arXiv subjects

Gene F. Mazenko

Publications and source records attributed to Gene F. Mazenko.

At least 37 records · Page 2Linked to original sources

arXiv2003

Defect Structures in the Growth Kinetics of the Swift-Hohenberg Model

The growth of striped order resulting from a quench of the two-dimensional Swift-Hohenberg model is studied in the regime of a small control parameter and quenches to zero temperature. We introduce an algorithm for finding and identifying the disordering defects (dislocations, disclinations and grain boundaries) at a given time. We can track their trajectories separately. We find that the coarsening of the defects and lowering of the effective free energy in the system are governed by a growth law $L(t)\approx t^{x}$ with an exponent x near 1/3. We obtain scaling for the correlations of the nematic order parameter with the same growth law. The scaling for the order parameter structure factor is governed, as found by others, by a growth law with an exponent smaller than x and near to 1/4. By comparing two systems with different sizes, we clarify the finite size effect. We find that the system has a very low density of disclinations compared to that for dislocations and fraction of points in grain boundaries. We also measure the speed distributions of the defects at different times and find that they all have power-law tails and the average speed decreases as a power law.

cond-mat.soft↗

arXiv2002

Granular clustering in a hydrodynamic simulation

We present a numerical simulation of a granular material using hydrodynamic equations. We show that, in the absence of external forces, such a system phase-separates into high density and low density regions. We show that this separation is dependent on the inelasticity of collisions, and comment on the mechanism for this clustering behavior. Our results are compatible with the granular clustering seen in experiments and molecular dynamic simulations of inelastic hard disks.

cond-mat.soft↗

arXiv2001

Defect Statistics in the Two Dimensional Complex Ginsburg-Landau Model

The statistical correlations between defects in the two dimensional complex Ginsburg-Landau model are studied in the defect-coarsening regime. In particular the defect-velocity probability distribution is determined and has the same high velocity tail found for the purely dissipative time-dependent Ginsburg-Landau (TDGL) model. The spiral arms of the defects lead to a very different behavior for the order parameter correlation function in the scaling regime compared to the results for the TDGL model.

cond-mat.stat-mech↗

arXiv2001

A nonlinear hydrodynamical approach to granular materials

We propose a nonlinear hydrodynamical model of granular materials. We show how this model describes the formation of a sand pile from a homogeneous distribution of material under gravity, and then discuss a simulation of a rotating sandpile which shows, in qualitative agreement with experiment, a static and dynamic angle of repose.

cond-mat.soft↗

arXiv2000

Spinodal Decomposition and the Tomita Sum Rule

The scaling properties of a phase-ordering system with a conserved order parameter are studied. The theory developed leads to scaling functions satisfying certain general properties including the Tomita sum rule. The theory also gives good agreement with numerical results for the order parameter scaling function in three dimensions. The values of the associated nonequilibrium decay exponents are given by the known lower bounds.

cond-mat.stat-mech↗

arXiv1999

Perturbation Expansion in Phase-Ordering Kinetics: II. N-vector Model

The perturbation theory expansion presented earlier to describe the phase-ordering kinetics in the case of a nonconserved scalar order parameter is generalized to the case of the $n$-vector model. At lowest order in this expansion, as in the scalar case, one obtains the theory due to Ohta, Jasnow and Kawasaki (OJK). The second-order corrections for the nonequilibrium exponents are worked out explicitly in $d$ dimensions and as a function of the number of components $n$ of the order parameter. In the formulation developed here the corrections to the OJK results are found to go to zero in the large $n$ and $d$ limits. Indeed, the large-$d$ convergence is exponential.

cond-mat.stat-mech↗

arXiv1998

Velocity Distribution for Strings in Phase Ordering Kinetics

The continuity equations expressing conservation of string defect charge can be used to find an explicit expression for the string velocity field in terms of the order parameter in the case of an O(n) symmetric time-dependent Ginzburg-Landau model. This expression for the velocity is used to find the string velocity probability distribution in the case of phase-ordering kinetics for a nonconserved order parameter. For long times $t$ after the quench, velocities scale as $t^{-1/2}$. There is a large velocity tail in the distribution corresponding to annihilation of defects which goes as $V^{-(2d+2-n)}$ for both point and string defects in $d$ spatial dimensions.

cond-mat.stat-mech↗

arXiv1998

Perturbation Expansion in Phase-Ordering Kinetics: I. Scalar Order Parameter

A consistent perturbation theory expansion is presented for phase-ordering kinetics in the case of a nonconserved scalar order parameter. At zeroth order in this expansion one obtains the theory due to Ohta, Jasnow and Kawasaki (OJK). At the next nontrivial order in the expansion, worked out in d dimensions, one has small corrections to the OJK result for the nonequilibrium exponent $λ$ and the introduction of a new exponent $ν$ governing the algebraic component of the decay of the order parameter scaling function at large scaled distances.

cond-mat.stat-mech↗

arXiv1997

Perturbation Expansion in Phase Ordering Kinetics

A consistent perturbation theory expansion is presented for phase ordering kinetics in the case of a nonconserved scalar order parameter. At lowest order in this formal expansion one obtains the theory due to Ohta, Jasnow and Kawasaki (OJK). At next order, worked out explicitly in d dimensions, one has small corrections to the OJK result for the nonequilibrium exponent $λ$ and the introduction of a new exponent $ν$ governing the algebraic component of the decay of the order parameter scaling function at large scaled distances.

cond-mat.stat-mech↗

arXiv1997

Vortex Velocity Pair Correlations

The vortex velocity probability distribution for two distinct vortices is determined for the case of phase-ordering kinetics in systems with point defects. The n-vector model driven by time-dependent Ginzburg-Landau dynamics for a nonconserved order parameter is considered. The description includes the effects of other vortices and order parameter fluctuations. At short distances the most probable configuration is that a vortex-antivortex pair have only a nonzero relative velocity which is inversely proportional to the distance between them. The coefficient of proportionality is determined explicitly.

cond-mat↗

arXiv1997

Ordering kinetics of defect structures

We show how the continuity equations expressing conservation of topological point or string defect charge can be used to determine the order-parameter correlation function for the phase-ordering kinetics of the O(n) model in the special case where the order parameter is constrained to be near a defect core. In this regime we find a self-consistent solution by assuming the order parameter is Gaussian. The resulting linear equation for the order-parameter correlation function has as its solution the Ohta-Jasnow-Kawasaki form.

cond-mat↗

arXiv1996

Vortex annihilation in the ordering kinetics of the O(2) model

The vortex-vortex and vortex-antivortex correlation functions are determined for the two-dimensional O(2) model undergoing phase ordering. We find reasonably good agreement with simulation results for the vortex-vortex correlation function where there is a short-scaled distance depletion zone due to the repulsion of like-signed vortices. The vortex-antivortex correlation function agrees well with simulation results for intermediate and long-scaled distances. At short-scaled distances the simulations show a depletion zone not seen in the theory.

cond-mat↗

arXiv1996

Vortex Velocities in the O(n) Symmetric TDGL Model

An explicit expression for the vortex velocity field as a function of the order parameter field is derived for the case of point defects in the O(n) symmetric time-dependent Ginzburg-Landau model. This expression is used to find the vortex velocity probability distribution in the gaussian closure approximation in the case of phase ordering kinetics for a nonconserved order parameter. The velocity scales as $L^{-1}$ in scaling regime where $L\approx t^{1/2}$ and t is the time after the quench.

cond-mat↗

arXiv1996

Fluctuations and defect-defect correlations in the ordering kinetics of the O(2) model

The theory of phase ordering kinetics for the O(2) model using the gaussian auxiliary field approach is reexamined from two points of view. The effects of fluctuations about the ordering field are included and we organize the theory such that the auxiliary field correlation function is analytic in the short-scaled distance (x) expansion. These two points are connected and we find in the refined theory that the divergence at the origin in the defect-defect correlation function $\tilde{g}(x)$ obtained in the original theory is removed. Modifications to the order-parameter autocorrelation exponent $λ$ are computed.

cond-mat↗

arXiv1996

Phase ordering of the O(2) model in the post-gaussian approximation

The gaussian closure approximation previously used to study the growth kinetics of the non-conserved O(n) model is shown to be the zeroth-order approximation in a well-defined sequence of approximations composing a more elaborate theory. This paper studies the effects of including the next non-trivial correction in this sequence for the case n=2. The scaling forms for the order-parameter and order-parameter squared correlation functions are determined for the physically interesting cases of the O(2) model in two and three spatial dimensions. The post-gaussian versions of these quantities show improved agreement with simulations. Post-gaussian formulae for the defect density and the defect-defect correlation function $\tilde{g}(x)$ are derived. As in the previous gaussian theory, the addition of fluctuations allows one to eliminate the unphysical divergence in $\tilde{g}(x)$ at short scaled-distances. The non-trivial exponent $λ$, governing the decay of order-parameter auto-correlations, is computed in this approximation both with and without fluctuations.

cond-mat↗

arXiv1994

Metastable Dynamics above the Glass Transition

The element of metastability is incorporated in the fluctuating nonlinear hydrodynamic description of the mode coupling theory (MCT) of the liquid-glass transition. This is achieved through the introduction of the defect density variable $n$ into the set of slow variables with the mass density $ρ$ and the momentum density ${\bf g}$. As a first approximation, we consider the case where motions associated with $n$ are much slower than those associated with $ρ$. Self-consistently, assuming one is near a critical surface in the MCT sense, we find that the observed slowing down of the dynamics corresponds to a certain limit of a very shallow metastable well and a weak coupling between $ρ$ and $n$. The metastability parameters as well as the exponents describing the observed sequence of time relaxations are given as smooth functions of the temperature without any evidence for a special temperature. We then investigate the case where the defect dynamics is included. We find that the slowing down of the dynamics corresponds to the system arranging itself such that the kinetic coefficient $γ_v$ governing the diffusion of the defects approaches from above a small temperature-dependent value $γ^c_v$.

cond-mat↗

arXiv1994

Density nonlinearities and a field theory for the dynamics of simple fluids

We study the role of the Jacobian arising from a constraint enforcing the nonlinear relation: ${\bf g}=ρ{\bf V}$, where $ρ,\: {\bf g}$ and ${\bf V}$ are the mass density, the momentum density and the local velocity field, respectively, in the field theoretic formulation of the nonlinear fluctuating hydrodynamics of simple fluids. By investigating the Jacobian directly and by developing a field theoretic formulation without the constraint, we find that no changes in dynamics result as compared to the previous formulation developed by Das and Mazenko (DM). In particular, the cutoff mechanism discovered by DM is shown to be a consequence of the $1/ρ$ nonlinearity in the problem not of the constraint. The consequences of this result for the static properties of the system is also discussed.

cond-mat↗

arXiv1994

Metastability, Mode Coupling and the Glass Transition

Mode coupling theory (MCT) has been successful in explaining the observed sequence of time relaxations in dense fluids. Previous expositions of this theory showing this sequence have required the existence of an ideal glass transition temperature $T_0$. Recent experiments show no evidence of $T_0$. We show here how the theory can be reformulated, in a fundamental way, such that one retains this sequence of relaxation behaviors but with a smooth temperature dependence and without any indication of $T_0$. The key ingredient in the reformulation is the inclusion of the metastable nature of the glass transition problem through a coupling of the mass density to the defect density. A main result of our theory is that the exponents governing the sequence of time relaxations are weak functions of the temperature in contrast to the results from conventional MCT.

cond-mat↗