Modelling of periodic electromagnetic structures bianisotropic materials with memory effects

We study the behavior of the electromagnetic field of a medium presenting periodic microstructures made of bianisotropic material. We reconsider the classical multi-scale homogenization technique by giving a new approach based upon the periodic unfolding method. The limiting homogeneous constitutive law is thus rigorously justified both in the time domain and in the frequency domain. In particular we show that the limit law differs from the initial one regarding the convolution term accounting for the memory effects.     

Control of synchronization and spiking regularity by heterogenous aperiodic high-frequency signal in coupled excitable systems

This paper investigates the synchronization and spiking regularity induced by heterogenous aperiodic (HA) signal in coupled excitable FitzHugh–Nagumo systems. We found new nontrivial effects of couplings and HA signals on the firing regularity and synchronization in coupled excitable systems without a periodic external driving. The phenomenon is similar to array enhanced coherence resonance (AECR), and it is shown that AECR-type behavior is not limited to systems driven by noises. It implies that the HA signal may be beneficial for the brain function, which is similar to the role of noise. Furthermore, it is also found that the mean frequencies, the amplitudes and the heterogeneity of HA stimuli can serve as control parameters in modulating spiking regularity and synchronization in coupled excitable systems. These results may be significant for the control of the synchronized firing of the brain in neural diseases like epilepsy.     

Elastic Wave Propagation in Soft Microstructured Composites Undergoing Finite Deformations

We consider the propagation of elastic waves in soft composite materials undergoing large deformations. The analysis is performed in terms of small amplitude motions superimposed on a deformed state. By consideration of 2D periodic laminates and 3D fiber composites, we find that an applied deformation influences the elastic waves through the change in the microstructure, and through the change in the local material properties. These effects can be significantly amplified by the deformation induced elastic instability phenomenon leading to microstructure transformations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Large-Deformation Phase-Field Approach for the Modeling of Magneto-Sensitive Elastomers

Magneto-sensitive materials show magneto-mechanical coupled response and are thus of increasing interest in the recent age of smart functional materials. Ferromagnetic particles suspended in an elastomeric matrix show realignment under the influence of an external applied field, in turn causing large deformations of the substrate material. The magneto-mechanical coupling in this case is governed by the magnetic properties of the inclusion and the mechancial properties of the matrix. The magnetic phenomenon in ferromagnetic materials is governed by the formation and evolution of domains on the micro scale. A better understanding of the behavior of these particles under the influence of an external applied field is required to accurately predict the behavior of such materials. In this context it is of particular importance to model the macro scopic magneto-mechanically coupled behavior based on the micro-magnetic domain evolution. The key aspect of this work is to develop a large-deformation micro-magnetic model that can accurately capture the microscopic response of such materials. Rigorous exploitation of appropriate rate-type variational principles and consequent incremental variational principles directly give us field equations including the time evolution equation of the magnetization, which acts as the order parameter in our formulation. The theory presented here is the continuation of the work presented in [1, 7] for small deformations. A summary of magneto-mechanical theories spanning over multiple scales has been presented in [4]. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micro‐Macro Modelling of Piezoelectric Fiber Composites

The present work deals with the numerical modeling of 1‐3 periodic composites made of piezoceramic (PZT) fibers embedded in a soft non‐piezoelectric matrix. We especially focus on predicting the effective co‐efficients of the periodic transversely isotropic piezoelectric fiber composites using representative volume element method (unit cell method). The results which are obtained from the FEM technique are compared with analytical homogenization method for different volume fractions. The effective co‐efficients are obtained for rectangular and hexagonal arrangement of unidirectional piezoelectric fiber composites. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of the phase on the dynamics of a perturbed bouncing ball system

The phase control method is a non-feedback control technique which has been used for different purposes in continuous periodically driven dynamical systems. One of the main goals of this paper is to apply this control technique to the bouncing ball system, which can be seen as a paradigmatic periodically driven discrete dynamical system, and has a rather simple physical interpretation. The main idea is to apply a periodic control signal including a phase difference with respect to the periodic forcing of the initial system and to analyze its effect on the dynamics of the bouncing ball system. The numerical simulations we have carried out clearly show the strong effect of the phase of the control signal in suppressing or generating chaotic behavior and in changing the period of a periodic orbit. We have also analyzed the effect of the phase in the phenomenon of the crisis-induced intermittency, showing how the phase enhances the size of the attractor near a crisis and can induce the intermittent behavior. Finally we have analyzed the scaling behavior of the crisis by varying the phase difference between the perturbation and the external forcing.     

Periodic and Almost Periodic Solutions for a Coupled System of Two Korteweg-de Vries Equations with Boundary Forces

In this paper, we investigate a coupled system of two Korteweg-de Vries equations on a bounded domain. We discuss the long-time behavior of this system with forces on the left Dirichlet boundary conditions. We obtain that if the forces are periodic (almost periodic) with small amplitude, then the solution of the coupled system is periodic (almost periodic).     

Dynamics of a coupled atmosphere–ocean model

We consider a coupled atmosphere–ocean model, which involves hydrodynamics, thermodynamics and nonautonomous interaction at the air–sea interface. First, we show that the coupled atmosphere–ocean system is stable under the external fluctuation in the atmospheric energy balance relation. Then, we estimate the atmospheric temperature feedback in terms of the freshwater flux, heat flux and the external fluctuation at the air–sea interface, as well as the earth's longwave radiation coefficient and the shortwave solar radiation profile. Finally, we prove that the coupled atmosphere–ocean system has time-periodic, quasiperiodic and almost periodic motions, whenever the external fluctuation in the atmospheric energy balance relation is time-periodic, quasiperiodic and almost periodic, respectively.     

Periodic Gibbs measures for the three-state SOS model on a Cayley tree with a translation-invariant external field

Theoretical and Mathematical Physics - We consider a three-state solid-on-solid (SOS) model on a Cayley tree in the presence of an external field. We show that periodic Gibbs measures are either...     

A discussion about the homogenization of moving interfaces

There has been considerable interest lately in the homogenization theory for first- and second-order partial differential equations in periodic/almost periodic and random, stationary, ergodic environments. Of special interest is the study of the averaged behavior of moving interfaces. In this note we revisit the last issue. We present several new results concerning interfaces moving by either oscillatory first-order or curvature dependent coupled with oscillatory forcing normal velocity in periodic environments and analyze in detail their behavior. Under sharp assumptions we show that such fronts may homogenize, get trapped or oscillate.     

Huddling behavior as critical phase transition triggered by low temperatures

Huddling is a grouping behavior where animals maintain close bodily contact and save energy. We tested the hypothesis that this thermoregulatory behavior behaves as a system with continuous (second‐order phase) transition called critical when the environmental temperature (driving parameter) is near a critical value. To do so, we followed theoretical and experimental approaches, examining data from geometrical models, metabolic rate during huddling in small mammals, and also conducting an experiment on thermoregulatory huddling behavior with white mice. Our results support all predictions for systems under continuous‐phase transition triggered by low temperatures, a phenomenon reported for first time in a biological system. We suggest that huddling behavior in social animals, a recognized adaptive behavior, may be considered a self‐organized system coupled with an external driving parameter. © 2011 Wiley Periodicals, Inc. Complexity, 2011     

Predicting the elastoplastic response of fiber-reinforced metal matrix composites

This paper aims to investigate the effect of microstructure parameters (such as the cross-sectional shape of fibers and fiber volume fraction) on the stress–strain behavior of unidirectional composites subjected to off-axis loadings. A micromechanical model with a periodic microstructure is used to analyze a representative volume element. The fiber is linearly elastic, but the matrix is nonlinear. The Bodner–Partom model is used to characterize the nonlinear response of the fiber-reinforced composites. The analytical results obtained show that the flow stress of composites with square fibers is higher than with circular or elliptic ones. The difference in the elastoplastic response, which is affected by the fiber shape, can be disregarded if the fiber volume fraction is smaller than 0.15. Furthermore, the effect of fiber shape on the stress–strain behavior of the composite can be ignored if the off-axis loading angle is smaller than 30°.     

Variational Structural and Material Stability Analysis in Finite Electro-Magneto-Mechanics of Active Materials

Soft matter electro-elastic, magneto-elastic and magneto-electro-elastic composites exhibit coupled material behavior at large strains. Examples are electro-active polymers and magneto-rheological elastomers, which respond by a deformation to applied electric or magnetic fields, and are used in advanced industrial environments as sensors and actuators. Polymer-based magneto-electro-elastic composites are a new class of tailor-made materials with promising future applications. Here, a magneto-electric coupling effect is achieved as a homogenized macro-response of the composite with electro-active and magneto-active constituents. These soft composite materials show different types of instability phenomena, which even might be exploited for future enhancement of their performance. This covers micro-structural instabilities, such as buckling of micro-fibers or particles, as well as material instabilities in the form of limit-points in the local constitutive response. Here, the homogenization-based scale bridging links long wavelength micro-structural instabilities to material instabilities at the macro-scale. This work outlines a comprehensive framework of an energy-based homogenization in electro-magneto-mechanics, which allows a tracking of postcritical solution paths such as those related to pull-in instabilities. Representative simulations demonstrate a tracking of inhomogenous composites, showing the development of postcritical zones in the microstructure and a possible instable homogenized material response. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stochastic resonance induced by novel random transitions of motion of FitzHugh–Nagumo neuron model

In contrast to the previous studies which have dealt with stochastic resonance induced by random transitions of system motion between two coexisting limit cycle attractors in the FitzHugh–Nagumo (FHN) neuron model after Hopf bifurcation and which have dealt with the phenomenon of stochastic resonance induced by external noise when the model with periodic input has only one attractor before Hopf bifurcation, in this paper we have focused our attention on stochastic resonance (SR) induced by a novel transition behavior, the transitions of motion of the model among one attractor on the left side of bifurcation point and two attractors on the right side of bifurcation point under the perturbation of noise. The results of research show: since one bifurcation of transition from one to two limit cycle attractors and the other bifurcation of transition from two to one limit cycle attractors occur in turn besides Hopf bifurcation, the novel transitions of motion of the model occur when bifurcation parameter is perturbed by weak internal noise; the bifurcation point of the model may stochastically slightly shift to the left or right when FHN neuron model is perturbed by external Gaussian distributed white noise, and then the novel transitions of system motion also occur under the perturbation of external noise; the novel transitions could induce SR alone, and when the novel transitions of motion of the model and the traditional transitions between two coexisting limit cycle attractors after bifurcation occur in the same process the SR also may occur with complicated behaviors types; the mechanism of SR induced by external noise when FHN neuron model with periodic input has only one attractor before Hopf bifurcation is related to this kind of novel transition mentioned above.     

Macroscopic finite element analyses of discretematerials based on directly evaluated micro‐macro transitions

We consider a homogenized macro‐continuum with locally attached microstructure of granules and derive specific micromacro transitions by a consistent transfer of discrete micro‐variables to field variables on a continuous macrostructure. Displacements and rotational constraints are imposed on the granules on the defined boundary frame of the microstructure. The constraints for linear displacements and uniform tractions on the surface yield upper and lower bound characteristics for periodic boundary conditions with regard to the aggregate stiffness. Secondly, we perform two‐scale analyses where we link simulations on the macro‐ and the microscales. Therein, coupled boundary‐value problems are solved on both scales. The macroscopic homogeneous problem is solved by a finite element method where the material model is implemented using the directly evaluated micro‐macro transitions on the basis of the discrete microstructures. Finally, a model problem is investigated to clarify the proposed method. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Short-term memories with a stochastic perturbation

We investigate short-term memories in linear and weakly nonlinear coupled map lattices with a periodic external input. We use locally coupled maps to present numerical results about short-term memory formation adding a stochastic perturbation in the maps and in the external input.     

Degenerate plasma in a half-space under an external electric field

An analytic solution is found for the problem on the behavior of a collisional plasma in a variable external electric field. We elucidate the structure of the screened electric field and investigate the case where the frequency of the external field is close to the plasma oscillation frequency (resonance). We show that there are two near-surface layers where the behavior of the screened field differs essentially. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 3, pp. 487–502, June, 2006.     

Four competing interactions for models with an uncountable set of spin values on a Cayley tree

We consider models with four competing interactions (external field, nearest neighbor, second neighbor, and three neighbors) and an uncountable set [0, 1] of spin values on the Cayley tree of order two. We reduce the problem of describing the splitting Gibbs measures of the model to the problem of analyzing solutions of a nonlinear integral equation and study some particular cases for Ising and Potts models. We also show that periodic Gibbs measures for the given models either are translation invariant or have the period two. We present examples where periodic Gibbs measures with the period two are not unique.     

Periodic Gibbs measures for the Potts model on the Cayley tree

We study the Potts model on the Cayley tree. We demonstrate that for this model with a zero external field, periodic Gibbs measures on some invariant sets are translation invariant. Furthermore, we find the conditions under which the Potts model with a nonzero external field admits periodic Gibbs measures.