共查询到20条相似文献,搜索用时 31 毫秒
1.
G. Migliorini V.G. Rostiashvili T.A. Vilgis 《The European physical journal. E, Soft matter》2001,4(4):475-487
A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain
in d dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when screening is not present,
in order to compute the end-to-end distance and the asymptotic properties of the chain as a function of the polymer chain
length N. We find R≃N
ν(log N)γ, where ν = and λ is the exponent which characterizes the long-range interaction U∝ 1/r
λ. The exponent γ is shown to be non-universal, depending on the strength of the Coulomb interaction. We check our findings
by a direct numerical minimization of the variational energy for chains of increasing size 24 < N < 215. The electrostatic blob picture, expected for small enough values of the interaction strength, is quantitatively described
by the variational approach. We perform a Monte Carlo simulation for chains of length 24 < N < 210. The non-universal behavior of the exponent γ previously derived within the variational method is also confirmed by the simulation
results. Non-universal behavior is found for a polyelectrolyte chain in d = 3 dimension. Particular attention is devoted to the homopolymer chain problem, when short-range contact interactions are
present.
Received 8 August 2000 and Received in final form 19 December 2000 相似文献
2.
The critical behavior of the two-dimensional O(N) model close to criticality is shown to be encoded in the fractal structure of the high-temperature graphs of the model. Based on Monte Carlo simulations and with the help of percolation theory, de Gennes' results for polymer rings, corresponding to the limit N-->0, are generalized to random loops for arbitrary -2相似文献
3.
Michelle Przedborski 《Phase Transitions》2013,86(1):85-93
For the spin models with continuous symmetry on regular lattices and finite range of interactions, the lower critical dimension is d?=?2. In two dimensions the classical XY-model displays Berezinskii–Kosterlitz–Thouless (BKT) transition associated with unbinding of topological defects (vortices and antivortices). We perform a Monte Carlo study of the classical XY-model on Sierpiński pyramids (SPs) whose fractal dimension is D = log?4/log?2?=?2 and the average coordination number per site is ≈ 7. The specific heat does not depend on the system size which indicates the absence of a long-range order. From the dependence of the helicity modulus on the cluster size and on boundary conditions, we draw a conclusion that in the thermodynamic limit there is no BKT transition at any finite temperature. This conclusion is also supported by our results for linear magnetic susceptibility. The lack of finite temperature phase transition is presumably caused by the finite order of ramification of SP. 相似文献
4.
At the critical point of the simple cubic Ising model, the radius of Coniglio-Klein clusters containings sites each is found by Monte Carlo simulation to be roughly 0.54s
0.4, consistent with the theoretically expected fractal dimension 2.5.Dedicated to Professor W. Brenig on the occasion of his 60th birthday 相似文献
5.
The effective dielectric constant of porous ultra low-k dielectrics is simulated by applying the fractal geometry and Monte Carlo technique in this work. Based on the fractal character of pore size distribution in porous media, the probability models for pore diameter and for effective dielectric constant are derived. The proposed model for the effective dielectric constant is expressed as a function of the dielectric coefficient of base medium and the volume fractions of pores and base medium, fractal dimension for pores, the pore size, as well as random number. The Monte Carlo simulations combined with the fractal geometry are performed. The predictions by the present simulations are shown in good accord with the available experimental data. The proposed technique may have the potential in analyzing other properties such as electrical conductivity and thermal conductivity in porous ultra low-k dielectrics. 相似文献
6.
三角格点基底上磁性分形团簇形貌演化规律 总被引:1,自引:1,他引:0
在扩散限制凝聚模型基础上引入粒子的自旋自由度,将磁耦合系数扩展为随自旋间距离幂次变化的非常数项J/ra,采用Monte Carlo方法研究在二维三角格点基底上具有幂次相互作用的磁性团簇形貌及其分形维数Df的演化规律.模拟结果表明,对于较大的幂指数α值,即α≥5时,团簇形貌随耦合参数J的变化较小,其分形维数Df在1.50~1.70之间;随着α值的减小,团簇形貌随参数J有一明显的演化过程,在模拟范围内,分形维数Df在1.20~1.90之间. 相似文献
7.
Thermal conductivity of nanofluids and size distribution of nanoparticles by Monte Carlo simulations 总被引:1,自引:0,他引:1
Yongjin Feng Boming Yu Kaiming Feng Peng Xu Mingqing Zou 《Journal of nanoparticle research》2008,10(8):1319-1328
Nanofluids, a class of solid–liquid suspensions, have received an increasing attention and studied intensively because of
their anomalously high thermal conductivites at low nanoparticle concentration. Based on the fractal character of nanoparticles
in nanofluids, the probability model for nanoparticle’s sizes and the effective thermal conductivity model are derived, in
which the effect of the microconvection due to the Brownian motion of nanoparticles in the fluids is taken into account. The
proposed model is expressed as a function of the thermal conductivities of the base fluid and the nanoparticles, the volume
fraction, fractal dimension for particles, the size of nanoparticles, and the temperature, as well as random number. This
model has the characters of both analytical and numerical solutions. The Monte Carlo simulations combined with the fractal
geometry theory are performed. The predictions by the present Monte Carlo simulations are shown in good accord with the existing
experimental data. 相似文献
8.
Using Monte Carlo molecular dynamics, a new, careful study is made of the approach of the trajectory of a typical particle in a hard sphere fluid to that of a Brownian particle, discussed before by Powles and Quirke and Rapaport. The apparent fractal dimension of the trajectory, as a function of reduced length scale,(), characterizes the transition from mechanical to Brownian motion and differs markedly from 2 in all present computer simulations. 相似文献
9.
In this article we review recent developments in computational methods for quantum statistical lattice problems. We begin by giving the necessary mathematical basis, the generalized Trotter formula, and discuss the computational tools, exact summations and Monte Carlo simulation, that will be used to examine explicit examples. To illustrate the general strategy, the method is applied to an analytically solvable, non-trivial, model: the one-dimensional Ising model in a transverse field. Next it is shown how to generalized Trotter formula most naturally leads to different path-integral representations of the partition function by considering one-dimensional fermion lattice models. We show how to analyze the different representations and discuss Monte Carlo simulation results for one-dimensional fermions. Then Monte Carlo work on one- and two-dimensional spin- models based upon the Trotter formula approach is reviewed and the more dedicated Handscomb Monte Carlo method is discussed. We consider electron-phonon models and discuss Monte Carlo simulation data on the Molecular Crystal Model in one, two and three dimensions and related one-dimensional polaron models. Exact numerical results are presented for free fermions and free bosons in the canonical ensemble. We address the main problem of Monte Carlo simulations of fermions in more than one dimension: the cancellation of large contributions. Free bosons on a lattice are compared with bosons in a box and the effects of finite size on Bose-Einstein condensation are discussed. 相似文献
10.
采用非格点珠簧球链模型, 结合Monte Carlo方法, 研究了半刚性高分子链受限于无限长圆柱体的构象性质. 模拟结果表明: 在圆柱体内表面附近具有吸附能的情况下, 当弯曲能b由小到大变化时, 发现半刚性高分子链由开始时的无规则被吸附在圆柱体内表面, 到逐渐出现螺旋结构, 最后伸展成类似棒状的结构. 同时计算了不同弯曲能b时的半刚性高分子链的平均螺旋数Nt, 平均每条链单体的螺旋百分比Ph和能量涨落. 发现高分子链螺旋结构的形成与转变, 不仅与圆柱体半径R的大小有关, 还与弯曲能b的大小有关. 研究结果能有助于加深对受限生物大分子构象的认识. 相似文献
11.
12.
《Surface science》1994,321(3):L261-L266
The surface of a catalyst is a fractal, and its fractal dimension can strongly influence the performance of a catalytic reaction. By means of the Monte Carlo method, the decompositions of N2O on a square lattice and a fractal surface are investigated in this paper. From the simulation it is found that the fractal surface can change both the reaction rate constant K and the reaction order α in the N2O decomposition, and all of these changes are caused by the abnormal diffusion of the surface species on the fractal surface. 相似文献
13.
By the fractal dimension method, the polaron properties in cylindrical GaAs/Al_xGa_(1-x)As core-shell nanowire are explored. In this study, the polaron effects in GaAs/Al_xGa_(1-x)As core-shell nanowire at different values of shell width and aluminum concentration are discussed. The polaron binding energy, polaron mass shift and fractal dimension parameter are numerically worked out each as a function of core radius. The calculation results show that the binding energy and mass shift of the polaron first increase and then decrease as the core radius increases, forming their corresponding maximum values for different aluminum concentrations at a given shell width. Polaron problems in the cylindrical GaAs/Al_xGa_(1-x)As core-shell nanowire are solved simply by using the fractal dimension method to avoid complex and lengthy calculations. 相似文献
14.
Joseph W. Haus Klaus W. Kehr Kazuo Kitahara 《Zeitschrift für Physik B Condensed Matter》1983,50(2):161-169
We consider a classical stochastic model describing particle transport on a lattice with randomly distributed nearest-neighbor transition rates. Applying an effective medium theory to the model, we determine average properties related to the particle's dynamics ind-dimensions. In particular, we calculate the mean-square displacement, and the fourth moment of the displacement in one-, two- and three dimensions. The results compare favorably with Monte Carlo simulations of the model. We also present preliminary results for the velocity autocorrelation function.An aspect of the bond percolation problem, which is a special case of the stochastic model is investigated; the average inverse cluster size, <N
c
–1>, is calculated. In one dimension the expression for this quantity is exact and in higher dimensions our results are very accurate not too close to the percolation concentration. 相似文献
15.
H. Nélisse C. Bourbonnais H. Touchette Y.M. Vilk A.-M.S. Tremblay 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,12(3):351-365
The temperature-dependent uniform magnetic susceptibility of interacting electrons in one dimension is calculated using several
methods. At low temperature, the renormalization group reveals that the Luttinger liquid spin susceptibility approaches zero temperature with an infinite slope in striking contrast with the Fermi liquid result and with the behavior
of the compressibility in the absence of umklapp scattering. This effect comes from the leading marginally irrelevant operator,
in analogy with the Heisenberg spin 1/2 antiferromagnetic chain. Comparisons with Monte Carlo simulations at higher temperature
reveal that non-logarithmic terms are important in that regime. These contributions are evaluated from an effective interaction
that includes the same set of diagrams as those that give the leading logarithmic terms in the renormalization group approach.
Comments on the third law of thermodynamics as well as reasons for the failure of approaches that work in higher dimensions
are given.
Received 2 March 1999 相似文献
16.
FORMATIONS OF FRACTAL ISLANDS AGGREGATED WITH DISCS IN GAUSSIAN DISTRIBUTION ON NONLATTICE SUBSTRATES 总被引:1,自引:0,他引:1
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The growth mechanism of fractal islands on a two-dimensional nonlattice substrate with periodic boundary conditions has been investigated by using Monte Carlo technique. Results show that the fractal dimension df of the final ramified islands is almost independent of the diffusion step length, mobility and rigid rotation of the islands. The characteristics of the size distribution of the discs in an island do not change the dimension df of the island. However, we find that df increases linearly with the surface coverage ρ of the system and its slope decreases with the increase of the mean diameter of the discs. 相似文献
17.
LI Rui ZHANG Duan-Ming HUANG Ming-Tao SU Xiang-Ying CHEN Zhi-Yuan ZHU Hong-Ying ZHANG Lin 《理论物理通讯》2007,48(2):343-347
We propose a two-dimensional model of polydisperse granular mixtures with a power-law size distribution in the presence of stochastic driving. A fractal dimension D is introduced as a measurement of the inhomogeneity of the size distribution of particles. We define the global and partial granular temperatures of the multi-component mixture. By direct simulation Monte Carlo, we investigate how the inhomogeneity of the size distribution influences the dynamic properties of the mixture, focusing on the granular temperature, dissipated energy, velocity distribution, spatial clusterization, and collision time. We get the following results: a single granular temperature does not characterize a multi-component mixture and each species attains its own "granular temperature"; The velocity deviation from Gaussian distribution becomes more and more pronounced and the partial density of the assembly is more inhomogeneous with the increasing value of the fractal dimension D; The global granular temperature decreases and average dissipated energy per particle increases as the value olD augments. 相似文献
18.
19.
A model for simulation of the three-dimensional morphology of nano-structured aggregates formed by concurrent coagulation and sintering is presented. Diffusion controlled cluster–cluster aggregation is assumed to be the prevailing coagulation mechanism which is implemented using a Monte–Carlo algorithm. Sintering is modeled as a successive overlapping of spherical primary particles, which are allowed to grow as to preserve overall mass. Simulations are characterized by individual ratios of characteristic collision to fusion time. A number of resulting aggregate-structures is displayed and reveals structure formation by coagulation and sintering for different values of . These aggregates are described qualitatively and quantitatively by their mass fractal dimension Df and radius of gyration. The fractal dimension increases from 1.86 for pure aggregation to 2.75 for equal characteristic time scales. As sintering turns out to be more and more relevant, increasingly compact aggregates start to form and the radius of gyration decreases significantly. The simulation results clearly reveal a strong dependence of the fractal dimension on the kinetics of the concurrent coagulation and sintering processes. Considering appropriate values of Df in aerosol process simulations may therefore be important in many cases. 相似文献
20.
LI Rui ZHANG Duan-Ming HUANG Ming-Tao SU Xiang-Ying CHEN Zhi-Yuan ZHU Hong-Ying ZHANG Lin 《理论物理通讯》2007,48(8):343-347
We propose a two-dimensional model of polydisperse granular mixtures with a power-law size distribution in the presence of stochastic driving. A fractal dimension D is introduced as a measurement of the inhomogeneity of the size distribution of particles. We define the global and partial granular temperatures of the multi-component mixture. By direct simulation Monte Carlo, we investigate how the inhomogeneity of the size distribution influences the dynamic properties of the mixture, focusing on the granular temperature, dissipated energy, velocity distribution, spatial clusterization, and collision time. We get the following results: a single granular temperature does not characterize a multi-component mixture and each species attains its own "granular temperature"; The velocity deviation from Gaussian distribution becomes more and more pronounced and the partial density of the assembly is more inhomogeneous with the increasing value of the fractal dimension D; The global granular temperature decreases and average dissipated energy per particle increases as the value of D augments. 相似文献