Translation drag coefficient of a self-similar assembly of spheres immersed in an incompressible fluid.

On the basis of deterministic fractals and the Rotne-Prager hydrodynamic interaction tensor, we confirm the asymptotic as well as the finite size scaling of the friction coefficient lambda of a self-similar structure. The fractal assembly is made of N spheres with its dimension varying from D < 1 to D = 3. The number of spheres can be as high as N approximately O(10(4)). The asymptotic scaling behavior of the friction coefficient per sphere is lambda approximately N(1/D-1) for D > 1, lambda approximately (lnN)(-1) for D = 1, and lambda approximately N(0) for D < 1. The crossover behavior indicates that while in the regime of D > 1 the hydrodynamic screening effect grows with the size, for D<1 it is limited in a finite range, which decays with decreasing D.     

New scaling of child-langmuir law in the quantum regime

This paper presents a consistent quantum mechanical model of Child-Langmuir (CL) law, including electron exchange-correlation interaction, electrode's surface curvature, and finite emitter area. The classical value of the CL law is increased by a larger factor due to the electron tunneling through the space-charge potential, and the electron exchange-correlation interaction becomes important when the applied gap voltage Vg and the gap spacing D are, respectively, on the order of Hartree energy level, and nanometer scale. It is found that the classical scaling of Vg(3/2) and D(-2) is no longer valid in the quantum regime, and a new scaling of Vg(1/2) and D(-4) is established. The smooth transition from the classical regime to the quantum regime is also demonstrated.     

An efficient flexible-order model for 3D nonlinear water waves

The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211–228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss–Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.     

GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model

The compute unified device architecture (CUDA) is a programming approach for performing scientific calculations on a graphics processing unit (GPU) as a data-parallel computing device. The programming interface allows to implement algorithms using extensions to standard C language. With continuously increased number of cores in combination with a high memory bandwidth, a recent GPU offers incredible resources for general purpose computing. First, we apply this new technology to Monte Carlo simulations of the two dimensional ferromagnetic square lattice Ising model. By implementing a variant of the checkerboard algorithm, results are obtained up to 60 times faster on the GPU than on a current CPU core. An implementation of the three dimensional ferromagnetic cubic lattice Ising model on a GPU is able to generate results up to 35 times faster than on a current CPU core. As proof of concept we calculate the critical temperature of the 2D and 3D Ising model using finite size scaling techniques. Theoretical results for the 2D Ising model and previous simulation results for the 3D Ising model can be reproduced.     

Size dependence of the Mössbauer effect in one-dimension

Employing a model of coupled harmonic oscillators we analyze the nature of recoilless emission in the Mössbauer effect for a finite sized 1D lattice. We demonstrate explicitly that under certain assumptions, recoilless probability first attains a maximum for a certain lattice size and then decreases with increasing lattice size. Further, we derive a scaling relation for this variation. Our treatment may have relevance to the recoilless probability in finite clusters such as nanocrystals and nanowires.     

Criticality of Epidemic Spreading in Mobile Individuals Mediated by Environment

We investigate the critical behaviour of an epidemical model in a diffusive population mediated by a static vector environment on a 2D network. It is found that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. Finite-size and short-time dynamic scaling relations are used to determine the critical population density and the critical exponents characterizing the behaviour near the critical point. The results are compatible with the universality class of directed percolation coupled to a conserved diffusive field with equal diffusion constants.     

含遮蔽抛射沉积模型的有限尺寸效应

含遮蔽抛射沉积模型是在抛射沉积(BD)模型的基础上考虑了粒子以一定的角度分布倾斜入射的情况.本文应用外推方法确定了大尺寸极限下含遮蔽抛射沉积模型的各标度指数,讨论了该模型的有限尺寸效应及其标度性质.从模拟结果可以看出含遮蔽BD模型的有限尺寸效应与BD模型有所不同,遮蔽这种非局域作用可以显著地改变BD模型的标度性质. 关键词： 遮蔽效应 抛射沉积模型 有限尺寸效应 动力学标度     

Scale dependent dimension of luminous matter in the universe

We suggest a geometrical model for the distribution of luminous matter in the Universe, where the apparent dimension, D(l), increases linearly with the logarithm of the scale l. Beyond the correlation length, xi, the Universe is homogeneous, and D = 3. Comparison with data from the SARS redshift catalog, and the LEDA database provides a good fit with a correlation length xi approximately 300 Mpc. This type of scaling structure was recently discovered in a simple reaction-diffusion "forest-fire" model, indicating a broad class of scaling phenomena.     

Scaling properties of three-dimensional magnetohydrodynamic turbulence

The scaling properties of three-dimensional magnetohydrodynamic turbulence with finite magnetic helicity are obtained from direct numerical simulations using 512(3) modes. The results indicate that the turbulence does not follow the Iroshnikov-Kraichnan phenomenology. The scaling exponents of the structure functions can be described by a modified She-Leveque model zeta(p) = p/9+1-(1/3)(p/3), corresponding to basic Kolmogorov scaling and sheetlike dissipative structures. In particular, we find zeta(2) approximately 0.7, consistent with the energy spectrum E(k) approximately k(-5/3) as observed in the solar wind, and zeta(3) approximately 1, confirming a recent analytical result.     

Three-Body Recombination with Two-Channel Contact Interactions

We use a two-channel contact interaction model to describe a system of three identical bosons. The two-channel model quantitatively describes the phenomena of Feshbach resonance in agreement with the phenomenological expression relating scattering length to magnetic detuning. The model also has a finite effective range. We investigate finite range effects in three-body recombination. The simpler one-channel contact interaction model predicts a characteristic geometric scaling of minima in the recombination coefficient as a function of scattering length with scaling parameter 22.7. We show that this factor is reduced when the effective range is included. We compare calculations to experiment.     

On the scaling behavior of the chiral phase transition in QCD in finite and infinite volume

We study the scaling behavior of the two-flavor chiral phase transition using an effective quark–meson model. We investigate the transition between infinite-volume and finite-volume scaling behavior when the system is placed in a finite box. We can estimate effects that the finite volume and the explicit symmetry breaking by the current quark masses have on the scaling behavior which is observed in full QCD lattice simulations. The model allows us to explore large quark masses as well as the chiral limit in a wide range of volumes, and extract information about the scaling regimes. In particular, we find large scaling deviations for physical pion masses and significant finite-volume effects for pion masses that are used in current lattice simulations.     

Universal fermionic spectral functions from string theory

We carry out the first holographic calculation of a fermionic response function for a strongly coupled d=3 system with an explicit D=10 or D=11 supergravity dual. By considering the supersymmetry current, we obtain a universal result applicable to all d=3 N=2 SCFTs with such duals. Surprisingly, the spectral function does not exhibit a Fermi surface, despite the fact that the system is at finite charge density. We show that it has a phonino pole and at low frequencies there is a depletion of spectral weight with a power-law scaling which is governed by a locally quantum critical point.     

The fully finite spherical model

A lattice sum technique is applied to the constraint equation of the finite size mean spherical model. It is shown that this allows the investigation of the model over a wide range of temperatures, for a wide range of system sizes. Correlation lengths and susceptibilities are shown to obey crossover scaling aroundT=0 below the lower critical dimension, and finite size scaling between the lower and upper critical dimensions. Universal scaling forms are suggested for the lower critical dimension. At and above the upper critical dimension, the behavior is identical to that of finite sized mean field theory. The scaling at and above the upper critical dimension is shown to be modified by the existence of a dangerous irrelevant variable which also governs the failure of hyperscaling. Implications for phenomenological renormalization experiments are discussed. Numerical results of scaling are displayed.     

New ordered phases in a class of generalized XY models

It is well known that the 2D XY model exhibits an unusual infinite order phase transition belonging to the Kosterlitz-Thouless (KT) universality class. Introduction of a nematic coupling into the XY Hamiltonian leads to an additional phase transition in the Ising universality class [D. H. Lee and G. Grinstein, Phys. Rev. Lett. 55, 541 (1985)]. Using a combination of extensive Monte Carlo simulations and finite size scaling, we show that the higher order harmonics lead to a qualitatively different phase diagram, with additional ordered phases originating from the competition between the ferromagnetic and pseudonematic couplings. The new phase transitions belong to the 2D Potts, Ising, or KT universality classes.     

Global quantum discord and matrix product density operators

In a previous study, we have proposed a procedure to study global quantum discord in 1D chains whose ground states are described by matrix product states [Z.-Y. Sun et al., Ann. Phys. 359, 115 (2015)]. In this paper, we show that with a very simple generalization, the procedure can be used to investigate quantum mixed states described by matrix product density operators, such as quantum chains at finite temperatures and 1D subchains in high-dimensional lattices. As an example, we study the global discord in the ground state of a 2D transverse-field Ising lattice, and pay our attention to the scaling behavior of global discord in 1D sub-chains of the lattice. We find that, for any strength of the magnetic field, global discord always shows a linear scaling behavior as the increase of the length of the sub-chains. In addition, global discord and the so-called “discord density” can be used to indicate the quantum phase transition in the model. Furthermore, based upon our numerical results, we make some reliable predictions about the scaling of global discord defined on the n × n sub-squares in the lattice.     

Wang-Landau study of the 3D Ising model with bond disorder

We implement a two-stage approach of the Wang-Landau algorithm to investigate the critical properties of the 3D Ising model with quenched bond randomness. In particular, we consider the case where disorder couples to the nearest-neighbor ferromagnetic interaction, in terms of a bimodal distribution of strong versus weak bonds. Our simulations are carried out for large ensembles of disorder realizations and lattices with linear sizes L in the range L=8-64L=8{-}64. We apply well-established finite-size scaling techniques and concepts from the scaling theory of disordered systems to describe the nature of the phase transition of the disordered model, departing gradually from the fixed point of the pure system. Our analysis (based on the determination of the critical exponents) shows that the 3D random-bond Ising model belongs to the same universality class with the site- and bond-dilution models, providing a single universality class for the 3D Ising model with these three types of quenched uncorrelated disorder.     

Dynamics of quantum phase transition in an array of Josephson junctions

We study the dynamics of the Mott insulator-superfluid quantum phase transition in a periodic 1D array of Josephson junctions. We show that crossing the critical point at a finite rate with a quench time tau(Q) induces finite quantum fluctuations of the current around the loop proportional to tau(-1/6)(Q). This scaling could be experimentally verified with an array of weakly coupled Bose-Einstein condensates or superconducting grains.     

Time distribution and loss of scaling in granular flow

Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling p) and deterministic critical slope processes with internal correlation time t_c equal to the avalanche lifetime, in model A, and ,in model B. In both cases nonuniversal scaling properties of avalanche distributions are found for , where is related to directed percolation threshold in d=3. Distributions of avalanche durations for are studied in detail, exhibiting multifractal scaling behavior in model A, and finite size scaling behavior in model B, and scaling exponents are determined as a function of p. At a phase transition to noncritical steady state occurs. Due to difference in the relaxation mechanisms, avalanche statistics at approaches the parity conserving universality class in model A, and the mean-field universality class in model B. We also estimate roughness exponent at the transition. Received: 29 May 1998 / Revised: 8 September 1998 / Accepted: 10 September 1998     

Energetics of 2D and 3D Repulsive Hubbard Model from Their 1D Counterpart using Dimensional Scaling for an Arbitrary Band Filling

A dimensional scaling computation of the electron concentration-dependent ground-state energy for the repulsive Hubbard model is presented, a generalization of Capelle’s analysis of the 2D and 3D Hubbard Hamiltonians with half-filled bands. The computed ground-state energies are compared with the results of mean-field and density-matrix functional theories and of quantum Monte Carlo calculations. The comparison indicates that dimensional scaling yields moderately accurate ground-state energies close to and at half filling over the wide range of interaction strengths in the study. By contrast, the accuracy becomes poor at low filling for strong interactions.