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
Materials Science, Multidisciplinary
Giovanni Alberto Ummarino, Antonio Gallerati
Summary: This study estimated the conjectured interaction between the Earth's gravitational field and a superconductor immersed in external, static electric and magnetic fields, proposing multiple measurable effects. The analysis included the local effect of the gravitational field inside the superconductor and the generation of a new component of a generalized electric field within the sample.
RESULTS IN PHYSICS
(2021)
Article
Optics
Salim B. Ivars, Muriel Botey, Ramon Herrero, Kestutis Staliunas
Summary: We propose a method to control turbulence by modifying the excitation cascade. The method is based on the asymmetric coupling between spatiotemporal excitation modes using non-Hermitian potentials. We demonstrate that unidirectional coupling towards larger or smaller wave numbers can increase or reduce the energy flow in turbulent states, thereby influencing the character of turbulence. The study uses the complex Ginzburg-Landau equation, a universal model for pattern formation and turbulence in various systems.
Article
Mathematics, Interdisciplinary Applications
Orazio Descalzi, Carlos Cartes
Summary: This article investigates the formation of localized spatiotemporal chaos in the complex cubic Ginzburg-Landau equation with nonlinear gradient terms and reviews the influence of multiplicative noise on stationary pulses stabilized by nonlinear gradients. Surprising results are obtained through numerical simulations and explained analytically, including the induction of velocity change in propagating dissipative solitons.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Tiemo Pedergnana, Nicolas Noiray
Summary: This study presents a detailed analysis of the transformation rules for Langevin equations under general nonlinear mappings, and shows how to identify systems with exact potentials by understanding their differential-geometric properties. The results imply a broad class of exactly solvable stochastic models for nonlinear oscillations.
Article
Mathematics, Interdisciplinary Applications
Ahmed H. Arnous, Anjan Biswas, Yakup Yildirim, Qin Zhou, Wenjun Liu, Ali S. Alshomrani, Hashim M. Alshehri
Summary: This paper implements the enhanced Kudryashov's method to address the solitons of the cubic-quartic complex Ginzburg-Landau equation. Different forms of self-phase modulation structures are studied, and the existence criteria for bright and singular solitons are indicated.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Philip Rosenau
Summary: The gradient-tempered Ginzburg-Landau free energy functional induces compact drops and phase transitions within a finite domain. It regulates the divergence of gradients in the ultra-violet limit. Crossing a critical value of the bulk energy strength parameter may lead to sharp jumps and finger structures in the forming drops.
PHYSICA D-NONLINEAR PHENOMENA
(2021)
Article
Mathematics, Applied
T. Rossides, D. J. B. Lloyd, S. Zelik, M. R. Turner
Summary: In this study, an effective numerical scheme is proposed to calculate the dynamics of weakly interacting multi-pulse solutions of the quintic complex Ginzburg-Landau equation (QCGLE) in one space dimension. The scheme overcomes the difficulties of other numerical schemes by utilizing a global center-manifold reduction and adaptive time-stepping. The results demonstrate various dynamics of two-pulse and three-pulse interactions.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
(2023)
Article
Engineering, Mechanical
Ahmed H. Arnous, Taher A. Nofal, Anjan Biswas, Yakup Yildirim, Asim Asiri
Summary: This paper presents a method for extracting cubic-quartic optical soliton solutions for the complex Ginzburg-Landau equation with five distinct forms of nonlinear refractive index. By utilizing the proposed algorithm, a diverse range of optical solitons, including hybrid types, that satisfy the specified parameter restrictions can be obtained.
NONLINEAR DYNAMICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Qingguo Hong, Limin Ma, Jinchao Xu, Longqing Chen
Summary: In this paper, a new finite element approach is proposed to simulate the time-dependent Ginzburg-Landau equations under the temporal gauge. An efficient preconditioner is designed for the Newton iteration of the resulting discrete system. The approach solves the magnetic potential in H(curl) space using the lowest order of the second kind Nedelec element. It offers a simple way to handle the boundary condition and demonstrates stable and reliable performance for superconductors with reentrant corners. Numerical simulations confirm the efficiency of the proposed preconditioner in significantly speeding up large-scale computations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Astronomy & Astrophysics
Chuan-Yin Xia, Hua-Bi Zeng, Yu Tian, Chiang-Mei Chen, Jan Zaanen
Summary: The AdS/CFT correspondence provides a unique method to study vortex matter phases in superconductors. By solving the dynamical evolution of a 2+1-dimensional superconductor at finite temperature and subjected to a magnetic field quench in terms of a gravitational hairy black hole in an asymptotic AdS 4 space, we can determine the nature of equilibrium states after the quench. Our results show the existence of Meissner phase and Abrikosov lattices under different external magnetic field conditions, consistent with the expectations of Ginzburg-Landau theory.
Article
Materials Science, Multidisciplinary
Anjan Biswas, Abdul H. Kara, Yunzhou Sun, Qin Zhou, Yakup Yildirim, Hashim M. Alshehri, Milivoj R. Belic
Summary: This paper discusses the conserved densities and quantities for the perturbed complex Ginzburg-Landau model using Lie symmetry analysis, and finds that for certain nonlinear forms, the Hamiltonian ceases to exist due to divergent integrals.
RESULTS IN PHYSICS
(2021)
Article
Mathematics
Ahmed H. Arnous, Luminita Moraru
Summary: In this paper, optical soliton solutions for the complex Ginzburg-Landau equation with Kudryashov's law of refractive index are derived using an improved modified extended tanh-function technique. Bright and dark solitons, as well as singular soliton solutions, are obtained. Additionally, as the modulus of ellipticity approaches unity or zero, solutions are expressed in terms of Jacobi's elliptic functions, which yield solitons and periodic wave solutions.
Article
Multidisciplinary Sciences
Bjoern Niedzielski, Dominik Schulz, Jamal Berakdar
Summary: This study demonstrates the potential of spintronic THz emitters based on metastructures to drive and modulate the superconducting order parameter, leading to the topological texture of THz fields. Numerical simulations illustrate the formation of Abrikosov vortices and the local modification of superconducting properties in nanoscale samples.
SCIENTIFIC REPORTS
(2022)
