Biomedical subjects

Gene F Mazenko

Publications and source records attributed to Gene F Mazenko.

8 recordsLinked to original sources

PubMed2006

Growth of order in an anisotropic Swift-Hohenberg model.

We have studied the ordering kinetics of a two-dimensional anisotropic Swift-Hohenberg (SH) model numerically. The defect structure for this model is simpler than for the isotropic SH model. One finds only dislocations in the aligned ordering striped system. The motion of these point defects is strongly influenced by the anisotropic nature of the system. We developed accurate numerical methods for following the trajectories of dislocations. This allows us to carry out a detailed statistical analysis of the dynamics of the dislocations. The average speeds for the motion of the dislocations in the two orthogonal directions obey power laws in time with different amplitudes but the same exponents. The position and velocity distribution functions are only weakly anisotropic.

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PubMed2004

Vortex kinetics of conserved and nonconserved On models.

We study the motion of vortices in the conserved and nonconserved phase-ordering models. We give an analytical method for computing the speed and position distribution functions for pairs of annihilating point vortices based on heuristic scaling arguments. In the nonconserved case this method produces a speed distribution function consistent with previous analytic results. As two special examples, we simulate numerically the conserved and nonconserved O(2) model in two-dimensional space. The numerical results for the nonconserved case are consistent with the theoretical predictions. The speed distribution of the vortices in the conserved case is measured. Our theory produces a distribution function with the correct large speed tail but does not accurately describe the numerical data at small speeds. The position distribution functions for both models are measured and we find good agreement with our analytic results. We are also able to extend this method to models with a scalar order parameter.

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PubMed2004

Vortex velocity probability distributions in phase-ordering kinetics.

The calculation of the point vortex velocity probability distribution function (VVPDF) is extended to a larger class of systems beyond the nonconserved time-dependent Ginzburg-Landau (TDGL) model treated earlier. The range is extended to include certain anisotropic models and the conserved order parameter case. The VVPDF still satisfies scaling with large velocity tails as for the nonconserved isotropic case. It is shown that the average vortex speed can be self-consistently expressed in terms of correlation functions associated with a Gaussian auxiliary field. In the conserved order parameter case the average vortex speed decays as t(-1) compared to the t(-1/2) decay for the nonconserved case.

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PubMed2004

Response functions in phase-ordering kinetics.

We discuss the behavior of response functions in phase-ordering kinetics within the perturbation theory approach developed earlier. At zeroth order the results agree with previous gaussian theory calculations. At second order the nonequilibrium exponents lambda and lambda(R) are changed but remain equal.

Kinetics↗

PubMed2004

Model for striped growth.

We introduce a model for describing the defected growth of striped patterns. This model, while roughly related to the Swift-Hohenberg model, generates a quite different mixture of defects during phase ordering. We find two characteristic lengths in the system: the scaling length L(t), and the average width of the domain walls. The growth law exponent is larger than the value of 1/2 found in typical point defect systems.

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PubMed2003

Vortex dynamics in a coarsening two-dimensional XY model.

The vortex velocity distribution function for a two-dimensional coarsening nonconserved O(2) time-dependent Ginzburg-Landau model is determined numerically and compared to theoretical predictions. In agreement with these predictions the distribution function scales with the average vortex speed which is inversely proportional to t(x), where t is the time after the quench and x is near 1/2. We find the entire curve, including a large speed algebraic tail, in good agreement with the theory.

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PubMed2003

Granular clustering in a hydrodynamic simulation.

We examine the hydrodynamics of a granular gas using numerical simulation. We demonstrate the appearance of shearing and clustering instabilities predicted by linear stability analysis, and show that their appearance is directly related to the inelasticity of collisions in the material. We discuss the rate at which these instabilities arise and the manner in which clusters grow and merge.

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PubMed2003

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) approximately 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.

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