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.     

Classical dynamics of polar diatomic molecules in external fields

In this paper, we present the study of the global classical dynamics of a rigid diatomic molecule in the presence of combined electrostatic and nonresonant polarized laser fields. In particular, we focus on the collinear field case, which is an integrable system because the z-component P_φ of the angular momentum is conserved. The study involves the complete analysis of the stability of the equilibrium points, their bifurcations and the evolution of the phase flow as a function of the field strengths and P_φ. Finally, the influence of the bifurcations on the orientation of the quantum states is studied.     

Control coherence resonance by noise recycling

We study the effect of recycled noise, generated by the superposition of a primary Gaussian noise source with a second component of constant delay, in a parameter region below the threshold of supercritical Hopf bifurcation, by focussing on the performance of noise induced oscillations and coherence resonance. For fixed noise intensity, the amplitude and signal-to-noise ratio of the oscillation show periodic dependences on the delay time. The optimal noise intensity for the occurrence of coherence resonance also shows a periodic dependence on the delay. A theoretical analysis based on the stochastic normal form theory is presented, which qualitatively reproduces the simulation results with good agreement. This work presents a possible strategy for controlling noise induced oscillations and coherence resonance by deliberately adjusting the parameters of the recycled noise.     

The study of banded spherulite patterns by coupled logistic map lattice model

Banded spherulite patterns are simulated in two dimensions by means of a coupled logistic map lattice model. Both target pattern and spiral pattern which have been proved to be existent experimentally in banded spherulite are obtained by choosing suitable parameters in the model. The simulation results also indicate that the band spacing is decreased with the increase of parameter μ in the logistic map and increased with the increase of the coupling parameter ε, which is quite similar to the results in some experiments. Moreover, the relationship between the parameters and the corresponding patterns is obtained, and the target patterns and spiral patterns are distinguished for a given group of initial values, which may guide the study of banded spherulite.     

A Brownian energy depot model of the basilar membrane oscillation with a braking mechanism

High auditory sensitivity, sharp frequency selectivity, and spontaneous otoacoustic emissions are signatures of active amplification of the cochlea. The human ear can also detect very large amplitude sounds without being damaged, as long as the exposed time is not too long. The outer hair cells are believed to be the best candidate for the active force generator of the mammalian cochlea. In this paper, we propose a new model for the basilar membrane oscillation which describes both an active and a protective mechanism by employing an energy depot concept and a critical velocity of the basilar membrane. The compressive response of the basilar membrane at the characteristic frequency and the dynamic response to the stimulation are consistent with the experimental results. Although our model displays a Hopf bifurcation, our braking mechanism results in a hyper-compressive response to intense stimuli which is not generically observed near a Hopf bifurcation. Asymmetry seen in experimental recordings between the onset and the offset of the basilar membrane response to a sound burst is also observed in this model.     

Description of nonrigid rotation in small atomic clusters

The dependence of the internal dynamics of triatomic van der Waals clusters on the rate of nonrigid rotation has been studied. The method of decomposition of the system's motion into orthogonal modes of the motion has been proposed. Additionally, a new method of separation of the kinetic energy, captured by the modes, into rotational and vibrational components has been developed. It has been found that the most significant factor for the chaotic behavior of the cluster is the partitioning of the vibrational and rotational energies among the modes.     

Quantum transport in armchair graphene ribbons: analytical tight-binding solutions for propagation through step-like and barrier-like potentials

Based on the nearest-neighbor tight-binding approximation, we present exact analytical expressions for transmission coefficients through piecewise constant step-like and barrier-like electrostatic potentials. In the case of single mode propagation through semiconducting ribbon families our analytical solutions predict a new kind of resonances. Its features substantially change the behavior of the transmission coefficients in the range of moderate potentials, which become family-dependent. For semimetal ribbons our approach predicts no unit propagation. The non-zero backscattering is derived to be proportional as the square of the potential amplitude applied.     

Statistical analysis of the transmission based on the DMPK equation: an application to Pb nano-contacts

The density of the transmission eigenvalues of Pb nano-contacts has been estimated recently in mechanically controllable break-junction experiments. Motivated by these experimental analyses, here we study the evolution of the density of the transmission eigenvalues with the disorder strength and the number of channels supported by the ballistic constriction of a quantum point contact in the framework of the Dorokhov-Mello-Pereyra-Kumar equation. We find that the transmission density evolves rapidly into the density in the diffusive metallic regime as the number of channels N_c of the constriction increase. Therefore, the transmission density distribution for a few N_c channels comes close to the known bimodal density distribution in the metallic limit. This is in agreement with the experimental statistical-studies in Pb nano-contacts. For the two analyzed cases, we show that the experimental densities are seen to be well described by the corresponding theoretical results.     

Simulating 3D intense beam dynamics simulation using the moments method

The program of the 3D intense beam dynamic simulation based on the moments method is presented. The text was submitted by the authors in English.     

Topologically non-trivial chiral transformations

The role of chiral transformations in effective theories modeling Quantum Chromo Dynamics is reviewed. In the context of the Nambu-Jona-Lasinio model the hidden gauge and massive Yang-Mills approaches to vector mesons are linked by a special chiral transformation which removes the chiral field from the scalar-pseudoscalar sector. The chirally rotated axial vector meson field (à _μ ) transforms homogeneously under flavor rotations and may thus be dropped without violating chiral symmetry. The fermion determinant for static meson field configurations is computed by summing the discretized eigenvalues of the Dirac Hamiltonian. It is discussed how the local chiral transformation loses its unitary character in a finite model space. This technical issue proves to be crucial for the construction of the soliton within the Nambu-Jona-Lasinio model when the chirally rotated axial vector field is neglected. In the background of this soliton the valence quark is strongly bound, and its eigenenergy turns out to be negative. This important feature, which usually is generated by non-vanishing axial vector profiles, is thus maintained by the simplificationà _μ = 0.     

Theory of intraband transition linewidths due to LO phonon scattering in triangular well based on the many body projection method

Utilizing the state dependent projection technique, we derive a formula for intraband transition linewidths due to longitudinal optical phonon scattering for the electrons in a triangular potential well. We find for GaN that the absorption power is keenly affected by the screening in such a way that the power increases with the electron density. We also find that the linewidth increases with the temperature, but decreases with the electric field applied to the system.     

Electronic structure and anomalous physical properties of metastable Al-Si solid solutions

Al-Si solid solutions synthesized under high pressure demonstrate striking physical properties, such as enhanced superconductivity and peculiarities of low-temperature transport coefficients. In order to understand the connection of these effects to the electronic structure changes we have performed a first-principles study of the electronic spectra and Fermi surfaces of Al-Si solid solutions. We show that two electronic topological transitions (ETT's) lead to unusual concentration dependencies of the resistivity, thermoelectric power and Hall constant of the system while a variety of other interesting phenomena such as lattice instability and superconductivity enhancement may be a result of the nesting features appearing upon Si doping. We present also the results of our theoretical calculations of the thermodynamic and transport properties of Al-Si solid solutions which are in good agreement with experiment and reproduce nicely the experimentally observed peculiarities. Received 31 January 2002     

Stochastic resonance and energy optimization in spatially extended dynamical systems

We investigate a class of nonlinear wave equations subject to periodic forcing and noise, and address the issue of energy optimization. Numerically, we use a pseudo-spectral method to solve the nonlinear stochastic partial differential equation and compute the energy of the system as a function of the driving amplitude in the presence of noise. In the fairly general setting where the system possesses two coexisting states, one with low and another with high energy, noise can induce intermittent switchings between the two states. A striking finding is that, for fixed noise, the system energy can be optimized by the driving in a form of resonance. The phenomenon can be explained by the Langevin dynamics of particle motion in a double-well potential system with symmetry breaking. The finding can have applications to small-size devices such as microelectromechanical resonators and to waves in fluid and plasma.     

Active Brownian motion models and applications to ratchets

We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircaselike and Mateos ratchet potentials, also with the additional loads modelled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This stochastically driven directionality effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed.     

Type-II intermittency characteristics in the presence of noise

We consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type-II intermittency and random dynamics. We analytically deduce the law for the distribution of the laminar phases, which has never been obtained hitherto. The already known dependence of the mean length of the laminar phases on the criticality parameter [Phys. Rev. E 68, 036203 (2003)] follows as a corollary of the carried out research. We also prove that this dependence obtained earlier under the assumption of the fixed form of the reinjection probability does not depend on the relaminarization properties, and, correspondingly, the obtained expression of the mean length of the laminar phases on the criticality parameter remains correct for different types of the reinjection probability.     

Electroconvection in nematics above the splay Fréedericksz transition

We present a basic model for an instability leading to a novel type of electroconvection patterns observed above the splay Fréedericksz transition in nematics. Such patterns, with wave vector perpendicular to the director easy axis, are found in planar sandwich cells under crossed polarizers, they do not produce shadowgraph images at onset. An adaptation of the classical Carr Helfrich mechanism is introduced. The ground state is a tilted director field uniform in the cell plane. The proposed mechanism destabilizes this director field and leads to a structure with modulated out-of-plane (twist) deformations. Experimental confirmation is provided by polarizing microscopy. All experimental observations are qualitatively explained with the proposed model.     

Fractal model of the atom and some properties of the matter through an extended model of scale relativity

The scale relativity model was extended for the motions on fractal curves of fractal dimension D _F and third order terms in the equation of motion of a complex speed field. It results that, in a fractal fluid, the convection, dissipation and dispersion are compensating at any scale (differentiable or non-differentiable), whereas a generalized Schrödinger type equation is obtained for an irrotational movement of the fractal fluid. For D _F = 2 and the dissipative approximation of the motions, the fractal model of atom is build: the real part of the complex speed field describes the electron motion on stationary orbits according to a quantification condition, while the imaginary part of the complex speed field gives the electron energy quantification. For D _F = 3 and the dispersive approximation of motions, some properties of the matter are explained: at the differentiable scale the flowing regimes (non-quasi-autonomous and quasi-autonomous) of the fractal fluids are separated by the experimental “0.7 structure”, while for the non-differentiable scale the fractal potential acts as an energy accumulator and controls through coherence the transport phenomena. Moreover, the compatibility between the differentiable and non-differentiable scales implies a Cantor space-time, and consequently a fractal at any scale. Thus, some properties of the matter (the anomaly of nano-fluids thermal conductivity, the superconductivity etc.) can be explained by this model.     

Global firing induced by network disorder in ensembles of active rotators

We study the influence of repulsive interactions on an ensemble of coupled excitable rotators. We find that a moderate fraction of repulsive interactions can trigger global firing of the ensemble. The regime of global firing, however, is suppressed in sufficiently large systems if the network of repulsive interactions is fully random, due to self-averaging in its degree distribution. We thus introduce a model of partially random networks with a broad degree distribution, where self-averaging due to size growth is absent. In this case, the regime of global firing persists for large sizes. Our results extend previous work on the constructive effects of diversity in the collective dynamics of complex systems.