arXiv subjects

O. V. Gendelman

Publications and source records attributed to O. V. Gendelman.

33 records · Page 2Linked to original sources

arXiv2016

Dynamics and stability of a discrete breather in a harmonically excited chain with vibro-impact on-site potential

We investigate the existence and stability of discrete breathers in a chain of masses connected by linear springs and subjected to vibro-impact on-site potentials. The latter are comprised of harmonic springs and rigid constraints limiting the possible motion of the masses. Local dissipation is introduced through a non-unit restitution coefficient characterizing the impacts. The system is excited by uniform time-periodic forcing. The present work is aimed to study the existence and stability of similar breathers in the space of parameters, if additional harmonic potentials are introduced. Existence-stability patterns of the breathers in the parameter space and possible bifurcation scenarios are investigated analytically and numerically. In particular, it is shown that the addition of harmonic on-site potential can substantially extend the stability domain, at least close to the anti-continuum limit. This result can be treated as an increase in the robustness of the breather from the perspective of possible practical applications.

nlin.SI↗

arXiv2016

Heat conduction in a chain of colliding particles with stiff repulsive potential

One-dimensional billiard, i.e. a chain of colliding particles with equal masses, is well-known example of completely integrable system. Billiards with different particles are generically not integrable, but still exhibit divergence of a heat conduction coefficient (HCC) in thermodynamic limit. Traditional billiard models imply instantaneous (zero-time) collisions between the particles. We lift this condition and consider the heat transport in a chain of stiff colliding particles with power-law potential of the nearest-neighbor interaction. The instantaneous collisions correspond to the limit of infinite power in the interaction potential; for finite powers, the interactions take nonzero time. This modification of the model leads to profound physical consequence -- probability of multiple, in particular, triple particle collisions becomes nonzero. Contrary to the integrable billiard of equal particles, the modified model exhibits saturation of the heat conduction coefficient for large system size. Moreover, identification of scattering events with the triple particle collisions leads to simple definition of characteristic mean free path and kinetic description of the heat transport. This approach allows prediction both of temperature and density dependencies for the HCC limit values. The latter dependence is quite counterintuitive - the HCC is inversely proportional to the particle density in the chain. Both predictions are confirmed by direct numeric simulations.

cond-mat.stat-mech↗

arXiv2016

Vibration Mitigation in Partially Liquid-Filled Vessel using Passive Energy Absorbers

This paper treats possible solutions for vibration mitigation in reduced-order model of partially-filled liquid tank under impulsive forcing. Such excitation may lead to hydraulic impacts applied on the tank inner walls. Finite stiffness of the tank walls is taken into account. We explore both linear (Tuned Mass Damper) and nonlinear (Nonlinear Energy Sink) passive vibration absorbers; mitigation performances are examined numerically. The liquid sloshing mass is modeled by equivalent massspring-dashpot system, which can both perform small-amplitude linear oscillations and impact the vessel walls. We use parameters of the equivalent mass-spring-dashpot system for well-explored case of cylindrical tanks. The hydraulic impacts are modeled by high-power potential and dissipation functions. Critical location in the tank structure is determined and expression of the corresponding local mechanical stress is derived. We use finite-elemet approach to assess the natural frequencies for specific system parameters and to figure out possibilities for internal resonances. Numerical evaluation criteria are suggested to determine the energy absorption performance.

physics.flu-dyn↗

arXiv2016

Response Regimes in Equivalent Mechanical Model of Strongly Nonlinear Liquid Sloshing

We consider equivalent mechanical model of liquid sloshing in partially-filled cylindrical vessel; the model treats both the regime of linear sloshing, and strongly nonlinear sloshing regime. The latter is related to hydraulic impacts applied to the vessel walls. These hydraulic impacts are commonly simulated with the help of high-power potential and dissipation functions. For the sake of analytic exploration, we substitute this traditional approach by treatment of an idealized vibro-impact system with velocity-dependent restitution coefficient. The obtained reduced model is similar to recently explored system of linear primary oscillator with attached vibro-impact energy sink. The ratio of modal mass of the first sloshing mode to the total mass of the liquid and the tank serves as a natural small parameter for multiple-scale analysis. In the case of external ground forcing, steady-state responses and chaotic strongly modulated responses are revealed. All analytical predictions of the reduced vibro-impact model are validated against direct numerical simulations of initial equivalent model with high-power smooth potential and dissipation functions, and good agreement is observed.

physics.flu-dyn↗

arXiv2016

Discrete breathers in an array of self-excited oscillators: exact solutions and stability

Dynamics of array of coupled self-excited oscillators is considered. Model of Franklin bell is adopted as a mechanism for the self-excitation. The model allows derivation of exact analytic solutions for discrete breathers (DBs), and extensive exploration of their stability in the space of parameters. The DB solutions exist for all frequencies in the attenuation zone, but lose stability via Neimark-Sacker bifurcation near the boundary of propagation zone. Besides the well-known DBs with exponential localization, the considered system possesses additional and novel type of solutions - discrete breathers with main frequency in the propagation zone of the chain. The amplitude of oscillations in this solution is maximal at the localization site and then exponentially approaches constant value at infinity. We also derive these solutions in closed analytic form. They are stable in a narrow region of system parameters bounded by Neimark-Sacker and pitchfork bifurcations.

nlin.PS↗

arXiv2016

Energy exchange and localization in essentially nonlinear oscillatory systems: canonical formalism

Over recent years, a lot of progress has been achieved in understanding of the relationship between localization and transport of energy in essentially nonlinear oscillatory systems. In this paper we are going to demonstrate that the structure of the resonance manifold can be conveniently described in terms of canonical action-angle variables. Such formalism has important theoretical advantages: all resonance manifolds may be described at the same level of complexity, appearance of additional conservation laws on these manifolds is easily proven both in autonomous and non-autonomous settings. The harmonic balance - based complexification approach, used in many previous studies on the subject, is shown to be a particular case of the canonical formalism. Moreover, application of the canonic averaging allows treatment of much broader variety of dynamical models. As an example, energy exchanges in systems of coupled trigonometrical and vibro-impact oscillators are considered.

nlin.SI↗

arXiv2015

Normal heat conductivity in two-dimensional scalar lattices

The paper revisits recent counterintuitive results on divergence of heat conduction coefficient in two-dimensional lattices. It was reported that in certain lattices with on-site potential, for which one-dimensional chain has convergent conductivity, for the 2D case it turns out to diverge. We demonstrate that this conclusion is an artifact caused by insufficient size of the simulated system. To overcome computational restrictions, a ribbon of relatively small width is simulated instead of the square specimen. It is further demonstrated that the heat conduction coefficient in the "long" direction of the ribbon ceases to depend on the width, as the latter achieves only 10 to 20 interparticle distances. So, one can consider the dynamics of much longer systems, than in the traditional setting, and still can gain a reliable information regarding the 2D lattice. It turns out that for all considered models, for which the conductivity is convergent in the 1D case, it is indeed convergent in the 2D case. In the same time, however, the length of the system, necessary to reveal the convergence in the 2D case, may be much bigger than in its 1D counterpart.

cond-mat.stat-mech↗

arXiv2015

Accelerating oscillatory fronts in a nonlinear sonic vacuum with strong non-local effects

In this Letter we describe a novel class of dynamical excitations -- accelerating oscillatory fronts in a new genre of nonlinear sonic vacua with strongly non-local effects. Indeed, it is surprising that such models naturally arise in dynamics of common and popular lattices. In this study, we address a chain of particles oscillating in the plane and coupled by linear springs, with fixed ends. When one end of this system is harmonically excited in the transverse direction, one observes accelerated propagation of the excitation front, accompanied by an almost monochromatic oscillatory tail. The front propagation obeys the scaling law $l \sim t^{4/3}$. The frequency of the oscillatory tail remains constant, and the wavelength scales as $λ\sim t^{1/3}$. These scaling laws result from the nonlocal effects; we derive them analytically (including the scaling coefficients) from a continuum approximation. Moreover, a certain threshold excitation amplitude is required in order to initiate the front propagation. The initiation threshold is rationalized on the basis of a simplified discrete model. This model is further reduced to a new completely integrable nonlinear system. The Letter introduces a new and yet unexplored class of nonlinear sonic vacua and explores the effects of strong non-locality on the initiation and propagation of oscillating fronts in these media. Given their simplicity, nonlinear sonic vacua of the type considered herein should be common in periodic lattices.

nlin.PS↗

arXiv2014

Heat conduction in a chain of dissociating particles: effect of dimensionality

The paper considers heat conduction in a model chain of composite particles with hard core and elastic external shell. Such model mimics three main features of realistic interatomic potentials - hard repulsive core, quasilinear behavior in a ground state and possibility of dissociation. It has become clear recently, that this latter feature has crucial effect on convergence of the heat conduction coefficient in thermodynamic limit. We demonstrate that in one-dimensional chain of elastic particles with hard core the heat conduction coefficient also converges, as one could expect. Then we explore effect of dimensionality on the heat transport in this model. For this sake, longitudinal and transversal motions of the particles are allowed in a long narrow channel. With varying width of the channel, we observe sharp transition from "one-dimensional" to "two-dimensional" behavior. Namely, the heat conduction coefficient drops by about order of magnitude for relatively small widening of the channel. This transition is not unique for the considered system. Similar phenomenon of transition to quasi-1D behavior with growth of aspect ratio of the channel is observed also in a gas of densely packed hard (billiard) particles, both for two- and three-dimensional cases. It is the case despite the fact that the character of transition in these two systems is not similar, due to different convergence properties of the heat conductivity. In the billiard model, the divergence of the heat conduction coefficient smoothly changes from logarithmic to power-like law with increase of the length.

cond-mat.stat-mech↗

arXiv2013

Normal heat conductivity in chains capable of dissociation

The paper suggests a resolution for recent controversy over convergence of heat conductivity in one-dimensional chains with asymmetric nearest-neighbor potential. We conjecture that the convergence is promoted not by the mere asymmetry of the potential, but due to ability of the chain to dissociate. In other terms, the attractive part of the potential function should approach a finite value as the distance between the neighbors grows. To clarify this point, we study the simplest model of this sort -- a chain of linearly elastic disks with finite diameter. If the distance between the disk centers exceeds their diameter, the disks cease to interact. Formation of gaps between the disks is the only possible mechanism for scattering of the oscillatory waves. Heat conduction in this system turns out to be convergent. Moreover, an asymptotic behavior of the heat conduction coefficient for the case of large densities and relatively low temperatures obeys simple Arrhenius-type law. In the limit of low densities, the heat conduction coefficient converges due to triple disk collisions. Numeric observations in both limits are grounded by analytic arguments. In a chain with Lennard-Jones nearest-neighbor potential the heat conductivity also saturates in a thermodynamic limit and the coefficient also scales according to the Arrhenius law for low temperatures. This finding points on a universal role played by the possibility of dissociation, as convergence of the heat conduction coefficient is considered.

cond-mat.stat-mech↗

arXiv2013

Propagation of stationary exothermic transition front with nonstationary oscillatory tail

We consider a propagation of exotermic transition front in a discrete conservative oscillatory chain. Adequate description of such fronts is a key point in prediction of important transient phenomena, including phase transitions and topochemical reactions. Due to constant energy supply, the transition front can propagate with high velocities, precluding any continuum-based considerations. Stationary propagation of the front is accompanied by formation of a non-stationary oscillatory tail with complicated internal structure. We demonstrate that the structure of the oscillatory tail is related to a relationship between phase and group velocities of the oscillations. We suggest also an approximate analytic procedure, which allows one to determine all basic characteristics of the propagation process: velocity and width of the front, frequency and amplitude of the after-front oscillations, as well as the structure of the oscillatory tail. As an example, we consider a simple case of biharmonic double-well on-site potential. Numeric results nicely conform to the analytic predictions.

nlin.PS↗

arXiv2012

Exact solutions for discrete breathers in forced-damped chain

Exact solutions for symmetric discrete breathers (DBs) are obtained in forced-damped linear chain with on-site vibro-impact constraints. The damping is related to inelastic impacts; the forcing may be chosen from broad class of periodic antisymmetric functions. Global conditions for existence and stability of the DB are established. Some unusual phenomena, like non-monotonous dependence of the stability boundary on the forcing amplitude, are revealed analytically for the full system and illustrated numerically for small periodic lattices.

nlin.PS↗

arXiv2011

Nonstationary heat conduction in one-dimensional models with substrate potential

The paper investigates non-stationary heat conduction in one-dimensional models with substrate potential. In order to establish universal characteristic properties of the process, we explore three different models --- Frenkel-Kontorova (FK), phi4+ ($ϕ^4$+) and phi4- ($ϕ^4-$). Direct numeric simulations reveal in all these models a crossover from oscillatory decay of short-wave perturbations of the temperature field to smooth diffusive decay of the long-wave perturbations. Such behavior is inconsistent with parabolic Fourier equation of the heat conduction and clearly demonstrates the necessity of hyperbolic models. The crossover wavelength decreases with increase of average temperature. The decay patterns of the temperature field almost do not depend on the amplitude of the perturbations, so the use of linear evolution equations for temperature field is justified. In all model investigated, the relaxation of thermal perturbations is exponential -- contrary to linear chain, where it follows a power law. However, the most popular lowest-order hyperbolic generalization of the Fourier law, known as Cattaneo-Vernotte (CV) or telegraph equation (TE) is not valid for description of the observed behavior of the models with on-site potential. In part of the models a characteristic relaxation times exhibit peculiar scaling with respect to the temperature perturbation wavelength. Quite surprisingly, such behavior is similar to that of well-known model with divergent heat conduction (Fermi-Pasta-Ulam chain) and rather different from the model with normal heat conduction (chain of rotators). Thus, the data on the non-stationary heat conduction in the systems with on-site potential do not fit commonly accepted concept of universality classes for heat conduction in one-dimensional models.

cond-mat.stat-mech↗

arXiv2003

Heat Conduction in One-Dimensional chain of Hard Discs with Substrate Potential

Heat conduction of one-dimensional chain of equivalent rigid particles in the field of external on-site potential is considered. Zero diameters of the particles correspond to exactly integrable case with divergent heat conduction coefficient. By means of simple analytical model it is demonstrated that for any nonzero particle size the integrability is violated and the heat conduction coefficient converges. The result of the analytical computation is verified by means of numerical simulation in a plausible diapason of parameters and good agreement is observed

cond-mat↗

arXiv2002

Heat conduction in 1D lattices with on-site potential

The process of heat conduction in one-dimensional lattice with on-site potential is studied by means of numerical simulation. Using discrete Frenkel-Kontorova, $ϕ$--4 and sinh-Gordon we demonstrate that contrary to previously expressed opinions the sole anharmonicity of the on-site potential is insufficient to ensure the normal heat conductivity in these systems. The character of the heat conduction is determined by the spectrum of nonlinear excitations peculiar for every given model and therefore depends on the concrete potential shape and temperature of the lattice. The reason is that the peculiarities of the nonlinear excitations and their interactions prescribe the energy scattering mechanism in each model. For models sin-Gordon and $ϕ$--4 phonons are scattered at thermalized lattice of topological solitons; for sinh-Gordon and $ϕ$--4 - models the phonons are scattered at localized high-frequency breathers (in the case of $ϕ$--4 the scattering mechanism switches with the growth of the temperature).

cond-mat.dis-nn↗