Nonlinear voter models: the transition from invasion to coexistence

In nonlinear voter models the transitions between two states depend in a nonlinear manner on the frequencies of these states in the neighborhood. We investigate the role of these nonlinearities on the global outcome of the dynamics for a homogeneous network where each node is connected to m = 4 neighbors. The paper unfolds in two directions. We first develop a general stochastic framework for frequency dependent processes from which we derive the macroscopic dynamics for key variables, such as global frequencies and correlations. Explicit expressions for both the mean-field limit and the pair approximation are obtained. We then apply these equations to determine a phase diagram in the parameter space that distinguishes between different dynamic regimes. The pair approximation allows us to identify three regimes for nonlinear voter models: (i) complete invasion; (ii) random coexistence; and – most interestingly – (iii) correlated coexistence. These findings are contrasted with predictions from the mean-field phase diagram and are confirmed by extensive computer simulations of the microscopic dynamics.     

Sexually transmitted infections and the marriage problem

We study an SIS epidemiological model for a sexually transmitted infection in a monogamous population where the formation and breaking of couples is governed by individual preferences. The mechanism of couple recombination is based on the so-called bar dynamics for the marriage problem. We compare the results with those of random recombination – where no individual preferences exist – for which we calculate analytically the infection incidence and the endemic threshold. We find that individual preferences give rise to a large dispersion in the average duration of different couples, causing substantial changes in the incidence of the infection and in the endemic threshold. Our analysis yields also new results on the bar dynamics, that may be of interest beyond the field of epidemiological models.     

A model based on <Emphasis Type="Italic">TTC</Emphasis> to describe how drivers controltheir vehicles

We have used the Penna ageing model to analyze how the differences in evolution of sex chromosomes depend on the strategy of reproduction. In panmictic populations, when females (XX) can freely choose the male partner (XY) for reproduction from the whole population, the Y chromosome accumulates defects and eventually the only information it brings is a male sex determination. As a result of shrinking Y chromosome the male genomes de facto loose one copy of the X chromosome information and, as a result, males are characterized by higher mortality, observed also in the human populations. If it is assumed in the model that the presence of the male is indispensable at least during the pregnancy of his female partner and he cannot be seduced by another female at least during the one reproduction cycle-the Y chromosome preserves its content, does not shrink and the lifespan of females and males is the same. Thus, Y chromosome shrinks not because of existing in one copy, without the possibility of recombination, but because it stays under weaker selection pressure; in panmictic populations without the necessity of being faithful, a considerable fraction of males is dispensable and they can be eliminated from the population without reducing its reproduction potential.     

Dynamical inference of hidden biological populations

Population fluctuations in a predator-prey system are analyzed for the case where the number of prey could be determined, subject to measurement noise, but the number of predators was unknown. The problem of how to infer the unmeasured predator dynamics, as well as the model parameters, is addressed. Two solutions are suggested. In the first of these, measurement noise and the dynamical noise in the equation for predator population are neglected; the problem is reduced to a one-dimensional case, and a Bayesian dynamical inference algorithm is employed to reconstruct the model parameters. In the second solution a full-scale Markov Chain Monte Carlo simulation is used to infer both the unknown predator trajectory, and also the model parameters, using the one-dimensional solution as an initial guess.     

Absorption measurements in InSe:Ho single crystal under an electric field

InSe:Ho single crystal was grown by Bridgman-Stockberger method. Electric field effects on the absorption measurements have been investigated as a function of temperature in InSe:Ho single crystal. The absorption edge shifted towards longer wavelengths and a decrease of intensity in absorption spectra occurred under an electric field of 7.5 kV/cm. Using absorption measurements, steepness parameter and Urbach energy were calculated under electric field. Applied electric field caused an increase in the Urbach energy. At 10 K and 320 K, the first exciton energies were calculated as 1.322 and 1.301 eV for zero voltage and 1.245 and 1.232 eV for applied electric field, respectively.     

Pattern formation,social forces,and diffusion instability in games with success-driven motion

A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the spreading and disappearance of strategies. In this paper, it is shown that success-driven motion can trigger such local agglomeration and may, therefore, be used to supplement other mechanisms supporting cooperation, like reputation or punishment. Success-driven motion is formulated here as a function of the game-theoretical payoffs. It can change the outcome and dynamics of spatial games dramatically, in particular as it causes attractive or repulsive interaction forces. These forces act when the spatial distributions of strategies are inhomogeneous. However, even when starting with homogeneous initial conditions, small perturbations can trigger large inhomogeneities by a pattern-formation instability, when certain conditions are fulfilled. Here, these instability conditions are studied for the prisoner’s dilemma and the snowdrift game. Furthermore, it is demonstrated that asymmetrical diffusion can drive social, economic, and biological systems into the unstable regime, if these would be stable without diffusion.     

Time evolution of non-lethal infectious diseases: a semi-continuous approach

A model describing the dynamics related to the spreading of non-lethal infectious diseases in a fixed-size population is proposed. The model consists of a non-linear delay-differential equation describing the time evolution of the increment in the number of infectious individuals and depends upon a limited number of parameters. Predictions are in good qualitative agreement with data on influenza, which is taken to be a representative type of non-lethal infectious disease.     

Editorial: Ecological complex systems

Main aim of this topical issue is to report recent advances in noisy nonequilibrium processes useful to describe the dynamics of ecological systems and to address the mechanisms of spatio-temporal pattern formation in ecology both from the experimental and theoretical points of view. This is in order to understand the dynamical behaviour of ecological complex systems through the interplay between nonlinearity, noise, random and periodic environmental interactions. Discovering the microscopic rules and the local interactions which lead to the emergence of specific global patterns or global dynamical behaviour and the noise’s role in the nonlinear dynamics is an important, key aspect to understand and then to model ecological complex systems.     

Momentum map and action-angle variables for Nambu dynamics

Momentum map is a reduction procedure that reduces the dimension of a Hamiltonian system to the lower ones. It is shown that behavior of the action-angle variables under the momentum map generates the new action-angle variables for the reduced system considered as a Nambu structure. The symmetrical top is given as an illustration. This work was supported in part by the Scientific and Technical Research Council of Turkey (TüBİTAK).     

Determination of erosion rates with cosmic ray produced36Cl

We present results of the determination of³⁶C1 (T _1/2=3.0·10⁵a) in rock samples produced in situ by cosmic rays and natural radioactivities. These experiments were designed to determine the feasibility of using³⁶Cl for studying erosion processes in calcium rich minerals like limestone or dolomite. The³⁶Cl/Cl ratios in the samples have been determined with accelerator mass spectrometry (AMS) at the Munich accelerator laboratory. A first application is the investigation of the erosion in the last million years in Allchar (Yugoslavia) for the feasibility study of the geochemical²⁰⁵Tl solar neutrino experiment.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday. Supported by DFG     

Martensitic phase transition from cubic to tetragonal V<Subscript>3</Subscript>Si: an electronic structure study

We analyze the epidemic spread via a contact infection process in an immobile population within the Susceptible-Infected-Removed (SIR) model. We present both the results of stochastic simulations assuming different numbers of individuals (degrees of freedom) per cell as well as the solution of the corresponding deterministic equations. For the last ones we show that the appropriate system of nonlinear partial differential equations (PDE) allows for a complete separation of variables and present the approximate analytical expressions for the infection wave in different ranges of parameters. Comparing these results with the direct Monte-Carlo simulations we discuss the domain of applicability of the PDE models and their restrictions.     

Noise-controlled slow–fast oscillations in predator–prey models with the Beddington functional response

The influence of environmental fluctuations (modeled as a multiplicative dichotomous noise) on predator–prey interaction is studied using a metapopulation model with N prey-subpopulations. Investigating the role that predator interference plays in the dynamics of such trophic systems, the Beddington functional response is considered. In case the growth rates of prey and predator are widely different, we obtain analytic results by a dynamical mean-field approximation. In some regions of the system parameters, variations of noise amplitude or correlation time can cause transitions of the mean field from a globally stable equilibrium to the stable limit cycle as well as in the opposite direction. The conditions for the occurrence of such a phenomenon are found and illustrated by phase diagrams. Implications of the results on the colored-noise-induced extinction of a predator population are also discussed.     

SIR model of epidemic spread with accumulated exposure

We study an extended and modified SIR model of epidemic spread in which susceptible agents during interactions with infectious neighbors are exposed to the disease and can consequently become infectious. The studied model is extended to include heterogeneity of interactions which is modelled assuming random character of the dose accumulated by susceptible agents in every interaction with infectious neighbors. When the accumulated exposure is larger than the individual’s resistance, an agent becomes infectious and consequently introduces a new source of an epidemic which is capable of passing the disease further. We study statistical properties characterizing the course of an epidemic. The examination of the modified SIR model reveals a possible “resonant activation”-like behavior of the system in the duration of the epidemic outbreak and a possible bistable behavior of the model with accumulated exposure. Furthermore, the linear scaling of the duration of the epidemic with the system size for a wide range of the model parameters is recorded.     

Spectrally selective splitters with metal-dielectric-metal surface plasmon waveguides

Spectrally selective splitters with metal-dielectric-metal (MDM) subwavelength waveguides are proposed in this paper. The method is based on the Bragg grating structure with periodically modulated MDM waveguide width, which delivers a stop band effect for the surface plasmon propagating in the waveguide. By adding appropriate Bragg grating structure in one or more arms of the waveguide splitters, light in a certain frequency range can be readily guided into the desired directions, as demonstrated numerically by the finite-difference time-domain method. Dependence and optimization of the geometrical parameters are also considered in this paper.     

The project of a Tau-Charm Factory with Crab Waist in Novosibirsk

The project of a new-generation TCF is now under consideration in Novosibirsk. A novel approach of the Crab Waist collision scheme allows reaching a luminosity of 1–2 × 10³⁵ cm⁻² s⁻¹. The other features of the facility are as follows: variable energy from 3 GeV to 4.5 GeV (c.m.), electron beam polarization, flexible usage of damping and excitation wigglers to keep high luminosity for all energy levels, etc. We discuss some of the challenges and opportunities available with the development of the project. for the Novosibirsk Tau-Charm Factory team The text was submitted by the author in English.     

Diode end pumped Nd:YAG laser at 946 nm with high pulse energy limited by thermal lensing

Diode lasers with peak powers in the kW range and pulse durations of micro- to milli-seconds have been available since several years. Pumping solid state lasers with such sources yield high output pulse energies in spiking or Q-switched operation. The output energy is limited by the thermal lens effects, which are measured and calculated. The time dependent heat conduction equation in the laser crystal is solved numerically to predict the overall temperature rise and thermal lensing. The thermally induced optical path difference is approximated by a quadratic distribution to obtain the focal length f of the thermal lens. The thermal lens coefficient K=1/(f⋅P _av), which depends only weakly on the heat transfer coefficient H of the laser crystal to the heat sink, decreases exponentially with increasing pump frequency until the steady state is reached. Experiments were done with a Nd:YAG crystal at different pump frequencies up to 100 Hz. The thermal lens coefficients obtained by the power maxima of asymmetric flat-flat resonators agree with our calculations.     

The development of a TESLA recirculator with superconducting accelerating structures in Ukraine

The recirculator project, which is to be built at the National Science Center, Kharkov Institute of Physics and Technology (NSC KIPT), is presented. The basic solutions incorporated in the design are given. The TESLA superconducting section is chosen as the accelerating structure of an accelerating complex. The text was submitted by the authors in English.     

Birth and death in a continuous opinion dynamics model

We here discuss the process of opinion formation in an open community where agents are made to interact and consequently update their beliefs. New actors (birth) are assumed to replace individuals that abandon the community (deaths). This dynamics is simulated in the framework of a simplified model that accounts for mutual affinity between agents. A rich phenomenology is presented and discussed with reference to the original (closed group) setting. Numerical findings are supported by analytical calculations.     

Picosecond lifetime measurements in147Pm

Half-lives of excited levels in¹⁴⁷Pm have been measured using BaF₂ scintillators. New values of t_1/2 are 2420(10), 43(5), 22(9), 17(10) and 17(10) ps for the 91.1, 410.5, 489.2, 531.0 and 685.9 keV level, respectively. E2 enhancement factors of -transitions have been deduced.