arXiv subjects
Publications and source records attributed to Michael W. Deem.
We describe a new, biased Monte Carlo scheme to determine the crystal structures of zeolites from powder diffraction data. We test the method on all publicly known zeolite materials, with success in all cases. We show that the method of parallel tempering is a powerful supplement to the biased Monte Carlo.
We address via numerical simulation the two-dimensional bimolecular annihilation reaction $A + A \to \emptyset$ in the presence of quenched, random impurities. Renormalization group calculations have suggested that this reaction displays anomalous kinetics at long times, $c_{A}(t) \sim at^{δ-1}$, for certain types of topological or charged reactants and impurities. Both the exponent and the prefactor depend on the strength of disorder. The decay exponents determined from our simulations agree well with the values predicted by theory. The observed renormalization of the prefactor also agrees well with the values predicted by theory.
We present computer simulations of anomalous diffusion, $< r^2(t) > \sim a t^{1-δ}$, in two dimensions. The Monte Carlo calculations are in excellent agreement with previous renormalization group calculations. Interestingly, use of a high quality pseudo-random number generator is necessary to observe the anomalous diffusion. A linear-feedback, shift-register method leads to incorrect, ballistic motion of the random walkers.
We analyze the reactions $A+A \to \emptyset$ and $A + B \to \emptyset$ occurring in a model of turbulent flow in two dimensions. We find the reactant concentrations at long times, using a field-theoretic renormalization group analysis. We find a variety of interesting behavior, including, in the presence of potential disorder, decay rates faster than that for well-mixed reactions.
We analyze the dynamics of the ion-dipole pairing reaction in the two-dimensional Coulomb gas in the presence of disorder. Sufficiently singular disorder forces the critical temperature of the Kosterlitz-Thouless-Berezinskii fixed point to be non-universal. This disorder leads to anomalous ion pairing kinetics with a continuously variable decay exponent. Sufficiently strong disorder eliminates the transition altogether. For ions that are chemically reactive, anomalous kinetics with a continuously variable decay exponent also occurs in the high-temperature regime. The Coulomb interaction inhibits reactant segregation, and so the ionic $A^+ +B^- \to \emptyset$ reaction behaves like the nonionic $A + A \to \emptyset$ reaction.
We derive the long-time behavior of the ${A} + {B} \to \emptyset$ reaction in two dimensions, finding a universal exponent and prefactor in the absence of disorder. Sufficiently singular disorder leads to a (sub)diffusion-limited reaction and a continuously variable decay exponent. Pattern matching between the reactant segregation and the disorder is not strong enough to affect the long-time decay.
We address the two-dimensional bimolecular annihilation reaction $A + A \to \emptyset$ in the presence of random impurities. Impurities with sufficiently long-ranged interaction energies are known to lead to anomalous diffusion, $ \sim t^{1-δ}$, in the absence of reaction. Applying renormalization group theory to a field theoretic description of this reaction, we find that this disorder also leads to anomalous kinetics in the long time limit: $c(t) \sim t^{δ-1}$. This kinetics results because the disorder forces the system into the (sub)diffusion controlled regime, in which the kinetics must become anomalous.
In this manuscript, we describe a new configurational bias Monte Carlo technique for the simulation of peptides. We focus on the biologically relevant cases of linear and cyclic peptides. Our approach leads to an efficient, Boltzmann-weighted sampling of the torsional degrees of freedom in these biological molecules, a feat not possible with previous Monte Carlo and molecular dynamics methods.
The behavior of a thin film of nematic liquid crystal with unequal Frank constants is discussed. Distinct Frank constants are found to imply unequal core energies for $+1/2$ and $-1/2$ disclinations. Even so, a topological constraint is shown to ensure that the bulk densities of the two types of disclinations are the same. For a system with free boundary conditions, such as a liquid membrane, unequal core energies simply renormalize the Gaussian rigidity and line tension.
We examine the shapes and energies of 5- and 7-fold disclinations in low-temperature hexatic membranes. These defects buckle at different values of the ratio of the bending rigidity, $κ$, to the hexatic stiffness constant, $K_A$, suggesting {\em two} distinct Kosterlitz-Thouless defect proliferation temperatures. Seven-fold disclinations are studied in detail numerically for arbitrary $κ/K_A$. We argue that thermal fluctuations always drive $κ/K_A$ into an ``unbuckled'' regime at long wavelengths, so that disclinations should, in fact, proliferate at the {\em same} critical temperature. We show analytically that both types of defects have power law shapes with continuously variable exponents in the ``unbuckled'' regime. Thermal fluctuations then lock in specific power laws at long wavelengths, which we calculate for 5- and 7-fold defects at low temperatures.