A Uniform Accurate Boundary Treatment for the One-Dimensional Non-Local Models

2022 ◽  
Author(s):  
Gang Pang ◽  
Songsong Ji ◽  
Jiwei Zhang ◽  
Dong Qian
Keyword(s):  
Local Models ◽  
One Dimensional ◽  
Boundary Treatment ◽  
Non Local ◽  
The One

scholarly journals Uniqueness of one-dimensional Néel wall profiles

2016 ◽  
Vol 472 (2187) ◽  
pp. 20150762 ◽  
Author(s):  
Cyrill B. Muratov ◽  
Xiaodong Yan
Keyword(s):  
Domain Wall ◽  
Energy Functional ◽  
Wall Structure ◽  
One Dimensional ◽  
Uniform Estimates ◽  
Limiting Behaviour ◽  
Non Local ◽  
The One ◽  
Wall Profile ◽  
Domain Wall Structure

We study the domain wall structure in thin uniaxial ferromagnetic films in the presence of an in-plane applied external field in the direction normal to the easy axis. Using the reduced one-dimensional thin-film micromagnetic model, we analyse the critical points of the obtained non-local variational problem. We prove that the minimizer of the one-dimensional energy functional in the form of the Néel wall is the unique (up to translations) critical point of the energy among all monotone profiles with the same limiting behaviour at infinity. Thus, we establish uniqueness of the one-dimensional monotone Néel wall profile in the considered setting. We also obtain some uniform estimates for general one-dimensional domain wall profiles.

scholarly journals Non-local Problems with Integral Displacement for Highorder Parabolic Equations

2021 ◽  
Vol 36 ◽  
pp. 14-28
Author(s):  
A.I. Kozhanov ◽  
◽  
A.V. Dyuzheva ◽  
◽  
Keyword(s):  
Parabolic Equations ◽  
High Order ◽  
Multidimensional Case ◽  
Integral Conditions ◽  
Spatial Variables ◽  
One Dimensional ◽  
Linear Parabolic Equations ◽  
Local Problems ◽  
Non Local ◽  
The One

The aim of this paper is to study the solvability of solutions of non-local problems with integral conditions in spatial variables for high-order linear parabolic equations in the classes of regular solutions (which have all the squared derivatives generalized by S. L. Sobolev that are included in the corresponding equation) . Previously, similar problems were studied for high-order parabolic equations, either in the one-dimensional case, or when certain conditions of smallness on the coefficients are met equations. In this paper, we present new results on the solvability of non-local problems with integral spatial variables for high-order parabolic equations a) in the multidimensional case with respect to spatial variables; b) in the absence of smallness conditions. The research method is based on the transition from a problem with non-local integral conditions to a problem with classical homogeneous conditions of the first or second kind on the side boundary for a loaded integro-differential equation. At the end of the paper, some generalizations of the obtained results will be described.

TWO-COMPONENT SUPERCONDUCTIVITY OF HEAVY FERMIONIC MATERIAL UPt3

2002 ◽  
Vol 16 (20n22) ◽  
pp. 3024-3024
Author(s):  
V. P. MINEEV ◽  
T. CHAMPEL
Keyword(s):  
Superconducting State ◽  
Hexagonal Crystal ◽  
Unconventional Superconductor ◽  
Crystal Axis ◽  
One Dimensional ◽  
Flux Lattice ◽  
Two Component ◽  
Non Local ◽  
Anisotropic Interactions ◽  
The One

The theory of the Abrikosov lattice structures in the unconventional superconductor UPt3 under magnetic field parallel to the hexagonal crystal axis is presented. Only the two-component E2 superconducting state among the other states of different symmetry is proved to be compatible with the recent observations1 of the flux lattice in the A phase misaligned with crystallographic directions. Unlike to the one-dimensional superconductivity where anisotropic interactions caused by non-local electrodynamic corrections are essential for the vortex ordering the formation of slightly distorted triangular flux lattice in UPt3 due to the two-dimensional nature of its superconducting state can be described already in local electrodynamics.2

One-dimensional Large-U Hubbard Model in Strong Coupling: Charge and Spin Separation

1991 ◽  
Vol 05 (10) ◽  
pp. 1801-1807
Author(s):  
Z. Y. Weng ◽  
D. N. Sheng ◽  
C. S. Ting
Keyword(s):  
Fixed Point ◽  
Hubbard Model ◽  
Weak Coupling ◽  
Composite Particle ◽  
Electron Hole ◽  
Integral Formalism ◽  
One Dimensional ◽  
Coupling Case ◽  
Non Local ◽  
The One

A path-integral formalism of the Hubbard model is used to study the one-dimensional large-U case. It is shown that the bare electron (hole) becomes a composite particle of two decoupled excitations, holon and spinon, together with the non-local string fields. Various correlation functions are analytically derived. The results strongly suggest a U*=∞ fixed point of Hubbard model which is distinct from the weak coupling case.

Stability of a non-local kinetic model for cell migration with density-dependent speed

2020 ◽  
Author(s):  
Nadia Loy ◽  
Luigi Preziosi
Keyword(s):  
Kinetic Model ◽  
One Dimensional ◽  
Dirac Delta ◽  
Finite Distance ◽  
Non Local ◽  
Sensing Radius ◽  
The Mean ◽  
The Stability ◽  
The One ◽  
Direction Of Polarization

Abstract The aim of this article is to study the stability of a non-local kinetic model proposed by Loy & Preziosi (2020a) in which the cell speed is affected by the cell population density non-locally measured and weighted according to a sensing kernel in the direction of polarization and motion. We perform the analysis in a $d$-dimensional setting. We study the dispersion relation in the one-dimensional case and we show that the stability depends on two dimensionless parameters: the first one represents the stiffness of the system related to the cell turning rate, to the mean speed at equilibrium and to the sensing radius, while the second one relates to the derivative of the mean speed with respect to the density evaluated at the equilibrium. It is proved that for Dirac delta sensing kernels centered at a finite distance, corresponding to sensing limited to a given distance from the cell center, the homogeneous configuration is linearly unstable to short waves. On the other hand, for a uniform sensing kernel, corresponding to uniformly weighting the information collected up to a given distance, the most unstable wavelength is identified and consistently matches the numerical solution of the kinetic equation.

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