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  • 1
    Electronic Resource
    Electronic Resource
    Singular solutions of the Zakharov equations for Langmuir turbulence (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 969-980 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A dynamic rescaling method is used to simulate numerically the dynamics of a collapsing wave packet in three-dimensional Langmuir turbulence, governed by the vector Zakharov equations. Subsonic and supersonic regimes are considered. For a large class of initial conditions with a single maximum for the field intensity, the collapse is found to be nearly self-similar and weakly anisotropic, while in the subsonic or near subsonic limit the electric field may develop strong anisotropy at early times and break apart into two peaks.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859852
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  • 2
    Electronic Resource
    Electronic Resource
    A random wave process (1984)
    Springer
    Applied mathematics & optimization 12 (1984), S. 97-114 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The parabolic or forward scattering approximation to the equation describing wave propagation in a random medium leads to a stochastic partial differential equation which has the form of a random Schrödinger equation. Existence, uniqueness and continuity of solutions to this equation are established. The resulting process is a Markov diffusion process on the unit sphere in complex Hilbert space. Using Markov methods a limiting Markov process is identified in the case of a narrow beam limit; this limiting process corresponds to a simple random translation of the beam known as “spot-dancing.”
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01449037
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  • 3
    Electronic Resource
    Electronic Resource
    Nonlinear diffusion limit for a system with nearest neighbor interactions (1988)
    Springer
    Communications in mathematical physics 118 (1988), S. 31-59 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider a system of interacting diffusions. The variables are to be thought of as charges at sites indexed by a periodic one-dimensional lattice. The diffusion preserves the total charge and the interaction is of nearest neighbor type. With the appropriate scaling of lattice spacing and time, a nonlinear diffusion equation is derived for the time evolution of the macroscopic charge density.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01218476
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  • 4
    Electronic Resource
    Electronic Resource
    A limit theorem for stochastic acceleration (1980)
    Springer
    Communications in mathematical physics 78 (1980), S. 19-63 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the motion of a particle in a weak mean zero random force fieldF, which depends on the position,x(t), and the velocity,v(t)= $$\dot x$$ (t). The equation of motion is $$\ddot x$$ (t)=ɛF(x(t),v(t), ω), wherex(·) andv(·) take values in ℝ d ,d≧3, and ω ranges over some probability space. We show, under suitable mixing and moment conditions onF, that as ɛ→0,v ɛ (t)≡v(t/ɛ2) converges weakly to a diffusion Markov processv(t), and ɛ2 x ɛ (t) converges weakly to $$\int\limits_0^t {v(s)ds + x} $$ , wherex=lim ɛ2 x ɛ (0).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01941968
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  • 5
    Electronic Resource
    Electronic Resource
    A limit theorem for turbulent diffusion (1979)
    Springer
    Communications in mathematical physics 65 (1979), S. 97-128 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We show under some specific conditions that the formal diffusion approximation for the motion of a particle in a random velocity field is valid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01225144
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  • 6
    Electronic Resource
    Electronic Resource
    Buckling of randomly imperfect beams (1989)
    Springer
    Acta applicandae mathematicae 17 (1989), S. 269-286 
    Details
    ISSN: 1572-9036
    Keywords: 58F14 ; 35C20 ; 35F20 ; Stochastic bifurcation ; buckling ; asymptotic expansion ; nonlinear equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The qualitative behavior of buckled states of two different models of elastic beams is studied. It is assumed that random imperfections affect the governing nonlinear equations. It is shown that near the first critical value of the buckling load the stochastic bifurcation is described asymptotically by an algebraic equation whose coeffficients are Gaussian random variables. The corresponding asymptotic expansion for the displacement is to lowest order a Gaussian stochastic process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00047074
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  • 7
    Electronic Resource
    Electronic Resource
    Dynamic crack propagation behaviour of rubber-toughened poly(methyl methacrylate) (1986)
    Springer
    Journal of materials science 21 (1986), S. 4281-4288 
    Details
    ISSN: 1573-4803
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Dynamic crack propagation has been studied in detail for a series of transparent rubber-toughened samples of poly(methyl methacrylate) using a combination of high-speed photography and the optical method of transmitted caustics. The dynamic stress intensity factor has been measured as a function of rubber content, crack length and loading rate. The dynamic stress intensity factor is found to increase significantly as the rubber content increases, which is consistent with the improvement in impact behaviour found on the addition of rubber particles. It is proposed that the toughening takes place through crack tip blunting caused by localized shear yielding induced by the presence of the rubber particles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01106542
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  • 8
    Electronic Resource
    Electronic Resource
    Rubber-modified polymer composites (1987)
    Springer
    Journal of materials science 22 (1987), S. 3417-3420 
    Details
    ISSN: 1573-4803
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The effect of rubber modification on the mechanical properties of a polymer composite consisting of polymethyl methacrylate (PMMA) beads embedded in a PMMA matrix was studied. The synthetic rubber used, a styrene-butadiene copolymer (SBR), was dissolved after mastication into the methyl methacrylate monomer, thus ensuring that rubber dispersion takes place in the matrix phase. The results obtained show that the mechanical properties of the rubber-modified material produced by the technique described are greatly dependent on the total rubber content, since it affects the form and particle size of the dispersed phase.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01161214
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  • 9
    Electronic Resource
    Electronic Resource
    Dynamic crack propagation in rubber-modified composite models (1988)
    Springer
    Journal of materials science 23 (1988), S. 3421-3434 
    Details
    ISSN: 1573-4803
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The dynamic crack propagation behaviour of several rubber-modified composite models has been studied. In all cases the method of high speed photography along with the method of dynamic caustics was used. Results of crack propagation mode observation, fracture toughness and crack propagation velocity measurements are presented here. Especially in the case of two “complex” inclusions it was found that the crack propagation mode is highly rate dependent. At low test rates the crack growth tends to follow an almost straight crack path while an increase in strain rate in general results in the formation of a kink in the interparticle area. In the same area a crack propagation delay, and in some cases arrest, was observed while both the crack propagation velocity v and dynamic stress intensity factor K i d showed an intense variation. For the sake of comparison, specimens with one and/or two press-fitting inclusions as well as with two holes were fractured under dynamic loads. In all cases both qualitative and quantitative results were obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00540474
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  • 10
    Electronic Resource
    Electronic Resource
    Viscoelastic modelling and strain-rate behaviour of plasticized poly(vinyl chloride) (1991)
    Springer
    Journal of materials science 26 (1991), S. 4323-4330 
    Details
    ISSN: 1573-4803
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The effect of four different types of plasticizers and four strain-rates on the tensile behaviour of poly(vinyl chloride) (PVC) has been studied. di(2-ethylhexyl phthalate), benzyl butyl phthalate, epoxidized soyabean oil and chloroparaffin were mixed at different ratios and were used as plasticizers in concentration levels of up to 77% of the PVC weight. The plasticized and unplasticized PVC were processed into sheets by compression moulding. Tensile tests were conducted at different strain rates. It was found that tensile modulus increases with increasing strain rate while it decreases with increasing plasticizer concentration. The rate of variation of tensile modulus either as a function of strain rate and/or the plasticizer concentration was, in all cases, dependent on the mixing ratio of the different types of plasticizers. Assuming the material to be a linearly viscoelastic one, a simple viscoelastic model along with a least-squares-based computer procedure was applied which enabled us to fit the experimentally obtained curves with the respective theoretical predictions as well as to study the strain-rate effect on the relaxation spectrum, H(τ), of the material under consideration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00543646
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