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We introduce the concept of time-coarse graining into Cartesian space simulations and investigate its application to flexible models of polymer systems. The technique, which was recently introduced in the context of a rigid model, is an approximate method for the accelerated equilibration of dense long-chain melts. It was demonstrated previously that the thermal equilibration of these systems can be enhanced by up to an order of magnitude with respect to sampling efficiency, while incurring only a moderate loss in the accuracy of the generated ensemble of long-time observables. In this contribution, we show how this technique can be extended to deal with the stiff bond-length and bond-angle interaction potentials that are present in flexible models of polymer chains.

We examine the vibrational density of states of atomistic models of polypropylene glasses containing a single impurity molecule of s‐tetrazine. We discuss existing methods and develop new ones to achieve significant data reduction and navigate through the complex spectrum of the normal modes of the glass. By calculating the participation ratio, the distribution of the kinetic energy of each mode on the atomic coordinates, and a mode‐proximity index to the solute it is possible to identify impurity‐related, polymer‐related, and mixed modes and assess their relative contributions to the vibrational density of states. Activation of specific modes using molecular dynamics allows the observation of anharmonicities in the doped glass, even at very low temperatures.

An effective‐potential approach is presented for improving sampling efficiency in simulations of atomistically detailed models of dense long‐chain liquids. The motion of atoms on short‐time scales is described as rapid fluctuations about the slowly moving mean conformations of the chain molecules. The distribution of these fluctuations is approximated by that of isotropic elastic motion. The interactions between nonbonded pairs of atoms are preaveraged over this distribution and a much softer, effective interaction is obtained, allowing a correspondingly faster exploration of configuration space. The approximate sampling scheme is then tested on two model systems of united‐atom liquid hydrocarbons—a melt of twenty C24 chains and one of ten C71 chains. In the C24 melt, where a comparison with fully equilibrated samples from rigorous algorithms is possible, the preaveraging is shown to produce an improvement in sampling efficiency of up to an order of magnitude at the expense of only a moderate loss in accuracy. The method is then applied to the C71 melt, where currently available, rigorous sampling algorithms fail to produce thorough equilibration. Also in this case, the preaveraging method proves to significantly enhance the sampling speed while producing satisfactory distributions of observables.

We undertake a numerical study of the Flory-Huggins-de Gennes functional ind=3 dimensions describing a polymer blend. By discretising the functional on a three-dimensional lattice and employing the hybrid Monte Carlo simulation algorithm, we investigate to what extent the inclusion of the term describing fluctuations in local polymer concentration alters the phase diagram of the model. We find that, despite the relatively small weight of the fluctuation term, the coexistence curve is shifted by an appreciable amount from that predicted by naive mean-field theory, which ignores such spatial fluctuations. The direction of the shift is consistent with that already observed in experiment and in simulations of microscopic models of polymer blends. A finite-size scaling analysis indicates that the critical behavior of the model seems to belong to the 3D Ising universality class rather than being mean-field in nature.

We investigate the efficiency of two recently introduced hybrid Monte Carlo algorithms for the off‐lattice simulation of dense polymer melts. Their performance is assessed both with respect to the molecular dynamics method and new single‐chain Monte Carlo techniques proposed recently. Our findings show that the long‐time behavior of both hybrid algorithms offer the possibility of calibration with respect to real time.

We describe a novel hybrid Monte Carlo algorithm for the off-lattice simulation of dense, atomistically detailed polymer systems. Bond lengths and bond angles are constrained to their equilibrium values and a generalized-coordinate description using the torsional degrees of freedom is employed. Simple, decoupled, Cartesian-like equations of motion are obtained by the introduction of fictitious angular momenta variables conjugate to the torsional degrees of freedom. A unique time scale, and hence a mapping onto real time, can be obtained by allocating time-independent, effective moments of inertia to each angular momentum variable.

Crossover scaling of the surface width in the Kardar-Parisi-Zhang equation for surface growth is studied numerically. By means of a perturbative solution of the discretized equation and by comparison with the exact solution of the corresponding linear equation, the finite-size effects due to the spatial discretization are carefully analyzed. The dependence on the nonlinearity of both the finite-size and asymptotic scaling forms is then investigated.

We present a numerical study of a neural network model with a low level of activity. Our findings confirm a previous replica-symmetric mean-field analysis which predicts a much higher storage capacity compared with the standard Hopfield model. Indeed our estimate of the critical storage ratio of the model lies above that yielded analytically. We also obtain good agreement with an analytical investigation of the dynamics of the model.

The equilibrium properties of the discreteφ 4-model ind=2 dimensions are investigated at critically using the hybrid Monte Carlo algorithm and the Ferrenberg-Swendsen extrapolation scheme. By combining the extrapolation scheme with a finite-size scaling analysis, the critical line of the model could be located very accurately. The universality of the model along the critical line is then explicity demonstrated both with respect to the universal nature of the probability distribution function of the global order parameter and by direct comparison with the critical two-dimensional Ising model.

A brief review of some recent results on a particular class of growth models is presented. Numerical estimates for the roughness exponents of a d-dimensional surface are discussed, as is the question of the existence of a non-equilibrium roughening transition for the experimentally relevant and theoretically controversial case of d=2.

The roughening behavior of moving surface under a deposition and evaporation dynamics is explored within the hypercube-stacking model. One limiting case of the model is an equilibrium surface, which exhibits thermal roughening for surface dimension d≤2. Another limiting case is nonequilibrium irreversible growth, where the model is shown to map exactly to zero-temperature directed polymers on a hypercubic lattice with a random energy distribution. Results of exact calculations for d=1 and of large-scale Monte Carlo simulations [N=220, 11 5202, and 2×1923 surface sites for d=1, 2, and 3, respectively] are presented that establish the Kardar-Parisi-Zhang equation as the correct continuum description of the growth process. For pure deposition (i.e., irreversible growth), careful analysis of surface width data yields the exponents β(2)=0.240±0.001 and β(3)=0.180±0.005, which violate a number of recent conjectures. By allowing for evaporation, we observe a less rapid increase of the surface roughness as a function of time. This phenomenon is consistently explained by a crossover scenario for d=1 and 2 but a nonequilibrium roughening transition for d=3, as predicted by a perturbative renormalization-group analysis of the Kardar-Parisi-Zhang equation. Detailed predictions on crossover scaling from the renormalization-group analysis are also confirmed by simulation data. In the d=1 case, some of the continuum parameters characterizing the renormalization-group flow are obtained explicitly in terms of the lattice parameters via the exact calculation of steady-state properties of the model.

Many growth processes in nature involve, on the molecular level, random attachment and detachment of particles at the interface. One such example is the growth of an amorphous film by the sputtering technique, where energetic atoms land on a cold substrate at the end of their ballistic flights. In the absence of rapid surface diffusion, fluctuations in the incoming flux of particles (known as “shot-noise”) lead to accumulation of excess material at parts of the surface, thereby create surface height fluctuations whose amplitude may diverge with the size of the substrate. Such growth-induced roughening can be different from thermal roughening due to the difference in either the noise spectrum or, perhaps more importantly, the way a growing surface responds to a given type of noise in comparison with its equilibrium counterpart.

We study in d+1 dimensions a new deposition and evaporation model of a d-dimensional surface which bears a Potts-spin representation. For the pure deposition case, our simulations on systems up to ${11520}^{2}$ sites in d=2 and 2\ifmmode\times\else\texttimes\fi{}${192}^{3}$ sites in d=3 yield roughness exponents which violate recent conjectures. Including evaporation, we observe a nonequilibrium surface-roughening transition in d=3, but only a smooth crossover behavior in d=2. A logarithmic anomalous scaling form for surface width at the transition is conjectured.

We present a deposition and evaporation model for surface growth under a solid-on-solid constraint. We generalize the Ising-spin representation of a two-dimensional surface by Blote and Hilhorst to ad-dimensional surface of a (d+1)-dimensional hypercubic lattice. The allowed surface configurations correspond to the (degenerate) ground states of a chirald-state Potts model. We describe a vectorized multisite-coding implementation for the corresponding kinetic Potts-spin model ford=2 andd=3. For thed=2 equilibrium surface our simulation results show excellent agreement with an exact analysis.