The uniformly driven kink in the damped ?4-chain

Magyari, E.

doi:10.1007/bf01420565

Cited by 10 publications

(3 citation statements)

References 27 publications

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“…The kink solution of the φ 4 equation with an external bias has already been found in the infinite-length limit [21,28,29,30,31]. The work [30] suggest that for a relatively weak applied field the kink shape is not affected but instead, is accelerated if its motion is shifted from its zero-field position by a finite spatial amount, equivalent to the effect of a "Goldstone translation". However, if the magnitude of the field is large enough the field can result into a deformation of the kink shape as shown in Fig.…”

Section: Domain-wall Solutions In the Presence Of An External Fieldmentioning

confidence: 93%

Domain Structure in Ferroelectric Thin Films

Yunga

Dikandé

2022

AJR2P

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At low temperatures, uniaxial perovskites exhibit a spontaneous polarization with a permanent dipole moment. The broken symmetry state involves an order parameter and dielectric properties of the materials which are strongly dominated by a one-dimensional physics. For the last sixty years there has been growing interest in these crystals for potential applications in communication technology. Very recently, renewed interest to ferroelectric memory devices has been remarkable with particular emphasis on miniaturized devices. This new perspective comes along with great challenges, one of which is the critical size for stable domains in thin ferroelectric crystals. Since the polarization switching involves a pre-existing spontaneous polarization, it is of fundamental importance to address the question of conditions under which polarized domains can develop in a ferroelectric thin film. From previous articles, it has been observed that most studies focus on numerical simulations which is a good approach but for the fact that numerical simulations involve approximation of physical quantities, which is limitation to comparing experimental with theoretical studies. This motivated the authors to look purely at an analytical approach taking advantage of the new mathematical approach in the study of nonlinear systems. In this work, the authors have considered the question from an analytical point of view, focusing on an interesting model introduced by Lu and Cao. We propose an analytical counterpart of the numerical simulations done in this previous study.

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Section: Domain-wall Solutions In the Presence Of An External Fieldmentioning

confidence: 93%

Domain Structure in Ferroelectric Thin Films

Yunga

Dikandé

2022

AJR2P

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“…(1) describes structural phase transitions in dissipative ferroelectrics in the presence of an electric field E (so that A & -E, y&0). The corresponding structure factor for small frequencies is Lorentzian and various authors [8,11,12], used a qualitative analysis of Eq.…”

Section: Introductionmentioning

confidence: 99%

“…(7) again. ] On the other hand, for subsonic velocities I( is negative and the transformation z =( -K) ' (xut) (8) leads to where aI +re Bf (9) I = yu(Dpu )- (10) y(x =+~) = q&2 and (p(x = +~) = g, , or between (12) Equation (9) describes the motion of a single particle of a unit mass in a potential P(p). We shallanalyze in detail solutions for P(y) defined by Eq.…”

Section: Introductionmentioning

confidence: 99%

Propagation and stability of relaxation modes and transition regions in the Landau-Ginzburg model with dissipation

1992

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Exact traveling-wave solutions of the nonlinear Klein-Gordon equation with dissipation are found. The solutions are discussed in the context of propagating nonlinear mechanical waves as well as domain walls (solutions interpolating between two local minima in the potential) and relaxation modes (solutions interpolating between a local minimum and a local maximum in the potential) in systems undergoing second-order phase transitions. Using the Lyapunov method the stability of traveling waves is analyzed.Explicit solutions for domain walls are found and shown to be asymptotically stable. While domain walls propagate with a velocity uniquely determined by the parameters of the model, relaxation modes can move with arbitrary velocities. Among those solutions only one solution propagating with a characteristic velocity u, is asymptotically stable. Other solutions are demonstrated to be Lyapunov unstable.It is found that relative values of the mass density and the damping coeScient are crucial for the dynamic critical behavior, which changes from U, -(T, -T)' for small densities to v. that is temperature independent for large densities.

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Dynamics of Ionic and Bonding Defects in Quasi‐One‐Dimensional Hydrogen‐Bonded Chains

Kristoforov

Zolotaryuk

1988

Physica Status Solidi (b)

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The motion of extended ion (orientational) defects in quasi-one-dimensional hydrogen-bondcd chains is studied for the double-well potential model of a proton in the prcsencc of applied external fields. ~CCJJenOBaHO HBAXeHIle llPOTR~eH11b1X IlOHHbIX (OPLleHTa4MOHHblX) ne@eKTOB KBa3LlOZ-HOMePHblX BO~OPORHOCBRBaHHbIX MOJleKyJIRplIbIX UenOYeK B MOnedlFIX C RBYXbRMHblM noTeiruaanoM a m npoToHa n p~ HanoxeHm BHetuHax nonel. l ) UI. Metrologicheskaya 14 b, Sd-252 130 Kiev, USSR. Dynamics of Ionic and Bonding Defects in Quasi-ID Hydrogen-Bonded Chains eters are introduced,

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The uniformly driven kink in the damped ?4-chain

Cited by 10 publications

References 27 publications

Domain Structure in Ferroelectric Thin Films

Domain Structure in Ferroelectric Thin Films

Propagation and stability of relaxation modes and transition regions in the Landau-Ginzburg model with dissipation

Dynamics of Ionic and Bonding Defects in Quasi‐One‐Dimensional Hydrogen‐Bonded Chains

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