Domain wall solutions for EHM model of crystal:

Abe, Kohji; Shigenari, Takeshi

doi:10.1016/s0167-2789(00)00158-5

Cited by 15 publications

(40 citation statements)

References 17 publications

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“…(c) For a large P, the periodic set of topological solitons separating the domains of four-periodic structure is formed. Equation (1) supports various modulated structures [10). Here, for the sake of illustration, we discuss the topological solitons in the four-periodic structure,…”

Section: Ehm Model Of Crystalmentioning

confidence: 97%

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Topological Soliton Dynamics in Media with Microscopic Rotations

Yoshikawa

Vasiliev

2004

Solid Mechanics and Its Applications

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Abstract. Microscopic rotations can play a very important role in the molecular crystals or in some dielectric crystals where atoms are joined in comparatively rigid clusters and the inter-cluster interactions are comparatively weak. The range of unusual phenomena observed in such materials is fascinating, from incommensurate phase to negative Poisson ratio. Here we focus on the topological soliton dynamics in such materials and describe a number of effects, such as the trigger off and propagation of autowaves, soliton multiplication in the metastable media, soliton collisions and annihilations. All these phenomena are addressed in frame of the elastically hinged mo lecule (EHM) model having microscopic particles with rotational degrees of freedom. For this model we construct various continuum approximations. New important features of the continuum models for media with microscopic rotations are the increase in number of equations of motion due to the increase in number of degrees of freedom and the appearance of the higher gradient terms in the resulting equations. We also construct the trulti-field continuum approximation capable of description not only long but also short waves.

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Section: Ehm Model Of Crystalmentioning

confidence: 97%

“…In these works, the constant amplitude approximation (CAA) has been employed to obtain the solitary wave solutions propagating in different commensurate periodic phases. Later we have demonstrated the importance of the so-called multi-field approximations [8,9] in constructing the soliton solutions [5,10].…”

Section: Introductionmentioning

confidence: 99%

Topological Soliton Dynamics in Media with Microscopic Rotations

Yoshikawa

Vasiliev

2004

Solid Mechanics and Its Applications

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“…[32]). Continuum approximation for the EHM model enabled us to describe the transition from commensurate to a modulated phase, dynamics of domain walls [26,31], a mechanism of transition between modulated phases with different modulation wave vectors [34], and mechanisms of the lock-in transition [26,38].…”

Section: Finite Size Particles Micropolar Continuummentioning

confidence: 99%

“…For example, the short wavelength end-effect for a periodic frame structure has been described [21] and the buckling phenomenon for the periodically strengthened cylindrical thin shell under external pressure has been investigated [22]. Recently a manyfield domain wall solution for a ferroelectric crystal has been given in [26] and compared with a single-field solution in [31]. It was demonstrated that there is a region of parameters where many-field domain wall solution can be significantly improved by retaining highorder gradient terms [31].…”

Section: D Many-field Theorymentioning

confidence: 99%

Many-Field Theory for Crystals Containing Particles with Rotational Degrees of Freedom

et al. 2003

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We give a brief review of some generalized continuum theories applied to the crystals with complicated microscopic structure. Three different ways of generalization of the classical elasticity theory are discussed. One is the high-gradient theory, another is the micropolar type theory and the third one is the many-field theory. The importance of the first two types of theories has already been established, while the theory of the third type still has to be developed. With the use of 1D and 2D examples we show for each of these theories where they can be and should be applied, separately or in a combination.

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“…has emerged in the geometry of surfaces [3] and then it has long been used in physics to describe propagation of magnetic flux on an array of superconducting Josephson junctions [4], to study the interacting mesons and baryons [5], fermions in the Thirring model [6], the properties of crystal dislocations [7], dynamics of domain walls in ferromagnetics [8] and ferroelectrics [9,10], the oscillations of an array of pendula [11], and others [2,7,12,13]. The SGE is capable of describing the dynamics of topological solitons such as a kink and an antikink, as well as their bound state called breather, a feature that distinguishes it from other continuum models [14].…”

Section: Introductionmentioning

confidence: 99%

High energy density in multisoliton collisions

Saadatmand

Kevrekidis

2015

Phys. Rev. D

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Solitons are very effective in transporting energy over great distances and collisions between them can produce high energy density spots of relevance to phase transformations, energy localization and defect formation among others. It is then important to study how energy density accumulation scales in multi-soliton collisions. In this study, we demonstrate that the maximal energy density that can be achieved in collision of N slowly moving kinks and antikinks in the integrable sineGordon field, remarkably, is proportional to N 2 , while the total energy of the system is proportional to N . This maximal energy density can be achieved only if the difference between the number of colliding kinks and antikinks is minimal, i.e., is equal to 0 for even N and 1 for odd N and if the pattern involves an alternating array of kinks and antikinks. Interestingly, for odd (even) N the maximal energy density appears in the form of potential (kinetic) energy, while kinetic (potential) energy is equal to zero. The results of the present study rely on the analysis of the exact multisoliton solutions for N = 1, 2, and 3 and on the numerical simulation results for N = 4, 5, 6, and 7. The effect of weak Hamiltonian and non-Hamiltonian perturbations on the maximal energy density in multi-kink collisions is also discussed as well as that of the collision relative phase. Based on these results one can speculate that the soliton collisions in the sine-Gordon field can, in principle, controllably produce very high energy density. This can have important consequences for many physical phenomena described by the Klein-Gordon equations.

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Domain wall solutions for EHM model of crystal:

Cited by 15 publications

References 17 publications

Topological Soliton Dynamics in Media with Microscopic Rotations

Topological Soliton Dynamics in Media with Microscopic Rotations

Many-Field Theory for Crystals Containing Particles with Rotational Degrees of Freedom

High energy density in multisoliton collisions

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