Cellular automata approach to site percolation on ℤ2. A numerical study

We present a cellular automata model as a new approach to Bernoulli site percolation on the square lattice. A new macroscopic quantity is defined and numerically computed at each level step of the automata dynamics. Its limit manifests a critical behavior at a value of the site occupancy probability quite close to those obtained for site percolation on ² with the best-known numerical methods.     

Diffusion in Lorentz lattice gas automata with backscattering

The probability of first return to the initial intervalx and the diffusion tensorD _x are calculated exactly for a ballistic Lorentz gas on a Bethe lattice or Cayley tree. It consists of a moving particle and a fixed array of scatterers, located at the nodes, and the lengths of the intervals between scatterers are determined by a geometric distribution. The same values forx andD _x apply also to a regular space lattice with a fraction of sites occupied by a scatterer in the limit of a small concentration of scatterers. If backscattering occurs, the results are very different from the Boltzmann approximation. The theory is applied to different types of lattices and different types of scatterers having rotational or mirror symmetries.     

A new Monte Carlo simulation for two models of self-avoiding lattice trees in two dimensions

By means of a new Monte Carlo sampling of a grand canonical ensemble, we verify universality for the critical exponents and of two models of lattice trees constrained to be self-avoiding on sites or on bonds. The attrition constants are also obtained. This algorithm, a generalization of that recently proposed by Berretti and Sokal for random walks, appears to optimize the critical slowing down in the scaling region. Systematic and statistical errors are carefully estimated.     

New Monte Carlo method for the self-avoiding walk

We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find=2.63820 ± 0.00004 ± 0.00030=1.352 ± 0.006 ± 0.025v=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length 166, using 340 hours CPU time on a CDC Cyber 170–730. We compare our results to previous work and indicate some directions for future research.     

On some variational approximations in two-dimensional classical lattice systems

A new derivation is presented of some variational approximations for classical lattice systems that belong to the class of cluster-variation methods, among them the well-known Bethe-Peierls and Kramers-Wannier approximations. The limiting behavior of a hierarchical sequence of cluster-variation approximations, the so-calledC hierarchy, is discussed. It is shown that this hierarchy provides a monotonically decreasing sequence of upper boundsf _n on the free energy per lattice sitef and thatf _n f asn . Our results are based on extension theorems for states given on subsets of the lattice, which might be of some independent interest, and on an application of transfer matrix concepts to the variational characterization of translation-invariant equilibrium states.     

Effect of molecular orientation distribution and crystallinity on the measurement of the crystal lattice modulus of nylon 6 by x-ray diffraction

The crystal lattice modulus of nylon 6 (-type) was measured by x-ray diffraction using nylon 6 films drawn up to five times. The measured crystal lattice modulus was 173–175 GPa for all specimens whose crystallinity and the Young's modulus were beyond 46% and 3.75 GPa, respectively. These results indicate that a state of homogenous stress can be achieved. In contrast, the values were scattered for the speciments whose crystallinity and Young's modulus are less than the above values. To study the origin, a numerical calculation of the crystal lattice modulus, as measured by x-ray diffraction, was carried out by considering effects on the orientation factors of molecular chains and crystallinity. In this calculation, a previously introduced model was employed, in which oriented crystalline layers are surrounded by oriented amorphous phases so that the strains of the two phases at the boundary are identical. The theoretical results calculated by the introduced model indicated that the crystal lattice modulus by x-ray diffraction is almost equal to the intrinsic crystal modulus if the morphology of the test specimen can be represented as a series model. In contrast, if a parallel model is more appropriate, the difference between the measured modulus and the intrinsic value can be pronounced. Such morphological dependence was found to be less pronounced with increasing high degree of molecular orientation and crystallinity.     

Rapidly converging lattice sums for nonelectrostatic interactions

The relative energies of one-, two-, and three-dimensional Bravais lattice Lennard-Jones particles can be calculated by lattice sums. The expression of lattice sums over a Lennard-Jones potential can be manipulated into a form that converges rapidly. A formalism capable of calculating the lattice potential at arbitrary points of a completely general lattice has been developed. This method provides an alternative way to calculate the relative energies from the surface and the interior bulk sites of many chemical systems. The method is illustrated with application to hcp and fcc Lennard-Jonesium, both for the relative binding energy and for calculating the potential along the geometric diffusion pathway between tetrahedral and octahedral interstitial sites. Diffusion from the tetrahedral site to the octahedral site experiences a barrier of 752.600 in units of 4 epsilon. The reverse pathway experiences a barrier of 1035.614 in units of 4 epsilon.     

Lattice models of peptide aggregation: evaluation of conformational search algorithms

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.     

聚合物微晶尺寸和晶格畸变

聚合物微晶尺寸和晶格畸变是对聚合物材料性能有着重要影响的结构参数。本文介绍了应用Ｘ射线衍射方法测定聚合物微晶尺寸和结构畸变的几种方法：近似函数、次晶模型法、方差法、矩法。     

Dynamics of the formation of two-dimensional ordered structures

The growth of ordered domains in lattice gas models, which occurs after the system is quenched from infinite temperature to a state below the critical temperatureT _c, is studied by Monte Carlo simulation. For a square lattice with repulsion between nearest and next-nearest neighbors, which in equilibrium exhibits fourfold degenerate (2×1) superstructures, the time-dependent energy E(t), domain size L(t), and structure functionS(q, t) are obtained, both for Glauber dynamics (no conservation law) and the case with conserved density (Kawasaki dynamics). At late times the energy excess and halfwidth of the structure factor decrease proportional tot ^–x, whileL(t) t ^x, where the exponent x=1/2 for Glauber dynamics and x1/3 for Kawasaki dynamics. In addition, the structure factor satisfies a scaling lawS(k,t)=t ^2xS(kt^x). The smaller exponent for the conserved density case is traced back to the excess density contained in the walls between ordered domains which must be redistributed during growth. Quenches toT>T _c, T=T_c (where we estimate dynamic critical exponents) andT=0 are also considered. In the latter case, the system becomes frozen in a glasslike domain pattern far from equilibrium when using Kawasaki dynamics. The generalization of our results to other lattices and structures also is briefly discussed.