International Journal of Modern Physics C

We show that there exists a simple solution to the density problem in cellular automata, under fixed boundary conditions, in contrast to previously used periodic ones.

The object-oriented middleware standard, CORBA, is a very useful platform for distributed computing, and in particular for sharing a workload among a collection of possibly polymorphic computers. CORBA has, however, received relatively little attention from the scientific computing community. In this article we demonstrate how CORBA and Java can be used to implement a distributed multi-dimensional Monte Carlo integration algorithm which runs on the internet.

The reverse Monte Carlo (RMC) technique has been used to generate atomic structures of amorphous carbon based on the radial distribution functions and the fraction of differently coordinated sites measured on experimental samples. The resulting structures have been subsequently relaxed via a Tight Binding Molecular Dynamics simulation (TBMD). The radial distribution function, the energy and the fraction of 2-, 3- and 4-fold coordinated sites, evaluated on the relaxed structures, have been compared to those calculated for atomic systems generated on the basis of the "conventional" numerical melt-quench technique. We thus suggest the possibility of using RMC modeling as a useful and convenient tool for generating amorphous structures to be used as initial configurations in Molecular Dynamics simulations.

We describe a method that allows an efficient determination of the density of states of one-dimensional heterostructures. We show that the propagation of an appropriate vector through the structure together with the use of the node theorem is much more effective than transfer matrix methods in those cases in which highly degenerate spectra are present. As a by-product, spatial behavior of solutions is also easily obtained. A case of elastic propagation is discussed in detail and application to Schrödinger's equation is presented.

In this paper we study the importance of parental care for the survival of semelparous species, that reproduce only once in life. We perform our simulations for sexual and asexual reproductions and show that catastrophic senescence (death soon after reproduction) is delayed if parental care is considered.

With the projector quantum Monte Carlo algorithm and the stochastic diagonalization it is possible to calculate the ground state of the Hubbard model for small finite clusters. Nevertheless the usual finite size scaling of the Hubbard model has problems of deducing the behavior of the infinite system correctly from the numerical data of small system sizes. Therefore we study the finite size scaling of the superconducting correlation functions in superconducting BCS-reduced Hubbard models to analyze the finite size behavior in small finite clusters. The ground state of the BCS-reduced Hubbard models is calculated with the stochastic diagonalization without any approximations. As result of these analyses we propose a new finite size scaling ansatz for the Hubbard model, which is able describe the finite size effects in a consistent way taking the corrections to scaling into account, which are dominant for weak interaction strength and small clusters. With this new finite size scaling ansatz it is possible to give evidence for superconductivity for all interaction strengths for both the attractive tt'-Hubbard model (with s-wave symmetry) and the repulsive tt'-Hubbard model (with d_x²-y²-wave symmetry).

Successive pairs of pseudo-random numbers generated by standard linear congruential transformations display ordered patterns of parallel lines. We study the "ordered" and "chaotic" distribution of such pairs by solving the eigenvalue problem for two-dimensional modular transformations over integers. We conjecture that the optimal uniformity for pair distribution is obtained when the slope of linear modular eigenspaces takes the value , where p is a prime number. We then propose a new generator of pairs of independent pseudo-random numbers, which realizes an optimal uniform distribution (in the "statistical" sense) of points on the unit square (0, 1] × (0, 1]. The method can be easily generalized to the generation of k-tuples of random numbers (with k>2).

We introduce a toy model for interacting populations connected by mutations and limited by a shared resource. We study the presence of Eigen's error threshold and mutational meltdown. The phase diagram of the system shows that the extinction of the whole population due to mutational meltdown can occur well before an eventual error threshold transition.

We demonstrate that the standard O(n) symmetric φ⁴ field theory does not correctly describe the leading finite-size effects near the critical point of spin systems with periodic boundary conditions on a d-dimensional lattice with d>4. We show that these finite-size effects require a description in terms of a lattice Hamiltonian. For n →∞ and n=1, explicit results are given for the susceptibility and for the Binder cumulant. They imply that these quantities do not have the universal properties predicted previously and that recent analyses of Monte Carlo results for the five-dimensional Ising model are not conclusive.

We investigate the long-time behavior of the drift velocity of two-dimensional biased diffusion with varying bias B and percentage p of allowed sites. A phase diagram for the drift/no-drift transition depending on B and p is presented.

A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age, confirming a general relation between Age and Area proposed by Willis. The ecology exhibits punctuated equilibrium. Analytic and numerical results show that the probability distribution of genera sizes, genera lifetimes, and extinction event sizes are the same power law P(x)~ 1/x², consistent with paleontological data.

Monte Carlo simulations suggest that dimensionless ratios of cumulants for the height of the surface depend on how randomness is used.

An empirical scheme for implementation of bond functions in heteronuclear diatomics is suggested and applied to HeBe using universal even-tempered functions. The effects of bond functions and core-correlation energy on the interaction potential of HeBe calculated at the uncorrelated (SCF) and correlated (MBPT and CC) levels are examined. The results confirm that an accuracy of sub μ Hartree level can be obtained using even-tempered functions with s-, p-, and d- symmetry and that bond functions of size {4s2p} for He and {6s3p} for Be recovers 100% of energy lowering obtained from the addition of 10d atom-centered functions to He and 13d atom centred functions to Be. The various treatments of the electron correlation, conclude that the system is interacting weakly with a well depth from 14.5–24.7 μE_h at a separation near 9.1a₀ compared with 20.7–25.5 μE_h previously reported with a rather limited basis set. The most reliable well depth corrected for BSSE (19.0 μE_h) was obtained at the CC-SD(T)level at separation of 8.71a₀ taking into account the effects of bond functions and core correlation energy. Potential energy curves at the CC-SD(T) valence and CC-SD(T) valence + core correlation levels are analyzed in analytical forms in terms of exchange repulsion, induction and dispersion components.

A family of new hybrid four-step tenth algebraic order methods with phase-lag of order fourteen is developed for accurate computations of the radial Schrödinger equation. Numerical results obtained for the integration of the phase shift problem for the well known case of the Lennard-Jones potential and for the numerical solution of the coupled equations arising from the Schrödinger equation show that these new methods are better than other finite difference methods.

We present a perturbative calculation of finite-size effects near T_c of the φ⁴ lattice model in a d-dimensional cubic geometry of size L with periodic boundary conditions for d>4. The structural differences between the φ⁴ lattice theory and the φ⁴ field theory found previously in the spherical limit are shown to exist also for a finite number of components of the order parameter. The two-variable finite-size scaling functions of the field theory are nonuniversal whereas those of the lattice theory are independent of the nonuniversal model parameters. One-loop results for finite-size scaling functions are derived. Their structure disagrees with the single-variable scaling form of the lowest-mode approximation for any finite ξ/L where ξ is the bulk correlation length. At T_c, the large-L behavior becomes lowest-mode like for the lattice model but not for the field-theoretic model. Characteristic temperatures close to T_c of the lattice model, such as T_max(L) of the maximum of the susceptibility χ, are found to scale asymptotically as T_c-T_max(L) ~L^-d/2, in agreement with previous Monte Carlo (MC) data for the five-dimensional Ising model. We also predict χ_max~L^d/2 asymptotically. On a quantitative level, the asymptotic amplitudes of this large-L behavior close to T_c have not been observed in previous MC simulations at d=5 because of nonnegligible finite-size terms ~L^(4-d)/2 caused by the inhomogeneous modes. These terms identify the possible origin of a significant discrepancy between the lowest-mode approximation and previous MC data. MC data of larger systems would be desirable for testing the magnitude of the L^(4-d)/2 and L^4-d terms predicted by our theory.

A Monte Carlo algorithm for partitioning graphs is presented. The algorithm is based on the self-organizing map, an unsupervised, competitive neural network. A mean-field analysis suggests that the complexity of the algorithm is at most is on the order of O(n³/|E|), where n is the number of vertices of the graph, and |E| the number of edges. This prediction is tested on a class of random graphs. Scaling laws that deviate from the mean-field prediction are obtained. Although the origin of these scaling laws is unclear, their consequences are discussed.