A note on differentiability of the cluster density for independent percolation in high dimensions

The cluster density function of independent percolation in ad-dimensional lattice is considered. For eachn, it is shown that(p) has finitenth leftderivative at critical probabilityp _c ifd is sufficiently large. This result agrees with the Bethe lattice approximation, where thenth one-sided derivative of(p) is bounded atp _c for alln.     

Some considerations of fluid interfaces in two dimensions

Basic assumptions of the capillary wave theory of fluid interfaces are examined critically as a function of space dimensionalityd. When the predictions of capillary wave theory are compared with those of the nonclassical Maxwell-van der Waals theory, agreement is found ind=3 and 4, but strong disagreement occurs ind=2. It is shown that the total effective mass density obtained from the Hamiltonian describing the collective capillary wave excitations has a logarithmic divergence ind=2. This result suggests the possibility of anomalous behavior for fluid interfaces ind=2.     

Random aggregation and random-walking center of mass

Two random aggregation models are used in demonstrating the properties of the random displacementsr _i of the center of mass of aggregating particles. It is found that r _i is a randomly decreasing sequence that scales with the cluster size (steps)s and _i ^=1/s r _i s ^1/D , whereD is the fractal dimension. The center-of-mass random walk is a consistent representation of the dynamics of aggregation.     

On the upper critical dimensions of random spin systems

A set of critical exponent inequalities is proved for a large class of classical random spin systems. The inequalities imply rigorous (and probably the optimal) lower bounds for the upper critical dimensions, i.e.,d _u4 for regular and random ferromagnets,d _u6 for spin glasses and random field systems.     

Fractal dimension and grand Universality of critical phenomena

Conformation of branched random fractals formed in equilibrium processes is discussed using a Flory-type theory. Within this approach we find only three distinct types or classes of random fractals. We call these theextended, thecompensated, and thecollapsed states. In particular, the critical clusters in thermal phase transitions are found to be of the compensated type and have approximately the same value of the fractal dimension. The Flory theory predicts the upper critical dimension for these clusters to be 6 instead of 4. This result and the apparent grand universality of the fractal geometry of the clusters in critical phenomena are discussed.     

Multiparticle fractal aggregation

Kinetic fractal aggregation in a particle bath where a fractionf of the sites are initially occupied is studied withd=2 computer simulations. Independent particles diffusing to a fixed cluster produce an aggregate with fractal dimensionD 1.7 up to a correlation length(f). At larger lengthsD2.(f) asf 0. When the particles remain fixed but the cluster undergoes a rigid random walkD appears constant at larger scales but varies withf. D 1.95 at largef andD 1.7 asf 0. In both cases, the aggregate sizeN(t) grows with timet ^(f) . Aggregation on a surface by independently diffusing particles produces shapes reminiscent of electrochemical dendritic growth. The dependence of growth rate and geometry is studied as a function of particle concentration and sticking probability.     

Post-deposition dynamics of multiple cluster aggregation on liquid surfaces

A comprehensive simulation model---deposition, diffusion, rotation and aggregation---is presented to demonstrate the post-deposition phenomena of multiple cluster growth on liquid surfaces, such as post-deposition nucleation, post-deposition growth and post-deposition coalescence. Emphasisis placed on the relaxations of monomer density, dimer density and cluster density as well as combined cluster-plus-monomer density with time after deposition ending. It is shown that post-deposition coalescence largely takes place after deposition due to the large mobility of clusters on liquid surfaces, while the post-deposition nucleation is only possible before the saturation cluster density is reached at the end of the deposition. The deposition flux and the moment of deposition ending play important roles in the post-deposition dynamics.     

Multifractal dimensions for branched growth

A recently proposed theory for diffusion-limited aggregation (DLA), which models this system as a random branched growth process, is reviewed. Like DLA, this process is stochastic, and ensemble averaging is needed in order to define multifractal dimensions. In an earlier work by Halsey and Leibig, annealed average dimensions were computed for this model. In this paper, we compute the quenched average dimensions, which are expected to apply to typical members of the ensemble. We develop a perturbative expansion for the average of the logarithm of the multifractal partition function; the leading and subleading divergent terms in this expansion are then resummed to all orders. The result is that in the limit where the number of particlesn, the quenched and annealed dimensions areidentical; however, the attainment of this limit requires enormous values ofn. At smaller, more realistic values ofn, the apparent quenched dimensions differ from the annealed dimensions. We interpret these results to mean that while multifractality as an ensemble property of random branched growth (and hence of DLA) is quite robust, it subtly fails for typical members of the ensemble.     

Critical Exponents for the Contact Process under the Triangle Condition

We show that a continuous-time version of the triangle condition for percolation implies mean-field values for several contact process critical exponents. Our results support the belief that the upper critical (spatial) dimension for the contact process is four.     

Phase transitions in a probabilistic cellular automaton: Growth kinetics and critical properties

We investigate a discrete-time kinetic model without detailed balance which simulates the phase segregation of a quenched binary alloy. The model is a variation on the Rothman-Keller cellular automaton in which particles of type A (B) move toward domains of greater concentration of A (B). Modifications include a fully occupied lattice and the introduction of a temperature-like parameter which endows the system with a stochastic evolution. Using computer simulations, we examine domain growth kinetics in the two-dimensional model. For long times after a quench from disorder, we find that the average domain sizeR(t) t ^1/3, in agreement with the prediction of Lifshitz-Slyozov-Wagner theory. Using a variety of methods, we analyze the critical properties of the associated second-order transition. Our analysis indicates that this model does not fall within either the Ising or mean-field classes.     

On the Unicity of Discontinuous Transitions in the Two-Dimensional Potts and Ashkin–Teller Models

Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following nontrivial power laws in experimentally relevant distributions. Previous numerical estimates on the critical exponents, when existing, are confirmed and superseded. A physical motivation for both models in the present framework is also discussed.     

Hyperscaling Inequalities for the Contact Process and Oriented Percolation

The contact process and oriented percolation are expected to exhibit the same critical behavior in any dimension. Above their upper critical dimension d _c, they exhibit the same critical behavior as the branching process. Assuming existence of the critical exponents, we prove a pair of hyperscaling inequalities which, together with the results of refs. 16 and 18, implies d _c=4.     

Anomalous aggregation growth of palladium nanosphere with SPR band in visible range

The morphology and properties of nanostructures are significantly influenced by the chemical coordination during their growth procedure. Using small molecule N-vinyl pyrolidone as stabilizer, this paper introduces a new strategy for synthesis of palladium nanospheres, which has a novel surface plasmon resonance band in the visible range. An aggregation growth mode was observed in the growth process. More specifically, the growth rate increases with increasing concentration of stabilizer. The absorption in visible region suggests new optical applications for these Pd nanospheres, such as photocatalysis, photothermal heating and surface enhanced Raman scattering.     

The number and size of branched polymers in high dimensions

We consider two models of branched polymers (lattice trees) on thed-dimensional hypercubic lattice: (i)the nearest-neighbor model in sufficiently high dimensions, and (ii) a spread-out or long-range model ford>8, in which trees are constructed from bonds of length less than or equal to a large parameterL. We prove that for either model the critical exponent for the number of branched polymers exists and equals 5/2, and that the critical exponentv for the radius of gyration exists and equals 1/4. This improves our earlier results for the corresponding generating functions. The proof uses the lace expansion, together with an analysis involving fractional derivatives which has been applied previously to the self-avoiding walk in a similar context.     

非线性聚集生长理论的研究及其应用

首先介绍了非线性聚集生长计算机模型与生长规则和非线性聚集生长的实验原理与装置,然后阐述了计算凝聚物分形维数的计算机模拟方法和实验方法,最后论述了非线性聚集生长理论在大气颗粒物、薄膜生长方面的应用。     

Critical dynamics of cluster algorithms in the dilute Ising model

Autocorrelation times for thermodynamic quantities atT _C are calculated from Monte Carlo simulations of the site-diluted simple cubic Ising model, using the Swendsen-Wang and Wolff cluster algorithms. Our results show that for these algorithms the autocorrelation timesdecrease when reducing the concentration of magnetic sites from 100% down to 40%. This is of crucial importance when estimating static properties of the model, since the variances of these estimators increase with autocorrelation time. The dynamical critical exponents are calculated for both algorithms, observing pronounced finite-size effects in the energy autocorrelation data for the algorithm of Wolff. We conclude that, when applied to the dilute Ising model, cluster algorithms become even more effective than local algorithms, for whichincreasing autocorrelation times are expected.     

Branched polymers in a wedge geometry in three dimensions

We investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge angles and. We show that the growth constant is equal to ^f , where is the self-avoiding walk limit. Thef and (, ) dependences of the corresponding critical exponent _f (, ) are studied using Monte Carlo techniques. In the casef=1, our results are compared with existing predictions obtained from series expansion and renormalization group methods. We have also estimated the amplitudes for the mean square radius of gyration and the mean square end-to-end branch length. Our results for the ratio of the mean square radius of gyration of anf-star to that of a linear polymer of the same degree of polymerization attached in a similar wedge, and the analogous ratio for the mean square end-to-end branch length, are consistent with these ratios being lattice-independent quantities.     

树状分形结构形成过程的实验研究

对大量金属小球在强电场作用下运动形态的演化全过程用联机摄像装置进行了实时拍摄,通过用Sandbox方法计算其稳定状态的分维数,系统地研究了分维数随电压的变化关系.结果表明：在一定电压范围内金属小球聚集体通过自组织过程形成稳定的树状分形结构,其分维数随外加电压的增加而减小.该结果对研究耗散结构的形成机理和外界动力对耗散结构的形貌影响具有参考价值.关键词：分形生长自组织过程树状结构分维数     

Very high upper critical fields of F-doped Fe-based layered superconductors NdO0.88F0.12FeAs and CeO0.88F0.12FeAs

Using the solid state reaction method, we have synthesized the polycrystalline F-doped NdO_0.88F_0.12FeAs and CeO_0.88F_0.12FeAs with the superconducting transition temperatures at about 48 and 40 K, respectively. To obtain the upper critical field H _c2 of Nd(Ce)O_0.88F_0.12FeAs samples, we measured the electrical resistivity under magnetic field up to 14 T. Based on the Werthamer-Helfand-Hohenberg (WHH) relation together with the H _c2(T) curves in a relatively high field, we estimated that these superconductors have a rather high upper critical field of about 115 T for Nd-based and 107 T for Ce-based samples, indicating the similarities between these ReO_1−x F _x FeAs (Re = rare earth element) superconductors and high T _c cuprate superconductors. Recommended by Prof. Nie Yuxin, Executive Editor of Science in China Series G-Physics, Mechanics & Astronomy Supported by the National Basic Research Program of China (973 Program)(Grant No. 2006CB9213001) and the National Natural Science Foundation of China (Grant No. 10774181)     

On the critical behavior of the magnetization in high-dimensional Ising models

We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT _c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y| couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.).