• 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
• 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
• 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
• 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
• 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
• 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 • 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 • 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 • 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 • 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 • 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 • 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
• 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
• 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
• 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
• 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
• 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
• 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
• Nonlinearity (IF 1.729) Pub Date : 2020-04-16

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] {$\begin{cases}-{\Delta}u={\vert x\vert }^{\alpha }f\left(u\right)\quad 更新日期：2020-04-16 • Nonlinearity (IF 1.729) Pub Date : 2020-04-16 Lijun Wei and Xiang Zhang For a planar analytic near-Hamiltonian system, whose unperturbed system has a family of periodic orbits filling a period annulus with the inner boundary an elementary centre and the outer boundary a homoclinic loop through a nilpotent singularity of arbitrary order, we characterize the coefficients of the terms with degree greater than or equal to 2 in the expansion of the first order Melnikov function 更新日期：2020-04-16 • Nonlinearity (IF 1.729) Pub Date : 2020-04-16 Kristian Bjerklöv We show that the quasi-periodic Schrödinger cocycle with a continuous potential is of parabolic type, with a unique invariant section, at all gap edges where the Lyapunov exponent vanishes. This applies, in particular, to the almost Mathieu equation with critical coupling. It also provides examples of real-analytic cocycles having a unique invariant section which is not smooth. 更新日期：2020-04-16 • Nonlinearity (IF 1.729) Pub Date : 2020-04-16 Tomasz Jakubowski and Grzegorz Serafin We provide two-sided pointwise estimates and uniform asymptotics of the solutions to the subcritical quasi-geostrophic equation with initial data in ##IMG## [http://ej.iop.org/images/0951-7715/33/6/2686/nonab7637ieqn1.gif] {${L}^{2/\left(\alpha -1\right)}\left({\mathbb{R}}^{2}\right)$} , α ∈ (1, 2). Furthermore, we give an upper bound of a similar type for any derivative of the solutions. Initial data 更新日期：2020-04-16 • Nonlinearity (IF 1.729) Pub Date : 2020-04-16 Fan Lü and Jun Wu Let β > 1 and x ∈ [0, 1) be two real numbers. For any y ∈ [0, 1), the maximal run-length function r x ( y , n ) (with respect to x ) is defined to be the maximal length of the prefix of x ’s β -expansion which appears in the first n digits of y ’s. In this paper, we study the metric properties of the maximal run-length function and apply them to the hitting time, which generalises many known results 更新日期：2020-04-16 • Nonlinearity (IF 1.729) Pub Date : 2020-04-16 Ayreena Bakhtawar, Philip Bos and Mumtaz Hussain In this article we calculate the Hausdorff dimension of the set ##IMG## {$\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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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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