Landau Ginzburg Research Articles

Solitary waves pattern appear in tropical tropospheres and mid-latitudes of nonlinear Landau–Ginzburg–Higgs equation with chaotic analysis

The objective of this research is to investigate the nonlinear Landau–Ginzburg–Higgs equation, which characterizes nonlinear solitary waves exhibiting distant and feeble scattering interactions among tropical tropospheres and mid-latitudes. Additionally, the study will examine the interchange of mid-latitude Rossby waves and equatorial waves within this context. In this research article, we focus on obtaining exact traveling wave solutions for the Landau–Ginzburg–Higgs equation using a new extended direct algebraic technique. The obtained soliton solutions include various types such as combined and multiple bright-dark, periodic, bright, and multiple bright-periodic. We present these soliton solutions graphically by varying the involved parameters using the advanced software program Wolfram Mathematica. The graphical representations allow us to visualize the behavior of the wave velocity and wave number as the parameters change. Additionally, we conduct a chaotic analysis to examine the wave profiles of the newly designed dynamical framework. The results of this analysis demonstrate the reliability and efficiency of the proposed method, which can be applied to find closed-form traveling wave solitary solutions for a wide range of nonlinear evolution equations.

Analytic inclined flow rule for determining granular rheology under strong non-local effects

This study theoretically establishes a flow rule for a granular flow down a rough inclined plane, capable of determining granular rheology in the presence of strong non-local effects resulting from grain cooperativity. To describe the non-local rheology, a Landau–Ginzburg model is formulated in terms of the fluidisation parameter represented by the granular inertial number. The exact solutions of the inertial-number field are solved and provide physical insights into the evolution of the internal rheology and the flow arrest process controlled by the flow height. Through asymptotic analysis in the regime dominated by strong non-locality, the exact solutions are further reduced to yield an analytical flow rule for the mean flow velocity. A comparison between the prediction of the flow rule and experimental data from the literature for sand grains determines the underlying rheology law and the relevant rheological parameters. Thus, the proposed flow rule serves as an effective tool for inferring granular rheology from strongly non-local inclined flow data, surpassing the limitations of the classical flow rule deduced from the local rheology framework.

Apéry extensions

AbstractThe Apéry numbers of Fano varieties are asymptotic invariants of their quantum differential equations. In this paper, we initiate a program to exhibit these invariants as (mirror to) limiting extension classes of higher cycles on the associated Landau–Ginzburg (LG) models — and thus, in particular, as periods. We also construct an Apéry motive, whose mixed Hodge structure is shown, as an application of the decomposition theorem, to contain the limiting extension classes in question. Using a new technical result on the inhomogeneous Picard–Fuchs equations satisfied by higher normal functions, we illustrate this proposal with detailed calculations for LG‐models mirror to several Fano threefolds. By describing the “elementary” Apéry numbers in terms of regulators of higher cycles (i.e., algebraic ‐theory/motivic cohomology classes), we obtain a satisfying explanation of their arithmetic properties. Indeed, in each case, the LG‐models are modular families of surfaces, and the distinction between multiples of and (or ) translates ultimately into one between algebraic and of the family.

On the dilemma between percolation processes and fluctuating pairs as the origin of the enhanced conductivity above the superconducting transition in cuprates

The confrontation between percolation processes and superconducting fluctuations to account for the observed enhanced in-plane electrical conductivity above but near T c in cuprates is revisited. This dilemma is currently an open and debated question, whose solution would contribute to the phenomenological understanding of the emergence of superconductivity in these compounds. The cuprates studied here, La1.85Sr0.15CuO4, Bi2Sr2CaCu2O, and Tl2Ba2Ca2Cu3O10, have a different number of superconducting CuO2 (ab)-layers per unit-cell length and different Josephson coupling between them, and are optimally-doped to minimize T c -inhomogeneities. The excellent chemical and structural quality of these optimally-doped samples also contribute to minimize the effect of extrinsic -inhomogeneities, a crucial aspect when analyzing the possible presence of intrinsic percolative processes. Our analyses also cover the so-called high reduced-temperature region, up to the resistivity rounding onset ɛ onset. By using the simplest form of the effective-medium theory, we show that possible emergent percolation processes alone cannot account for the measured enhanced conductivity. In contrast, these measurements can be quantitatively explained using the Gaussian–Ginzburg–Landau (GGL) approach for the effect of superconducting fluctuations in layered superconductors, extended to ɛ onset by including a total energy cutoff, which takes into account the limits imposed by the Heisenberg uncertainty principle to the shrinkage of the superconducting wavefunction. Our present analysis confirms the adequacy of this cutoff, which was introduced heuristically, and that the effective periodicity length is controlled by the relative Josephson coupling between superconducting layers, two long standing debated aspects of the GGL approaches for multilayered superconductors. These conclusions are reinforced by analyzing, as an example, one of the recent works that allegedly discards the superconducting fluctuations scenario while supporting a percolative scenario for the enhanced conductivity above T c in cuprates.

Nambu Jona-Lasinio model of relativistic superconductivity

Abstract We propose a Nambu Jona-Lasinio (NJL) effective model of relativistic superconductivity. In this framework, we discuss possible electromagnetic (EM) behaviors of (specifically) type-II superconductivity in line with the nonrelativistic Ginzburg–Landau (GL) theory. We comment on possible solitonic solutions of this model. Our investigation could be of relevance to describe type-II proton superconductivity in neutron-star crusts.

Fully extended $r$-spin TQFTs

We prove the r -spin cobordism hypothesis in the setting of (weak) 2-categories for every positive integer r : the 2-groupoid of 2-dimensional fully extended r -spin TQFTs with given target is equivalent to the homotopy fixed points of an induced \mathrm{Spin}_2^r -action. In particular, such TQFTs are classified by fully dualisable objects together with a trivialisation of the r th power of their Serre automorphisms. For r=1 , we recover the oriented case (on which our proof builds), while ordinary spin structures correspond to r=2 . To construct examples, we explicitly describe \mathrm{Spin}_2^r -homotopy fixed points in the equivariant completion of any symmetric monoidal 2-category. We also show that every object in a 2-category of Landau–Ginzburg models gives rise to fully extended spin TQFTs and that half of these do not factor through the oriented bordism 2-category.

Criteria sensitive analysis of transport critical current density in BZO mixed YBCO

In this paper, we have extracted transport critical current density ([Formula: see text]) of BaZrO3 (BZO) added YBa2Cu3O[Formula: see text] (YBCO) by using several low electric field (E)-based criteria. By varying E-based criteria in order of magnitude, we have extracted [Formula: see text](T) and granular critical current density, [Formula: see text](T) by using JE (IV) characteristics. The temperature (T) dependence of [Formula: see text] and [Formula: see text] is found to be affected strongly as a result of the choice of E as criterion. The sensitiveness of [Formula: see text] and [Formula: see text] becomes prominent with the lowering of T. The Ambegaokar–Baratoff (AB) and the Ginzburg–Landau (GL) descriptions of [Formula: see text](T) and [Formula: see text](T) have been studied to understand how varying criteria may change the extraction of several associated coefficients. Extrapolated [Formula: see text]([Formula: see text]) and [Formula: see text]([Formula: see text]) is also highly sensitive to criteria used.

Hybrid Schrödinger-Ginzburg-Landau (Sch-GL) approach to study of superconducting integrated structures

Hybrid Schrödinger-Ginzburg-Landau approach is based on the fact of the mathematical similarity of Ginzburg-Landau (GL) and Schrödinger formalisms. Starting from Schrödinger approach by replacing the term V (x)−E with the term α(x)+β(x)|ψ(x)|2 we get the Ginzburg-Landau equation. In the proposed relaxation algorithm, we use one- and two-dimensional ground energy solutions of the Schrödinger equation and apply them as a starting trial solution for the GL relaxation method. The obtained numerical results and used methodology form the basis of the simulation platform for studying superconducting integrated structures and modeling various superconducting devices, including their time-dependent geometry.

Interlayer Interaction and Coercivity of Three-Layer Films Оbtained bу Chemical Deposition

Abstract—The results of experimental and theoretical studies of the coercivity and the displacement field of the hysteresis loop on the thickness of the nonmagnetic interlayer in magnetic films obtained by electroless plating are presented. With the help of model calculations based on the Landau–Ginzburg equations, the exchange interactions between magnetic layers with the participation of atoms of the nonmagnetic layer are studied. The resulting expression for the displacement field describes well the exponential changes in the displacement field as a function of the interlayer thickness in structures with both magnetically soft layers and layers with significantly different values of the coercivity.

Analytical solution for ginzburg–landau equation in discrete solitons laser arrays lattices via non-perturbation methods

Analytical solution for ginzburg–landau equation in discrete solitons laser arrays lattices via non-perturbation methods

Superconductivity with T c of 116K discovered in antimony polyhydrides.

Superconductivity (SC) was experimentally observed for the first time in antimony polyhydride. The diamond anvil cell combined with a laser heating system was used to synthesize the antimony polyhydride sample at high pressure and high temperature. In-situ high pressure transport measurements as a function of temperature with an applied magnetic field were performed to study the SC properties. It was found that the antimony polyhydride samples show superconducting transition with critical temperature T c 116K at184GPa. The investigation of SC at magnetic field revealed the superconducting coherent length of ∼40Å based on the Ginzburg Landau (GL) equation. Antimony polyhydride superconductor has the second highest T c in addition to sulfur hydride among the polyhydrides of elements from main groups IIIA to VIIA in the periodic table.

Superheating field in superconductors with nanostructured surfaces

We report calculations of a DC superheating field Hsh in superconductors with nanostructured surfaces. Numerical simulations of the Ginzburg–Landau (GL) equations were performed for a superconductor with an inhomogeneous impurity concentration, a thin superconducting layer on top of another superconductor, and superconductor–insulator–superconductor (S-I-S) multilayers. The superheating field was calculated taking into account the instability of the Meissner state with a non-zero wavelength along the surface, which is essential for the realistic values of the GL parameter κ. Simulations were performed for the material parameters of Nb and Nb3Sn at different values of κ and the mean free paths. We show that the impurity concentration profile at the surface and thicknesses of S-I-S multilayers can be optimized to enhance Hsh above the bulk superheating fields of both Nb and Nb3Sn. For example, an S-I-S structure with a 90-nm-thick Nb3Sn layer on Nb can boost the superheating field up to ≈500 mT, while protecting the superconducting radio-frequency (SRF) cavity from dendritic thermomagnetic avalanches caused by local penetration of vortices.

Fundamental Factorization of a GLSM Part I: Construction

We define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases these invariants recover both the Gromov–Witten type invariants defined by Chang–Li and Fan–Jarvis–Ruan using cosection localization as well as the FJRW type invariants constructed by Polishchuk–Vaintrob. The invariants are defined by constructing a “fundamental factorization” supported on the moduli space of Landau–Ginzburg maps to a convex hybrid model. This gives the kernel of a Fourier–Mukai transform; the associated map on Hochschild homology defines our theory.

Matrix factorizations, Reality and Knörrer periodicity

AbstractMotivated by periodicity theorems for Real ‐theory and Grothendieck–Witt theory and, separately, work of Hori and Walcher on the physics of Landau–Ginzburg orientifolds, we introduce and study categories of Real matrix factorizations. Our main results are generalizations of Knörrer periodicity to categories of Real matrix factorizations. These generalizations are structurally similar to (1,1)‐periodicity for ‐theory and 4‐periodicity for Grothendieck–Witt theory. We use techniques from Real categorical representation theory, which allow us to incorporate into our main results equivariance for a finite group and discrete torsion twists.

Solving Nonlinear Fractional Models in Superconductivity Using the q-Homotopy Analysis Transform Method

The Ginzburg–Landau (GL) equation and the Ginzburg–Landau couple system are important models in the study of superconductivity and superfluidity. This study describes the q-homotopy analysis transform method (q-HATM) as a powerful technique for solving nonlinear problems, which has been successfully used with a set of mathematical models in physics, engineering, and biology. We apply the q-HATM to solve the Ginzburg–Landau equation and the Ginzburg–Landau coupled system and derive analytical solutions in terms of the q-series. Also, we investigate the convergence and accuracy of the obtained solutions. Our results show 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. Several graphs have been presented for the solutions obtained utilizing different levels of the fractional-order derivative and at various points in time.

R-Symmetries and Curvature Constraints in A-Twisted Heterotic Landau–Ginzburg Models

In this paper, we discuss various aspects of a class of A-twisted heterotic Landau–Ginzburg models on a Kähler variety X. We provide a classification of the R-symmetries in these models which allow the A-twist to be implemented, focusing on the case in which the gauge bundle is either a deformation of the tangent bundle of X or a deformation of a sub-bundle of the tangent bundle of X. Some anomaly-free examples are provided. The curvature constraint imposed by supersymmetry in these models when the superpotential is not holomorphic is reviewed. Constraints of this nature have been used to establish properties of analogues of pullbacks of Mathai–Quillen forms which arise in the correlation functions of the corresponding A-twisted or B-twisted heterotic Landau–Ginzburg models. The analogue most relevant to this paper is a deformation of the pullback of a Mathai–Quillen form. We discuss how this deformation may arise in the class of models studied in this paper. We then comment on how analogues of pullbacks of Mathai–Quillen forms not discussed in previous work may be obtained. Standard Mathai–Quillen formalism is reviewed in an appendix. We also include an appendix which discusses the deformation of the pullback of a Mathai–Quillen form.

New waves solutions of a nonlinear Landau–Ginzburg–Higgs equation: The Sardar-subequation and energy balance approaches

This article investigates the significance of the unsteady nonlinear Landau–Ginzburg–Higgs equation in the context of superfluids and Bose–Einstein condensates. The problem of interest is the search for new exact solutions within this equation. To tackle this problem, the Sardar-subequation and energy balance approaches are employed. Through these methods, a variety of new exact solutions are obtained, expressed in terms of cosine functions, generalized hyperbolic functions, and generalized trigonometric functions. The obtained solutions encompass different types of solitons, including bright and dark solitons, singular periodic soliton, and hybrid solitons. The solutions are then visualized through 2D and 3D simulations. The findings of this study contribute to the understanding of the Landau–Ginzburg–Higgs equation and its application to superfluids and Bose–Einstein condensates. The novelty of this work lies in the utilization of the Sardar-subequation and energy balance approaches to obtain diverse traveling wave solutions, surpassing previous efforts in the literature.

Phase field study on the flexoelectric response of dielectric–ferroelectric multilayers

We report a theoretical modeling of the flexoelectric response of dielectric–ferroelectric (DE–FE) multilayers based on phase field simulations in the framework of the Landau–Ginzburg–Devonshire (LGD) theory. The correlation between negative capacitance and flexoelectric response is revealed, and the single-domain and multi-domain models are compared. It shows that the dielectric layers drive the ferroelectric layer into a negative capacitance regime, and the flexoelectric response of the multilayer is maximal when the negative capacitance of the ferroelectric layer has a minimal absolute value. Moreover, the flexoelectric response peak will be shifted to a lower temperature by increasing the thickness of dielectric layer, indicating a possibility of achieving a stronger flexoelectric response at room temperature compared with that of pure ferroelectric. However, while the single-domain model shows that the flexoelectric response peak is simply shifted to a lower temperature with near constant peak value and width, the multi-domain model reveals a significant suppressing of the flexoelectric peak by the dielectric layer. This is attributed to the formation of the vortex domain state, which eases the depolarization effect and leads to large absolute value of negative capacitance of the ferroelectric layer. Our work provides new insights into flexoelectricity in ferroelectric heterostructures.

Electrocaloric Effect in Multilayer Ferroelectric Structures

Introduction. Ferroelectric films are widely used for radiotechnical, microwave microelectronic, sensoric, and energy conversion purposes. Such a diverse application range demands film materials with specific electrophysical properties. For instance, while energy storage applications require materials with a high dielectric constant, energy conversion devices largely use those with a low dielectric constant. The necessary physical properties can be achieved using multicomponent ferroelectric structures, such as solid solutions, composites, and multilayer film structures. Mechanical stresses between the substrate and ferroelectric layers play an extremely important role in dielectric properties of multilayer structures.Aim. Development of a mathematical model quantifying the ferroelectric polarization, static dielectric constant, as well as pyroelectric and electrocaloric properties of multilayered ferroelectric film structures.Materials and methods. The presented model is based on the Landau–Ginzburg–Devonshire model (LGD) considering elasticity equations and using electric induction as the order parameter.Results. The developed mathematical model based on LGD provides for a quantifiable description of dielectric, pyroelectric, and electrocaloric properties of layered ferroelectric structures. This model displays the effect of the thickness ratio of polycrystalline layers and grain size distribution on the dielectric properties of films.Conclusion. The developed quantitative model demonstrates the dependence of the thickness, grain size, and stacking order of ferroelectric layers on the dielectric constant and pyroelectric coefficient of multilayered polycrystalline film structures. The presented model can be applied when optimizing the parameters of multilayer structures with respect to their application area.

A Compact Model for Ferroelectric Capacitors Based on Multidomain Phase-Field Framework

A generalized and fast multidomain phase-field-based compact model for the metal-ferroelectric-metal (MFM) capacitor is presented. Time-dependent Landau–Ginzburg (TDGL) and Poisson’s equations are solved self-consistently to model the polarization dynamics. Additionally, physics-based empirical relationships for voltage-dependent kinetic and gradient energy coefficients are formulated. It is also demonstrated how gradient energy coefficient needs to be modified to accurately capture the physics of the device when a coarse simulation grid is used for fast computation. The developed model is 30 000 times faster than our prior multidomain phase-field model with no degradation in accuracy. Moreover, a further computational speedup has been achieved by decreasing the number of Poisson solver nodes with a slight compromise of accuracy. The model shows a good agreement with the experimental results of both transient characteristics and minor hysteresis loops. The proposed model has the potential to facilitate fast and accurate simulations of large-scale circuits containing ferroelectric capacitors.