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  • Inorganic Chemistry  (9,032)
  • Cell & Developmental Biology  (3,455)
  • Engineering  (2,961)
  • Earth model, also for more shallow analyses !
  • Elasticity
  • LUNAR AND PLANETARY EXPLORATION
  • 1995-1999  (7,526)
  • 1935-1939  (3,966)
  • 1930-1934  (4,275)
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Keywords
Publisher
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Year
  • 1
    Electronic Resource
    Electronic Resource
    A Contact Problem of the Interaction of a Semi-Finite Inclusion with a Plate (1999)
    Springer
    Georgian mathematical journal 6 (1999), S. 489-500 
    Details
    ISSN: 1572-9176
    Keywords: Elasticity ; elastic mixtures ; general representations ; integral Fredholm equations ; boundary value problems ; splitted boundary value problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A piece wise-homogeneous plane made up of twodifferent materials and reinforced by an elastic unclusion is considered on a semi-finite section where the different materials join. Vertical and horizontal forces are applied to the inclusion which haz a variable thichness and a variable elasticity modulus. Under certain conditions the problem is reduced to integrodifferential equations of third order. The solution is constructed effectively by applying the methods of theory of analytic functions to a boundary value problem of the Carleman type for a strip. Asymptotic estimates of normal contact stress are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022932902050
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  • 2
    Electronic Resource
    Electronic Resource
    Application of Analogues of General Kolosov–Muskhelishvili Representations in the Theory of Elastic Mixtures (1999)
    Springer
    Georgian mathematical journal 6 (1999), S. 1-18 
    Details
    ISSN: 1572-9176
    Keywords: Elasticity ; elastic mixtures ; general representations ; Fredholm integral equations ; boundary value problems ; splitted boundary value problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The existence and uniqueness of a solution of the first, the second and the third plane boundary value problem are considered for the basic homogeneous equations of statics in the theory of elastic mixtures. Applying the general Kolosov–Muskhelishvili representations from [1], these problems can be split and reduced to the first and the second boundary value problem for an elliptic equation which structurally coincides with the equation of statics of an isotropic elastic body.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022904308409
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  • 3
    Electronic Resource
    Electronic Resource
    Elasticity and movements of the cockroach tarsus in walking (1999)
    Springer
    Journal of comparative physiology 185 (1999), S. 157-172 
    Details
    ISSN: 1432-1351
    Keywords: Key words Insect ; Walking ; Elasticity ; Tarsus ; Joints
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Abstract Anatomical, kinematic and ablation studies were performed to evaluate the contribution of elasticity in use of the cockroach tarsus (foot) in walking. The distal tarsus (claws and arolium) engages the substrate during the stance phase of walking by the action of a single muscle, the retractor unguis. Kinematic and ablation studies demonstrated that tarsal disengagement occurs at the end of stance, in part via the action of elastic elements at the penultimate tarsal joint. In isolated legs, this joint exhibits very rapid (less than 20 ms duration) recoil to extension when released from the engaged position, and recoil is even more rapid (less than 10 ms) after removal of the retractor tendon (apodeme). The joint also possesses an enlarged cuticular condyle which is the attachment for ligaments and articular membranes, some of which fulfill morphological criteria consistent with the presence of the elastic protein resilin. Measurements of restoring forces generated by joint displacement indicate that they are graded but could readily lift the mass of the distal tarsus. This biomechanical design can facilitate efficient use of the tarsus in walking while under active control by only a single muscle and may also be highly advantageous when cockroaches very rapidly traverse irregular terrain.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s003590050374
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  • 4
    Electronic Resource
    Electronic Resource
    A method based on singularity theory to predict edge delamination of laminates (1999)
    Springer
    International journal of fracture 100 (1999), S. 105-120 
    Details
    ISSN: 1573-2673
    Keywords: Elasticity ; composite materials ; delamination.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Delamination starting from a stress free edge is the main mode of failure of cross-ply laminates. The analysis of singularities and resulting stress concentrations at interfaces along these edges are not sufficient to provide a satisfying model of onset mechanisms. In particular, the model is by far less sensitive to the layers thickness than observed in traction experiments. A refined asymptotic process is proposed which takes into account the existence of surface flaws (micro-cracks or notches). Numerical results prove that this model is much more in agreement with the experiments. Moreover, the knowledge of the interface toughness, in addition with the experiments, allows to estimate a characteristic fracture length, a kind of process zone. It is a material property and in a first approximation it arises to be of the same order of magnitude than the characteristic inhomogeneity length of the components, i.e. the fibers diameter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018382422833
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  • 5
    Electronic Resource
    Electronic Resource
    On 3D Cracks Intersecting a Free Surface in Laminated Composites (1999)
    Springer
    International journal of fracture 99 (1999), S. 25-40 
    Details
    ISSN: 1573-2673
    Keywords: Elasticity ; brittle fracture ; singularities.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In two- and three-dimensional linear elasticity, the singularities together with matched asymptotic expansions allow to extend the brittle fracture mechanics. Although there exist some difference between 2D and 3D approaches, the usual crack tip singularity exponent $$\frac{1}{2}$$ remains in both cases the hinge value between strong and weak singularities. In 3D, 0 was expected to be also a hinge, but it seems difficult to exhibit solutions with a negative exponent. One aim of this paper is to investigate numerically such specific cases and to derive some asymptotics of the classical stress intensity factors. The second part is dedicated to prove that, in case of a small linear ligament, negative exponents cannot exist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018366720722
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  • 6
    Electronic Resource
    Electronic Resource
    The interface crack problem for bonded piezoelectric and orthotropic layers under antiplane shear loading (1999)
    Springer
    International journal of fracture 98 (1999), S. 87-102 
    Details
    ISSN: 1573-2673
    Keywords: Elasticity ; fracture mechanics ; integral transform ; piezoelectric material ; layered material ; interface crack ; stress intensity factor ; energy release rate.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The primary objective of this paper is to study the influence of the electroelastic interactions on the stress intensity factor in bonded layers of piezoelectric and orthotropic materials containing a crack along the interface under antiplane shear. Attention is given to a two-layer hybrid laminate formed by adding a layer of piezoelectric ceramic to a unidirectional graphite/epoxy composite or an aluminum layer. Electric displacement or electric field is prescribed on the surfaces of the piezoelectric layer. The problem is formulated in terms of a singular integral equation which is solved by using a relatively simple and efficient technique. A number of examples are given for various material combinations. The results show that the effect of the electroelastic interactions on the stress intensity factor and the energy release rate can be highly significant.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018755614151
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  • 7
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    The tensile dislocation problem in a layered elastic medium (1999)
    In:  Geophys. J. Int., Taipei, Elsevier, vol. 136, no. 2, pp. 341-356, pp. 2091, (ISBN: 0-12-018847-3)
    Details
    Publication Date: 1999
    Keywords: cracks and fractures (.NE. fracturing) ; Dislocation ; Modelling ; Layers ; rifting ; Elasticity ; Stress ; Inhomogeneity ; Volcanology ; GJI
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    BIBLIOGRAPHY SEISMOLOGY
  • 8
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    Staggered mesh for the anisotropic and viscoelastic wave equation (1999)
    In:  Geophysics, Luxembourg, Conseil de l'Europe, vol. 64, no. 6, pp. 1863-1866, pp. 1972, (ISBN: 0-12-018847-3)
    Details
    Publication Date: 1999
    Keywords: Waves ; Synthetic seismograms ; Anisotropy ; Inelastic ; Rheology ; Elasticity
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  • 9
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    The lithospheric structure and evolution of the Pannonian/Carpathian/Dinaride region (1999)
    In:  Tectonophysics, London, Army Corps of Engineers, Woodward-Clyde Consultants, vol. 297, no. 1-4, pp. 1-293, pp. 1062, (ISBN: 0-12-018847-3)
    Details
    Publication Date: 1999
    Keywords: EUROPROBE (Geol. and Geophys. in eastern Europe) ; Earth model, also for more shallow analyses ! ; Velocity depth profile ; Deep seismic sounding (espec. cont. crust) ; Geol. aspects
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  • 10
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    Time-dependence of the stress shadowing effect and its relation to the structure of the lower crust (1999)
    In:  Geology, New York, Allerton Press, vol. 27, no. 2, pp. 119-122, pp. L13315, (ISSN: 1340-4202)
    Details
    Publication Date: 1999
    Keywords: Inelastic ; Rheology ; Modelling ; Finite Element Method ; Fault zone ; SAF ; Tectonics ; Stress ; Earth model, also for more shallow analyses !
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  • 11
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    Body waveform modeling of east Mediterranean earthquakes at intermediate distances (17°-30°) with a Gaussian beam summation method (1999)
    In:  J. Geophys. Res., Tulsa, 450 pp.; 2nd modified and expanded ed., Society of Exploration Geophysics, vol. 104, no. B12, pp. 28813-28828, pp. L21319, (ISSN: 1340-4202)
    Details
    Publication Date: 1999
    Keywords: Body waves ; Ray seismics ; Source time function ; Fault plane solution, focal mechanism ; Inversion ; Earth model, also for more shallow analyses ! ; JGR
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  • 12
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    Proposed project would give unprecedented look under North America (1999)
    In:  Eos, Trans., Am. Geophys. Un., Luxembourg, Conseil de l'Europe, vol. 80, no. 22, pp. 245, 250 & 251, pp. B02405, (ISSN: 1340-4202)
    Details
    Publication Date: 1999
    Keywords: Seismology ; Deep seismic sounding (espec. cont. crust) ; Velocity depth profile ; Earth model, also for more shallow analyses ! ; Rheology ; IReservoir induced seismicity ; Ekstroem ; Ekstrom
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  • 13
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    Effects of lateral viscosity variations on postglacial rebound: an analytical approach (1999)
    In:  Geophys. J. Int., Amsterdam, Univ. Tokyo, vol. 137, no. 2, pp. 489-500, pp. B12306, (ISSN: 1340-4202)
    Details
    Publication Date: 1999
    Keywords: Rheology ; Crustal deformation (cf. Earthquake precursor: deformation or strain) ; Inelastic ; Elasticity ; Inhomogeneity ; Modelling ; GJI
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  • 14
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    Beno Gutenberg - June 4, 1889 - January 25, 1960 (1999)
    In:  DGG Mittlg., New York, Conseil de l'Europe, vol. 93, no. 4, pp. 2-15, pp. B07307, (ISSN: 1340-4202)
    Details
    Publication Date: 1999
    Keywords: Seismology ; history ; NOISE ; Magnitude ; Earth model, also for more shallow analyses ! ; Physical properties of rocks
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  • 15
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    Petrographic interpretation of a complex seismic crust-mantle transition in the central-eastern Alps (1999)
    In:  Tectonophys., Amsterdam, Elsevier Science Publishers B.V., vol. 294, no. 1-2, pp. 75-88, pp. B09407, (ISSN: 1340-4202)
    Details
    Publication Date: 1999
    Keywords: petrology ; Mineralogy ; Earth model, also for more shallow analyses ! ; Velocity depth profile ; EUROPROBE (Geol. and Geophys. in eastern Europe)
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  • 16
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    Strain compatibility and shear zones: is there a problem? (1999)
    In:  Journal of Structural Geology, Taipei, Am. Inst. Min. Metal. Petr. Eng., vol. 21, no. 8-9, pp. 923-932, pp. 2324, (ISSN 0343-5164)
    Details
    Publication Date: 1999
    Keywords: Strain ; Fault zone ; Elasticity ; Structural geology ; JSG
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  • 17
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    Gravitational viscoelastic relaxation of eccentrically nested spheres (1999)
    In:  Geophys. J. Int., Zagreb, 3-4, vol. 138, no. 1, pp. 45-66, pp. B06305, (ISSN: 1340-4202)
    Details
    Publication Date: 1999
    Keywords: NOModelling ; Gravimetry, Gravitation ; Inelastic ; Rheology ; Elasticity ; Modelling ; GJI
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  • 18
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    On tensile cracks close to and across the interface between two welded elastic half-spaces (1999)
    In:  Geophys. J. Int., Taipei, Elsevier, vol. 138, no. 2, pp. 410-434, pp. 2091, (ISBN: 0-12-018847-3)
    Details
    Publication Date: 1999
    Keywords: cracks and fractures (.NE. fracturing) ; Dislocation ; Modelling ; Layers ; rifting ; Elasticity ; Stress ; Inhomogeneity ; Volcanology ; GJI
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  • 19
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    Effects of plate bending and fault strength at subduction zones on plate dynamics (1999)
    In:  Journal of Geophysical Research, Roma, Elsevier, vol. 104, no. B8, pp. 17551-17571, pp. 2099, (ISBN: 0-12-018847-3)
    Details
    Publication Date: 1999
    Keywords: Plate tectonics ; Strength ; Fault zone ; Subduction zone ; Inelastic ; Rheology ; Finite Element Method ; Modelling ; velocity ; Strain ; Elasticity ; JGR
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  • 20
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    Displacement and flexural stresses of a loaded elastic plate on a viscous liquid (1999)
    In:  Journal of Geophysical Research, Tübingen, Europ. Ass. Exploration Geophys., vol. 104, no. B5, pp. 10,827-10,839, pp. TC4007, (ISSN: 1340-4202)
    Details
    Publication Date: 1999
    Keywords: Modelling ; Elasticity ; Inelastic ; Rheology ; Stress ; Fluids ; buckling ; JGR
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  • 21
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    Seismic velocity and density jumps across the 410- and 660-kilometer discontinuities (1999)
    In:  Science, Luxembourg, Inst. Electrical & Electronics Engineers, vol. 285, no. 5433, pp. 1545-1548, pp. B06303, (ISSN: 1340-4202)
    Details
    Publication Date: 1999
    Keywords: Velocity depth profile ; Earth model, also for more shallow analyses ! ; earth mantle ; Seismology ; Reflectivity
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  • 22
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    A successfully stress-forecast earthquake (1999)
    In:  Geophys. J. Int., Roma, Acad. Roy. des Sciences, vol. 138, no. 1, pp. F1-F5, pp. B04102, (ISBN: 0-12-018847-3)
    Details
    Publication Date: 1999
    Keywords: Earthquake precursor: prediction research ; AnisotropyS ; Iceland ; fracture ; criticality ; SOC ; Seismology ; APE ; anisotropic ; poro-elasticity ; Elasticity ; Iceland ; Stefansson ; GJI
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  • 23
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    Nonlinear mesoscopic elasticity: Evidence for a new class of materials (1999)
    In:  Phys. Today, Warszawa, Zaklad Geofizyki Polskiej Akademii Nauk, vol. 52, no. 4, pp. 30-36, pp. L24306, (ISBN: 0534351875, 2nd edition)
    Details
    Publication Date: 1999
    Keywords: Elasticity ; Fracture ; Laboratory measurements ; Non-linear effects ; hysteresis ; Stress ; Strain ; Strong motions ; Spectrum
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  • 24
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    Relevance of hot underlying asthenosphere to the occurrence of Latur earthquake and Indian peninsular shield seismicity (1999)
    In:  J. of Geodynamics, Dresden, H.-J. Vogt, vol. 28, no. 2-3, pp. 303-316
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    Publication Date: 1999
    Keywords: Inelastic ; Earth model, also for more shallow analyses ! ; Earthquake ; Seismicity ; Asthenosphere
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  • 25
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    The skin effect of the anelastic earth (1999)
    In:  Pageoph, Luxembourg, Conseil de l'Europe, vol. 156, no. 3, pp. 371-393, pp. 2501, (ISBN: 0-12-018847-3)
    Details
    Publication Date: 1999
    Keywords: Inelastic ; Rheology ; Earth model, also for more shallow analyses ! ; loading ; Seismicity ; Stress ; Modelling ; PAG
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  • 26
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    Surface loading of a viscoelastic earth - I. General theory (1999)
    In:  Geophys. J. Int., Warszawa, EGS, vol. 137, no. 3, pp. 847-855, pp. 2292, (ISSN: 1340-4202)
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    Publication Date: 1999
    Keywords: Rheology ; Inelastic ; Elasticity ; NOModelling ; GJI
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  • 27
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    Thermoelastic stresses with reference to scale and morphology of the Earth's surface (1999)
    In:  Geophys. Res. Lett., Kunming, China, 3-4, vol. 26, no. 1, pp. 267-270, pp. 2180, (ISSN: 1340-4202)
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    Publication Date: 1999
    Keywords: Geothermics ; Elasticity ; Stress ; GRL
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  • 28
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    Source-receiver reciprocity and empirical Green's functions from chemical blasts (1999)
    In:  Bulletin of the Seismological Society of America, Dordrecht, Martinus Nijhoff Publishers, vol. 89, no. 2, pp. 538-543, pp. B05S20, (ISSN: 1340-4202)
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    Publication Date: 1999
    Keywords: Elasticity ; Waves ; Seismology ; explosions ; BSSA
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  • 29
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    Evidence of nonlinear elasticity of the crust from the Mw7.6 Manyi (Tibet) earthquake (1999)
    In:  Science, Basle, Wiley, vol. 286, no. 5438, pp. 272-276, pp. L06315, (ISSN: 1340-4202)
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    Publication Date: 1999
    Keywords: Non-linear effects ; Elasticity ; China ; Earthquake
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  • 30
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    Surface loading of a viscoelastic earth - II. Spherical models (1999)
    In:  Geophys. J. Int., Warszawa, EGS, vol. 137, no. 3, pp. 856-872, pp. 2292, (ISSN: 1340-4202)
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    Publication Date: 1999
    Keywords: Rheology ; Inelastic ; Elasticity ; NOModelling ; GJI
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  • 31
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    Cracks and Fracture (1999)
    Academic Press
    In:  San Diego, London, Cambridge, Academic Press, vol. 11, pp. 503, (ISBN 0121341305)
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    Publication Date: 1999
    Keywords: Rock mechanics ; Fracture ; criteria ; cracks and fractures (.NE. fracturing) ; Coulomb ; Textbook of geophysics ; Textbook of engineering ; Modelling ; Elasticity ; Energy (of earthquakes) ; Stress ; Strain
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  • 32
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    Postseismic deformation in Chile: Constraints on the asthenospheric viscosity (1999)
    In:  Geophys. Res. Lett., Darmstadt, Wissenschaftliche Buchgesellschaft, vol. 26, no. 20, pp. 3157-3160, pp. L11308, (ISSN: 1340-4202)
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    Publication Date: 1999
    Keywords: Modelling ; Crustal deformation (cf. Earthquake precursor: deformation or strain) ; Elasticity ; spherical ; Inelastic ; GRL
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  • 33
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    Porous Media: Theory and Experiments (1999)
    Kluwer
    In:  Dordrecht, 336 pp., Kluwer, vol. 31, no. 3, pp. 2-203, (ISBN 0-7923-5692-6)
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    Publication Date: 1999
    Keywords: Textbook of geophysics ; Physical properties of rocks ; Laboratory measurements ; Elasticity
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  • 34
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    Analyse und Interpretation von Brunnenspiegelschwankungen als Folge des Roermond-Erdbebens vom April 1992 (1999)
    Math.-Naturwiss. Fak. Rhein. Friedr.-Wilh.-Univ.
    In:  Dissertation, Bonn, Math.-Naturwiss. Fak. Rhein. Friedr.-Wilh.-Univ., vol. 10, no. GL-TR-89-0157, pp. 5777-5782, (ISBN 3-933346-037)
    Details
    Publication Date: 1999
    Description: Shaker Verlag, Aachen; Ph.D. Thesis
    Keywords: Dislocation ; Earthquake ; Fluids ; TIDES ; Elasticity ; poro-elastic ; Finite Element Method ; Modelling ; hydraulic ; tests ; Laboratory measurements
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  • 35
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    Composition, Deep Structure and Evolution of Continents (1999)
    Elsevier
    In:  200 pp., Elsevier, vol. 24, no. ALEX(01)-FR-77-01, AFTAC Contract F08606-76-C-0025, pp. 329, (ISBN: 0-444-50309-9)
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    Publication Date: 1999
    Keywords: Plate tectonics ; Textbook of geology ; Textbook of geophysics ; Earth model, also for more shallow analyses ! ; Geol. aspects ; Mineralogy
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  • 36
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    Gravito-Viskoelastodynamik für verallgemeinerte Rheologien mit Anwendungen auf den Jupitermond Io und die Erde (1999)
    FB Physik, Math.-Natw. Fak., Westf. Wilhelms-Univ.
    In:  Dissertation, Münster, FB Physik, Math.-Natw. Fak., Westf. Wilhelms-Univ., vol. 10, no. GL-TR-89-0259, pp. 29-43, (ISBN 0 08 042822 3)
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    Publication Date: 1999
    Keywords: Elasticity ; Rheology ; Inelastic ; Planetology ; Gravimetry, Gravitation
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  • 37
    Electronic Resource
    Electronic Resource
    Thermoelastic Equilibrium of Bodies in Generalized Cylindrical Coordinates (1998)
    Springer
    Georgian mathematical journal 5 (1998), S. 521-544 
    Details
    ISSN: 1572-9176
    Keywords: Elasticity ; thermoelasticity ; transversally isotropic body ; thermoelastic equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Using the method of separation of variables, an exact solution is constructed for some boundary value and boundary-contact problems of thermoelastic equilibrium of one- and multilayer bodies bounded by the coordinate surfaces of generalized cylindrical coordinates ρ, α, z. ρ, α are the orthogonal coordinates on the plane and z is the linear coordinate. The body, occupying the domain Ω = {ρ0 〈 ρ 〈 ρ1, α0 〈 α 〈 α1, 0 〈 z 〈 z 1}, is subjected to the action of a stationary thermal field and surface disturbances (such as stresses, displacements, or their combinations) for z = 0 and z = z 1. Special type homogeneous conditions are given on the remainder of the surface. The elastic body is assumed to be transversally isotropic with the plane of isotropy z = const and nonhomogeneous along z. The same assumption is made for the layers of the multilayer body which contact along z = const.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/B:GEOR.0000008130.94207.f5
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  • 38
    Electronic Resource
    Electronic Resource
    Transverse Decay of Solutions in an Elastic Cylinder (1998)
    Springer
    Meccanica 33 (1998), S. 577-585 
    Details
    ISSN: 1572-9648
    Keywords: Circular cylinder ; Transverse decay ; Elasticity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract In a semi‐infinite cylinder composed of anisotropic linearised elastic material, loaded on the base and clamped along the lateral surface, it is known that the solution as measured, for example, by the strain‐energy flux through a plane cross‐ection decays longitudinally at most exponentially with respect to the axial distance from the base. There is, however, also a transverse radial decay of the solution, again measured for example by the strain‐energy, occurring from the region close to the cylinder's axis to the region near the lateral surface, where the energy vanishes. This problem is considered in the present paper which discusses a circular semi‐infinite cylinder and derives an estimate for the strain‐energy contained in a cylindrical annulus at a given distance from the base and of variable height, and whose outer surface coincides with the lateral surface of the cylinder. It is shown that the strain‐energy decays at most algebraically to zero as the inner radius of the annulus increases to that of the cylinder. Sommario. E'noto che in un cilindro semi‐infinito composto da materiale elastico lineare anisotropo, caricato sulla base ed incastrato lungo la superficie laterale, la soluzione elastica, misurata, per esempio, dal flusso di energia di deformazione attraverso una sezione trasversale piana, decade con legge al più esponenziale con la distanza dalla base. C'è tuttavia, anche un decadimento radiale della soluzione, misurato, per esempio, dall'energia di deformazione che passa dalla regione vicina all'asse del cilindro a quella vicin alla superficie laterale dove l'energia si annulla Questo problema è qui studiato. Si discute in particolare un cilindro circolare semi‐infinito e si deduce una stima per l'energia di deformazione contenuta in un anello cilindrico ad una distanza assegnata dalla base e di altezza variabile, e la cui superficie esterna coincide con la superficie laterale del cilindro. Si dimostra che l'energia di deformazione decade al più con legge algebrica a zero quando il raggio interno del cilindro si avvicina a quello esterno.
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    URL: http://dx.doi.org/10.1023/A:1004343004833
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    Modeling elastic properties of microtubule tips and walls (1998)
    Springer
    European biophysics journal 27 (1998), S. 501-513 
    Details
    ISSN: 1432-1017
    Keywords: Key words Microtubule ; Elasticity ; Competing curvatures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract Electron micrographs of tips of growing and shrinking microtubules are analyzed and interpreted. The many shapes observed are all consistent with a simple mechanical model, a flexible tube with competing intrinsic curvatures. Observations are also consistent with growing and shrinking microtubules having the same intrinsic curvature for protofilaments, the one observed in oligomers peeling off shrinking microtubules. If this is so, the lateral bonds between protofilaments are responsible for the difference between shapes of tips on growing and shrinking microtubules.
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    URL: http://dx.doi.org/10.1007/s002490050160
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    Elasticity of an upper mantle clinopyroxene (1998)
    Springer
    Physics and chemistry of minerals 26 (1998), S. 7-13 
    Details
    ISSN: 1432-2021
    Keywords: Key words Pyroxene ; Elasticity ; Monoclinic ; Systematics ; ISS
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract  The ambient pressure elastic properties of a natural clinopyroxene (C2/c symmetry) from Kilbourne Hole, NM have been determined. In terms of end-members, diopside (CaMgSi2O6), hedenbergite (CaFeSi2O6), jadeite (NaAlSi2O6), cosmochlor (NaCrSi2O6), and Mg-Tschermak (MgAl(AlSi)O6), its composition is Di72He9Jd3Cr3Ts12. The analytic density, based on chemistry and cell parameters is 3.327 (0.003) g/cm3. The elastic constants [c11, c12, c13, c15, c22, c23, c25, c33, c35, c44, c46, c55, c66] are [273.8 (0.9), 83.5 (1.3), 80.0 (1.1), 9.0 (0.6), 183.6 (0.9), 59.9 (1.6), 9.5 (1.0), 229.5 (0.9), 48.1 (0.6), 76.5 (0.9), 8.4 (0.8), 73.0 (0.4), 81.6 (1.0)] GPa where uncertainties are reported at the 95% confidence level. The aggregate (mean of Hashin-Strikman bounds) adiabatic bulk modulus is 117.2 (0.7) GPa, and the shear modulus is 72.2 (0.2) GPa. Although measured moduli are broadly consistent with trends in elasticity versus atomic volume, deviations from the systematics would produce significant (percent level) changes in calculated velocities for candidate mantle mineral assemblages. The compositional dependence of elasticity for several clinopyroxenes is explored on the basis of just the Di+He and Jd+Ts mole fractions. The bulk modulus lies within experimental uncertainties of the linear mixture of end-member properties while the shear modulus deviates by 3%.
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    URL: http://dx.doi.org/10.1007/s002690050156
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    The behaviour of real resonances under perturbation in a semi-strip (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1-24 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the large time asymptotics of solutions u(x, t) of the wave equation with time-harmonic force density f(x)e-iωt, ω≥0, in the semi-strip Ω= (0, ∞)×(0, 1) for a given f∊C∞0(Ω). We assume that u satisfies the initial condition u=(∂/∂t)u=0 for t=0 and the boundary conditions u=0 for x2=0 and x2=1, and (∂/∂x1)u=αu for x1=0, with given α, -π≤α〈∞. Let Dα be the self-adjoint realization of -Δ in Ω with this boundary condition. For -π≤α〈0, Dα has eigenvalues λj=π2j2-α2, j=1, 2, … For j≥2 these eigenvalues are embedded in the continuous spectrum of Dα, σc(Dα)=[π2, ∞]. For α≥0, Dα has no eigenvalues. We consider the asymptotic behaviour of u(x, t), t→∞, as a function of α. In the case α=0 resonances of order √t at ω=πj, j=1, 2, …, were found in References 5 and 10. We prove that for α=-π there is a resonance of order t2 for ω=0 and resonances of order t for every ω〉0 (note that 0 is an eigenvalue of D-π). Moreover, for -π〈α〈0 there are resonances of order t at ω=√λj. The resonance frequencies are continuous functions of α for -π〈α〈0 and tend to πj, j=1, 2, … as α goes to zero.On the contrary in the case α〉0 there are no real resonances in the sense that the solution remains bounded in time as t→∞. Actually in this case, the limit amplitude principle is valid for all frequencies ω≥0. This rather striking behaviour of the resonances is explained in terms of the extension of the resolvent R(κ)=(Dα-κ2)-1 as a meromorphic function of κ into an appropriate Riemann surface. We find that as α crosses zero the real poles of R(κ) associated with the eigenvalues remain real, but go into a second sheet of the Riemann surface. This behaviour under perturbation is rather different from the case of complex resonances which has been extensively studied in the theory of many-body Schrödinger operators where the (real) eigenvalues embedded in the continuous spectrum turn under a small perturbation into complex poles of the meromorphic extension of the resolvent, as a function of the spectral parameter κ2. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Existence and uniqueness of steady motions of a third-grade fluid (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 117-128 
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    ISSN: 0170-4214
    Keywords: third-grade fluid ; existence ; uniqueness ; classical solution ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The global existence and uniqueness of classical solution of steady motions of a third-grade fluid provided assumptions on positivness of μ (coefficient of viscosity) and α1, γ (material coefficients) is proved. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On Laplace and Stokes potentials (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 227-249 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Integral equations associated with the basic boundary value problems for the Laplace and Stokes equations are considered. The integral operators for these integral equations are interpreted as the pseudodifferential operators, and their principal symbols are calculated. The symbols are obtained in terms of the principal curvatures and the coefficients of the first quadratic form of the boundary. As a consequence, the initial approximation is suggested for the iterative methods solving the integral equations. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Small chirality behaviour of solutions to electromagnetic scattering problems in chiral media (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 327-359 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The boundary integral equation method is used to prove the convergence of the Drude-Born-Fedorov equations with variable coefficients, possibly non-smooth, to Maxwell's equations as chirality admittance tends to zero. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Explicit stability conditions for integro-differential equations with periodic coefficients (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 565-588 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: New explicit stability conditions are derived for a linear integro-differential equation with periodic operator coefficients. The equation under consideration describes oscillations of thin-walled viscoelastic structural members driven by periodic loads. To develop stability conditions two approaches are combined. The first is based on the direct Lyapunov method of constructing stability functionals. It allows stability conditions to be derived for unbounded operator coefficients, but fails to correctly predict the critical loads for high-frequency excitations. The other approach is based on transforming the equation under consideration in such a way that an appropriate ‘differential’ part of the new equation would possess some reserve of stability. Stability conditions for the transformed equation are obtained by using a technique of integral estimates. This method provides acceptable estimates of the critical forces for periodic loads, but can be applied to equations with bounded coefficients only. Combining these two approaches, we derive explicit stability conditions which are close to the Floquet criterion when the integral term vanishes. These conditions are applied to the stability problem for a viscoelastic bar compressed by periodic forces. The effect of material and structural parameters on the critical load is studied numerically. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Optimal control computation for integro-differential aerodynamic equations (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 653-664 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In order to maintain spectrally accurate solutions, the grids on which a non-linear physical problem is to be solved must also be obtained by spectrally accurate techniques. The purpose of this paper is to describe a pseudospectral computational method of solving integro-differential systems with quadratic performance index. The proposed method is based on the idea of relating grid points to the structure of orthogonal interpolating polynomials. The optimal control and the trajectory are approximated by the m th degree interpolating polynomial. This interpolating polynomial is spectrally constructed using Legendre-Gauss-Lobatto grid points as the collocation points, and Lagrange polynomials as trial functions. The integrals involved in the formulation of the problem are calculated by Gauss-Lobatto integration rule, thereby reducing the problem to a mathematical programming one to which existing well-developed algorithms may be applied. The method is easy to implement and yields very accurate results. An illustrative example is included to confirm the convergence of the pseudospectral Legendre method, and a comparison is made with an existing result in the literature. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Trapped-mode solutions for gravity-capillary water waves in channels of arbitrary cross-section (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 701-718 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article establishes the existence of a trapped-mode solution to a linearized water-wave problem. The fluid occupies a symmetric horizontal channel that is uniform everywhere apart from a confined region which either contains a thin vertical plate spanning the depth of the channel or has indentations in the channel walls; the forces of gravity and surface tension are operative. A trapped mode corresponds to an eigenvalue of the composition of an inverse differential operator and a Neumann-Dirichlet operator for an elliptic boundary-value problem in the fluid domain. The existence of such an eigenvalue is established by extending previous results dealing with the case when surface tension is absent. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Initial-boundary-value problem for the Broadwell model of a gas mixture with bimolecular reaction (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 501-517 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper an initial-boundary-value problem in one-space dimension is studied for the Broadwell model extended to a gas mixture undergoing bimolecular reactions. Techniques of semigroup of bounded positive operators in a suitable Banach space are used to prove existence and uniqueness of the solution on bounded time intervals whose length depends on the initial data. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A spectral-theoretic approach for the solution of Maxwell's equations in stratified media (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 685-700 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the present work, the problem of electromagnetic wave propagation in three-dimensional stratified media is studied. The method of decoupling the electric and magnetic fields is implemented, and the spectral approach is adopted, componentwise, to the vector equation involving the electric field. Operational calculus of self-adjoint, positive operators in suitable Hilbert spaces is used to solve the corresponding initial value problems. The spectral families of these operators for the cases of the whole space and of a finite layer are constructed. A discussion on the applicability of the obtained results to physical problems is also included. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Existence theory to the equations in viscoelasticity at finite deformations (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 757-780 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we prove under the assumption of small initial data the global existence of a classical solution to the equations in viscoelasticity, associated with a free damping boundary condition. We also show that if we choose the initial data large enough, blow up will occur in finite time. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Regularizing properties and propagations of singularities for thermoelastic plates (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 797-821 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the thermoelastic plate system,utt-γΔutt+Δ2u+αΔθ=0,θt-κΔθ-αΔut=0 and we make a comparison between the models in which γ=0 and γ〉0. We conclude that in the first case the plate system is of a parabolic type, while when γ〉0 the corresponding system has a hyperbolic behaviour. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Orbital stability of solitary waves of the long wave-short wave resonance equations (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 883-894 
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    ISSN: 0170-4214
    Keywords: solitary wave ; stability ; long wave-short wave resonance equations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper concerns the orbital stability for solitary waves of the Long Wave-Short Wave resonance equations. Since the abstract results of Grillakis et al. [7, 8] cannot be applied directly, we can extend the abstract stability theory and use the detailed spectral analysis to obtain the stability of the solitary waves. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    A particle transport problem with non-homogeneous reflection boundary conditions (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1049-1066 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider particle transport in a three-dimensional convex region V, bounded by the regular surface ∂V. We assume that particles are specularly reflected by ∂V and that a source q is assigned on ∂V; more general non-homogeneous boundary conditions are also discussed. The problem is non-linear because the boundary condition is not homogeneous. We prove existence of a unique strict solution and by using the theory of semigroups we derive the explicit expression of such a solution in terms of the boundary source q. In the appendix, we indicate how some properties of affine operators can be used to derive the solution. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Regularity and convergence results for a phase-field model with memory (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1085-1105 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A phase-field model based on the Coleman-Gurtin heat flux law is considered. The resulting system of non-linear parabolic equations, associated with a set of initial and Neumann boundary conditions, is studied. Existence, uniqueness, and regularity results are proved. An asymptotic analysis is also carried out, in the case where the coefficient of the interfacial energy term tends to 0. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    The Child-Langmuir asymptotics applied to a bipolar diode (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1115-1148 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We apply the Child-Langmuir asymptotics of the Vlasov-Poisson system to the case of a bipolar diode, i.e. a vacuum diode where two species of particles of opposite electric charge are flowing. This leads to a simplified model which, if at least one of the two injected currents is not too large, has a unique solution. Moreover, in that case, the currents flowing inside the diode are limited by the so-called bipolar Child-Langmuir currents. In the case of large currents, other solutions may appear, and the formation of virtual electrodes may occur inside the diode. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    On the existence of shock fronts for a Burgers equation with a singular source term (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1107-1113 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the Cauchy problem for the equation∂u/∂t + u ∂u/∂x + u/x = 0 for x 〉 0, t ≥ 0, with u(x, 0) = u0-(x) for x 〈 x0, u(x, 0) = u0+(x) for x 〉 x0, u0-(x0) 〉 u0+(x0). Following the ideas of Majda, 1984 and Lax, 1973, we construct, for smooth u0- and u0+, a global shock front weak solution u(x, t) = u-(x, t) for x 〈 φ(t), u(x, t) = u+(x, t) for x 〉 φ(t), where u- and u+ are the strong solutions corresponding (respectively) to u0- and u0+ and the curve t → φ(t) is defined by dφ/dt (t) = 1/2[u-(φ(t), t) + u+(φ(t), t)], t ≥ 0 and φ(0) = x0.© 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Variational approach to a non-local identification problem related to non-linear ion transport (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1195-1206 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A variational approach to a non-linear non-local identification problem related to the non-linear transport equation is studied. Introducing a similarity transformation, the problem is formulated as an identification problem for a non-linear differential equation of second order with an additional non-local condition. For the solution of the forward problem stability in H1-norm with respect to the identification parameter is obtained. Using this result the existence of a solution to the identification problem is proved. Some results of computational experiments are given. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Prewavelet approximations for a system of boundary integral equations for plates with free edges on polygons (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1233-1267 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the plate equation in a polygonal domain with free edges. Its resolution by boundary integral equations is considered with double layer potentials whose variational formulation was given in Reference 25. We approximate its solution (u, (∂u/∂n)) by the Galerkin method with approximated spaces made of piecewise polynomials of order 2 and 1 for, respectively, u and (∂u/∂n). A prewavelet basis of these subspaces is built and equivalences between some Sobolev norms and discrete ones are established in the spirit of References 14, 16, 30 and 31. Further, a compression procedure is presented which reduces the number of nonzero entries of the stiffness matrix from O(N2) to O(N log N), where N is the size of this matrix. We finally show that the compressed stiffness matrices have a condition number uniformly bounded with respect to N and that the compressed Galerkin scheme converges with the same rate than the Galerkin one. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    On the one and one-half dimensional relativistic Vlasov-Maxwell-Fokker-Planck system with non-vanishing viscosity (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1287-1296 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The relativistic Vlasov-Maxwell-Fokker-Planck system is used in modelling distribution of charged particles in plasma. It consists of a transport equation coupled with the Maxwell system. The diffusion term in the equation models the collisions among particles, whereas the viscosity term signifies the dynamical frictional forces between the particles and the background reservoir. In the case of one space variable and two momentum variables, we prove the existence of a classical solution when the initial density decays fast enough with respect to the momentum variables. The solution which shares this same decay condition along with its first derivatives in the momentum variables is unique. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    The local Cauchy problem for multicomponent reactive flows in full vibrational non-equilibrium (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1415-1439 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider reactive mixtures of dilute polyatomic gases in full vibrational non-equilibrium. The governing equations are derived from the kinetic theory and possesses an entropy. We recast this system of conservation laws into a symmetric conservative form by using entropic variables. Following a formalism developed by the authors in a previous paper, the system is then rewritten into a normal form, that is, in the form of a quasilinear symmetric hyperbolic-parabolic system. Using a result of Vol'pert and Hudjaev, we prove local existence and uniqueness of a bounded smooth solution to the Cauchy problem. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Trimodal approximate solutions of the non-linear Boltzmann equation (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1479-1494 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Approximate solutions of the non-linear Boltzmann equation, which have the structure of the linear combination of three global Maxwellians with arbitrary hydrodynamical parameters, are considered. Some sufficient conditions which allow the error between the left- and the right-hand sides of the equation tend to zero, and which are calculated either in the mixed metric or in the pure integral metric, are obtained. The class of the distributions, which minimized this error for the arbitrary Knudsen number, is found. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Analysis of a non-hyperbolic system modelling two-phase fluid flows: the effects of surface tension (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1519-1542 
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    ISSN: 0170-4214
    Keywords: non-hyperbolic systems ; two-phase flows ; dispersion terms ; symmetrization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper considers a system of partial differential equations of convection dispersion type, modelling a stratified two-phase fluid flow. Local existence in time is proved for a sufficiently smooth initial data, given in the set of physically admissible states. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Small vibrations of an elastic conductor in a magnetic field (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1559-1569 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we study the motion of an elastic conducting wire in a magnetic field. The motion of the conductor induces a current in the wire (Faraday's law) which, in turn produces a force on the wire. We consider the linear equation obtained by linearizing the resulting equations of motion about an equilibrium solution. This is a hyperbolic partial differential equation with a non-local term. We prove existence and uniqueness of a weak solution of an initial-boundary value problem for this equation. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Error analysis of a weighted least-squares finite element method for 2-D incompressible flows in velocity-stress-pressure formulation (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1637-1654 
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    ISSN: 0170-4214
    Keywords: generalized Stokes equations ; incompressible flow ; least-squares ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we are concerned with a weighted least-squares finite element method for approximating the solution of boundary value problems for 2-D viscous incompressible flows. We consider the generalized Stokes equations with velocity boundary conditions. Introducing the auxiliary variables (stresses) of the velocity gradients and combining the divergence free condition with some compatibility conditions, we can recast the original second-order problem as a Petrovski-type first-order elliptic system (called velocity-stress-pressure formulation) in six equations and six unknowns together with Riemann-Hilbert-type boundary conditions. A weighted least-squares finite element method is proposed for solving this extended first-order problem. The finite element approximations are defined to be the minimizers of a weighted least-squares functional over the finite element subspaces of the H1 product space. With many advantageous features, the analysis also shows that, under suitable assumptions, the method achieves optimal order of convergence both in the L2-norm and in the H1-norm. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Asymptotic profiles of variational eigenvalues of two-parameter non-linear Sturm-Liouville problems (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1619-1635 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the two-parameter non-linear Sturm-Liouville problems. By using the variational method on general level sets, the variational eigenvalues are obtained. The purpose of this paper is to study the properties of these variational eigenvalues with respect to the parameter of general level sets. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Asymptotic analysis of Poisson's equation in a thin domain and its application to thin-walled elastic beams and tubes (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 187-226 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the limit behaviour of solution of Poisson's equation in a class of thin two-dimensional domains, both simply connected or single-hollowed, as its thickness becomes very small. The method is based on a transformation of the original problem into another posed on a fixed domain, obtention of a priori estimates and convergence results when thickness parameter tends to zero. As an important application of abstract results we obtain the limit expressions for functions appearing in elastic beam theories as torsion and warping functions. In this way, we provide a mathematical justification and a correct definition of torsion, warping and Timoshenko functions and constants that should be used in the open and closed thin-walled elastic beam theories. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Möbius inversion on a multiplicative semigroup and inverse lattice problems in physics (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 269-279 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The generalized Möbius function and Möbius inversion formula are applied to a multiplicative semigroup. A general mathematical method based on this Möbius inversion is presented to solve inversion problems of expansions with unequally weighted terms. By this method, all the inverse lattice problems in physics can be solved concisely. The solutions of four inverse lattice problems: the Fibonacci structure, the square lattice structure, the bcc and the hcp lattice structures are given. These are difficult to be solved by other methods. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    One and multidimensional sampling theorems associated with Dirichlet problems (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 361-374 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We use the eigenfunction expansion of Green's function of Dirichlet problems to obtain sampling theorems. The analytic properties of the sampled integral transforms as well as the uniform convergence of the sampling series are proved without any restrictions on the integral transforms. We obtain a one- and multi-dimensional versions of sampling theorems. In both cases the sampling series are written in terms of Lagrange-type interpolation expansions. Some examples and the truncation error as well as the stability of the obtained sampling expansions are discussed at the end of the paper. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On exponential stability for von Kármán equations in the presence of thermal effects (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 393-416 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a dynamical von Kármán system in the presence of thermal effects. Our model includes the possibility of a rotational inertia term in the system. We show that the total energy of the solution of such system decays exponentially as t→+∞. The decay rates we obtain are uniform on bounded sets of the energy space. The main ingredients of our method of proof are suitable properties of a decoupled system, the energy method and the compactness of the nonlinear map associated to the von Kármán system. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Examples of embedded eigenvalues for problems in acoustic waveguides (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 479-488 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This short article discusses the spectrum of the Neumann Laplacian in the infinite domain Ω⊂∝n, n ≥2 created by inserting a compact obstacle P into the uniform cylinder Ω0 =(-∞, ∞)×Ω′. The main result is the existence of at least one embedded eigenvalue when P is an (n -2)-dimensional surface whose unit normal is parallel to Ω′ at each point of P . The special case when P is symmetric about {0}×Ω′ is also treated. It is shown that there is at least one symmetric eigenvector and, when P is sufficiently long, at least one antisymmetric eigenvector. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Regularization and existence of solutions of three-dimensional elastoplastic problems (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 551-564 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the existence of solutions to the three-dimensional elastoplastic problem with Hencky's law and Neumann boundary conditions by elliptic regularization and the penalty method, both for the case of a smooth boundary and of an interior two dimensional crack. It is shown, in particular, that the variational solution satisfies all boundary conditions. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On the propagation of Hölder regularity for the 3D Euler equations (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 251-268 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: The propagation of Hölder regularity of the solutions to the 3D Euler equations is discussed. Our method is a special semi-linearization of the vorticity equation combined with the classical Schauder interior estimates. © 1998 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Existence, uniqueness and analyticity properties for electromagnetic scattering in a two-layered medium (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 433-461 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with the solution of Maxwell equations in the modelling of the scattering of a time-harmonic electromagnetic wave by an obstacle located in a two-layered medium. The use of the Silver-Müller radiation condition in each layer is shown to provide a well-posed scattering problem. The analysis is based on the study of the Green tensor, which allows to relate the radiation condition to an integral representation formula. The analyticity properties of the scattering problem with respect to the frequency are then investigated. This gives rise to a limiting absorption principle and furnishes a characterization of the resonances. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Moment expansion analysis for time-domain asymptotics (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 489-499 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We apply our recently developed distributional technique [2, 3] to study time-domain asymptotics. This enables us to present a rigorous mathematical discussion and extensions of the results given by Chapman [1] and subsequent workers in this field. The present analysis is facilitated by defining functions which are distributionally small at infinity. We find that one of the advantages of using this technique is that multidimensional extensions can be derived very easily. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 519-549 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with a specific finite element strategy for solving elliptic boundary value problems in domains with corners and edges. First, the anisotropic singular behaviour of the solution is described. Then the finite element method with anisotropic, graded meshes and piecewise linear shape functions is investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates for functions from anisotropically weighted spaces are derived. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Liapunov stability analysis of a rotor-bearing system with a flexible attachment of appendage to shaft (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 605-617 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper presents a general method of analysis for investigating the whirl stability of a rotor-bearing system whose appendage is flexibly attached to the spinning shaft. Sufficient conditions of asymptotic stability involving system different parameters are derived based on Liapunov's theory. An inclusive analysis of the effect of the combined flexibilities of the elastic attachment of the appendage to the shaft and the two end bearings coupled with the other various parameters of the system on the dynamic stability is presented. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Steady compressible Navier-Stokes equations with large potential forces via a method of decomposition (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 665-684 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate the steady compressible Navier-Stokes equations near the equilibrium state v = 0, ρ = ρ0 (v the velocity, ρ the density) corresponding to a large potential force. We introduce a method of decomposition for such equations: the velocity field v is split into a non-homogeneous incompressible part u (div (ρ0u) = (0) and a compressible (irrotational) part ∇φ. In such a way, the original complicated mixed elliptic-hyperbolic system is split into several ‘standard’ equations: a Stokes-type system for u, a Poisson-type equation for φ and a transport equation for the perturbation of the density σ = ρ - ρ0. For ρ0 = const. (zero potential forces), the method coincides with the decomposition of Novotny and Padula [21]. To underline the advantages of the present approach, we give, as an example, a ‘simple’ proof of the existence of isothermal flows in bounded domains with no-slip boundary conditions. The approach is applicable, with some modifications, to more complicated geometries and to more complicated boundary conditions as we will show in forthcoming papers. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On recovering obstacles inside inhomogeneities (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 619-651 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider acoustic scattering from an obstacle inside an inhomogeneous structure. We prove in the paper that if the outside inhomogeneity is known then the obstacle and possible inside inhomogeneity are uniquely determined by the fixed energy far field data. The proof is based on new mapping properties of layer potentials in spaces that specify one point. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    About singularities at angular points of a trailing edge under the Joukowskii-Kutta Condition (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 939-967 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The linear problem for the velocity potential around a slightly curved thin finite wing is considered under the Joukowskii-Kutta hypothesis. The exponents of possible singularities of solutions at angular points on wing's trailing edge are expressed in terms of eigenvalues of mixed boundary value problems for the Beltrami-Laplace operator on the hemisphere and the semicircle. These singularities have a structure such that the circulation function turns out to be continuous in interior angular points of the trailing edge. In the case of trapezoidal shape of the wing ends there occur square-root singularities of the velocity field at the trailing edge endpoints and the same singularities, of course, are extended along the lateral sides of the wake behind the wing. It is proved that for any angular point on the trailing edge the exponents of all above-mentioned singularities form a countable set in the upper complex half-plane with the only accumulation point at infinity. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Long-time behaviour for solutions of the Vlasov-Poisson-Fokker-Planck equation (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 985-1014 
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    ISSN: 0170-4214
    Keywords: Vlasov-Poisson-Fokker-Planck ; long-time behaviour ; fundamental solutions ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the long-time behaviour of solutions of the Vlasov-Poisson-Fokker-Planck equation for initial data small enough and satisfying some suitable integrability conditions. Our analysis relies on the study of the linearized problems with bounded potentials decaying fast enough for large times. We obtain global bounds in time for the fundamental solutions of such problems and their derivatives. This allows to get sharp bounds for the decay of the difference between the solutions of the Vlasov-Poisson-Fokker-Planck equation and the solution of the free equation with the same initial data. Thanks to these bounds, we get an explicit form for the second term in the asymptotic expansion of the solutions for large times. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Existence and uniqueness results for the non-autonomous coagulation and multiple-fragmentation equation (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1067-1084 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An initial-value problem modelling coagulation and fragmentation processes is studied. The results of earlier papers are extended to models where either one or both of the rates of coagulation and fragmentation depend on time. An abstract integral equation, involving the solution operator to the linear fragmentation part, is investigated via the contraction mapping principle. A unique global, non-negative, mass-conserving solution to this abstract equation is shown to exist. The latter solution is used to generate a global, non-negative, mass-conserving solution to the original non-autonomous coagulation and multiple-fragmentation equation. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Global existence and energy decay for a damped quasi-linear wave equation (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1185-1194 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we prove the global existence and study decay property of the solutions to the initial boundary value problem for the quasi-linear wave equation with a dissipative term without the smallness of the initial data. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Modulation equations and parabolic limits of reaction random-walk systems (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1207-1226 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Reaction random-walk systems are hyperbolic models to describe spatial motion (in one dimension) with finite speed and reactions of particles. Here we present two approaches which relate reaction random-walk equations with reaction diffusion equations. First, we consider the case of high particle speeds (parabolic limit). This leads to a singular perturbation analysis of a semilinear damped wave equation. A initial layer estimate is given. Secondly, we consider the case of a transcritical bifurcation. We use techniques similar to that of the Ginzburg-Landau method to find a modulation equation for the amplitude of the first unstable mode. It turns out that the modulation equation is Fisher's equation, hence near the bifurcation point travelling wave solutions are obtained. The approximation result and the corresponding estimate is given in terms of the bifurcation parameter. Both results are based on an a priori estimate for classical solutions which follows from explicit representations of the solution of the linear telegraph equation. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Problem of regulation of the cardiovascular system as a bilinear control problem (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1365-1377 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the article the problem of regulation of the cardiovascular system is investigated from the point of view of control process theory. This problem was reduced to finding the optimal control in the sense of speed in a bilinear system. In the first part of the article the possibility of applying Saburov's method for the solution to bilinear control problems is considered. The second part of the article is devoted to the application of this method to a concrete problem from practical medicine. The method has allowed the complete synthesis of an optimal control to be carried out  -  the sliding mode takes place and it was investigated completely. The results obtained are interesting from the point of view of control process theory, and testify to the high efficiency of the method. The final results allow concrete recommendations about the regulation of the cardiovascular system. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    A steady-state system in non-equilibrium thermodynamics including thermal and electrical effects (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1399-1413 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The steady-state equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear elliptic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet-Neumann boundary conditions are prescribed. The existence of generalized solutions is proven. The key of the proof is a transformation of the problem by using the entropic variables, or electro-chemical potentials, which symmetrize the equations. The uniqueness of weak solutions is shown under the assumption that the boundary data are not far from the thermal equilibrium. A general uniqueness result cannot be expected for physical reasons. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Shape sensitivity analysis of stress intensity factors by Generalized J-integrals (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1343-1363 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider an elastic plate with the non-deformed shape ΩΣ := Ω \ Σ, where Ω is a domain bounded by a smooth closed curve Γ and Σ ⊂ Ω is a curve with the end points {γ1, γ2}. If the force g is given on the part ΓN of Γ, the displacement u is fixed on ΓD := Γ \ ΓN and the body force f is given in Ω, then the displacement vector u(x) = (u1(x), u2(x)) has unbounded derivatives (stress singularities) near γk, k = 1, 2   u(x) = ∑2k, l=1 Kl(γk)r1/2kSCkl(θk) + uR(x)     near γk.Here (rk, θk) denote local curvilinear polar co-ordinates near γk, k = 1, 2, SCkl (θk) are smooth functions defined on [-π, π] and uR(x) ∊ {H2(near γk)}2. The constants Kl(γk),   l = 1, 2, which are called the stress intensity factors at γk (abbr. SIFs), are important parameters in fracture mechanics. We notice that the stress intensity factors Kl(γk) (l = 1, 2;  k = 1, 2) are functionals Kl(γk) = Kl(γk; L, Ω, Σ) depending on the load L, the shape of the plate Ω and the shape of the crack Σ. We say that the crack Σ is safe, if Kl(γk; Ω)2 + K2(γk; Ω)2 〈 RẼ. By a small change of Ω the shape Σ can change to a dangerous one, i.e. we have K1(γk; Ω)2 + K2(γk; Ω)2 ≥ RẼ. Therefore it is important to know how Kl(γk) depends on the shape of Ω.For this reason, we calculate the Gâteaux derivative of Kl(γk) under a class of domain perturbations which includes the approximation of domains by polygonal domains and the Hadamard's parametrization Γ(τ) := {x + τφ(x)n(x);  x ∊ Γ}, where φ is a function on Γ and n is the outward unit normal on Γ. The calculations are quite delicate because of the occurrence of additional stress singularities at the collision points {γ3, γ4} = ΓD ∩ ΓN.The result is derived by the combination of the weight function method and the Generalized J-integral technique (abbr. GJ-integral technique). The GJ-integrals have been proposed by the first author in order to express the variation of energy (energy release rate) by extension of a crack in a 3D-elastic body. This paper begins with the weak solution of the crack problem, the weight function representation of SIF's, GJ-integral technique and finish with the shape sensitivity analysis of SIF's. GJ-integral Jω(u; X) is the sum of the P-integral (line integral) Pω(u, X) and the R-integral (area integral) Rω(u, X). With the help of the GJ-integral technique we derive an R-integral expression for the shape derivative of the potential energy which is valid for all displacement fields u ∊ H1. Using the property that the GJ-integral vanishes for all regular fields u ∊ H2 we convert the R-integral expression for the shape derivative to a P-integral expression. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    The Boltzmann-Grad limit for a particle system in a slab with stochastic walls (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1543-1558 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that a stochastic system of N interacting particles in a slab approximates, in the Boltzmann-Grad limit, a one-dimensional Boltzmann equation with diffusive boundary conditions. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Bounds and decay results for some second-order semilinear elliptic problems (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1571-1591 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The asymptotic behaviour of solutions of certain semilinear elliptic Dirichlet boundary value problems defined on a semi-infinite cylinder is investigated by means of energy arguments and maximum principles. Various hypotheses are made on the form of the semilinear term, and in some cases it is found that the rate of decay of solutions is faster than the optimal decay rate for harmonic functions. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Hazard and safety regions for paths with constrained curvature (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1655-1679 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper the problem of collision analysis for a mobile robot operating in a planar environment with moving objects (obstacles) is addressed. The pattern of motion of the potential obstacles cannot be predicted; only a bound on their maximum velocity is available. Based on this information, at its current position the robot constructs the Hazard Region that corresponds to the path it contemplates. If the Hazard Region contains at least one obstacle, then there is a potential for this obstacle to collide with the robot (in which case perhaps another path should be planned). We first derive the solution for Hazard Region for two standard path primitives, a straight line segment and a circular arc segment; the solution is exact, except for one special case (for which the approximation error is estimated). This result is then applied to a more complex case when the path presents a combination of those primitives. Such are, for example, the optimal (shortest) paths with constrained curvature (known as Dubins paths [3]), which connect two points, each with a prescribed direction of motion. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    A perturbative method for the spectral analysis of an acoustic multistratified strip (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1681-1704 
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    ISSN: 0170-4214
    Keywords: stratified medium ; acoustic waves ; self-adjoint operators ; spectrum ; limiting absorption principle ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the acoustic propagator A=-∇·c2∇ in the strip Ω={(x, z)∊∝2∣0〈z〈H} with finite width H〉0. The celerity c depends for large ∣x∣ only on the variable z and describes the stratification of Ω: it is assumed to be in L∞(Ω), bounded from below by cmin〉0, such that there exists M〉0 with c(x, z)=c1(z) if x〈 -M and c(x, z)=c2(z) if x〉M. We look at the propagator A as a ‘perturbation’ of the free propagators Aj in Ω associated to the velocities cj, j=1, 2, and implement a ‘perturbative’ method, adapting ideas of Majda and Vainberg. The spectrum of A is defined in section 2, a limiting absorption principle is proved in section 3 outside of a countable set Γ(A). The points of Γ(A) can only accumulate at the left of the thresholds of the free propagators. The needed material about Aj, j=1, 2, and some technical estimates for A are given in Appendix. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    On the controllability of a robot arm (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 25-42 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Considered is the rotation of a robot arm or rod in a horizontal plane about an axis through the arm's fixed end and driven by a motor whose torque is controlled. The model was derived and investigated computationally by Sakawa and co-authors in [7] for the case that the arm is described as a homogeneous Euler beam. The resulting equation of motion is a partial differential equation of the type of a wave equation which is linear with respect to the state, if the control is fixed, and non-linear with respect to the control.Considered is the problem of steering the beam, within a given time interval, from the position of rest for the angle zero into the position of rest under a certain given angle.At first we show that, for every L2-control, there is exactly one (weak) solution of the initial boundary value problem which describes the vibrating system without the end condition.Then we show that the problem of controllability is equivalent to a non-linear moment problem. This, however, is not exactly solvable. Therefore, an iteration method is developed which leads to an approximate solution of sufficient accuracy in two steps. This method is numerically implemented and demonstrated by an example. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Models of superconducting-normal-superconducting junctions (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 59-91 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A time-dependent Ginzburg-Landau-type model of a superconducting-normal-superconducting junction is presented. The existence and the uniqueness of the solutions are proved. When the data of the model are symmetric of some kinds, the solutions turns out to be symmetric of some kinds. In this symmetric case, an approximate model with the small thickness of the normal material in the middle of the junction as coefficients of a differential system is established for the sake of numerical computations. And also the existence and the uniqueness of the solution to this approximate model are set up. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A system of boundary integral equations for polygonal plates with free edges (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 165-185 
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    ISSN: 0170-4214
    Keywords: boundary integral equations ; boundary finite element ; free edge polygonal plate ; hypersingular kernels ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the problem of a polygonal plate with free edges. It is a boundary value problem for the biharmonic operator on a polygon with Neumann boundary conditions. Its resolution is studied via boundary integral equations. A variational formulation of the boundary problem obtained by a double-layer potential is given. Finally, we implement the method and give numerical results. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Wavelet approximations on closed surfaces and their application to boundary-value problems of potential theory (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 129-163 
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    ISSN: 0170-4214
    Keywords: wavelets on closed surfaces ; Dirichlet's and Neumann's problem ; scaling function ; scale discrete wavelets ; integral formulas ; exact fully discrete wavelet transform ; band-limited harmonic wavelets ; Runge-Walsh approximation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Wavelets on closed surfaces in Euclidean space ∝3 are introduced starting from a scale discrete wavelet transform for potentials harmonic down to a spherical boundary. Essential tools for approximation are integration formulas relating an integral over the sphere to suitable linear combinations of function values (resp. normal derivatives) on the closed surface under consideration. A scale discrete version of multiresolution is described for potential functions harmonic outside the closed surface and regular at infinity. Furthermore, an exact fully discrete wavelet approximation is developed in case of band-limited wavelets. Finally, the role of wavelets is discussed in three problems, namely (i) the representation of a function on a closed surface from discretely given data, (ii) the (discrete) solution of the exterior Dirichlet problem, and (iii) the (discrete) solution of the exterior Neumann problem. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A reaction-diffusion problem with a reaction front (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 417-432 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We state a 1D model with quasi-stationary gas flows approximation for a carbon reactivity test in the production of silicon. The mathematical problem we formulate is a non-linear boundary value problem for a third-order ordinary differential equation with non-linear boundary conditions, which are non-local in time. We prove existence and uniqueness of a classical solution and provide a numerical example. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical justification of a one-dimensional model for general elastic shallow arches (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 281-325 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present a bending model for a shallow arch, namely the type of curved rod where the curvature is of the order of the diameter of the cross section. The model is deduced in a rigorous mathematical way from classical tridimensional linear elasticity theory via asymptotic techniques, by taking the limit on a suitable re-scaled formulation of that problem as the diameter of the cross section tends to zero. This model is valid for general cases of applied forces and material, and it allows us to calculate displacements, axial stresses, bending moments and shear forces. The equations present a more general form than in the classical Bernoulli-Navier bending theory for straight slender rods, so that flexures and extensions are proved to be coupled in the most general case. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Integro-differential equation modelling heat transfer in conducting, radiating and semitransparent materials (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 375-392 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this work we analyse a model for radiative heat transfer in materials that are conductive, grey and semitransparent. Such materials are for example glass, silicon, water and several gases. The most important feature of the model is the non-local interaction due to exchange of radiation. This, together with non-linearity arising from the well-known Stefan-Boltzmann law, makes the resulting heat equation non-monotone. By analysing the terms related to heat radiation we prove that the operator defining the problem is pseudomonotone. Hence, we can prove the existence of weak solution in the cases where coercivity can be obtained. In the general case, we prove the solvability of the system using the technique of sub and supersolutions. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Control of the thermoelastic model of a plate activated by shape memory alloy reinforcements (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 589-603 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the paper we study the problem of control by means of a heat source g for a thermoelastic system of equationsutt - ρ∇·p(θ, ∇u) - νΔut + DΔ2 u = f, cv(θ, ∇u)θt - κΔθ - ρθ[pθ (θ, ∇u)·∇ut] - ν∣∇ut∣2 = g, in a two-dimensional domain, where both viscosity ν and rigidity D are positive. Such a system has been considered in our former papers, and existence of solutions as well as uniqueness have been obtained. Here we prove the continuity and differentiability of solutions under somewhat stronger assumptions. An example of a control problem and necessary optimality conditions are presented. The system has an interpretation as a plate reinforced with shape memory alloy (SMA) wire mesh. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Bäcklund transformations: exact solutions for the KdV and the Calogero-Degasperis-Fokas mKdV equations (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 719-731 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The exact solutions for the KdV and the Calogero-Degasperis-Fokas mKdV equations can be obtained by the AKNS class. The technique developed relies on the construction of the wave functions which are solutions of the associated AKNS system; that is, a linear eigenvalue problem in the form of a system of first order partial differential equations. The method of characteristics is used and Bäcklund transformations (BTs) are employed to generate two new solutions from the old. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On the existence of a global classical solution of the boundary value problem for □u-μu+aum=0 in the interior domain (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 781-795 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the boundary value problem for a semilinear equation□u(t, x)-μu(t, x)+aum(t, x)=0, μ〉0, a∊ℜ in the interior domain. We find a time global classical solution with exponential decay property by using singular hyperbolic equation. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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