Article
Mathematics
Khalid K. Ali, M. Maneea, Mohamed S. Mohamed
Summary: This study applies the q-homotopy analysis transform method (q-HATM) to solve the Ginzburg-Landau equation and the Ginzburg-Landau coupled system, obtaining analytical solutions in terms of the q-series. The results demonstrate that q-HATM is a reliable and promising approach for solving nonlinear differential equations and provides a valuable tool for researchers in the field of superconductivity.
JOURNAL OF MATHEMATICS
(2023)
Article
Physics, Mathematical
Dmitry Doryn, Calin Iuliu Lazaroiu
Summary: We prove the non-degeneracy of the cohomological bulk and boundary traces for general open-closed Landau-Ginzburg models associated with a pair (X, W), where X is a non-compact complex manifold with a trivial canonical line bundle and W is a complex-valued holomorphic function defined on X. These results can be seen as deformed versions of Serre duality.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Physics, Applied
Arkady P. Levanyuk, Sergey A. Minyukov, I. Burc Misirlioglu, M. Baris Okatan
Summary: In previous Landau-type models, the existence of interphase boundaries in clamped systems undergoing first-order phase transitions was neglected. Through a Ginzburg-Landau one-dimensional model, it was discovered that the transition to the two-phase state is abrupt rather than continuous from both symmetrical and nonsymmetrical phases, with the formation of the two-phase state beginning in a region proportional to square root L. This study also showed that the latent heat of the transition and the temperature width of the two-phase region are proportional to square root L in infinite systems.
JOURNAL OF APPLIED PHYSICS
(2021)
Correction
Mathematics, Applied
Dirk Hennig, Nikos I. Karachalios
Summary: In this note, we present a new result that completes the proof of Hennig and Karachalios (2022, Lemma 2.3) by addressing the critical value of the damping parameter for the non-local Discrete Ginzburg-Landau equation. We also provide a corrigendum for the proof of case 1 of Hennig and Karachalios (2022, Lemma 2.3) based on the specified conditions on the parameters.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Physics, Multidisciplinary
Antonio Gallerati
Summary: The study focuses on the mutual interaction between a superconducting sample and Earth's weak, static gravitational field, using the gravito-Maxwell formalism and time-dependent Ginzburg-Landau model. The research aims to enhance the desired gravity/superfluid interplay by analyzing thermal fluctuations and optimizing superconductor parameters and sample geometry.
Article
Physics, Applied
C. A. Aguirre, M. R. Joya, J. Barba-Ortega
Summary: In this study, we investigated the magnetization and Cooper pairs density in a conventional superconducting thin film under an external magnetic field H. By considering a topological-type coupling between the bands, we solved the p-wave-two-band Ginzburg-Landau equations. We varied the sample size L, the coupling weight gamma, and the effective Ginzburg-Landau parameter kappa eff as functions of the magnetic field. We observed interesting vortex configurations and the generation of vortex clusters due to the coupling between condensates. The first and second critical fields showed high and weak dependence on the coupling weight, respectively. We also identified interesting magnetization curves and their relationships with sample size, coherence length, penetration length, and the coupling weight between the bands (gamma).
MODERN PHYSICS LETTERS B
(2023)
Article
Optics
Khaled A. Gepreel, E. M. E. Zayed, M. E. M. Alngar
Summary: The researchers have successfully recovered optical soliton solutions (OSS) to the nonlinear complex Ginzburg-Landau (CGL) equation with Hamiltonian perturbation terms in birefringent fibers having Kerr law nonlinearity using the extended Kudryashov's (AEK) method and the Kudryashov's (AK) method. Various soliton solutions and their combinations have been retrieved and enumerated efficiently and powerfully using these two methods.
Article
Mathematics
Jishan Fan, Yuxi Hu, Gen Nakamura
Summary: This work proves the local well-posedness of local strong solutions to an isentropic compressible Ginzburg-Landau-Navier-Stokes system with vacuum in a bounded domain omega subset of R3.
MATHEMATISCHE NACHRICHTEN
(2021)
Article
Physics, Multidisciplinary
Giovanni Alberto Ummarino, Antonio Gallerati
Summary: In this study, the potential interaction between a superconductor and the Earth's gravitational fields was calculated using the gravito-Maxwell formalism and the time-dependent Ginzburg-Landau theory. The researchers aimed to determine the most favorable conditions for enhancing the effect by optimizing the superconductor parameters of the chosen sample. Additionally, a qualitative comparison was made between the behavior of high-Tc and classical low-Tc superconductors in the context of gravity/superfluid interplay.
Article
Mathematics
Radu Ignat, Matthias Kurzke
Summary: The paper discusses the importance of Jacobian and global Jacobian in the theory of 2D Ginzburg-Landau vortices, as well as their stability properties. The analysis and asymptotic expansion of boundary vortices in a specific scenario is also demonstrated.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Mathematics, Applied
Hengfei Ding, Changpin Li
Summary: In this paper, a new generating function is constructed and used to establish a fourth-order numerical differential formula for approximating the Riesz derivative with order gamma is an element of (1, 2]. The formula is then applied to study the two-dimensional nonlinear spatial fractional complex Ginzburg-Landau equation and a convergence order of O(tau 2 + h4x + h4) is obtained. The unique solvability, unconditional stability, and convergence of the numerical algorithm are proved using discrete energy method and newly derived discrete fractional Sobolev embedding inequalities. Numerical results confirm the theoretical correctness and effectiveness of the proposed scheme. (c) 2023 Elsevier B.V. All rights reserved.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Huadong Gao, Wen Xie
Summary: This paper focuses on the numerical analysis of a finite element method for the time-dependent Ginzburg-Landau equations under the Coulomb gauge. The main challenge lies in the divergence-free property of the magnetic potential A and its Stokes-like structure. The proposed method utilizes linear Lagrange elements and Nedelec edge elements to approximate the order parameter psi, magnetic potential A, and electric potential phi, respectively. The paper aims to establish the second order spatial convergence for the most important variable.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Physics, Multidisciplinary
Yu Li, Vivek Mishra, Yi Zhou, Fu-Chun Zhang
Summary: This study examines the unconventional superconductivity in strongly correlated electrons and its relation to non-Fermi liquid states. By investigating the Hatsugai-Kohomoto model, the researchers identify a non-Fermi liquid ground state and analyze its effects on superconductivity.
NEW JOURNAL OF PHYSICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Mohammed Alabedalhadi, Mohammed Al-Smadi, Shrideh Al-Omari, Yeliz Karaca, Shaher Momani
Summary: In this paper, a fractional complex Ginzburg-Landau equation is discussed using the parabolic law and the law of weak non-local nonlinearity. The dynamic behaviors of the model under certain parameter regions are derived using the planar dynamical system theory. Soliton, bright and kinked solitons are obtained using the ansatz method and their existence is verified under certain conditions. The graphical representations of the established solutions at different fractional derivatives are compared and the impact of the fractional derivative on the investigated soliton solutions is illustrated.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Min Zhang, Guo-Feng Zhang
Summary: In this work, an ADI scheme and a matrix splitting iteration method for solving 2D spatial fractional Ginzburg-Landau equations were proposed. The method demonstrated better performance in terms of iterative steps and computing time compared to existing iteration methods.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Ross G. Lund, Cyrill B. Muratov, Valeriy V. Slastikov
JOURNAL OF NONLINEAR SCIENCE
(2020)
Article
Chemistry, Physical
Mona M. Alyobi, Chris J. Barnett, Cyrill B. Muratov, Vitaly Moroz, Richard J. Cobley
Article
Mathematics, Applied
Anne Bernand-Mantel, Cyrill B. Muratov, Theresa M. Simon
Summary: This study characterizes skyrmions in ultrathin ferromagnetic films as local minimizers of a reduced micromagnetic energy suitable for quasi two-dimensional materials. The research demonstrates the existence of minimizers within a specific range of model parameters, and investigates the asymptotic profiles of skyrmions in the conformal limit. Additionally, a quantitative rigidity result for harmonic maps is obtained as a byproduct of the analysis.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2021)
Article
Biophysics
Yinbo Chen, Cyrill B. Muratov, Victor Matveev
BIOPHYSICAL JOURNAL
(2020)
Article
Mathematics, Applied
Cyrill B. Muratov, Matteo Novaga, Berardo Ruffini
Summary: We study a geometric variational problem that models the behavior of two-dimensional charged drops in the presence of an external potential. The semicontinuous envelope of the energy is characterized by a parameter measuring the relative strength of the Coulomb interaction. We demonstrate the existence and regularity estimates for volume-constrained minimizers when the potential is confining and the Coulomb repulsion strength is below a critical value. We also derive the Euler-Lagrange equation satisfied by regular critical points, expressing the first variation of the Coulombic energy in terms of the normal 1/2-derivative of the capacitary potential.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2022)
Correction
Physics, Mathematical
Cyrill B. Muratov, Theresa M. Simon
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Multidisciplinary Sciences
Anne Bernand-Mantel, Cyrill B. Muratov, Valeriy V. Slastikov
Summary: In this study, the continuum micromagnetic framework is used to derive formulas for compact skyrmion lifetime in ultrathin ferromagnetic films. The formulas take into account the effect of thermal noise and the relatively weak interfacial Dzyaloshinskii-Moriya interaction. When there is no saddle point connecting the skyrmion solution to the ferromagnetic state, the skyrmion collapse event is interpreted as capture by a microscale absorber.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2022)
Article
Mathematics, Applied
Jean-Francois Babadjian, Giovanni Di Fratta, Irene Fonseca, Gilles A. Francfort, Marta Lewicka, Cyrill B. Muratov
Summary: This article presents mathematical contributions to the behavior of thin films. It focuses on viewing thin film behavior as the variational limit of a three-dimensional domain, and explores the changes in behavior when the thickness of the domain approaches zero. The article reviews the different regimes that can arise in the classical elastic case, and discusses various extensions of those initial results, including brittleness and delamination, micromagnetics, and the presence of pre-strain in the model.
QUARTERLY OF APPLIED MATHEMATICS
(2022)
Article
Acoustics
Cyrill B. Muratov, Joseph Rogers, Michael Khasin
Summary: The acoustic response of a thin-walled spherical flight tank filled with water is studied as a testbed for the application of Weyl's law to measure propellant mass in zero-gravity conditions. The study shows that the liquid modes in the tank correspond to a slightly larger spherical tank with infinitely compliant wall, where Weyl's law can be directly applied.
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
(2022)
Article
Physics, Mathematical
Antonin Monteil, Cyrill B. Muratov, Theresa M. Simon, Valeriy V. Slastikov
Summary: We present a variational treatment of confined magnetic skyrmions and characterize their properties in the limit of vanishing DMI strength. The results show that the skyrmions are strongly repelled from the domain boundaries, providing them with stability desirable for applications.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Mathematics, Applied
Pearson W. Miller, Daniel Fortunato, Matteo Novaga, Stanislav Y. Shvartsman, Cyrill B. Muratov
Summary: This paper investigates the cell polarization in reaction-diffusion models with nonlocal constraints under the limit of slow surface diffusion. By using formal asymptotics and calculus of variations, the characteristic behavior of this system on three dynamical timescales is studied. The results show that an interface separating high- and low-concentration domains can be generated under suitable conditions on the short timescale, and on the intermediate timescale, the domains exhibit uniform growth or shrinking to fixed sizes determined by global parameters. On the long timescale, the dynamics reduce to area-preserving geodesic curvature flow, potentially leading to multi-interface steady state solutions.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
(2023)
Article
Computer Science, Interdisciplinary Applications
Pearson W. Miller, Daniel Fortunato, Cyrill Muratov, Leslie Greengard, Stanislav Shvartsman
Summary: This study investigates how altering the symmetry of a model impacts the dynamics of cell polarization. Through numerical and analytical techniques, non-trivial solutions for symmetry breaking are discovered.
NATURE COMPUTATIONAL SCIENCE
(2022)
Article
Mathematics, Applied
Giovanni Di Fratta, Cyrill B. Muratov, Filipp N. Rybakov, Valeriy V. Slastikov
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2020)
Article
Materials Science, Multidisciplinary
Anne Bernand-Mantel, Cyrill B. Muratov, Thilo M. Simon
Article
Materials Science, Multidisciplinary
Valeriy V. Slastikov, Cyrill B. Muratov, Jonathan M. Robbins, Oleg A. Tretiakov
