Co-existence in the two-dimensional May-Leonard model with random rates

We employ Monte Carlo simulations to numerically study the temporal evolution and transient oscillations of the population densities, the associated frequency power spectra, and the spatial correlation functions in the (quasi-)steady state in two-dimensional stochastic May--Leonard models of mobile individuals, allowing for particle exchanges with nearest-neighbors and hopping onto empty sites. We therefore consider a class of four-state three-species cyclic predator-prey models whose total particle number is not conserved. We demonstrate that quenched disorder in either the reaction or in the mobility rates hardly impacts the dynamical evolution, the emergence and structure of spiral patterns, or the mean extinction time in this system. We also show that direct particle pair exchange processes promote the formation of regular spiral structures. Moreover, upon increasing the rates of mobility, we observe a remarkable change in the extinction properties in the May--Leonard system (for small system sizes): (1) As the mobility rate exceeds a threshold that separates a species coexistence (quasi-)steady state from an absorbing state, the mean extinction time as function of system size N crosses over from a functional form ~ e^{cN} / N (where c is a constant) to a linear dependence; (2) the measured histogram of extinction times displays a corresponding crossover from an (approximately) exponential to a Gaussian distribution. The latter results are found to hold true also when the mobility rates are randomly distributed.Comment: 9 pages, 4 figures; to appear in Eur. Phys. J. B (2011

Spontaneous symmetry breaking in a two-lane model for bidirectional overtaking traffic

First we consider a unidirectional flux \omega_bar of vehicles each of which is characterized by its `natural' velocity v drawn from a distribution P(v). The traffic flow is modeled as a collection of straight `world lines' in the time-space plane, with overtaking events represented by a fixed queuing time tau imposed on the overtaking vehicle. This geometrical model exhibits platoon formation and allows, among many other things, for the calculation of the effective average velocity w=\phi(v) of a vehicle of natural velocity v. Secondly, we extend the model to two opposite lanes, A and B. We argue that the queuing time \tau in one lane is determined by the traffic density in the opposite lane. On the basis of reasonable additional assumptions we establish a set of equations that couple the two lanes and can be solved numerically. It appears that above a critical value \omega_bar_c of the control parameter \omega_bar the symmetry between the lanes is spontaneously broken: there is a slow lane where long platoons form behind the slowest vehicles, and a fast lane where overtaking is easy due to the wide spacing between the platoons in the opposite direction. A variant of the model is studied in which the spatial vehicle density \rho_bar rather than the flux \omega_bar is the control parameter. Unequal fluxes \omega_bar_A and \omega_bar_B in the two lanes are also considered. The symmetry breaking phenomenon exhibited by this model, even though no doubt hard to observe in pure form in real-life traffic, nevertheless indicates a tendency of such traffic.Comment: 50 pages, 16 figures; extra references adde

A model for bidirectional traffic of cytoskeletal motors

We introduce a stochastic lattice gas model including two particle species and two parallel lanes. One lane with exclusion interaction and directed motion and the other lane without exclusion and unbiased diffusion, mimicking a micotubule filament and the surrounding solution. For a high binding affinity to the filament, jam-like situations dominate the system's behaviour. The fundamental process of position exchange of two particles is approximated. In the case of a many-particle system, we were able to identify a regime in which the system is rather homogenous presenting only small accumulations of particles and a regime in which an important fraction of all particles accumulates in the same cluster. Numerical data proposes that this cluster formation will occur at all densities for large system sizes. Coupling of several filaments leads to an enhanced cluster formation compared to the uncoupled system, suggesting that efficient bidirectional transport on one-dimensional filaments relies on long-ranged interactions and track formation.Comment: 20 pages, 9 figure

Who Should Do Replication Labor?

. Scientists, for the most part, want to get it right. However, the social structures that govern their work undermine that aim, and this leads to nonreplicable findings in many fields. Because the social structure of science is a decentralized system, it is difficult to intervene. In this article, I discuss how we might do so, focusing on self-corrective-labor schemes (i.e., ways of distributing replication efforts within the scientific community). First, I argue that we need to implement a scheme that makes replication work outcome independent, systematic, and sustainable. Second, I use these three criteria to evaluate extant proposals, which place the responsibility for replication on original researchers, consumers of their research, students, or many labs. Third, on the basis of a philosophical analysis of the reward system of science and the benefits of the division of cognitive labor, I propose a scheme that satisfies the criteria better: the professional scheme. This scheme has two main components. First, the scientific community is organized into two groups: discovery researchers, who produce new findings, and confirmation researchers, whose primary function is to do confirmation work (i.e., replication, reproduction, meta-analysis). Second, a distinct reward system is established for confirmation researchers so that their career advancement is separated from whether they obtain positive experimental results

How to determine a quantum state by measurements: The Pauli problem for a particle with arbitrary potential

The problem of reconstructing a pure quantum state ¿¿> from measurable quantities is considered for a particle moving in a one-dimensional potential V(x). Suppose that the position probability distribution ¿¿(x,t)¿2 has been measured at time t, and let it have M nodes. It is shown that after measuring the time evolved distribution at a short-time interval ¿t later, ¿¿(x,t+¿t)¿2, the set of wave functions compatible with these distributions is given by a smooth manifold M in Hilbert space. The manifold M is isomorphic to an M-dimensional torus, TM. Finally, M additional expectation values of appropriately chosen nonlocal operators fix the quantum state uniquely. The method used here is the analog of an approach that has been applied successfully to the corresponding problem for a spin system

Synchronization Gauges and the Principles of Special Relativity

The axiomatic bases of Special Relativity Theory (SRT) are thoroughly re-examined from an operational point of view, with particular emphasis on the status of Einstein synchronization in the light of the possibility of arbitrary synchronization procedures in inertial reference frames. Once correctly and explicitly phrased, the principles of SRT allow for a wide range of `theories' that differ from the standard SRT only for the difference in the chosen synchronization procedures, but are wholly equivalent to SRT in predicting empirical facts. This results in the introduction, in the full background of SRT, of a suitable synchronization gauge. A complete hierarchy of synchronization gauges is introduced and elucidated, ranging from the useful Selleri synchronization gauge (which should lead, according to Selleri, to a multiplicity of theories alternative to SRT) to the more general Mansouri-Sexl synchronization gauge and, finally, to the even more general Anderson-Vetharaniam-Stedman's synchronization gauge. It is showed that all these gauges do not challenge the SRT, as claimed by Selleri, but simply lead to a number of formalisms which leave the geometrical structure of Minkowski spacetime unchanged. Several aspects of fundamental and applied interest related to the conventional aspect of the synchronization choice are discussed, encompassing the issue of the one-way velocity of light on inertial and rotating reference frames, the GPS's working, and the recasting of Maxwell equations in generic synchronizations. Finally, it is showed how the gauge freedom introduced in SRT can be exploited in order to give a clear explanation of the Sagnac effect for counter-propagating matter beams.Comment: 56 pages, 3 eps figures, invited paper; to appear in Foundations of Physics (Special Issue to honor Prof. Franco Selleri on his 70th birthday

Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model

Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see e.g. B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature {\bf 418}, 171 (2002)] and B. Kirkup and M. A. Riley [Nature {\bf 428}, 412 (2004)]. Through analytical methods supported by numerical simulations, we address this issue by studying the properties of a paradigmatic non-spatial three-species stochastic system, namely the `rock-paper-scissors' or cyclic Lotka-Volterra model. While the deterministic approach (rate equations) predicts the coexistence of the species resulting in regular (yet neutrally stable) oscillations of the population densities, we demonstrate that fluctuations arising in the system with a \emph{finite number of agents} drastically alter this picture and are responsible for extinction: After long enough time, two of the three species die out. As main findings we provide analytic estimates and numerical computation of the extinction probability at a given time. We also discuss the implications of our results for a broad class of competing population systems.Comment: 12 pages, 9 figures, minor correction

Molecular Spiders in One Dimension

Molecular spiders are synthetic bio-molecular systems which have "legs" made of short single-stranded segments of DNA. Spiders move on a surface covered with single-stranded DNA segments complementary to legs. Different mappings are established between various models of spiders and simple exclusion processes. For spiders with simple gait and varying number of legs we compute the diffusion coefficient; when the hopping is biased we also compute their velocity.Comment: 14 pages, 2 figure

Time on a Rotating Platform

Traditional clock synchronisation on a rotating platform is shown to be incompatible with the experimentally established transformation of time. The latter transformation leads directly to solve this problem through noninvariant one-way speed of light. The conventionality of some features of relativity theory allows full compatibility with existing experimental evidence.Comment: 12 pages, Latex, no figure. Copies available at [email protected] accepted for publication in Found. Phys. Let

Decoherence, Correlation, and Unstable Quantum States in Semiclassical Cosmology

It is demonstrated that almost any S-matrix of quantum field theory in curved spaces posses an infinite set of complex poles (or branch cuts). These poles can be transformed into complex eigenvalues, the corresponding eigenvectors being Gamow vectors. All this formalism, which is heuristic in ordinary Hilbert space, becomes a rigorous one within the framework of a properly chosen rigged Hilbert space. Then complex eigenvalues produce damping or growing factors. It is known that the growth of entropy, decoherence, and the appearance of correlations, occur in the universe evolution, but only under a restricted set of initial conditions. It is proved that the damping factors allow to enlarge this set up to almost any initial conditions.Comment: 19 pgs. Latex fil