Journal of Nonlinear Science最新文献

Abstract

Assessment of the stability/boundedness of solutions to nonlinear systems with variable coefficients brings long-standing and challenging problems which emerge in various application domains. These problems naturally evolved into more arduous and largely open problems concerned with the estimation of the corresponding stability/boundedness regions. This paper develops a novel approach furnishing computationally tractable boundedness/stability criteria which underscores a methodology providing recursive estimation of the boundaries of the trapping/stability regions for a broad class of multidimensional and nonlinear systems with variable nonperiodic coefficients. Furthermore, our approach naturally conveys the bilateral bounds for the norms of solutions to the corresponding systems via the application of successive approximations which are introduced in this paper. The developed techniques are validated in inclusive simulations which endorse their applications to systems with large and complex nonlinear components and bounded in-norm time-varying disturbances.

We study a nonlinear-nudging modification of the Azouani–Olson–Titi continuous data assimilation (downscaling) algorithm for the 2D incompressible Navier–Stokes equations. We give a rigorous proof that the nonlinear-nudging system is globally well posed and, moreover, that its solutions converge to the true solution exponentially fast in time. Furthermore, we also prove that once the error has decreased below a certain order one threshold, the convergence becomes double exponentially fast in time, up until a precision determined by the sparsity of the observed data. In addition, we demonstrate the applicability of the analytical and sharpness of the results computationally.

Abstract

We consider the initial value problem for a two-component Sasa–Satsuma equation associated with a (4times 4) Lax pair with decaying initial data on the line. By utilizing the spectral analysis, the solution of the two-component Sasa–Satsuma system is transformed into the solution of a (4times 4) matrix Riemann–Hilbert problem. Then, the long-time asymptotics of the solution is obtained by means of the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann–Hilbert problems. We show that there are three main regions in the half-plane (-infty<x<infty ) , (t>0) , where the asymptotics has qualitatively different forms: a left fast decaying sector, a central Painlevé sector where the asymptotics is described in terms of the solution to a system of coupled Painlevé II equations, which is related to a (4times 4) matrix Riemann–Hilbert problem, and a right slowly decaying oscillatory sector.

The characterization of the self-supporting slender structure with the furthest length is of interest both from a mechanical and biological point of view. Indeed, from a mechanical perspective, this classical problem was developed and studied with different methods, for example using similarity solutions and stable manifolds. However, none of them led to a complete analytical solution. On the other hand, plant structures such as tree branches or searcher shoots in climbing plants can be considered elastic cantilevered beams. In this paper, we formulate the problem as a non-convex optimisation problem with mixed state constraints. The problem is solved by analysing the corresponding relaxation. With this method, it is possible to obtain an analytical characterization of the cross-section

Divisive Normalization and the Wilson–Cowan equations are well-known influential models of nonlinear neural interaction (Carandini and Heeger in Nat Rev Neurosci 13(1):51, 2012; Wilson and Cowan in Kybernetik 13(2):55, 1973). However, they have been always treated as different approaches and have not been analytically related yet. In this work, we show that Divisive Normalization can be derived from the Wilson–Cowan dynamics. Specifically, assuming that Divisive Normalization is the steady state of the Wilson–Cowan differential equations, we find that the kernel that controls neural interactions in Divisive Normalization depends on the Wilson–Cowan kernel but also depends on the signal. A standard stability analysis of a Wilson–Cowan model with the parameters obtained from our relation shows that the Divisive Normalization solution is a stable node. This stability suggests the appropriateness of our steady state assumption. The proposed theory provides a mechanistic foundation for the suggestions that have been done on the need of signal-dependent Divisive Normalization in Coen-Cagli et al. (PLoS Comput Biol 8(3):e1002405, 2012). Moreover, this theory explains the modifications that had to be introduced ad hoc in Gaussian kernels of Divisive Normalization in Martinez-Garcia et al. (Front Neurosci 13:8, 2019) to reproduce contrast responses in V1 cortex. Finally, the derived relation implies that the Wilson–Cowan dynamics also reproduce visual masking and subjective image distortion, which up to now had been explained mainly via Divisive Normalization.

We consider a viscous incompressible fluid interacting with a linearly elastic shell of Koiter type which is located at some part of the boundary. Recently models with stochastic perturbation in the shell equation have been proposed in the literature but only analysed in simplified cases. We investigate the full model with transport noise, where (a part of) the boundary of the fluid domain is randomly moving in time. We prove the existence of a weak martingale solution to the underlying system.

We describe all metrics geodesically compatible with a (textrm{gl})-regular Nijenhuis operator L. The set of such metrics is large enough so that a generic local curve (gamma ) is a geodesic for a suitable metric g from this set. Next, we show that a certain evolutionary PDE system of hydrodynamic type constructed from L preserves the property of (gamma ) to be a g-geodesic. This implies that every metric g geodesically compatible with L gives us a finite-dimensional reduction of this PDE system. We show that its restriction onto the set of g-geodesics is naturally equivalent to the Poisson action of (mathbb {R}^n) on the cotangent bundle generated by the integrals coming from geodesic compatibility.

This study formulates a host–pathogen model driven by cross-diffusion to examine the effect of chemotaxis on solution dynamics and spatial structures. The negative binomial incidence mechanism is incorporated to illustrate the transmission process by pathogens. In terms of the magnitude of chemotaxis, the global solvability of the model is extensively studied by employing semigroup methods, loop arguments, and energy estimates. In a limiting case, the necessary conditions for chemotaxis-driven instability are established regarding the degree of chemotactic attraction. Spatial aggregation may occur along strong chemotaxis in a two-dimensional domain due to solution explosion. We further observe that spatial segregation appears for short-lived free pathogens in a one-dimensional domain, whereas strong chemotactic repulsion homogenizes the infected hosts and thus fails to segregate host groups effectively.

Abstract

A single hydrodynamic vortex on a surface will in general move unless its Riemannian metric is a special “Steady Vortex Metric” (SVM). Metrics of constant curvature are SVM only in surfaces of genus zero and one. In this paper:

1. I show that K. Okikiolu’s work on the regularization of the spectral zeta function leads to the conclusion that each conformal class of every compact surface with a genus of two or more possesses at least one steady vortex metric (SVM).

2. I apply a probabilistic interpretation of the regularized zeta function for surfaces, as developed by P. G. Doyle and J. Steiner, to extend the concept of SVM to higher dimensions.

Background: We aim to explore the effect of the score for the targeting of atrial fibrillation (STAF) combined with the serum D-dimer (DD) level in screening acute ischemic stroke patients with atrial fibrillation (AF).

Methods: This study is a retrospective case observation study. This study consecutively selected patients with acute ischemic stroke who were hospitalized in the Department of Neurology at Zhuhai Hospital Affiliated with Jinan University from February 2019 to February 2021. Venous blood was drawn from all patients within 24 hours of hospitalization for DD detection. In accordance with the medical records, the patients were classified into an AF group and a non-AF group and were scored according to the STAF standard. A combined test method was used to estimate the diagnostic screening value of the STAF combined with the DD value for acute ischemic stroke patients with AF.