Biomedical subjects

Moshe Schwartz

Publications and source records attributed to Moshe Schwartz.

8 recordsLinked to original sources

PubMed2004

What is the connection between ballistic deposition and the Kardar-Parisi-Zhang equation?

Ballistic deposition (BD) is believed to belong to the Kardar-Parisi-Zhang (KPZ) universality class. In this paper we study the validity of this belief by rigorously deriving a continuum equation from the BD microscopic rules, which deviates from the KPZ equation. We show that in one dimension and in the presence of noise the deviation is not important. This is not the case in the absence of noise. In more than one dimension and in the presence of noise we obtain an equation that superficially seems to be a continuum equation but in which the symmetry under rotations around the growth direction is broken.

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PubMed2004

Persisting roughness when deposition stops.

Useful theories for growth of surfaces under random deposition of material have been developed by several authors. The simplest theory is that introduced by Edwards and Wilkinson (EW), which is linear and soluble. Its nonlinear generalization by Kardar, Parisi, and Zhang (KPZ) resulted in many subsequent studies. Yet both EW and KPZ theories contain an unphysical feature. When deposition of material is stopped, both theories predict that as time tends to infinity, the surface becomes flat. In fact, of course, the final surface is not flat, but simply has no gradients larger than the gradient related to the angle of repose. We modify the EW and KPZ theories to accommodate this feature and study the consequences for the simpler system which is a modification of the EW equation. In spite of the fact that the equation describing the evolution of the surface is not linear, we find that the steady state in the presence of noise is not very different in the long-wavelength limit from that of the linear EW equation. The situation is quite different from that of EW when deposition stops. Initially there is still some rearrangement of the surface, but that stops as everywhere on the surface the gradient is less than that related to the angle of repose. The most interesting feature observed after deposition stops is the emergence of history-dependent steady-state distributions.

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PubMed2004

Bose-Einstein condensation and the glassy state.

The distinction between a classical glass and a classical liquid is difficult, since both are disordered. The difference is in the fact that a glass is frozen while the liquid is not. In this Letter an equilibrium measure is suggested that distinguishes between a glass and a liquid. The choice of this measure is based on the idea that in a system which is not frozen symmetry under permutation of particles is physically relevant, because particles can be permuted by actual physical motion. This is not the case in a frozen system. In this Letter it is shown how to generalize naturally the quantum mechanical concept of Bose condensed fraction to classical systems in order to distinguish between the glass and the liquid. It is finite in the liquid and zero in the frozen state. The actual value of the condensed fraction in the liquid may serve also as a measure of the glassiness in the liquid.

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PubMed2004

Kardar-Parisi-Zhang equation with temporally correlated noise: a self-consistent approach.

In this paper we discuss the well known Kardar-Parisi-Zhang (KPZ) equation driven by temporally correlated noise. We use a self-consistent approach to derive the scaling exponents of this system. We also draw general conclusions about the behavior of the dynamic structure factor Phiq(t) as a function of time. The approach we use here generalizes the well known self-consistent expansion (SCE) that was used successfully in the case of the KPZ equation driven by white noise, but unlike SCE, it is not based on a Fokker-Planck form of the KPZ equation, but rather on its Langevin form. A comparison to two other analytical methods, as well as to the only numerical study of this problem is made, and a need for an updated extensive numerical study is identified. We also show that a generalization of this method to any spatiotemporal correlations in the noise is possible, and two examples of this kind are considered.

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PubMed2004

Numerical evidence for stretched exponential relaxations in the Kardar-Parisi-Zhang equation.

We present results from extensive numerical integration of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions aimed to check the long-time behavior of the dynamical structure factor of that system. Over a number of decades in the size of the structure factor we confirm scaling and stretched exponential decay. We also give an analytic expression that yields a very good approximation to the numerical data. Our result clearly favors stretched exponential decay over recent results claiming to yield the exact time dependent structure factor of the 1+1 -dimensional KPZ system. We suggest a possible solution to that contradiction.

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PubMed2003

Shape fluctuations of a deformable body in a randomly stirred host fluid.

We consider a deformable body immersed in an incompressible fluid that is randomly stirred. Sticking to physical situations in which the body departs only slightly from its spherical shape, we investigate the deformations of the body. The shape is decomposed into spherical harmonic modes. We study the correlations of these modes for a general class of random flows that include, as a special case, the flow due to thermal agitation. Our results are general, in the sense that they are applicable to a large class of deformable bodies with energy that depends only on the shape of the body, and a general class of random flows.

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PubMed2003

Full reduction of large finite random Ising systems by real space renormalization group.

We describe how to evaluate approximately various physical interesting quantities in random Ising systems by direct renormalization of a finite system. The renormalization procedure is used to reduce the number of degrees of freedom to a number that is small enough, enabling direct summing over the surviving spins. This procedure can be used to obtain averages of functions of the surviving spins. We show how to evaluate averages that involve spins that do not survive the renormalization procedure. We show, for the random field Ising model, how to obtain Gamma(r)= - , the "connected" correlation function, and S(r)= , the "disconnected" correlation function. Consequently, we show how to obtain the average susceptibility and the average energy. For an Ising system with random bonds and random fields, we show how to obtain the average specific heat. We conclude by presenting our numerical results for the average susceptibility and the function Gamma(r) along one of the principal axes. (In this work, the full three-dimensional (3D) correlation is calculated and not just parameters such nu or eta). The results for the average susceptibility are used to extract the critical temperature and critical exponents of the 3D random field Ising system.

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PubMed2002

Diffusion of a nearly spherical deformable body in a randomly stirred host fluid.

The motion of a deformable body is investigated for cases in which the body is immersed in an incompressible fluid that is randomly stirred. Sticking to physical situations in which the body departs only slightly from its spherical shape, we show that the motion of its center is decoupled from its deformation degrees of freedom. We study the general case in which the velocity field, imposed on the system, is correlated both in space and time. We derive the mean-squared displacement of the body for the general random velocity field, and consider several useful cases including: white-noise flow, turbulence-like flow, and thermal agitation.

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