International Journal of Modern Physics C

We systematically investigate how symplectic integrator schemes are effective when applied to molecular dynamics method. The performances are estimated from a point of view of the total energy conservation by investigating molecular dynamics of one-component Lennard–Jones system in constant volume and constant temperature and pressure. It is shown that numerical simulations by the symplectic integrator scheme are better than those by classical schemes for a long-time simulation even in the case of large step size. The performances of various orders of symplectic integrator are evaluated.

The availability of efficient Krylov subspace solvers plays a vital role in the solution of a variety of numerical problems in computational science. Here we consider lattice field theory. We present a new general numerical method to compute many Green's functions for complex non-singular matrices within one iteration process. Our procedure applies to matrices of structure A = D − m, with m proportional to the unit matrix, and can be integrated within any Krylov subspace solver. We can compute the derivatives x⁽ⁿ⁾ of the solution vector x with respect to the parameter m and construct the Taylor expansion of x around m. We demonstrate the advantages of our method using a minimal residual solver. Here the procedure requires one intermediate vector for each Green's function to compute. As real-life example, we determine a mass trajectory of the Wilson fermion matrix for lattice QCD. Here we find that we can obtain Green's functions at all masses ≥ m at the price of one inversion at mass m.

We apply the method of State-dependent Diagonalization to study the eigenstates of the relativistic quantum harmonic oscillator in the low relativistic limit. The relativistic corrections of the energy eigenvalues of the quantum harmonic oscillator are evaluated for different values of the relativistic parameter α ≡ ħω₀ / m₀c². Unlike the conventional exact diagonalization, this new method is shown to be very efficient for evaluating the energy eigenvalues and eigenfunctions. We have also found that for non-zero α the eigenfunctions of the system become more localized in space and that the ground state of the SHO (i.e., the α = 0 case) turns into a squeezed state. Furthermore, since our system is a special case of the quantum harmonic oscillator with a velocity-dependent anharmonic potential, this new approach should be very useful for investigating the cases with more complicated velocity-dependent anharmonic potentials.

We present algorithmic procedures for generating systematically ideas and solutions to problems which are perceived as creative.

Our method consists of identifying and characterizing the most creative ideas among a vast pool. We show that they fall within a few large classes (archetypes) which share the same conceptual structure (Macros). We prescribe well defined abstract algorithms which can act deterministically on arbitrary given objects. Each algorithm generates ideas with the same conceptual structure characteristic to one of the Macros. The resulting new ideas turn out to be perceived as highly creative.

We support our claims by experiments in which senior advertising professionals graded advertisement ideas produced by our method according to their creativity. The marks (grade 4.6±0.2 on a 1–7 scale) obtained by laymen applying our algorithms (after being instructed for only two hours) were significantly better than the marks obtained by advertising professionals using standard methods (grade 3.6±0.2)).

The method, which is currently taught in USA, Europe, and Israel and used by advertising agencies in Britain and Israel has received formal international recognition.

This paper presents calculations of the rate constant for the unimolecular isomerization of cyclobutanone using the theory of Gray and Rice as extended by Zhao and Rice. Such calculations are also carried out from classical trajectory and from local Lyapunov function analysis. The results of the calculations as a function of energy are compared, and the agreement is found to be uniformly good. The present approach is considered as a computationally feasible alternative to Davis' turnstile approach to the calculations of intramolecular energy transfer.

A lattice Boltzmann model for two-phase fluids is used to find the equilibrium distribution of density and pressure across a vertical column under the action of terrestrial gravitational field. At low temperatures and without surface tension, the density distribution has a discontinuity point due to phase separation, while the pressure is always continuous. At temperatures far above the critical point, the fluid column behaves as an ideal gas and the well-known barometric formula is recovered. When surface tension is considered, this model gives also the correct behavior of a Van der Waals fluid placed in a tank subjected to terrestrial or space conditions in both cases, when the tank walls are wetted or not by the fluid.

The two-parent reproduction model of Derrida and Peliti is simulated on a rugged fitness landscape. Fixed fitness values for each possible genotype are assigned randomly, with all fit individuals having the same probability of reproduction. The previously observed transition to a self-organized state of the population with less recombinational load, implies an abrupt change of genetic overlap distributions, showing up characteristics of a phase transition. A crossover variant of the model has a smoother transition to the adapted regime, with a residual collective adaptation for small values of the threshold in fitness. When a geographical constraint (shortest possible distance) on pairwise reproduction in a population arranged one-dimensionally is imposed, a poised state results, suggestive of self-organized criticality.

This paper describes an extension into three dimensions of an existing two-dimensional technique for simulating brittle solid fracture. The fracture occurs on a simulated solid created by "gluing" together space-filling polyhedral elements with compliant interelement joints. Such a material can be shown to have well-defined elastic properties. However, the "glue" can only support a specified tensile stress and breaks when that stress is exceeded. In this manner, a crack can propagate across the simulated material. A comparison with experiment shows that the simulation can accurately reproduce the size distributions for all fragments with linear dimensions greater than three element sizes.

We investigate the effect of an age-dependent mutation rate in the Penna model of ageing and then we observe that the high mortality for human babies can be reproduced by the model if one assumes babies to be weaker than adults.

We confirm the results of Chaves and collaborators of very large size effects in the case when a site on the triangular lattice is permanently emptied if it has less than three occupied neighbors. We also show that the relaxation time peaks at an initial concentration different from the percolation threshold.

We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom.

While the previous systems were linear and exploded exponentially for certain parameter ranges, the new systems fulfill nonlinear time evolution equations similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics and evolve spontaneously towards "fixed trajectories" indexed by the average value of their degrees of freedom (which corresponds to the SSB order parameter). The "fixed trajectories" dynamics evolves on the edge between explosion and collapse/extinction.

The systems present power laws with exponents which in a wide range (α < –2.) are universally determined by the ratio between the minimal and the average values of the degrees of freedom. The time fluctuations are governed by Levy distributions of corresponding power. For exponents α > −2 there is no "thermodynamic limit" and the fluctuations are dominated by a few, largest degrees of freedom which leads to macroscopic fluctuations, chaos, and bursts/intermittency.

The two-dimensional simulations of Majumdar, Bray, Cornell, and Sire are confirmed and generalized to three to five dimensions. They agree with their epsilon expansion.