International Journal of Modern Physics C

An iterative algorithm to determine the dynamic user equilibrium with respect to link costs defined by a traffic simulation model is presented. Each driver's route choice is modeled by a discrete probability distribution which is used to select a route in the simulation. After each simulation run, the probability distribution is adapted to minimize the travel costs. Although the algorithm does not depend on the simulation model, a queuing model is used for performance reasons. The stability of the algorithm is analyzed for a simple example network. As an application example, a dynamic version of Braess's paradox is studied.

The Monte Carlo (MC) method is applied to the modeling of a liquid crystal display based on the in-plane switching effect. This is the first attempt to simulate this device features starting from purely microscopic molecular interactions. The optical textures are obtained from the Monte Carlo generated microscopic equilibrium configurations by means of a Müller matrix approach. Suitable order parameters are also calculated to quantify the ordering and the molecular organization across the display cell.

Using the Penna bit-string model for biological ageing we compare two kinds of reproductive regimes: Sexual reproduction (SR) and meiotic parthenogenesis (MP). The last one is a common type of asexual reproduction with recombination, found in diploid organisms. We show that although both regimes present roughly the same survival rates, the diversity generated by SR is much larger, and can prevent the extinction of a population submitted to a natural disaster. The fixation of bad genes inside an MP population, after many generations, explains our results. We also study the consequences of cloning (simple copy) on population diversity.

Discrete scale invariance, which corresponds to a partial breaking of the scaling symmetry, is reflected in the existence of a hierarchy of characteristic scales l₀,l₀λ,l₀λ²,…, where λ is a preferred scaling ratio and l₀ a microscopic cut-off. Signatures of discrete scale invariance have recently been found in a variety of systems ranging from rupture, earthquakes, Laplacian growth phenomena, "animals" in percolation to financial market crashes. We believe it to be a quite general, albeit subtle phenomenon. Indeed, the practical problem in uncovering an underlying discrete scale invariance is that standard ensemble averaging procedures destroy it as if it was pure noise. This is due to the fact, that while λ only depends on the underlying physics, l₀ on the contrary is realization-dependent. Here, we adapt and implement a novel so-called "canonical" averaging scheme which re-sets the l₀ of different realizations to approximately the same value. The method is based on the determination of a realization-dependent effective critical point obtained from, e.g., a maximum susceptibility criterion. We demonstrate the method on diffusion limited aggregation and a model of rupture.

We investigate the asymptotic density of living cells as dependent on an initial density, the results of scattering of gliders on small stable configurations and the damage spreading in an open system, subjected to a stream of gliders with the rules of the cellular automaton "Game of Life." We find that a damage increases approximately with the second power of time through about the first ten steps; later its time dependence becomes almost linear.

We simulate dopant profiles for phosphorus implantation into silicon using a new model for electronic stopping power. In this model, the electronic stopping power is factorized into a globally averaged effective charge , and a local charge density dependent electronic stopping power for a proton. There is only a single adjustable parameter in the model, namely the one electron radius which controls . By fine tuning this parameter, we obtain excellent agreement between simulated dopant profiles and the SIMS data over a wide range of energies for the channeling case. Our work provides a further example of implant species, in addition to boron and arsenic, to verify the validity of the electronic stopping power model and to illustrate its generality for studies of physical processes involving electronic stopping.

We present a preprocessor for attractor neural networks consisting of a chaotic cellular automaton. We show that this preprocessor improves on the ability to recognize correlated memories. The preprocessor, although chaotic, is reversible because the patterns have a finite number of neurons and appropriate boundary conditions were chosen. The performance of the present model was checked using numerical simulations in both the RS and the Hopfield models of neural networks. However, this is a very general approach that can be used in any other architecture with different learning rules.

In this work the Eigen model of quasispecies is reconsidered. Our main aim is to find to what extent mutational meltdown changes previously presented results, when the finite population can decrease or increase during evolution.

Using computer simulations of a bit-string model for age-structured populations, we found that sexual selection of older males is advantageous, from an evolutionary point of view. These results are in opposition to a recent proposal of females choosing younger males. Our simulations are based on findings from recent studies of polygynous bird species. Since secondary sex characters are found mostly in males, we could make use of asexual populations that can be implemented in a fast and efficient way.

We revisit here a new Monte Carlo approach, namely the Broad Histogram Method. It is based on two quantities, the numbers N_up and N_dn of potential modifications which could be performed starting from the system's current state, increasing or decreasing its energy E, respectively. Thus, the energy degeneracy g(E) can be directly determined from the microcanonical averages <N_up(E)> and <N_dn(E)> of these two quantities. This method was first tested by sampling states from a random walk along the energy axis, for which the control of possible correlations between successive averaging states is not an easy task. Neverthless, the resulting microcanonical averages could not depend upon the particular dynamics used to sample the Markovian chain of averaging states. Here, we test the same method within an alternative dynamics for which the quoted control becomes trivial.

The recent stimulating proposal of a "Gauge Theory of Finance" by Ilinsky et al. is connected here with traditional approaches. First, the derivation of the log-normal distribution is shown to be equivalent both in information and mathematical content to the simpler and well-known derivation, dating back from Bachelier and Samuelson. Similarly, the re-derivation of Black–Scholes equation is shown equivalent to the standard one because the limit of no uncertainty is equivalent to the standard risk-free replication argument. Both re-derivations of the log-normality and Black–Scholes result do not provide a test of the theory because it is not uniquely specified in the limits where these results apply. Third, the choice of the exponential form a la Boltzmann, of the weight of a given market configuration, is a key postulate that requires justification. In addition, the "Gauge Theory of Finance" seems to lead to "virtual" arbitrage opportunities for a pure Markov random walk market when there should be none. These remarks are offered in the hope to improve the formulation of the "Gauge Theory of Finance" into a coherent and useful framework.

Using a classic example proposed by G. I. Taylor, we reconsider through the use of computer algebra, the mathematical analysis of a fundamental process in turbulent flow, namely: How do large scale eddies evolve into smaller scale ones to the point where they are effectively absorbed by viscosity? The explicit symbolic series solution of this problem, even for cleverly chosen special cases, requires daunting algebra, and so numerical methods have become quite popular. Yet an algebraic approach can provide substantial insight, especially if it can be pursued with modest human effort.

The specific example we use dates to 1937 when Taylor and Green⁸ first published a method for explicitly computing successive approximations to formulas describing the three-dimensional evolution over time of what is now called a Taylor–Green vortex.

With the aid of a computer algebra system, we have duplicated Taylor and Green's efforts and obtained more detailed time-series results. We have extended their approximation of the energy dissipation from order 5 in time to order 14, including the variation with viscosity.

Rather than attempting additional interpretation of results for fluid flow (for which, see papers by Brachet et al.,^2,3 we examine the promise of computer algebra in pursuing such problems in fluid mechanics.