Dynamical phase transition in the simplest molecular chain model

We consider the dynamics of the simplest chain of a large number N of particles. In the double scaling limit, we find the partition of the parameter space into two domains: for one domain, the supremum over the time interval (0,∞) of the relative extension of the chain tends to 1 as N → ∞, and for the other domain, to infinity.     

A phase field model in electrowetting and related phenomena

The term electrowetting is commonly used for some techniques to change the shape and wetting behaviour of liquid droplets by the application of electric fields and charges. We developand analyze a model for electrowetting that combines the Navier-Stokes system for fluid flow, a phase-field model of Cahn-Hilliard type for the movement of the interface, a charge transport equation, and the potential equation of electrostatics. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamical magnetic susceptibility of the periodic anderson model in the chaotic phase approximation

Using the diagram technique in the atomic representation in the generalized chaotic phase approximation, we solve the problem of calculating the dynamical magnetic susceptibility of the periodic Anderson model in the strong electron correlation regime. We express the dynamical magnetic susceptibility in terms of four Matsubara Green’s functions describing partial contributions, which are calculated based on exact solutions of integral equations.     

Spiral chaos in the nonholonomic model of a Chaplygin top

This paper presents a numerical study of the chaotic dynamics of a dynamically asymmetric unbalanced ball (Chaplygin top) rolling on a plane. It is well known that the dynamics of such a system reduces to the investigation of a three-dimensional map, which in the general case has no smooth invariant measure. It is shown that homoclinic strange attractors of discrete spiral type (discrete Shilnikov type attractors) arise in this model for certain parameters. From the viewpoint of physical motions, the trace of the contact point of a Chaplygin top on a plane is studied for the case where the phase trajectory sweeps out a discrete spiral attractor. Using the analysis of the trajectory of this trace, a conclusion is drawn about the influence of “strangeness” of the attractor on the motion pattern of the top.     

Dynamical analysis of an anemoscope in the phase plane

We study the dynamical aspects of an anemoscope indicating a wind direction by constructing a model in the discrete view of fluid. Due to the non-linearity of the rotational equation, the geometrical method is applied for the qualitative analysis. For a given wind direction, there are two fixed points of the parallel and anti-parallel configurations. Near the anti-parallel configuration of the stable fixed point, the anemoscope performs a damped harmonic oscillation. It can be noteworthy that there is always the damping term for both the configurations even in the absence of the non-aerodynamic frictional force from, for example, the axis of rotation. The argument using the index of a closed curve in the phase portrait seems to support the non-existence of periodic solution.     

Aerodynamic and aeroacoustic phenomena due to non-uniform flow of wind turbines

Stall control and pitch control are the most commonly used methods of regulating power. However, through the opportunities presented by the flexible (or teetered) hub of a two–bladed teetered rotor one can also utilize yaw control to regulate power. This is achieved by adjusting the capture area of the rotor disk relative to the prevailing wind direction. This paper presents the aerodynamic and aeroacoustic results obtained from theoretical models for a rotor when is yawed to the undisturbed flow. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Critical phenomena in the fermionic hierarchical model

The dynamics of the renormalization-group transformation in the coupling-constant space of the fermionic hierarchical model are discussed. The critical behavior of this model is described in terms of the complex behavior of the Grassmann-valued mean-spin distribution density with the proper normalization. Some critical indices are calculated. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 3, pp. 471–488, December, 1998.     

Resonances of the SD oscillator due to the discontinuous phase

Resonant phenomenon of a harmonically excited system with multiple well dynamics plays a very important role in nonlinear dynamics research. In this paper, we investigate resonant behaviors of a discontinuous forced SD system with snap-through buckling and double-well dynamics. Firstly, a discontinuous time dependent Hamiltonian is derived from the discontinuous stage of SD oscillator providing a Du±ng type nonlinearity with snap-through buckling and double-well dynamics. This system comprises two subsystems connected at x = 0, where the system is discontinuous. We construct a series of generating functions and canonical transformations to get the canonical form of the system to reveal the complicated resonant behavior of the system. Furthermore, we introduce a composed winding number to explorer the complicated resonant phenomena of the system.This formulation for resonant phenomena given in this paper generalizes the formulation of n!0 = m! in regular perturbation theory, where n and m are relative prime integers,!0 and ! are the natural frequency and external frequencies respectively. Understanding the resonant behaviors of the SD oscillator at discontinuous stage enables us to further reveal the vibrational energy transition mechanism of the smooth and discontinuous nonlinear dynamic system.     

A continuum model for transport phenomena in convective flow of solid–liquid phase change material suspensions

Heat and mass transport is modeled in convective flow of a dilute binary mixture of a continuous fluid with mono-dispersed particles (PCM suspensions), in which solid–liquid phase change can take place. The model is based on the mixture continuum approach together with an approximate enthalpy formulation, in which the temporal and spatial variations of phase change fraction in the particles are considered explicitly. Derivations are given for a set of equations governing conservation of mass, momentum, species, and energy of the suspensions, as well as the evolution of phase change fraction of the dispersed particles.     

Dynamical properties of cluster in the Hamiltonian Mean Field model

We investigate some properties of the trapping/untrapping mechanism of a single particle into/outside the cluster in the Hamiltonian Mean Field model. Particle are clustered in the ordered low-energy phase in this model. However, when the number of particles is finite, some particles can acquire a high energy and leave the cluster. Hence, below the critical energy, the fully-clustered and excited states appear by turns. First, we show that the numerically computed time-averaged trapping ratio agrees with that obtained by a statistical average performed for the Boltzmann–Gibbs stationary solution of the Vlasov equation. Second, we found numerically that the probability distribution of the lifetime of the fully-clustered state is not exponential but follows instead a power law. This means that the excitation of a particle from the cluster is not a Poisson process and might be controlled by some type of collective motion with long memory. Therefore, although an average trapping ratio exists, there appear to be no typical trapping ratio in the probabilistic sense. Finally, we discuss the dynamical mechanism using a modified model.     

Concentration phenomena for the volume functional in unbounded domains: identification of concentration points

We study the variational problem

     

The rise of complex phenomena in Cournot duopoly games due to demand functions without inflection points

In this paper, we propose Cournot duopoly games where quantity-setting firms use non-linear demand functions that have no inflection points. Two different kinds of repeated games are introduced based on rationality process of firms and Puu’s incomplete approach. First, a model of two rational firms that are in competition and produce homogenous commodities is introduced. The equilibrium points of this model are obtained and their dynamical characteristics such as stability, bifurcation and chaos are investigated. By using rationality process firms do not need to solve any optimization problem but they adjust their production based on estimation of the marginal profit. Using Puu’s incomplete information approach a new model is introduced. As in the first model, the equilibrium points are obtained and their dynamical characteristics are investigated. By using Puu’s approach firms only need to know their profits and the quantities produced in the past two times. We compare the properties of the two models under the two approaches. The paper extends and generalizes the results of other authors that consider similar processes.     

Dynamical magnetic susceptibility in the spin-fermion model for cuprate superconductors

Using the method of diagram techniques for the spin and Fermi operators in the framework of the SU(2)-invariant spin-fermion model of the electron structure of the CuO₂plane of copper oxides, we obtain an exact representation of the Matsubara Green’s function D_⊥(k, iω _m ) of the subsystem of localized spins. This representation includes the Larkin mass operator Σ_L(k, iω _m ) and the strength and polarization operators P(k, iω _m ) and Π(k, iω _m ). The calculation in the one-loop approximation of the mass and strength operators for the Heisenberg spin system in the quantum spin-liquid state allows writing the Green’s function D_⊥(k, iω _m ) explicitly and establishing a relation to the result of Shimahara and Takada. An essential point in the developed approach is taking the spin-polaron nature of the Fermi quasiparticles in the spin-fermion model into account in finding the contribution of oxygen holes to the spin response in terms of the polarization operator Π(k, iω _m ).     

Dynamical behaviors of the chaotic Brushless DC motors model

This article is concerned with the boundedness solutions of the brushless DC motor system. For this system, the global attractive set and positively invariant set are obtained based on generalized Lyapunov function stability theory and the extremum principle of function. Furthermore, the rate of the trajectories is also obtained. Numerical simulations are presented to show the effectiveness of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 79–85, 2016     

Finite-volume corrections to magnetization in the spin-glass phase of the Derrida model

We consider the random energy model, where in the spin-glass phase, magnetization falls off exponentially as the volume increases. This magnetization corresponds to the probability of correct decoding in the case where the information transmission rate exceeds the channel capacity.Translated from Theoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 422–426, December, 1996.     

Dynamical analysis of a Lotka-Volterra learning-process model

A Lotka-Volterra learning-process model was proposed by Monteiro and Notargiacomo in [{\it Commum. Nonlinear Sci. Numer. Simulat.} {\bf 47}(2017), 416-420] to approach learning process as an interplay between understanding and doubt. They studied the stability of the boundary equilibria and gave some numerical simulations but no further discussion for bifurcations. In this paper, we study the qualitative properties of the interior equilibria and a singular line segment completely. Moreover, we discuss their bifurcations such as transcritical, pitchfork, Hopf bifurcation on isolated equilibria and transcritical bifurcation without parameters on non-isolated equilibria. Finally, we also demonstrate these analytical theory by numerical simulations.     

Transitions from bursting to spiking due to depolarizing current in the Chay neuronal model

Distinct transitions of firing activities from bursting to spiking induced by the depolarizing current I are explored near the Hopf bifurcations in the Chay neuronal system. The period-1 “circle/homoclinic” bursting at one rest state makes a transition slowly to repetitive spiking with the parameter I increasing. However, the “Hopf/homoclinic” bursting via a “fold/homoclinic” hysteresis loop at another rest state may transit to continuous spiking abruptly by increasing I.