Monte Carlo simulation of a lyotropic first-order isotropic-nematic phase transition in a lattice polymer model

We present a Monte Carlo simulation of the bond-fluctuation lattice model, using a Hamiltonian which introduces a change in the conformational statistics of the polymer chains from Gaussian behavior at high temperatures to rigid rod behavior at low temperatures. We do not introduce any attractive interaction between the chains. Upon cooling, the aspect ratio of the chains increases above the critical value for the density employed in the simulation, and we observe an entropically driven phase transition into a nematic phase. We examine this transition quantitatively by a careful finite size scaling study using an optimized cumulant intersection method, and show that the transition is of fir…

Efficient computation of stable bifurcating branches of nonlinear eigenvalue problems

Numerical solution of a class of nonlinear boundary value problems for analytic functions

We analyse a numerical method for solving a nonlinear parameter-dependent boundary value problem for an analytic function on an annulus. The analytic function to be determined is expanded into its Laurent series. For the expansion coefficients we obtain an operator equation exhibiting bifurcation from a simple eigenvalue. We introduce a Galerkin approximation and analyse its convergence. A prominent problem falling into the class treated here is the computation of gravity waves of permanent type in a fluid. We present numerical examples for this case.

Numerische Behandlung von Verzweigungsproblemen bei gew�hnlichen Differentialgleichungen

We present a new method for the numerical solution of bifurcation problems for ordinary differential equations. It is based on a modification of the classical Ljapunov-Schmidt-theory. We transform the problem of determining the nontrivial branch bifurcating from the trivial solution into the problem of solving regular nonlinear boundary value problems, which can be treated numerically by standard methods (multiple shooting, difference methods).

Small-Angle Excess Scattering: Glassy Freezing or Local Orientational Ordering?

We present Monte Carlo simulations of a dense polymer melt which shows glass-transition-like slowing-down upon cooling, as well as a build up of nematic order. At small wave vectors q this model system shows excess scattering similar to that recently reported for light-scattering experiments on some polymeric and molecular glass-forming liquids. For our model system we can provide clear evidence that this excess scattering is due to the onset of short-range nematic order and not directly related to the glass transition.

Gas transport through polymer membranes and free volume percolation

We consider the influence of structural and dynamical properties of a polymer membrane on the gas transport through this matrix. The diffusant and the polymer only interact through repulsive interactions. In the case of a glassy polymer, when one can consider the matrix as frozen, the gas particle diffusion is determined by the free volume structure of the system. We show how the percolation properties of the free volume show up in a subdiffusive behavior of the diffusant. When one takes matrix mobility into account the ideal percolation transition vanishes but its trace can still be found in a subdiffusive regime in the gas particle mean square displacement. In the statically non-percolati…

A Singular Multi-Grid Iteration Method for Bifurcation Problems

We propose an efficient technique for the numerical computation of bifurcating branches of solutions of large sparse systems of nonlinear, parameter-dependent equations. The algorithm consists of a nested iteration procedure employing a multi-grid method for singular problems. The basic iteration scheme is related to the Lyapounov-Schmidt method and is widely used for proving the existence of bifurcating solutions. We present numerical examples which confirm the efficiency of the algorithm.

Competition between liquid-crystalline ordering and glassy freezing in melts of semiflexible polymers: A monte carlo simulation

We present results of a Monte Carlo simulation of dense melts of semiflexible polymers using the bond-fluctuation model. The chosen Hamiltonian increases the chain stiffness upon cooling which in turn leads to glass-transition like freezing of the polymer mobility. Employing an efficient simulation algorithm, which is able to equilibrate the simulated systems to lower temperature than the Rouse-type algorithm showing the glassy freezing, we are able to observe an isotropic-nematic phase transition. This transition lies above the glass transition temperature one would extrapolate from the observed freezing behavior.

On the accurate determination of nonisolated solutions of nonlinear equations

A simple but efficient method to obtain accurate solutions of a system of nonlinear equations with a singular Jacobian at the solution is presented. This is achieved by enlarging the system to a higher dimensional one whose solution in question is isolated. Thus it can be computed e. g. by Newton's method, which is locally at least quadratically convergent and selfcorrecting, so that high accuracy is attainable.

Measurement of thett¯production cross section inpp¯collisions ats=1.96  TeVusing soft electronb-tagging

The authors present a measurement of the t{bar t} production cross section using events with one charged lepton and jets from p{bar p} collisions at a center-of-mass energy of 1.96 TeV. A b-tagging algorithm based on the probability of displaced tracks coming from the event interaction vertex is applied to identify b quarks from top decay. Using 318 pb{sup -1} of data collected with the CDF II detector, they measure the t{bar t} production cross section in events with at least one restrictive (tight) b-tagged jet and obtain 8.9{sub -1.0}{sup +1.0}(stat.){sub -1.0}{sup +1.1}(syst.) pb. The cross section value assumes a top quark mass of m{sub t} is presented in the paper. This result is cons…

Melting transition in two dimensions: A finite-size scaling analysis of bond-orientational order in hard disks

We describe a general and efficient method, based on computer simulations and applicable to a general class of fluids, that allows us to determine (i) bounds on the transition densities of the melting transition that are valid in the thermodynamic limit and (ii) the order of the phase transition. The bond-orientational order parameter, its susceptibility, and the compressibility are measured simulataneously on many length scales, and the latter two quantities are extrapolated to the thermodynamic limit by application of the subblock analysis method of finite-size scaling. We include a detailed analysis, related to the subblock method, of the cross correlations of the fluctuations of the den…

Two-Dimensional Melting Approached via Finite-Size Scaling of Bond-Orientational Order

Relying on Monte Carlo simulations, we investigate the hard-disk melting transition. The finite-size scaled values of the bond-orientational order parameter moments are obtained with the block analysis technique. The behaviour of Binder's cumulant and the susceptibility favour an interpretation in terms of a first-order transition.

On the numerical solution of some finite-dimensional bifurcation problems

We consider numerical methods for solving finite-dimensional bifurcation problems. This paper includes the case of branching from the trivial solution at simple and multiple eigenvalues and perturbed bifurcation at simple eigenvalues. As a numerical example we treat a special rod buckling problem, where the boundary value problem is discretized by the shooting method.

Interactions between yield stability and seed composition

Determination of DNA single strand breaks and selective DNA amplification by N-nitrodimethylamine and analogs, and estimation of the indicator cells' metabolic capacities.

N-nitrodimethylamine is metabolized oxidatively to N-nitrohydroxymethylmethylamine, which decomposes to yield formaldehyde and N-nitromethylamine. All four compounds and N-nitromethylamine were tested for their ability to induce DNA single strand breaks in hepatocytes and in SV 40-transformed Chinese hamster embryo cell lines. Only the two monoalkylnitramines were positive. They induced single strand breaks in hepatocytes, but were not effective in the other cells. Formaldehyde and N-nitrohydroxymethylmethylamine were toxic to the cells. None of the compounds tested was able to induce selective DNA amplification in the two transformed cell lines. Enzymes involved in drug metabolism were ass…

Local structure analysis of the hard-disk fluid near melting

The local structure of the hard-disk fluid is studied across its melting transition by means of Monte Carlo simulations and measurement of a local order parameter. Evidence for a linear behavior of this quantity in an intermediate density range is found, as well as indications for a possible ensemble difference between constant volume and constant pressure simulations within the presently accessible system sizes.

Penetrant diffusion in frozen polymer matrices: A finite-size scaling study of free volume percolation

The diffusion of penetrant particles in frozen polymer matrices is investigated by means of Monte Carlo simulations of the bond fluctuation model. By applying finite-size scaling to data obtained from very large systems it is demonstrated that the diffusion process takes place on a percolating free volume cluster describable by a correlated site percolation model which falls into the same universality class as random percolation. The diverging correlation length entails a pronounced dependence of the diffusion constant on the size of the simulated system. It is shown that this dependence is appreciable for a wide range of parameters around the transition. \textcopyright{} 1996 The American …