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Layered nanocomposite material having fcc-bcc interface with Kurdjumov-Sachs interface ori- entation relation has shown great potential as radiation resistant structural material for future fusion energy reactors. The superior radiation resistant properties of this material are attributed to it’s special fcc-bcc interface structure. In this study we have reported a stable interface between conventional bcc phase of Nb and transformed bcc phase of Cu. This bcc-bcc interface is found to be stable from both strain-energy and dynamical stability analysis. We have also shown that the bcc-bcc interface has different defect energetics behaviour compared to previously reported fcc-bcc interface which has a negative impact on the self annihilation property of the material against radiation induced defects. These aspects should be carefully considered in the future design of robust layered material for extreme radiation environment.

We present explicit formulas for total crossing events in the multi-species asymmetric exclusion process ($r$-ASEP) with underlying $U_q(\widehat{\mathfrak{sl}}_{r+1})$ symmetry. In the case of the two-species TASEP these can be derived using an explicit expression for the general transition probability on $\mathbb{Z}$ in terms of a multiple contour integral derived from a nested Bethe ansatz approach. For the general $r$-ASEP we employ a vertex model approach within which the probability of total crossing can be derived from partial symmetrization of an explicit high rank rainbow partition function. In the case of $r$-TASEP, the total crossing probability can be show to reduce to a multiple integral over the product of $r$ determinants. For $2$-TASEP we additionally derive convenient formulas for cumulative total crossing probabilities using Bernoulli-step initial conditions for particles of type 2 and type 1 respectively., Comment: 41 pages, 4 figures. Version 2 adds references and referee suggestions

We address the existence, stability, and propagation dynamics of both one- and two-dimensional defect solitons supported by optical lattice with saturable nonlinearity in fractional Schrödinger equation. Under the influence of fractional effect, in one dimension, solitons exist stably in limited regions in the semi-infinite bandgap with high and low power both for a negative and positive defect lattice. In the first bandgap, solitons are stable for negative defect lattice, while unstable for positive defect lattice. In the second bandgap, only stable solitons can propagate in small regions for the positive defect lattice. With increasing the Lévy index from 1 to 2, the power of the defect solitons decreases in the semi-infinite bandgap and increases in the first bandgap. Linear stability analyses show that, the domains of stability for defect solitons strongly depend on the Lévy index, defect strength and different bandgaps. In two dimension, defect solitons can exist stably at high and moderate power regions in the semi-infinite bandgap and all regions in the first bandgap with negative defect lattice, while they are stable at high, moderate and low power regions in the semi-infinite bandgap and unstable in the first bandgap with positive defect lattice.

Improving effective and thrifty photocatalysts was deemed an outstanding approach for pollution handling. Here, a novel magnetic Co0.5Mg0.5LaxFe2-xO4 nanoparticle photocatalysts were synthesized via a combustion approach for the harmful methylene blue (MB) dye degradation. These samples were labeled as Co0.5Mg0.5Fe2O4 (CMLF0), Co0.5Mg0.5La0.03Fe1.97O4 (CMLF1), Co0.5Mg0.5La0.06Fe1.94O4 (CMLF2), Co0.5Mg0.5La0.09Fe1.91O4 (CMLF3), Co0.5Mg0.5La0.12Fe1.88O4 (CMLF4), and Co0.5Mg0.5La0.15Fe1.85O4 (CMLF5). A sequence of characterizations, including XRD, STEM, and UV–Vis-DRS, was exploited to examine the structure, morphology, constituent elements, and optical features of the CMLF ferrite nanoparticles. Despite the substitution process, an amazing decrement result for the lattice parameter (8.3748 to 8.3610 Å) and crystallite size (21.87 to 13.95 nm) is a large La cation at the expense of a smaller Fe one. The band-gap behavior of the CMLF nanoferrites is unique; it increases from 1.528 eV at the CMLF0 to 1.547 eV at the CMLF3 and decreases to 1.526 eV at the CMLF4 and 1.520 eV at the CMLF5. Two justifications accounted for this behavior. The nanoferrite CMLF5 has the highest photodegradation efficiency, 96.09 %, after 60 minutes. Three hypotheses were introduced to explain this result. After five cycles, the degradation efficiency of the nanoferrite CMLF5 maintained its high performance with 95.09 %, 94.87 %, 94.76 %, 93.59 %, and 93.44 %, respectively. These outcomes validate the outstanding photocatalytic efficiency, recyclability, and stability of the CMLF5 photocatalyst in its task to degrade the harmful MB dye, making it acceptable for wastewater treatment applications.

Room-temperature exciton-polariton is observed in GaN/InGaN core-shell microrods grown by metal-organic vapor phase epitaxy. We demonstrate a large Rabi splitting in the core-shell microrod structure over 265 meV. Room-temperature lasing in core-shell microrods is confirmed by power-dependent photoluminescence spectra. The lasing in the shell layer results to a modulated lasing wavelength and takes one step further to more stable polariton lasing in MQW core-shell microrods.

The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV regularization, and show that the resulting enhanced TV minimization model is particularly effective for reducing the loss of contrast. The main purpose of this paper is to establish stable reconstruction guarantees for the enhanced TV model from noisy subsampled measurements with two sampling strategies, non-adaptive sampling for general linear measurements and variable-density sampling for Fourier measurements. In particular, under some weaker restricted isometry property conditions, the enhanced TV minimization model is shown to have tighter reconstruction error bounds than various TV-based models for the scenario where the level of noise is significant and the amount of measurements is limited. Advantages of the enhanced TV model are also numerically validated by preliminary experiments on the reconstruction of some synthetic, natural, and medical images., 29 pages, 8 figures

We describe topological T-duality and Poisson-Lie T-duality in terms of QP (differential graded symplectic) manifolds and their canonical transformations. Duality is mediated by a QP-manifold on doubled non-abelian ``correspondence'' space, from which we can perform mutually dual symplectic reductions, where certain canonical transformations play a vital role. In the presence of spectator coordinates, we show how the introduction of a bibundle structure on correspondence space realises changes in the global fibration structure under Poisson-Lie duality. Our approach can be directly translated to the worldsheet to derive dual string current algebras. Finally, the canonical transformations appearing in our reduction procedure naturally suggest a Fourier-Mukai integral transformation for Poisson-Lie T-duality.

In this article, using gravitational decoupling under vanishing complexity condition, an anisotropic solution to spherically symmetric compact stars has been investigated. After obtaining the solution, a detailed physical analysis including thermodynamic parameters, mass-radius ratio, and stability analysis of the model corresponding to the secondary component of the GW190814 event has been done. To test the effect of gravitational decoupling on the mass-radius ratio, we fixed the mass of the secondary component of the GW190814 event corresponding to the pure general relativity scenario. Alongside this, we also predicted the radii and mass-radius ratio of 11 different compact stars using observational data of their masses for different values of $\beta$. Furthermore, the hydrostatic balance has been analyzed using the modified Tolman-Oppenheimer-Volkoff (TOV) Equation. The physical analysis shows that our results are in good agreement as far as observational data is concerned.

Two important mathematical methods for addressing uncertainty in data processing are multigranulation rough set (MGRS) and fuzzy bipolar soft set (FBSS). This paper describes a certain kind of multigranulation rough set in the context of multiple soft binary relations. We first define the multigranulation roughness of fuzzy bipolar soft sets in the two universes. Moreover, a detailed study of structural properties has been conducted in order to explore this concept. The key characteristics of the traditional MGRS model are completely preserved in this new approach. Following that, we suggest two decision-making algorithms with respect to aftersets and foresets of the soft binary relations over dual universes. This approach appears to be better suited and more adaptable than other available methods, making it a favorable option for addressing decision-making problems. Finally, we provide a practical application of the suggested approach to a real-world problem.

This paper presents a blended ferron in a ferromagnetic cluster where the electric polarization and magnetization tailor the quasi-particle characteristics. The resulting quasi-particle has coupled acoustic-polaron and ferron characteristics. The constant competition between electric polarization and magnetization alters the effective mass thereby reducing the global inertia of the quasi-particle. The impurity significantly affects the environment, and the resulting defects in the polarization and magnetization are soliton-like. It was observed that any gain in electric polarization is conveyed by a drop in magnetization, where the hybridization of magnetization and polarization gives rise to a new quasi-particle concept: a blended ferron. The latter is manifested by the local deformation of the electric polarization and depletion of the magnetization in the cluster’s signature of magnetic reordering

Data driven modelling is vital to many analyses at collider experiments, however the derived inference of physical properties becomes subject to details of the model fitting procedure. This work brings a principled Bayesian picture, based on the marginal likelihood, of both data modelling and signal extraction to a common collider physics scenario. First the marginal likelihood based method is used to propose a more principled construction of the background process, systematically exploring a variety of candidate shapes. Second the picture is extended to propose the marginal likelihood as a useful tool for anomaly detection challenges in particle physics. This proposal offers insight into both precise background model determination and demonstrates a flexible method to extend signal determination beyond a simple bump hunt., 10 pages, 6 figures, accepted to JINST

Determination of temperature-dependent nucleation rate is a crucial parameter to accessing the kinetic and thermodynamic barrier linked with developing subatomic-sized nuclei, which tend to restrain the nucleation process. In this study, we exclusively compute the nucleation rate, thermodynamic parameters, and interfacial energy of ultra-small gadolinium oxide nanoclusters at high temperatures. Here, the apparent value of activation energy (Ea.) and pre-exponential kinetic factor (Aa) was precisely computed by utilizing the most accurate Vyazovkin advanced and KAS iso-conversional method, which was further exploited to estimate the thermodynamic parameters, nucleation rate, and interfacial energy of ~1 nm-sized gadolinium nanoclusters, in the temperature ranging from 555 to 780 K by appraising thermogravimetric data. The obtained Z (α) master plot suggested the existence of random nucleation within the BSA matrix of Gd2O3 nanoclusters at high temperature over a specified conversion value. Additionally, four mathematical models were proposed using the above finding to interpret the nucleation rate and interfacial energy concerning high temperature and specified conversion points for the first time.

In this paper, we propose an effective numerical method, based on the use of two-dimensional Shifted fractional-order Gegenbauer Multi-wavelets, for finding the approximate solutions of the time-fractional distributed order non-linear partial differential equations. The method is applied to solve fractional distributed order non-linear Klein-Gordon equation, numerically. We derive an exact formula for the Riemann–Liouville fractional integral operator for the Shifted fractional Gegenbauer Multi-wavelets. Applying function approximations obtained by this method turns the considered equation into a system of algebraic equations. Error estimation and convergence analysis of the method are also studied. Some numerical examples are included to show and check the effectiveness of the proposed method.

We investigate the existence and nonexistence of weak solutions to a (3+1)-dimensional equation of plasma drift waves perturbed by a singular potential. The considered equation is posed in an infinite parallelepiped, under an inhomogeneous Dirichlet boundary condition. We show that the dividing line with respect to existence or nonexistence is given by a critical exponent.

In this paper, we investigate a predator–prey system with nonlinear prey-taxis under Neumann boundary condition. For a class of chemotactic sensitive functions, we obtain the existence and boundedness of global classical solutions for initial boundary value problems in arbitrary dimensional space. In addition, we also study the local stability of the constant steady state solution, and obtain the global asymptotic stability of the steady state solution under different predation intensity by constructing appropriate Lyapunov functions. Furthermore, the steady state bifurcation, Hopf bifurcation and fold-Hopf Singularity are analysed in detail by using Lyapunov–Schmidt reduction method.

In this article, we prove that a sum of solitons and breathers of the modified Korteweg–de Vries equation (mKdV) is orbitally stable. The orbital stability is shown inH2. More precisely, we will show that if a solution of mKdV is close enough to a sum of solitons and breathers with distinct velocities att= 0 in theH2sense, then it stays close to this sum of solitons and breathers for any timet⩾ 0 in theH2sense, up to space translations for solitons or space and phase translations for breathers, provided the condition that the considered solitons and breathers are sufficiently decoupled from each other and that the velocities of the considered breathers are all positive, except possibly one. The constants that appear in this stability result do not depend on translation parameters. From this, we deduce the orbital stability of any multi-breather of mKdV, provided the condition that the velocities of the considered breathers are all positive, except possibly one (the condition about the decoupling of the considered solitons and breathers between each other is not required in this setting). The constants that appear in this stability result depend on translation parameters of the considered solitons and breathers.

We investigate the computability (in the sense of computable analysis) of the topological pressure $P_{\rm top}(\phi)$ on compact shift spaces $X$ for continuous potentials $\phi:X\to {\mathbb R}$. This question has recently been studied for subshifts of finite type (SFTs) and their factors (Sofic shifts). We develop a framework to address the computability of the topological pressure on general shift spaces and apply this framework to coded shifts. In particular, we prove the computability of the topological pressure for all continuous potentials on S-gap shifts, generalized gap shifts, and particular Beta-shifts. We also construct shift spaces which, depending on the potential, exhibit computability and non-computability of the topological pressure. We further prove that the generalized pressure function $(X,\phi)\mapsto P_{\rm top}(X,\phi\vert_{X})$ is not computable for a large set of shift spaces $X$ and potentials $\phi$. In particular, the entropy map $X\mapsto h_{\rm top}(X)$ is computable at a shift space $X$ if and only if $X$ has zero topological entropy. Along the way of developing these computability results, we derive several ergodic-theoretical properties of coded shifts which are of independent interest beyond the realm of computability., Comment: The statement of Theorem A has been updated. In particular, Theorem A holds now for all coded shifts. This follows from recent work by Beal, Perrin and Restivo (reference [3]) who show that every coded shift is uniquely representable. Further, we revised the proof of Theorem A fixing a mistake in the previous version

Bézier surface has been commonly applied to represent the complex geometric shape. Generally, all control points are dealt with by the same blending functions, regardless of the effect of independent coordinate. It causes to lack the modeling flexibility. Therefore, this paper proposes an equivalent parameter geometric shape representation method using the independent coordinates of control points. Since the coordinate components of control points are independent, the geometric modeling becomes more flexible. Firstly, a general Bézier curve is described in detail. Related expression is brought out in the form of independent coordinates by introducing two parameters. Then, their geometric meanings are analyzed in detail. Since both parameters are independent to parametric variables u and v, Bézier curve possess the same interval in the discrete parametric space, namely equivalent parameter. Next, a bicubic Bézier subsurface patch representation is discussed, including regular and non-regular subsurface patch. A general surface expression is given out in the form of independent coordinates, as well as the parameter structure and the geometric transformations. Finally, an example of ‘Bézier tree branch’ is constructed by using the proposed method. Results shows that the proposed method is feasible and reasonable.

In this paper, we study the pointwise equidistribution properties of measures μ p defined by digit restrictions on the b-adic expansion, where b ⩾ 2 is an integer. We prove that, if a sequence ( α n ) n ⩾ 1 satisfies a certain b-adic diversity condition, then the sequence ( α n x ) n ⩾ 1 is uniformly distributed modulo one for μ p -a.e. x. We also find some sufficient conditions to ensure the b-adic diversity. Moreover, we apply these results to establish the b-adic diversity for the sequences that can be written as certain combination of polynomial and exponential functions.

In this paper, we study the topological properties and the gap sequences of Bedford–McMullen sets. First, we introduce a topological condition, the component separation condition (CSC), and a geometric condition, the exponential rate condition (ERC). Then we prove that the CSC implies the ERC, and that both of them are sufficient conditions for obtaining the asymptotic estimate of gap sequences. We also explore topological properties of Bedford–McMullen sets and prove that all normal Bedford–McMullen sets with infinitely many connected components satisfy the CSC, from which we obtain the asymptotic estimate of the gap sequences of Bedford–McMullen sets without any restrictions. Finally, we apply our result to Lipschitz equivalence.

In this paper a generalised Rayleigh–Liénard oscillator is consider and lower bounds for the number of limit cycles bifurcating from weak focus equilibria and saddle connections are provided. By assuming some open conditions on the parameters of the considered system the existence of up to twelve limit cycles is provided. More precisely, the approach consists in perform suitable changes in the sign of some specific parameters and apply Poincaré–Bendixson theorem for assure the existence of limit cycles. In particular, the algorithm for obtaining the limit cycles through the referred approach is explicitly exhibited. The main techniques applied in this study are the Lyapunov constants and the Melnikov method. The obtained results contemplate the simultaneity of limit cycles of small amplitude and medium amplitude, the former emerging from a weak focus equilibrium and the latter from homoclinic or heteroclinic saddle connections.

In Jayanti and Trivisa (2022 J. Math. Fluid Mech. 24 46), the authors proved the existence of local-in-time weak solutions to a model of superfluidity. The system of governing equations was derived in Pitaevskii (1959 Sov. Phys. JETP 8 282–287) and couples the nonlinear Schrödinger equation and the Navier–Stokes equations. In this article, we prove a weak–strong type uniqueness theorem for these weak solutions. Only some of their regularity properties are used, allowing room for improved existence theorems in the future, with compatible uniqueness results.

This paper is concerned with the critical sharp traveling wave for doubly nonlinear diffusion equation with time delay, where the doubly nonlinear degenerate diffusion is defined by $\Big(\big|(u^m)_x\big|^{p-2}(u^m)_x\Big)_x$ with $m>0$ and $p>1$. The doubly nonlinear diffusion equation is proved to admit a unique sharp type traveling wave for the degenerate case $m(p-1)>1$, the so-called slow-diffusion case. This sharp traveling wave associated with the minimal wave speed $c^*(m,p,r)$ is monotonically increasing, where the minimal wave speed satisfies $c^*(m,p,r)0$. The sharp front is $C^1$-smooth for $\frac{1}{p-1}, Comment: arXiv admin note: text overlap with arXiv:1909.11751

We investigate orbital and asymptotic stability of solitary wave solutions to the U(1)-invariant nonlinear Klein–Gordon equation with mean field interaction.

We propose a novel semi-discrete Kadomtsev--Petviashvili equation with two discrete and one continuous independent variables, which is integrable in the sense of having the standard and adjoint Lax pairs, from the direct linearisation framework. By performing reductions on the semi-discrete Kadomtsev--Petviashvili equation, new semi-discrete versions of the Drinfel'd--Sokolov hierarchies associated with Kac--Moody Lie algebras $A_r^{(1)}$, $A_{2r}^{(2)}$, $C_r^{(1)}$ and $D_{r+1}^{(2)}$ are successfully constructed. A Lax pair involving the fraction of $\mathbb{Z}_\mathcal{N}$ graded matrices is also found for each of the semi-discrete Drinfel'd--Sokolov equations. Furthermore, the direct linearisation construction guarantees the existence of exact solutions of all the semi-discrete equations discussed in the paper, providing another insight into their integrability in addition to the analysis of Lax pairs., 18 pages

In this paper we study the quenched distributions of hitting times for a class of random dynamical systems. We prove that hitting times to dynamically defined cylinders converge to a Poisson point process under the law of random equivariant measures with super-polynomial decay of correlations. In particular, we apply our results to uniformly aperiodic random subshifts of finite type equipped with random invariant Gibbs measures. We emphasize that we make no assumptions about the mixing property of the marginal measure.

We study the non relativistic and ultra relativistic limits in the two-dimensional nonlinear damped Klein–Gordon equation driven by a space-time white noise on the torus. In order to take the limits, it is crucial to clarify the parameter dependence in the estimates of solution. In this paper we present two methods to confirm this parameter dependence. One is the classical, simple energy method. Another is the method via Strichartz estimates.

In this work we study the Hausdorff dimension of hyperbolic attractors that are given by skew-products. We prove that if the contraction is sufficiently strong, the weak-contraction is conformal and the attractor satisfies a geometric condition of transversality between its components, then the Hausdorff dimension and the box-counting dimension of the attractor satisfy Bowen’s formula. We also prove that for any attractor whose contraction is sufficiently strong, there exist dynamics C r -close such that the Hausdorff dimension and the box-counting dimension of the attractor have the same value given by Bowen’s formula.

We consider an initial value problem of the multi-dimensional Boussinesq equations with velocity damping for strongly stratified fluids. We prove the global-in-time existence of the classical solution to the stratified damped Boussinesq equations with initial data near the stationary stratified solution ( v s , ρ s , p s ) = ( 0 , … , 0 , x d , x d 2 / 2 ) . We also show the asymptotic stability of the solutions near the stratified solution and obtain the temporal decay for the fluid velocity and the temperature by providing estimates for the Green function associated with the linear operator in any dimension.

Motivated by questions originating from the study of a class of shallow student-teacher neural networks, methods are developed for the analysis of spurious minima in classes of gradient equivariant dynamics related to neural networks. In the symmetric case, methods depend on the generic equivariant bifurcation theory of irreducible representations of the symmetric group on k symbols, S k ; in particular, the standard representation of S k . It is shown that spurious minima (non-global local minima) do not arise from spontaneous symmetry breaking but rather through a complex deformation of the landscape geometry that can be encoded by a generic S k -equivariant bifurcation. We describe minimal models for forced symmetry breaking that give a lower bound on the dynamic complexity involved in the creation of spurious minima when there is no symmetry. Results on generic bifurcation when there are quadratic equivariants are also proved; this work extends and clarifies results of Ihrig & Golubitsky and Chossat, Lauterbach & Melbourne on the instability of solutions when there are quadratic equivariants.

In this paper, we consider certain partially hyperbolic diffeomorphisms (PHDs) with centre of arbitrary dimension and obtain continuity properties of the topological entropy under C 1 perturbations. The systems considered have subexponential growth in the centre direction and uniform exponential growth along the unstable foliation. Our result applies to PHDs which are Lyapunov stable in the centre direction. It applies to another important class of systems which do have subexponential growth in the centre direction, for which we develop a technique to use exponential mixing property of the systems to get uniform distribution of unstable manifolds. A primary example are the translations on homogeneous spaces which may have centre of arbitrary dimension and of polynomial orbit growth.

In this paper, we consider the global existence and convergence of smooth solutions for the three dimensional spherically symmetric compressible Euler equations with time-dependent damping and physical vacuum. The damping coefficient decays with time and the sound speed is C 1/2-Hölder continuous across the physical vacuum boundary. Both the degeneration of the damping coefficient at time infinity and the non C 1 continuity of the sound speed across the vacuum boundary will cause difficulty in proving the global existence of smooth solutions. Under suitable assumptions on the decayed damping coefficients, the globally in-time smooth solutions and convergence to the modified Barenblatt solution will be given. Also obtained are the pointwise convergence rate of the density, velocity and the expanding rate of the physical vacuum boundary. Our result extends that in Zeng (2017 Arch. Ration. Mech. Anal. 226 33–82) by considering the degenerate damping coefficient instead of the constant damping coefficient and that in Pan (2021 Calc. Var. Partial Differ. Equ. 60 5) from the one dimensional case to the three dimensional case with spherically symmetric data.

We extend Margulis–Ruelle inequality to the general setting of semigroup actions which are finitely generated either by Lipschitz continuous maps acting on a compact metric space or by smooth maps on a compact Riemannian manifold. We also discuss a few examples to illustrate the sharpness of our estimates.

Let μ be a Borel probability measure with compact support on R d . We say that μ is a spectral measure if there exists Λ ⊆ R d , called a spectrum of μ, such that E ( Λ ) ≔ { e − 2 π i ⟨ λ , x ⟩ } λ ∈ Λ forms an orthonormal basis for L 2(μ). In this paper, we study the structure of spectra for a class of self-similar spectral measure μ R,B with product form on R . We first give a partially characterize for E Λ to be a maximal orthogonal family in L 2(μ R,B ) by using the notion of maximal tree mapping. Based on this, we give a sufficient condition for a maximal orthogonal family E Λ (which corresponds to a maximal tree mapping) to be an orthonormal basis of L 2(μ R,B ). Moreover, we completely settle two types of spectral eigenvalue problems for μ R,B . Precisely, on the first case, for the model spectrum (simplest spectrum) of μ R,B , we characterize all possible real numbers t such that tΛ is also a spectrum of μ R,B . On the other case, we characterize all possible real numbers t such that there exists a countable set Λ such that Λ and tΛ are both spectra of μ R,B .

The goal of this paper is twofold. First, we give a simple proof that sufficiently sparse Navier--Stokes solutions do not develop singularities. This provides an alternative to the approach of \cite{Grujic2013}, which is based on analyticity and the `harmonic measure maximum principle'. Second, we analyze the claims in \cite{algebraicreduction,grujic2019asymptotic} that \emph{a priori} estimates on the sparseness of the vorticity and higher velocity derivatives reduce the 'scaling gap' in the regularity problem., Comment: 20 pages, 1 figure. Revised version, to appear in Nonlinearity

We show that for any topological dynamical system with the approximate product property, the set of points whose forward orbits do not accumulate to any point in a large set Z carries full topological entropy, as well as full topological pressure for any continuous potential. For instance, the set Z can include a finite union of the basins of any given invariant measures.

This corrigendum corrects a mistake in the paper (Baesens and MacKay 2018 Nonlinearity 31 2928–81) and the consequent conclusions. The corrected conclusions are confirmed by numerically computed bifurcation diagrams.

In this paper, we prove an exponential long time stability result for the derivative nonlinear Schödinger equation (DNLS) in some Sobolev space by using Birkhoff normal form technique and some suitable nonresonant conditions.

In this manuscript, we establish C loc α , α θ regularity estimates for bounded weak solutions of a certain class of doubly degenerate evolution PDEs, whose simplest model case is given by ∂ u ∂ t − d i v ( m | u | m − 1 | ∇ u | p − 2 ∇ u ) = f ( x , t ) in Ω T ≔ Ω × ( 0 , T ) , where m ⩾ 1, p ⩾ 2 and f belongs to a suitable anisotropic Lebesgue space. Employing intrinsic scaling techniques and geometric tangential methods, we derive sharp regularity estimates for such models, which depend only on universal and compatibility parameters of the problem. In this scenario, our results are natural improvements for former ones in the context of nonlinear evolution PDEs with degenerate structure via a unified approach. As a consequence of our findings and approach, we address a Liouville type result for entire weak solutions of a related homogeneous problem with frozen coefficients and asymptotic estimates under a certain approximating regime, which may have their own mathematical interest. We also present examples of degenerate PDEs where our results can be applied.

In the context of the Cauchy problem for the Korteweg-de Vries equation we extend the inverse scattering transform to initial data that behave at plus infinity like a sum of Wigner-von Neumann type potentials with small coupling constants. Our arguments are based on the theory of Hankel operators., To appear in Nonlinearity

Let f t be a flow satisfying Smale’s Axiom A (in short, A-flow) on a closed orientable three-manifold M 3, and Ω a two-dimensional basic set of f t . First, we prove that Ω is either an expanding attractor or contracting repeller. Next, one considers an A-flow f t with a two-dimensional non-mixing attractor Λ a . We construct a casing M(Λ a ) of Λ a that is a special compactification of the basin of Λ a by a collection of circles L(Λ a ) = {l 1, …, l k } such that M(Λ a ) is a closed three-manifold and L(Λ a ) is a fibre link in M(Λ a ). In addition, f t is extended on M(Λ a ) to a nonsingular structurally stable flow with the non-wandering set consisting of the attractor Λ a and the repelling periodic trajectories l 1, …, l k . We show that if a closed orientable three-manifold M 3 has a fibred link L = {l 1, …, l k } then M 3 admits an A-flow f t with the non-wandering set containing a two-dimensional non-mixing attractor and the repelling isolated periodic trajectories l 1, …, l k . This allows us to prove that any closed orientable n-manifold, n ⩾ 3, admits an A-flow with a two-dimensional attractor. We prove that the pair M ( Λ a ) ; L ( Λ a ) consisting of the casing M(Λ a ) and the corresponding fibre link L(Λ a ) is an invariant of conjugacy of the restriction f t | W s ( Λ a ) of the flow f t on the basin of the attractor Λ a .

We introduce a new approach to denoising correlation matrices that imposes a block structure with a fixed block-dependent pair-wise correlation within each block and a constant correlation specified for each pair of blocks. We characterize the eigenvalue spectrum and modify the Marchenko-Pastur distribution of eigenvalues. We present approximate analytic solutions for the inverse problem of determining the block sizes and the correlation parameters under a broad set of assumptions. Our solution is based on a novel unsupervised approach for improving correlation matrix estimation by a functional transformation of the original data rather than popular shrinkage estimation or standard random-matrix-theory-based techniques. However, a correlation matrix produced by our method can serve as an attractive target correlation matrix within shrinkage frameworks. Our correlation matrix denoising method has broad applications for global portfolio management with a large number of assets from many diverse asset classes.

In this article we consider resummed expressions for the heat-kernel's trace of a Laplace operator, the latter including a potential and imposing Dirichlet semitransparent boundary conditions on a surface of codimension one in flat space. We obtain resummed expressions that correspond to the first and second order expansion of the heat-kernel in powers of the potential. We show how to apply these results to obtain the bulk and surface form factors of a scalar quantum field theory in $d=4$ with a Yukawa coupling to a background. Additionally, we discuss a connection between heat-kernels for Dirichlet semitransparent, Dirichlet and Robin boundary conditions.

We develop the phase field model to simulate precipitation of secondary phase in ternary alloys with extra-small content of doping. This approach is applied to study $\beta$-phase precipitation in the model system of commercial alloy Zr-Nb-Sn at thermal treatment. An analysis of local rearrangement of doping and equilibrium vacancies during precipitation has shown that the dissolved Tin is mostly segregated around phase interface by trapping vacancies. Kinetics of precipitation, size and distribution of the precipitates, concentration of the species in precipitates and matrix are studied where it is revealed that Lifshits-Slyozov-Wagner distribution can be used to predicate statistical properties of precipitates. Mechanical response including the plastic deformations in precipitated solid is discussed. It is shown that yield strength change increases during precipitation. Yield and ultimate stresses are studied at different shear rates for the annealed alloy. A transition to plastic flow is described by means of dislocation structure evolution. Formation and growth of slip planes and dislocation loop-precipitate interaction governed by elastic moduli difference is analyzed. It is shown that emergence of dislocation loops around precipitates follows the Orowan mechanism.

Aiming at the problem that medical image information is easy to be stolen, tampered and maliciously destroyed in the transmission process, a selective region medical image encryption algorithm based on cascade chaos is proposed. The encryption algorithm consists of two stages: region of interest (ROI) encryption and full image encryption. First, the Cubic map is cascaded with an improved Cosine map. Through the analysis of dynamic characteristics, the cascade map has better chaotic performance than the traditional chaotic systems. The key sequence is generated by the cascade map and the image. Then edge detection is performed on the image to determine ROI. ROI is divided into multiple image blocks, and a new gradient algorithm is used to label the sub-blocks containing important information. A modified two-dimensional Joseph traversal method is used to scramble the positions of pixels in each sub-block, and further modify their pixel values with a round of diffusion. Finally, we use a block V-shape scrambling method to scramble the entire image. The final encrypted image is obtained through a round of bidirectional diffusion of all pixels using chaotic sequences. Simulation results and security analysis show that the algorithm has large key space and sufficient security. It can effectively resist various malicious attacks.

Crystalline alloys of Cu2-Se containing a transition metal, earth-abundant and eco-friendly element, are studied in this article as promising eco-friendly thermoelectric materials. Thermoelectric and transport properties of Cu2-xAgxSe (x = 0.00, 0.01, 0.03, 0.05, 0.07) bulk alloys were studied in the temperature range 273-473 K. Crystal structure and surface morphology were tested by X-ray diffraction analysis and scanning electron microscope analyses. Electrical conductivity measurements showed metallic conduction behaviour besides a tremendous decrease in its values with increasing Ag content (x). In contrast, doping increased the Seebeck coefficient to a large extent. Calculations of the electronic thermal conductivity showed that phonon scattering is increased due to the Ag-doping. The incorporation of Ag-atoms resulted in existence of point defects, introduced secondary phases which significantly reduced the thermal conductivity. Such effects resulted in enhanced ZT by the excess Ag-content. The largest ZT value of 0.25 was achieved for x = 0.07 at 473 K, which is about two times of that of the pristine Cu2Se sample. Increasing of the Ag content helps to maintain good TE properties of cubic Cu2-xAgxSe at higher temperatures.

Low-energy electron collisions with normal-pentane (n-C5H12) that initiate the plasma to assist combustion are critical in understanding the underlying physics and chemistries. In the present work, we studied this collisional process using the R-matrix method at the static-exchange plus polarization and close-coupling model levels. The scattering calculation was performed by running the UKRmol+ code using the Quantemol Electron Collision interface to obtain elastic differential, momentum transfer, integral, and electronic excitation cross sections up to 20 eV and ionization cross sections up to 1000 eV. Our computed cross-section data are in better agreement with the available experimental results both regarding the magnitude and shape. We also demonstrated the importance of using a diffuse basis set in describing the scattering due to the Rydberg nature of the lowest unoccupied molecular orbitals of n-C5H12.

The main purpose of this paper is to examine the viable attributes of charged compact stellar objects with anisotropic matter configuration in the framework of $f(\mathcal{R},\mathbf{T}^{2})$ theory. For this purpose, we use Tolman V solution and consider a specific functional form of this modified theory to examine the geometry of compact stars. The values of unknown parameters are found by the smooth matching of interior (static spherical metric) and exterior (modified Reissner-Nordstrom metric) spacetimes. We investigate the behavior of effective matter variables, anisotropy, equation of state parameters and energy bounds in the interior of the charged stellar objects. The stability of the compact stars is examined by speed of sound and adiabatic index. We find that the considered stars are viable as well as stable with all the required conditions in this modified theory of gravity.

A mechanical-thermal-chemical coupled peridynamic (PD) modeling for analyzing the damage and non-shock ignition behavior of polymer bonded explosives (PBXs) subject to impact loading has been presented. The friction and heat conduction and Arrenhenius law are embedded into the PD theory, ensuring that the simulation model is capable of capturing major features of dynamic damage response of PBX. A PD material model considering plasticity and the asymmetric behaviors of PBX under tensile and compressive loadings is proposed in this study. For a ring-shaped PBX 9501 sample confined by the steel structures, the simulation results indicate that the PBX 9501 in the regions towards the impact face and support face suffers from the serious damage. Meanwhile, the corresponding average temperatures in these two regions are also higher than their counterparts in other regions due to the more intense interaction between PBX 9501 and the steel confinement structures. The ignition time decreases with the increasing impact velocity within the range of 40-120 m/s. The internal steel shell response is analyzed according to its velocity history within a representative box. It is found that the deformation process of internal steel shell is closely related to the complicated flow behaviors of PBX 9501.