Regular Domain Perturbation

2020 ◽  
pp. 35-52
Author(s):  
Antonio André Novotny ◽  
Jan Sokołowski
Keyword(s):  
Regular Domain ◽  
Domain Perturbation

The Formation of Regular Domain Structures in Ferroelectrics under Switching Polarization in High-nonequilibrium Conditions

2017 ◽  
Vol 9 (2) ◽  
pp. 02032-1-02032-7
Author(s):  
L. I. Stefanovich ◽  
◽  
O. Yu. Mazur ◽  
Keyword(s):  
Regular Domain ◽  
Domain Structures ◽  
Nonequilibrium Conditions

Formation of Regular Domain Structures in Quenched Ferroelectrics Under the Influence of an External High-frequency Electric Field

2019 ◽  
Vol 9 (3) ◽  
pp. 344-352 ◽  
Author(s):  
L.I. Stefanovich ◽  
O.Y. Mazur ◽  
V.V. Sobolev
Keyword(s):  
Lithium Niobate ◽  
Electric Field ◽  
Domain Structure ◽  
High Frequency ◽  
Evolution Equations ◽  
Regular Domain ◽  
Field Frequency ◽  
Domain Structures ◽  
Alternating Electric Field ◽  
Lithium Niobate Crystals

Introduction: Within the framework of the phenomenological theory of phase transitions of the second kind of Ginzburg-Landau, the kinetics of ordering of a rapidly quenched highly nonequilibrium domain structure is considered using the lithium tantalate and lithium niobate crystals as an example. Experimental: Using the statistical approach, evolution equations describing the formation of the domain structure under the influence of a high-frequency alternating electric field in the form of a standing wave were obtained. Numerical analysis has shown the possibility of forming thermodynamically stable mono- and polydomain structures. It turned out that the process of relaxation of the system to the state of thermodynamic equilibrium can proceed directly or with the formation of intermediate quasi-stationary polydomain asymmetric phases. Results: It is shown that the formation of Regular Domain Structures (RDS) is of a threshold character and occurs under the influence of an alternating electric field with an amplitude less than the critical value, whose value depends on the field frequency. The conditions for the formation of RDSs with a micrometer spatial scale were determined. Conclusion: As shown by numerical studies, the RDSs obtained retain their stability, i.e. do not disappear even after turning off the external electric field. Qualitative analysis using lithium niobate crystals as an example has shown the possibility of RDSs formation in high-frequency fields with small amplitude under resonance conditions

scholarly journals Rigidity and trace properties of divergence-measure vector fields

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Gian Paolo Leonardi ◽  
Giorgio Saracco
Keyword(s):  
Vector Fields ◽  
Extremal Solution ◽  
Divergence Measure ◽  
Higher Dimension ◽  
Regular Domain ◽  
Curvature Equation ◽  
Mean Curvature Equation ◽  
Divergence Free Vector ◽  
Prescribed Mean Curvature Equation ◽  
Rigidity Property

AbstractWe consider a φ-rigidity property for divergence-free vector fields in the Euclidean n-space, where {\varphi(t)} is a non-negative convex function vanishing only at {t=0}. We show that this property is always satisfied in dimension {n=2}, while in higher dimension it requires some further restriction on φ. In particular, we exhibit counterexamples to quadratic rigidity (i.e. when {\varphi(t)=ct^{2}}) in dimension {n\geq 4}. The validity of the quadratic rigidity, which we prove in dimension {n=2}, implies the existence of the trace of a divergence-measure vector field ξ on an {\mathcal{H}^{1}}-rectifiable set S, as soon as its weak normal trace {[\xi\cdot\nu_{S}]} is maximal on S. As an application, we deduce that the graph of an extremal solution to the prescribed mean curvature equation in a weakly-regular domain becomes vertical near the boundary in a pointwise sense.

Ferroelectric and magnetic media with nanoscale regular domain structures

2011 ◽  
Vol 75 (5) ◽  
pp. 642-644 ◽  
Author(s):  
Kh. G. Bogdanova ◽  
A. R. Bulatov ◽  
A. V. Golenishchev-Kutuzov ◽  
V. A. Golenishchev-Kutuzov ◽  
R. I. Kalimuilin ◽  
...  
Keyword(s):  
Magnetic Media ◽  
Regular Domain ◽  
Domain Structures

scholarly journals Existence results for a nonlinear nonautonomous transmission problem via domain perturbation

2021 ◽  
pp. 1-26
Author(s):  
Matteo Dalla Riva ◽  
Riccardo Molinarolo ◽  
Paolo Musolino
Keyword(s):  
Boundary Value Problem ◽  
Laplace Equation ◽  
Boundary Value ◽  
Perturbation Parameter ◽  
Existence Results ◽  
Transmission Problem ◽  
Perforated Domain ◽  
Analytic Dependence ◽  
Domain Perturbation ◽  
Fixed Domain

In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism $\phi$ . First we analyse the case in which the inclusion is a fixed domain. Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter $\phi$ .

Review of the Secondary Flows of Complex Fluids

2003 ◽  
Author(s):  
Dennis A. Siginer
Keyword(s):  
Secondary Flow ◽  
Cross Sections ◽  
Secondary Flows ◽  
Laboratory Setting ◽  
Transfer Enhancement ◽  
Domain Perturbation ◽  
Novel Approach ◽  
Viscoelastic Liquids ◽  
First Time ◽  
Secondary Flow Field

A survey of secondary flows of viscoelastic liquids in straight tubes is given including recent work pointing at striking analogies with transversal deformations associated with the simple shearing of solid materials. The importance and implications of secondary flows of viscoelastic fluids in heat transfer enhancement are explored together with the difficulties in detecting weak secondary flows (dilute, weakly viscoelastic solutions) in a laboratory setting. Recent new work by the author and colleagues which explores for the first time the structure of the secondary flow field in the pulsating flow of a constitutively nonlinear simple fluid in straight tubes of arbitrary cross-sections is summarized. Arbitrary conduit contours are obtained through a novel approach to the concept of domain perturbation. Time averaged, mean secondary flow streamline contours are presented for the first time for triangular, square and hexagonal pipes.

Czochralski-grown lithium niobate with regular domain structure

1997 ◽  
Vol 190 (1) ◽  
pp. 107-112 ◽  
Author(s):  
I. I. Naumova ◽  
N. F. Evlanova ◽  
O. A. Gliko ◽  
S. V. Lavrichev
Keyword(s):  
Lithium Niobate ◽  
Domain Structure ◽  
Regular Domain ◽  
Regular Domain Structure

Recording of domains and regular domain patterns in strontium–barium niobate crystals in the field of atomic force microscope

2009 ◽  
Vol 95 (3) ◽  
pp. 505-512 ◽  
Author(s):  
R. V. Gainutdinov ◽  
T. R. Volk ◽  
O. A. Lysova ◽  
I. I. Razgonov ◽  
A. L. Tolstikhina ◽  
...  
Keyword(s):  
Atomic Force Microscope ◽  
Regular Domain ◽  
Strontium Barium Niobate ◽  
Strontium Barium ◽  
Atomic Force
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