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This article brings up an introduction to computational physics and scientific programming through an application, the radioactive decay problem. This problem is solved computationally through two different approaches: numerical integration and stochastic simulation. The numerical integration is realised via the Runge-Kutta method, used to obtain numerical solutions of the ordinary differential equation describing the model dynamics, while the stochastic simulations are implemented via Monte Carlo simulations, where random numbers are used to guide decision making. A comparicion of the advantages of each method and its convenience is made and some examples of implementation of the algorithms presented in this work are also exhibited in different programming languages. [ABSTRACT FROM AUTHOR]

Quantification of chaos is a challenging issue in complex dynamical systems. In this paper, we discuss the chaotic properties of generalized Lotka–Volterra and May–Leonard models of biodiversity, via the Hamming distance density. We identified chaotic behavior for different scenarios via the specific features of the Hamming distance and the method of q-exponential fitting. We also investigated the spatial autocorrelation length to find the corresponding characteristic length in terms of the number of species in each system. In particular, the results concerning the characteristic length are in good accordance with the study of the chaotic behavior implemented in this work. [ABSTRACT FROM AUTHOR]

We consider nonlocal effects, obtained by incorporating fractional derivatives in the kinetic energy of a conventional Hamiltonian, to analyze physical properties of non-crystalline solids at very low temperature. By using thermal Green functions, we deduce some experimentally observable quantities such as the particle momentum distribution function, the particle energy distribution function, and the specific heat. The agreement between the results obtained for the specific heat and the experimental data suggests that the approach presented here may be useful as a phenomenological model to investigate thermal properties of non-crystalline solids at low temperature. [ABSTRACT FROM AUTHOR]

We obtain time dependent solutions for a Schröndiger equation in the presence of a nonlocal term by using the Green function approach. These solutions are compared with recent results obtained for the fractional Schrödinger equation as well as for the usual one. The nonlocal term incorporated in the Schrödinger equation may also be related to the spatial and time fractional derivative and introduces different regimes of spreading of the solution with the time evolution. [ABSTRACT FROM AUTHOR]

We investigate the problem of the predominance and survival of "weak" species in the context of the simplest generalization of the spatial stochastic rock-paper-scissors model to four species by considering models in which one, two, or three species have a reduced predation probability. We show, using lattice based spatial stochastic simulations with random initial conditions, that if only one of the four species has its probability reduced, then the most abundant species is the prey of the "weakest" (assuming that the simulations are large enough for coexistence to prevail). Also, among the remaining cases, we present examples in which "weak" and "strong" species have similar average abundances and others in which either of them dominates--the most abundant species being always a prey of a weak species with which it maintains a unidirectional predator-prey interaction. However, in contrast to the three-species model, we find no systematic difference in the global performance of weak and strong species, and we conjecture that a similar result will hold if the number of species is further increased. We also determine the probability of single species survival and coexistence as a function of the lattice size, discussing its dependence on initial conditions and on the change to the dynamics of the model which results from the extinction of one of the species. [ABSTRACT FROM AUTHOR]

We revisit the problem of the predominance of the "weakest" species in the context of Lotka-Volterra and May-Leonard formulations of a spatial stochastic rock-paper-scissors model in which one of the species has its predation probability reduced by 0

Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of competitors we may face a novel situation because beside the mentioned unidirectional predator-prey-like dominance a balanced or peer relation can emerge between some competitors. By utilizing this possibility in the present work we generalize a four-state predator-prey-type model where we establish two groups of species labeled by even and odd numbers. In particular, we introduce different invasion probabilities between and within these groups, which results in a tunable intensity of bidirectional invasion among peer species. Our study reveals an exceptional richness of pattern formations where five quantitatively different phases are observed by varying solely the strength of the mentioned inner invasion. The related transition points can be identified with the help of appropriate order parameters based on the spatial autocorrelation decay, on the fraction of empty sites, and on the variance of the species density. Furthermore, the application of diverse, alliance-specific inner invasion rates for different groups may result in the extinction of the pair of species where this inner invasion is moderate. These observations highlight that beyond the well-known and intensively studied cyclic dominance there is an additional source of complexity of pattern formation that has not been explored earlier. [ABSTRACT FROM AUTHOR]

We investigate a six-species class of May-Leonard models leading to the formation of two types of competing spatial domains, each one inhabited by three species with their own internal cyclic rock-paper-scissors dynamics. We study the resulting population dynamics using stochastic numerical simulations in two-dimensional space. We find that as three-species domains shrink, there is an increasing probability of extinction of two of the species inhabiting the domain, with the consequent creation of one-species domains. We determine the critical initial radius beyond which these one-species spatial domains are expected to expand. We further show that a transient scaling regime, with a slower average growth rate of the characteristic length scale L of the spatial domains with time t, takes place before the transition to a standard L∝t1/2 scaling law, resulting in an extended period of coexistence. [ABSTRACT FROM AUTHOR]

In this work we investigate the development of stable dynamical structures along interfaces separating domains belonging to enemy partnerships in the context of cyclic predator-prey models with an even number of species N ≥ 8. We use both stochastic and field theory simulations in one and two spatial dimensions, as well as analytical arguments, to describe the association at the interfaces of mutually neutral individuals belonging to enemy partnerships and to probe their role in the development of the dynamical structures at the interfaces. We identify an interesting behavior associated with the symmetric or asymmetric evolution of the interface profiles depending on whether N/2 is odd or even, respectively. We also show that the macroscopic evolution of the interface network is not very sensitive to the internal structure of the interfaces. Although this work focuses on cyclic predator-prey models with an even number of species, we argue that the results are expected to be quite generic in the context of spatial stochastic May-Leonard models. [ABSTRACT FROM AUTHOR]

This work deals with a system of three distinct species that changes in time under the presence of mobility, selection, and reproduction, as in the popular rock-paper-scissors game. The novelty of the current study is the modification of the mobility rule to the case of directional mobility, in which the species move following the direction associated to a larger (averaged) number density of selection targets in the surrounding neighborhood. Directional mobility can be used to simulate eyes that see or a nose that smells, and we show how it may contribute to reduce the probability of coexistence. [ABSTRACT FROM AUTHOR]

In this work, the frequency dependence of the known mechano-optical effect which occurs in the micellar isotropic phases (I) of mixtures of potassium laurate (KL), decanol (DeOH), and water is investigated in the range from 200mHz to 200Hz. In order to fit the experimental data, a model of superimposed damped harmonic oscillators is proposed. In this phenomenological approach, the micelles (microscopic oscillators) interact very weakly with their neighbors. Due to shape anisotropy of the basic structures, each oscillator i (i=1,2,3,...,N) remains in its natural oscillatory rotational movement around its axes of symmetry with a frequency ω0i. The system will be in the resonance state when the frequency of the driving force ω reaches a value near ω0i. This phenomenological approach shows excellent agreement with the experimental data. One can find f~2.5, 9.0, and 4.0Hz as fundamental frequencies of the micellar isotropic phases I, I1, and I2, respectively. The different micellar isotropic phases I, I1, and I2 that we find in the phase diagram of the KL-DeOH-water mixture are a consequence of possible differences in the intermicellar correlation lengths. This work reinforces the possibilities of technological applications of these phases in devices such as mechanical vibration sensors. [ABSTRACT FROM AUTHOR]