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  • 1
    Electronic Resource
    Electronic Resource
    Three-dimensional frictionless contact between layered elastic bodies and incorporating sharp edges (1991)
    Springer
    Computational mechanics 8 (1991), S. 257-268 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The roller coating system used in industry to apply paint to sheet metal involves two contacting rolling cylinders, one of which is rubber covered and through which the sheet metal travels. Of particular concern in the industry is the effect of high pressures upon the flow of paint at the ends of the rollers. In an elastohydrodynamic-lubrication analysis of the paint flow, it is the corresponding “dry-contact pressure” which is of major concern. In this paper we present a numerical solution to the three-dimensional contact problem for both smooth profiled layered bodies and those which involve sharp edges but in both cases ignoring the effects of curvature. The procedure adopted is based on one previously developed by a number of authors for homogeneous bodies. An understanding of the consequences of changing the operating variables is of prime importance in an industrial scenario. The numerical scheme described here provides complete measurements of both the deformation and the contact pressure distribution for given operating variables, which are the elastic properties and dimensions of both rolls and the total applied force.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00577379
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  • 2
    Electronic Resource
    Electronic Resource
    Utilization of nonlinear diffusion solutions forn-diffusion and power-law materials (1992)
    Springer
    Acta mechanica 91 (1992), S. 193-208 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The equation ofn-diffusion, as originally formulated by J. R. Philip for various problems involving unsteady turbulent flows, applies directly to the one-dimensional flow of a non-Newtonian power-law fluid as well as indirectly to the laminar boundary layer flow of such fluids over a flat plate. The purpose of this note is to utilize a simple relation between one-dimensionaln-diffusion and nonlinear diffusion with power-law diffusivity such that ifp(x, t) denotes ann-diffusion pressure thenc(x, t)=|ϖp/ϖx| satisfies the nonlinear diffusion equation with power law diffusivity. This means in particular that the large number of solutions presently known for nonlinear diffusion can be utilized in the context ofn-diffusion. Known solutions ofn-diffusion are obtained via this procedure as well as newn-diffusion solutions, including the source solution and a solution of the problem of fluid withdrawal at a constant flow rate for a non-Newtonian fluid in a porous medium of infinite extent. Solutions arising from other exact nonlinear diffusion profiles are also investigated as well as the limiting case ofn-diffusion forn tending to infinity and the results are displayed graphically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01194109
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  • 3
    Electronic Resource
    Electronic Resource
    An approximate solution for planar solidification with Newton cooling at the surface (1985)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 36 (1985), S. 637-647 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Das klassische Problem der Bestimmung der variablen Grenze beim Gefrieren eines halbunendlich gesättigten Fluids mit Newton-Kühlung an der Wand besitzt bekanntlich keine geschlossene Lösung. Näherungslösungen sind nur für große Stefan-Zahlen bekannt. Bei Newton Kühlung erfordern die gängigen numerischen Methoden eine Schrittweite, die so klein ist, daß genaue Resultate große Rechenzeiten erfordern. Hier werden zwei Näherungslösungen konstruiert, die eine für kleine und die andere für große Zeiten. Im Fall einer großen Stefan-Zahlα erhalten wir mit beiden Lösungen einen pseudostationären Zustand mit Korrekturen erster Ordnung. Der Grenzfall der verschwindenden Newton-Kühlung ergibt genau die bekannte Stefan-oder Neumann-Lösung. Im allgemeinen Fall wird die Gültigkeit der Näherung durch Vergleich mit Resultaten früherer Arbeiten sowie mit bekannten oberen und unteren Schranken verifiziert.
    Notes: Summary The classical moving boundary problem for the planar freezing of a semi-infinite saturated liquid with Newton cooling at the wall is well known not to admit an exact solution. Existing perturbation solutions are valid only when the Stefan number is large. Further, since the implementation of the Newton cooling condition involves the step size, numerical solutions are only accurate if extremely small sizes are taken which involves large computing times. Here two new approximate analytic solutions are obtained, the first is an initial or starting solution while the second is valid for subsequent times. In the limit of large Stefan numberα the pseudo-steady state and first order corrected motions arise from both approximations. Further, in the limit of no Newton cooling at the wall the large time solution gives rise to precisely the well known Stefan or Neumann solution. The validity of the approximations is illustrated numerically with reference to previous work and known upper and lower bounds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00960376
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  • 4
    Electronic Resource
    Electronic Resource
    Molecular dynamics simulation of granular flows: Slip along rough inclined planes (1998)
    Springer
    Computational mechanics 22 (1998), S. 160-166 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Although the velocity slip of granular flows on an inclined plane has been observed in many experiments, sufficient detail is not available for comparison with theoretical predictions. In this paper, we employ a molecular dynamics simulation technique to model the flow of a granular material down a rough inclined plane, with attention being focused on the effect of the boundary roughness and the angle of inclination of the plane. We find that the parameter θ proposed in the literature, which characterises the extent of flowing particles “penetrating” into the boundary, is not the decisive factor for the measurement of the boundary roughness. Slip velocity is found to be linearly proportional to the angle of inclination, but there is a non-linear relation with the boundary parameter θ. The average shear rate produced depends non-linearly on the inclination angle but the influence of the boundary parameter θ on the shear rate is not obvious.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050349
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  • 5
    Electronic Resource
    Electronic Resource
    Similarity solutions for nonlinear diffusion — further exact solutions (1990)
    Springer
    Journal of engineering mathematics 24 (1990), S. 109-124 
    Details
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract Although the nonlinear diffusion equation has been extensively studied and there exists substantial literature in many diverse areas of science and technology, the number of exact concentration profiles is nevertheless limited. In a recent article in this journal (Hill [1]) a brief review of known exact results is given, as well as an elementary integration procedure which appears to be a general device for obtaining integrals associated with similarity solutions. This paper extends the results given in [1] and for particular power law diffusivitiesc m (such asm = −/12, −1, −/32 and −2) presents a number of new exact solutions obtained by fully integrating the ordinary differential equations derived in [1]. In addition new results are found for a general nonlinear diffusion equation which includes one-dimensional diffusion with an inhomogenouus and nonlinear diffusivityc mxmas well as symmetric nonlinear diffusion in cylinders and spheres. Moreover by a separate and ad-hoc procedure a new solution is obtained of the travelling wave type but with a variable wave speed. Some of the new exact solutions obtained for one-dimensional nonlinear diffusion with power law diffusivitiesc mare illustrated graphically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00129869
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  • 6
    Electronic Resource
    Electronic Resource
    Recent progress on the Columbus Project and the Miror Laboratory program (1989)
    Springer
    Astrophysics and space science 160 (1989), S. 55-70 
    Details
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper summarizes recent advances on the Columbus Project telescope and in the University of Arizona Mirror Lab. The Columbus telescope structure has been re-optimized to allow rapid changes between foci, while still maintaining high rigidity. Room has been made to translate secondary and tertiary spiders out of the light path to the center. A bill allowing construction of the telescope on Mt. Graham, Arizona, has been passed by Congress and signed into law. Two alternative enclosure designs, one with a co-rotating building and a second which opens like a flower, are being explored. A common baseline design for the 8 m honeycomb mirrors for both the Columbus and Magellan telescopes has been developed. It has stiffness comparable to that of the Palomar 200 inch mirror. The Mirror Lab has successfully cast two 3.5 m honeycomb blanks and expects to begin casting at the 6.5 and 8 m scale at the end of 1990. Interferometric tests of the Vatican f/1 1.8 m borosilicate honeycomb mirror show good stability of figure with the air jet ventilation system. A 60 cm stressed lap has been completed, and will be used to parabolize this mirror which is now polished as an f/1 sphere. Plans for a polishing facility to house two 8 m machines and a test tower are complete, with construction starting in April 1989.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00642755
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  • 7
    Electronic Resource
    Electronic Resource
    Geographic information systems as applied to the manipulation of environmental data (1983)
    Springer
    The environmentalist 3 (1983), S. 33-38 
    Details
    ISSN: 1573-2991
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Energy, Environment Protection, Nuclear Power Engineering
    Notes: Summary As the nationwide and worldwide shortages of natural resources become more apparent, and demand rises, there is little doubt that managers will need to better acquire, organize and manipulate environmental data for decision-making purposes. A Geographic Information System (GIS) is a computerized system for processing geographic and/or mapped data. In the development of a GIS it is felt that the system should be capable of processing a wide variety of pertinent data including points, maps, lines, and aircraft or satellite derived information. The Remote Sensing and Image Processing Laboratory (RSIP), Louisiana State University, had a basic system for image processing that was expanded to incorporate the needed functions for utilizing GIS oriented capabilities. This paper will focus on two aspects of a GIS; (1) the components of and implementation of a GIS, and (2) the actual demonstration of a GIS in the management of natural resources. Demonstrations related to lignite mining, permit requirements in the coastal zone, and location of potential landfills and hazardous waste sites will be presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02240042
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  • 8
    Electronic Resource
    Electronic Resource
    Similarity solutions for nonlinear diffusion — a new integration procedure (1989)
    Springer
    Journal of engineering mathematics 23 (1989), S. 141-155 
    Details
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract The nonlinear diffusion equation arises in many important areas of science and technology and most of the known exact solutions turn out to be similarity solutions. For a general similarity solution involving an arbitrary parameter λ, a new integration procedure is proposed which enables first integrals to be obtained for special values of λ. The best known exact solutions arise from this analysis when the integration constant is taken to be zero and the procedure provides a natural way of deducing other special exact solutions. A new exact solution is obtained for the power law diffusivity of index —4/3 and new first integrals are deduced for a general equation which includes nonlinear cylindrical and spherical symmetrical diffusion and one-dimensional nonlinear diffusion with an inhomogeneous diffusivity. The procedure has given rise to an extensive number of first-order ordinary differential equations which include a wide variety of differing physical situations and which warrant further study either analytically to determine exact integrals or numerically for particular boundary value problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00128865
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  • 9
    Electronic Resource
    Electronic Resource
    Symmetry Reductions of Equations for Solute Transport in Soil (2000)
    Springer
    Nonlinear dynamics 22 (2000), S. 15-27 
    Details
    ISSN: 1573-269X
    Keywords: solute transport ; saturated soil ; dispersion ; Fokker–Planck
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Solute transport in saturated soil is represented by anonlinear system consisting of a Fokker–Planck equation coupled toLaplace's equation. Symmetries, reductions and exact solutions are foundfor two dimensional transient solute transport through some nontrivialwedge and spiral steady water flow fields. In particular, the mostgeneral complex velocity potential is determined, such that the soluteequation admits a stretching group of transformations that wouldnormally be possessed by a point source solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008309107295
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  • 10
    Electronic Resource
    Electronic Resource
    Finite elastic eversion of a thick-walled incompressible spherical cap (2000)
    Springer
    Journal of engineering mathematics 37 (2000), S. 93-109 
    Details
    ISSN: 1573-2703
    Keywords: perfectly elastic ; incompressible ; Varga strain-energy ; spherical eversion ; exact solution.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract For perfectly elastic rubber-like materials, which are capable of undergoing extremely large deformations, the number of exact solutions remains limited, especially in the context of fully three-dimensional deformations. Here a simple exact solution describing the finite elastic eversion of a sector of a thick-walled incompressible spherical shell is determined for the modified Varga elastic material. This new solution, which describes a portion of a spherical shell being turned inside out, is deduced from a known simplified system and it is shown, by solving the full equilibrium equations, that no further solutions of this type can be deduced for this particular material. Further, a general family of response functions is considered, which involves an arbitrary index n, and which incorporates standard materials such as the neo-Hookean and Varga strain-energy functions. It is established that other than n=1 (namely the Varga material) only the special case n=2 admits nontrivial solutions to the eversion problem, but the resulting second-order highly nonlinear ordinary differential equation appears not to admit any simple analytical solutions. Finally, the new solution is examined as a potential solution of the 'snap-buckling' problem of a spherical cap. Unfortunately, the solution appears not to be applicable to this problem and instead it is presented in the specific context of the eversion of a thick-walled spherical cap, with no applied forces acting on one of the surfaces of the deformed configuration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004713707083
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