Phase separation of symmetrical polymer mixtures in thin-film geometry

Monte Carlo simulations of the bond fluctuation model of symmetrical polymer blends confined between two neutral repulsive walls are presented for chain lengthN _A=N _B=32 and a wide range of film thicknessD (fromD=8 toD=48 in units of the lattice spacing). The critical temperaturesT _c (D) of unmixing are located by finite-size scaling methods, and it is shown that , wherev ₃0.63 is the correlation length exponent of the three-dimensional Ising model universality class. Contrary to this result, it is argued that the critical behavior of the films is ruled by two-dimensional exponents, e.g., the coexistence curve (difference in volume fraction of A-rich and A-poor phases) scales as , where ₂ is the critical exponent of the two-dimensional Ising universality class ( ₂=1/8). Since for largeD this asymptotic critical behavior is confined to an extremely narrow vicinity ofT _c (D), one observes in practice effective exponents which gradually cross over from ₂ to ₃ with increasing film thickness. This anomalous flattening of the coexistence curve should be observable experimentally.     

A goldstone mode in the Kawasaki-Ising model

The hydrodynamic regime of superfluids is dominated by a Goldstone mode corresponding to a spontaneously brokenU(1) symmetry. In this article we map the Kawasaki-Ising model for a classical lattice gas into a quantum model for a superfluid and establish a connection between the normal density fluctuations of the first and the Goldstone mode of the second. The fact that the quantum model we obtain describes a superfluid derives from an inequality by Penrose and Onsager which gives a lower bound to the Bose-Einstein condensate density. Mathematically, the Goldstone mode can be described by means of a quantum extension of the local algebra of the Ising model. The classification of its irreducible representations requires an additionalU(1) phase factor and the correspondingU(1) gauge symmetry is spontaneously broken for all finite values of the temperature and of the density.     

Random walk on distant mesh points Monte Carlo methods

A new technique for obtaining Monte Carlo algorithms based on the Markov chains with a finite number of states is suggested. Instead of the classical random walk on neighboring mesh points, a general way of constructing Monte Carlo algorithms that could be called random walk on distant mesh points is considered. It is applied to solve boundary value problems. The numerical examples indicate that the new methods are less laborious and therefore more efficient.In conclusion, we mention that all Monte Carlo algorithms are parallel and could be easily realized on parallel computers.     

Renormalization group for Markov chains and application to metastability

In this paper we introduce a new renormalization group method for the study of the long-time behavior of Markov chains with finite state space and with transition probabilities exponentially small in an external parameter. A general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two-dimensional Ising system at low temperature,     

Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm

We present a Monte Carlo algorithm to find approximate solutions of the traveling salesman problem. The algorithm generates randomly the permutations of the stations of the traveling salesman trip, with probability depending on the length of the corresponding route. Reasoning by analogy with statistical thermodynamics, we use the probability given by the Boltzmann-Gibbs distribution. Surprisingly enough, using this simple algorithm, one can get very close to the optimal solution of the problem or even find the true optimum. We demonstrate this on several examples.We conjecture that the analogy with thermodynamics can offer a new insight into optimization problems and can suggest efficient algorithms for solving them.The author acknowledges stimulating discussions with J. Piút concerning the main ideas of the present paper. The author is also indebted to P. Brunovský, J. erný, M. Hamala, . Peko, . Znám, and R. Zajac for useful comments.     

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.     

Surface tension and universality in the three-dimensional Ising model

The amplitude ₀ of the interfacial free energy per unit area (or surface tension) of the body-centered-cubic Ising model is found using a direct monte carlo simulation technique. The combination ²/k_BT_c, where is the correlation length, is shown to agree within the precision of the simulations with a previously reported estimate for the simple cubic lattice. Evidence is also presented for the universality of the finite-size scaling amplitude for the surface tension.     

用计算模拟方法研究Al_3P_4O_(16)~(3-)计量比的二维层状磷酸铝中的有机胺模板能力

将快速 Monte Carlo方法与分子动力学方法相结合 ,研究了不同种类有机分子在 Al3P4 O3- 1 6 计量比的二维层状磷酸铝形成中的模板能力 .依据主 -客体之间非键相互作用能 (包括范德华能、氢键能和库仑能 ) ,可合理地解释已知实验现象 ,并能有效地预测出适于形成某一特定无机层结构的有机胺模板剂 .通过选择理论预测的有机胺分子作为模板剂 ,成功地合成了二维层状磷酸铝化合物 Al3P4 O1 6 · 1 .5 H3NC6 H1 0 NH3.     

Computer experiments on crystalline nylons: structural analysis of nylons with large aliphatic segments

A theoretical study based on force-field calculations has been performed to investigate the structural preferences of crystalline even nylons n with large and very large aliphatic segments. Atomistic energy calculations and Monte Carlo simulations were carried out considering the conventional and forms of nylons 10, 12, 18, 24, and 32. Results indicated that the form is the most favored for nylons 10, 12, 18, and 24. However, the structure was unstable for nylon 32, a polymer in which the density of hydrogen bonds is almost negligible. In this case, the arrangement is energetically more favored than the one.     

水煤气变换反应的微观动力学分析──Cu基催化剂上H_2S中毒失活原因的 Monte Carlo 模拟研究

用ＢＯＣＭＰ方法及ＭｏｎｔｅＣａｒｌｏ模拟技术，对Ｈ２Ｓ导致Ｃｕ基催化剂失活的原因进行了计算分析。研究结果表明，当原料气中存在Ｈ２Ｓ时，ＷＧＳ反应的活化能明显高于无Ｈ２Ｓ时的活化能，随着表面Ｈ２Ｓ浓度的增大（θ＝０，０．１０，０．２５），反应的活化能也逐渐变大（其大小比为１∶１．３４∶３．３），究其原因可归结为Ｈ２Ｓ的存在使得反应物分子的吸附热减小，从而使Ｈ２Ｏ的解离吸附（ＷＧＳ反应的速控步骤）活化能增大。