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  • The profile of chiral skyrmions of small radius
    Nonlinearity (IF 1.729) Pub Date : 2020-05-28
    Stavros Komineas, Christof Melcher and Stephanos Venakides

    Chiral skyrmions are stable particle-like solutions of the Landau–Lifshitz equation for ferromagnets with the Dzyaloshinskii–Moriya (DM) interaction, characterized by a topological number. We study the profile of an axially symmetric skyrmion and give exact formulae for the solution of the corresponding far-field and near-field equations, in the asymptotic limit of small DM parameter (alternatively

    更新日期:2020-05-28
  • Nonadditive topological pressure for flows
    Nonlinearity (IF 1.729) Pub Date : 2020-05-28
    Luis Barreira and Carllos Holanda

    We introduce a version of the nonadditive topological pressure for flows and we describe some of its main properties. In particular, we discuss how the nonadditive topological pressure varies with the data and we establish a variational principle in terms of the Kolmogorov–Sinai entropy. We also consider corresponding capacity topological pressures. In the particular case of subadditive families of

    更新日期:2020-05-28
  • Existence of a solution to the stochastic nonlocal Cahn–Hilliard Navier–Stokes model via a splitting-up method
    Nonlinearity (IF 1.729) Pub Date : 2020-05-28
    G Deugoué, B Jidjou Moghomye and T Tachim Medjo

    We consider a stochastic diffuse interface model which describes the motion of an incompressible isothermal mixture of two immiscible fluids under the influence of stochastic external forces in a bounded domain of ##IMG## [http://ej.iop.org/images/0951-7715/33/7/3424/nonab8020ieqn1.gif] {${\mathbb{R}}^{d}$} , d = 2, 3. The model consists of the stochastic Navier–Stokes equations coupled with a nonlocal

    更新日期:2020-05-28
  • Equilibrium states for certain partially hyperbolic attractors
    Nonlinearity (IF 1.729) Pub Date : 2020-05-28
    Todd Fisher and Krerley Oliveira

    We prove that a class of partially hyperbolic attractors introduced by Castro and Nascimento have unique equilibrium states for natural classes of potentials. We also show if the attractors are C 2 and have invariant stable and centre-unstable foliations, then there is a unique equilibrium state for the geometric potential and its 1-parameter family. We do this by applying general techniques developed

    更新日期:2020-05-28
  • Global weak solutions in a three-dimensional degenerate chemotaxis-Navier–Stokes system modeling coral fertilization
    Nonlinearity (IF 1.729) Pub Date : 2020-05-26
    Ji Liu

    In this paper, we study a three-dimensional chemotaxis-Navier–Stokes system which characterizes the fertilization process of coral. It is proved that in the context of the nonlinear diffusion of cells with the index ##IMG## [http://ej.iop.org/images/0951-7715/33/7/3237/nonab834eieqn1.gif] {$m{ >}\frac{10}{9}$} the corresponding initial-boundary problem is globally solvable in the weak sense.

    更新日期:2020-05-26
  • Singular elliptic problems with unbalanced growth and critical exponent
    Nonlinearity (IF 1.729) Pub Date : 2020-05-26
    Deepak Kumar, Vicenţiu D Rădulescu and K Sreenadh

    In this article, we study the existence and multiplicity of solutions of the following ( p , q )-Laplace equation with singular nonlinearity: ##IMG## [http://ej.iop.org/images/0951-7715/33/7/3336/nonab81edieqn1.gif] {$\left\{\begin{aligned}\hfill -{{\Delta}}_{p}u-\beta {{\Delta}}_{q}u& =\lambda {u}^{-\delta }+{u}^{r-1},\quad u{ >}0,\;\;\text{in}\;{\Omega}\hfill \\ \hfill u& =0\quad \;\text{on}\;\partial

    更新日期:2020-05-26
  • Flat trace statistics of the transfer operator of a random partially expanding map
    Nonlinearity (IF 1.729) Pub Date : 2020-05-26
    Luc Gossart

    We consider the skew-product of an expanding map E on the circle ##IMG## [http://ej.iop.org/images/0951-7715/33/7/3303/nonab81efieqn1.gif] {$\mathbb{T}$} with an almost surely ##IMG## [http://ej.iop.org/images/0951-7715/33/7/3303/nonab81efieqn2.gif] {${\mathcal{C}}^{k}$} random perturbation τ = τ 0 + δτ of a deterministic function τ 0 : ##IMG## [http://ej.iop.org/images/0951-7715/33/7/3303/nonab81efueqn1

    更新日期:2020-05-26
  • Global well-posedness for the primitive equations coupled to nonlinear moisture dynamics with phase changes
    Nonlinearity (IF 1.729) Pub Date : 2020-05-26
    Sabine Hittmeir, Rupert Klein, Jinkai Li and Edriss S Titi

    In this work we study the global solvability of the primitive equations for the atmosphere coupled to moisture dynamics with phase changes for warm clouds, where water is present in the form of water vapor and in the liquid state as cloud water and rain water. This moisture model contains closures for the phase changes condensation and evaporation, as well as the processes of auto conversion of cloud

    更新日期:2020-05-26
  • Boundedness for reaction–diffusion systems with Lyapunov functions and intermediate sum conditions
    Nonlinearity (IF 1.729) Pub Date : 2020-05-26
    Jeff Morgan and Bao Quoc Tang

    We study the uniform boundedness of solutions to reaction–diffusion systems possessing a Lyapunov-like function and satisfying an intermediate sum condition . This significantly generalizes the mass dissipation condition in the literature and thus allows the nonlinearities to have arbitrary polynomial growth. We show that two dimensional reaction–diffusion systems, with quadratic intermediate sum conditions

    更新日期:2020-05-26
  • Discontinuous shock solutions of the Whitham modulation equations as zero dispersion limits of traveling waves
    Nonlinearity (IF 1.729) Pub Date : 2020-05-26
    Patrick Sprenger and Mark A Hoefer

    Whitham modulation theory describes the zero dispersion limit of nonlinear disperesive partial differential equations (PDEs) by a system of conservation laws for the parameters of modulated periodic traveling waves (TWs). In this work, admissible, discontinuous, weak solutions of the Whitham modulation equations—termed Whitham shocks —are identified with zero dispersion limits of TW solutions to higher

    更新日期:2020-05-26
  • Dynamics at the threshold for blowup for supercritical wave equations outside a ball
    Nonlinearity (IF 1.729) Pub Date : 2020-05-26
    Piotr Bizoń and Maciej Maliborski

    We consider spherically symmetric supercritical focusing wave equations outside a ball. Using mixed analytical and numerical methods, we show that the threshold for blowup is given by a codimension-one stable manifold of the unique static solution with exactly one unstable direction. We analyse in detail the convergence to this critical solution for initial data fine-tuned to the threshold.

    更新日期:2020-05-26
  • A predator–prey model with taxis mechanisms and stage structure for the predator
    Nonlinearity (IF 1.729) Pub Date : 2020-05-26
    Jianping Wang and Mingxin Wang

    We study the initial-boundary value problem of a predator–prey model with two taxis strategies and stage structure for the predator: ##IMG## [http://ej.iop.org/images/0951-7715/33/7/3134/nonab8692ieqn1.gif] {$\begin{cases}{u}_{t}={d}_{1}{\Delta}u-\chi \nabla \cdot \left(u\nabla w\right)+bv-cu,\hfill & x\in {\Omega},t{ >}0,\hfill \\ {v}_{t}={d}_{2}{\Delta}v-\rho \nabla \cdot \left(v\nabla u\right)+kuw-v

    更新日期:2020-05-26
  • On the rigidity of Zoll magnetic systems on surfaces
    Nonlinearity (IF 1.729) Pub Date : 2020-05-26
    Luca Asselle and Christian Lange

    In this paper we study rigidity aspects of Zoll magnetic systems on closed surfaces. We characterize magnetic systems on surfaces of positive genus given by constant curvature metrics and constant magnetic functions as the only magnetic systems such that the associated Hamiltonian flow is Zoll, i.e. every orbit is closed, on every energy level below the Mañe critical value. We also prove the persistence

    更新日期:2020-05-26
  • Improved regularity for the p -Poisson equation
    Nonlinearity (IF 1.729) Pub Date : 2020-05-11
    Edgard A Pimentel, Giane C Rampasso and Makson S Santos

    In this paper we produce new, optimal, regularity results for the solutions to p -Poisson equations. We argue through a delicate approximation method, under a smallness regime for the exponent p , that imports information from a limiting profile driven by the Laplace operator. Our arguments contain a novelty of technical interest, namely a sequential stability result; it connects the solutions to p

    更新日期:2020-05-11
  • The Rovella attractor is asymptotically sectional-hyperbolic
    Nonlinearity (IF 1.729) Pub Date : 2020-05-11
    B San Martín and K Vivas

    The Rovella attractor is a compact invariant set for a vector field X 0 that mimics the construction of the geometric Lorenz attractor, but considering a central contractive singularity instead of a central expansive one. In this paper we will prove that the Rovella attractor is asymptotically sectional-hyperbolic. Furthermore, it is proved that for a generic two-parameter family of vector fields containing

    更新日期:2020-05-11
  • Velocity decay estimates for Boltzmann equation with hard potentials
    Nonlinearity (IF 1.729) Pub Date : 2020-05-04
    Stephen Cameron and Stanley Snelson

    We establish pointwise polynomial decay estimates in velocity space for the spatially inhomogeneous Boltzmann equation without cutoff, in the case of hard potentials ( γ + 2 s > 2), under the assumption that the mass, energy, and entropy densities are bounded above, and the mass density is bounded below. These estimates are self-generating, i.e. they do not require corresponding decay assumptions on

    更新日期:2020-05-04
  • Γ-convergence of a mean-field model of a chiral doped nematic liquid crystal to the Oseen–Frank description of cholesterics
    Nonlinearity (IF 1.729) Pub Date : 2020-05-04
    Jamie M Taylor

    Systems of elongated molecules, doped with small amounts of molecules lacking mirror symmetry can form macroscopically twisted cholesteric liquid crystal phases. The aim of this work is to rigorously derive the Oseen–Frank model of cholesterics from a more fundamental model concerned with pairwise molecular interactions. A non-local mean-field model of the two-species nematic host/chiral dopant mixture

    更新日期:2020-05-04
  • Intrinsic stability: stability of dynamical networks and switched systems with any type of time-delays
    Nonlinearity (IF 1.729) Pub Date : 2020-04-20
    David Reber and Benjamin Webb

    In real-world networks, interactions between network elements are inherently time-delayed. These time-delays can both slow and destabilize the network, leading to poor performance. However, not all networks can be destabilized by time-delays. Previously, it has been shown that if a network is intrinsically stable, it maintains stability when constant time-delays are introduced. Here we show that intrinsically

    更新日期:2020-04-20
  • On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE’s: II
    Nonlinearity (IF 1.729) Pub Date : 2020-04-16
    Anna Lisa Amadori and Francesca Gladiali

    By using a characterization of the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem given in Amadori A L and Gladiali F (2018 arXiv:1805.04321), we give a lower bound for the Morse index of radial solutions to Hénon type problems ##IMG## [http://ej.iop.org/images/0951-7715/33/6/2541/nonab7639ieqn1.gif] {$\begin{cases}-{\Delta}u={\vert x\vert }^{\alpha }f\left(u\right)\quad

    更新日期:2020-04-16
  • Limit cycles bifurcating from periodic orbits near a centre and a homoclinic loop with a nilpotent singularity of Hamiltonian systems
    Nonlinearity (IF 1.729) Pub Date : 2020-04-16
    Lijun Wei and Xiang Zhang

    For a planar analytic near-Hamiltonian system, whose unperturbed system has a family of periodic orbits filling a period annulus with the inner boundary an elementary centre and the outer boundary a homoclinic loop through a nilpotent singularity of arbitrary order, we characterize the coefficients of the terms with degree greater than or equal to 2 in the expansion of the first order Melnikov function

    更新日期:2020-04-16
  • Some remarks on the dynamics of the almost Mathieu equation at critical coupling
    Nonlinearity (IF 1.729) Pub Date : 2020-04-16
    Kristian Bjerklöv

    We show that the quasi-periodic Schrödinger cocycle with a continuous potential is of parabolic type, with a unique invariant section, at all gap edges where the Lyapunov exponent vanishes. This applies, in particular, to the almost Mathieu equation with critical coupling. It also provides examples of real-analytic cocycles having a unique invariant section which is not smooth.

    更新日期:2020-04-16
  • Uniform pointwise asymptotics of solutions to quasi-geostrophic equation
    Nonlinearity (IF 1.729) Pub Date : 2020-04-16
    Tomasz Jakubowski and Grzegorz Serafin

    We provide two-sided pointwise estimates and uniform asymptotics of the solutions to the subcritical quasi-geostrophic equation with initial data in ##IMG## [http://ej.iop.org/images/0951-7715/33/6/2686/nonab7637ieqn1.gif] {${L}^{2/\left(\alpha -1\right)}\left({\mathbb{R}}^{2}\right)$} , α ∈ (1, 2). Furthermore, we give an upper bound of a similar type for any derivative of the solutions. Initial data

    更新日期:2020-04-16
  • Maximal run-length function for real numbers in beta-dynamical system
    Nonlinearity (IF 1.729) Pub Date : 2020-04-16
    Fan Lü and Jun Wu

    Let β > 1 and x ∈ [0, 1) be two real numbers. For any y ∈ [0, 1), the maximal run-length function r x ( y , n ) (with respect to x ) is defined to be the maximal length of the prefix of x ’s β -expansion which appears in the first n digits of y ’s. In this paper, we study the metric properties of the maximal run-length function and apply them to the hitting time, which generalises many known results

    更新日期:2020-04-16
  • Hausdorff dimension of an exceptional set in the theory of continued fractions
    Nonlinearity (IF 1.729) Pub Date : 2020-04-16
    Ayreena Bakhtawar, Philip Bos and Mumtaz Hussain

    In this article we calculate the Hausdorff dimension of the set ##IMG## {$\mathcal{F}\left({\Phi}\right)=\left\{x\in \left[0,1\right):\begin{array}{c}\hfill {a}_{n+1}\left(x\right){a}_{n}\left(x\right){\geqslant}{\Phi}\left(n\right)\quad \mathrm{f}\mathrm{o}\mathrm{r}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{i}\mathrm{n}\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{e}

    更新日期:2020-04-16
  • Open set condition and pseudo Hausdorff measure of self-affine IFSs
    Nonlinearity (IF 1.729) Pub Date : 2020-04-16
    Xiaoye Fu, Jean-Pierre Gabardo and Hua Qiu

    Let A be an n × n real expanding matrix and ##IMG## [http://ej.iop.org/images/0951-7715/33/6/2592/nonab7725ieqn1.gif] {$\mathcal{D}$} be a finite subset of ##IMG## [http://ej.iop.org/images/0951-7715/33/6/2592/nonab7725ieqn2.gif] {${\mathbb{R}}^{n}$} with ##IMG## [http://ej.iop.org/images/0951-7715/33/6/2592/nonab7725ieqn3.gif] {$0\in \mathcal{D}$} . The family of maps ##IMG## [http://ej.iop.org/i

    更新日期:2020-04-16
  • Spectral stability and semiclassical measures for renormalized KAM systems
    Nonlinearity (IF 1.729) Pub Date : 2020-04-16
    Víctor Arnaiz

    An exact semiclassical version of the classical KAM theorem about small perturbations of vector fields on the torus is given. Moreover, a renormalization theorem based on counterterms for some semiclassical systems that are close to being completely integrable is obtained. We apply these results to characterize the sets of semiclassical measures and quantum limits for sequences of L 2 -eigenfunctions

    更新日期:2020-04-16
  • Transition of blow-up mechanisms in k -equivariant harmonic map heat flow
    Nonlinearity (IF 1.729) Pub Date : 2020-04-13
    Paweł Biernat and Yukihiro Seki

    In the present article, we consider blow-up phenomena appearing in k -equivariant harmonic map heat flow from ##IMG## [http://ej.iop.org/images/0951-7715/33/6/2756/nonab74f4ieqn001.gif] to a unit sphere ##IMG## [http://ej.iop.org/images/0951-7715/33/6/2756/nonab74f4ieqn002.gif] : ##IMG## [http://ej.iop.org/images/0951-7715/33/6/2756/nonab74f4ieqn003.gif] Here the scalar variable u stands for latitudinal

    更新日期:2020-04-13
  • SCALING LIMITS OF A MODEL FOR SELECTION AT TWO SCALES.
    Nonlinearity Pub Date : 2017-09-05
    Shishi Luo,Jonathan C Mattingly

    The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is

    更新日期:2019-11-01
  • The effect of spontaneous curvature on a two-phase vesicle.
    Nonlinearity Pub Date : 2015-06-23
    Geoffrey Cox,John Lowengrub

    Vesicles are membrane-bound structures commonly known for their roles in cellular transport and the shape of a vesicle is determined by its surrounding membrane (lipid bilayer). When the membrane is composed of different lipids, it is natural for the lipids of similar molecular structure to migrate towards one another (via spinodal decomposition), creating a multi-phase vesicle. In this article, we

    更新日期:2019-11-01
  • Ionic Size Effects: Generalized Boltzmann Distributions, Counterion Stratification, and Modified Debye Length.
    Nonlinearity Pub Date : 2014-01-28
    Bo Liu,Pei Liu,Zhenli Xu,Shenggao Zhou

    Near a charged surface, counterions of different valences and sizes cluster; and their concentration profiles stratify. At a distance from such a surface larger than the Debye length, the electric field is screened by counterions. Recent studies by a variational mean-field approach that includes ionic size effects and by Monte Carlo simulations both suggest that the counterion stratification is determined

    更新日期:2019-11-01
  • Yukawa-Field Approximation of Electrostatic Free Energy and Dielectric Boundary Force.
    Nonlinearity Pub Date : 2011-11-01
    Hsiao-Bing Cheng,Li-Tien Cheng,Bo Li

    A Yukawa-field approximation of the electrostatic free energy of a molecular solvation system with an implicit or continuum solvent is constructed. It is argued through the analysis of model molecular systems with spherically symmetric geometries that such an approximation is rational. The construction extends non-trivially that of the Coulomb-field approximation which serves as a basis of the widely

    更新日期:2019-11-01
  • Nonlinear modelling of cancer: bridging the gap between cells and tumours.
    Nonlinearity Pub Date : 2010-09-03
    J S Lowengrub,H B Frieboes,F Jin,Y-L Chuang,X Li,P Macklin,S M Wise,V Cristini

    Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth

    更新日期:2019-11-01
  • A delay model for noise-induced bi-directional switching.
    Nonlinearity Pub Date : 2010-07-02
    Jinzhi Lei,Guowei He,Haoping Liu,Qing Nie

    Many biological systems can switch between two distinct states. Once switched, the system remains stable for a period of time and may switch back to its original state. A gene network with bistability is usually required for the switching and stochastic effect in the gene expression may induce such switching. A typical bistable system allows one-directional switching, in which the switch from the low

    更新日期:2019-11-01
  • Dynamic mechanisms of blood vessel growth.
    Nonlinearity Pub Date : 2006-01-01
    Roeland M H Merks,James A Glazier

    The formation of a polygonal configuration of proto-blood-vessels from initially dispersed cells is the first step in the development of the circulatory system in vertebrates. This initial vascular network later expands to form new blood vessels, primarily via a sprouting mechanism. We review a range of recent results obtained with a Monte Carlo model of chemotactically migrating cells which can explain

    更新日期:2019-11-01
  • A stochastic adding machine and complex dynamics.
    Nonlinearity Pub Date : 2000-11-01
    Peter R Killeen,Thomas J Taylor

    This paper considers properties of a Markov chain on the natural numbers which models a binary adding machine in which there a non-zero probability of failure each time a register attempts to increment the succeeding register and resets. This chain has a family of natural quotient Markov chains, and extends naturally to a chain on the 2-adic integers. The transition operators of these chains have a

    更新日期:2019-11-01
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