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  • Recursion and Hamiltonian operators for integrable nonabelian difference equations
    Nonlinearity (IF 1.505) Pub Date : 2020-11-13
    Matteo Casati and Jing Ping Wang

    In this paper, we carry out the algebraic study of integrable differential-difference equations whose field variables take values in an associative (but not commutative) algebra. We adapt the Hamiltonian formalism to nonabelian difference Laurent polynomials and describe how to obtain a recursion operator from the Lax representation of an integrable nonabelian differential-difference system. As an

    更新日期:2020-11-13
  • Hyperbolicity of asymmetric lemon billiards
    Nonlinearity (IF 1.505) Pub Date : 2020-11-13
    Xin Jin and Pengfei Zhang

    Asymmetric lemon billiards was introduced in Chen et al (2013 Chaos 23 043137), where the billiard table Q ( r , b , R ) is the intersection of two round disks with radii r ⩽ R , respectively, and b measures the distance between the two centres. It is conjectured Bunimovich et al (2016 Commun. Math. Phys. 341 781–803) that the asymmetric lemon billiards is hyperbolic when the arc Γ r is a major arc

    更新日期:2020-11-13
  • The unique global solvability and optimal time decay rates for a multi-dimensional compressible generic two-fluid model with capillarity effects
    Nonlinearity (IF 1.505) Pub Date : 2020-11-13
    Fuyi Xu and Meiling Chi

    The present paper deals with the Cauchy problem of a compressible generic two-fluid model with capillarity effects in any dimension N ⩾ 2. We first study the unique global solvability of the model in spaces with critical regularity indices with respect to the scaling of the associated equations. Due to the presence of the capillary terms, we exploit the parabolic properties of the linearized system

    更新日期:2020-11-13
  • Extreme value distributions of observation recurrences
    Nonlinearity (IF 1.505) Pub Date : 2020-11-13
    Th Caby, D Faranda, S Vaienti and P Yiou

    We study analytically and numerically the extreme value distribution of observables defined along the temporal evolution of a dynamical system. The convergence to the Gumbel law of observable recurrences gives information on the fractal structure of the image of the invariant measure by the observable. We provide illustrations on idealized and physical systems.

    更新日期:2020-11-13
  • On some rigorous aspects of fragmented condensation
    Nonlinearity (IF 1.505) Pub Date : 2020-11-13
    Daniele Dimonte, Marco Falconi and Alessandro Olgiati

    In this paper we discuss some aspects of fragmented condensation from a mathematical perspective. We first propose a simple way of characterizing finite fragmentation. Then, inspired by recent results of semiclassical analysis applied to bosonic systems with infinitely many degrees of freedom, we address the problem of persistence of fragmented condensation. We show that the latter occurs in interacting

    更新日期:2020-11-13
  • Breather solutions of the cubic Klein–Gordon equation
    Nonlinearity (IF 1.505) Pub Date : 2020-11-11
    Dominic Scheider

    We obtain real-valued, time-periodic and radially symmetric solutions of the cubic Klein–Gordon equation ##IMG## [http://ej.iop.org/images/0951-7715/33/12/7140/nonabb78bieqn8.gif] {${\partial }_{t}^{2}U-{\Delta}U+{m}^{2}U={\Gamma}\left(x\right){U}^{3}\;\text{on}\;\mathbb{R}{\times}{\mathbb{R}}^{3},$} which are weakly localized in space. Various families of such ‘breather’ solutions are shown to bifurcate

    更新日期:2020-11-12
  • On topological classification of Morse–Smale diffeomorphisms on the sphere S n ( n > 3)
    Nonlinearity (IF 1.505) Pub Date : 2020-11-10
    V Grines, E Gurevich, O Pochinka and D Malyshev

    We consider the class G ( S n ) of orientation preserving Morse–Smale diffeomorphisms of the sphere S n of dimension n > 3, assuming that invariant manifolds of different saddle periodic points have no intersection. For any diffeomorphism f ∈ G ( S n ), we define a coloured graph Γ f that describes a mutual arrangement of invariant manifolds of saddle periodic points of the diffeomorphism f . We enrich

    更新日期:2020-11-12
  • On existence and uniqueness of a carrying simplex in Kolmogorov differential systems
    Nonlinearity (IF 1.505) Pub Date : 2020-11-10
    Zhanyuan Hou

    This paper deals with global asymptotic behaviour of the dynamics for N -dimensional competitive Kolmogorov differential systems of equations ##IMG## [http://ej.iop.org/images/0951-7715/33/12/7067/nonabb03cieqn1.gif] {$\frac{\mathrm{d}{x}_{i}}{\mathrm{d}t}={x}_{i}{f}_{i}\left(x\right),\quad 1{\leqslant}i{\leqslant}N,\enspace x\in {\mathbb{R}}_{+}^{N}$} . A theory based on monotone dynamical systems

    更新日期:2020-11-12
  • A nonexistence result for anisotropic problems
    Nonlinearity (IF 1.505) Pub Date : 2020-11-10
    Phuong Le, Kim Anh T Le and Phuoc Vinh Dinh

    We study the anisotropic problem ##IMG## [http://ej.iop.org/images/0951-7715/33/12/7040/nonabaca1ieqn1.gif] {$-\sum _{i=1}^{N}\frac{\partial }{\partial {x}_{i}}\left({\left\vert \frac{\partial u}{\partial {x}_{i}}\right\vert }^{{p}_{i}-2}\frac{\partial u}{\partial {x}_{i}}\right)=wf\left(u\right)\enspace \text{in}\;{\Omega},\enspace u=0\enspace \;\text{on}\;\partial {\Omega},$} where p i ⩾ 2, Ω is

    更新日期:2020-11-12
  • The direct scattering problem for the perturbed Gr(1, 2) ⩾ 0 Kadomtsev–Petviash-vili II solitons
    Nonlinearity (IF 1.505) Pub Date : 2020-10-21
    Derchyi Wu

    Regular Kadomtsev–Petviashvili II (KPII) solitons have been investigated and classified successfully by the Grassmannian. We complete rigorous analysis for the direct scattering problem of perturbed Gr(1, 2) ⩾0 KPII solitons by providing a λ -uniform estimate for the Green function and a Cauchy integral equation with controllable singularities.

    更新日期:2020-11-02
  • Oscillatory orbits in the restricted planar four body problem
    Nonlinearity (IF 1.505) Pub Date : 2020-10-29
    Tere M Seara and Jianlu Zhang

    The restricted planar four body problem describes the motion of a massless body under the Newtonian gravitational force of other three bodies (the primaries), and the motion of the primaries gives us general solutions of the three body problem. A trajectory is called oscillatory if it goes arbitrarily faraway but returns infinitely many times to the same bounded region. We prove the existence of such

    更新日期:2020-10-30
  • The r -Hunter–Saxton equation, smooth and singular solutions and their approximation
    Nonlinearity (IF 1.505) Pub Date : 2020-10-27
    Colin J Cotter, Jacob Deasy and Tristan Pryer

    In this work we introduce the r -Hunter–Saxton equation, a generalisation of the Hunter–Saxton equation arising as extremals of an action principle posed in L r . We characterise solutions to the Cauchy problem, quantifying the blow-up time and studying various symmetry reductions. We construct piecewise linear functions and show that they are weak solutions to the r -Hunter–Saxton equation.

    更新日期:2020-10-30
  • On the differential geometry of numerical schemes and weak solutions of functional equations
    Nonlinearity (IF 1.505) Pub Date : 2020-10-23
    Jean-Pierre Magnot

    We exhibit differential geometric structures that arise in numerical methods, based on the construction of Cauchy sequences, that are currently used to prove explicitly the existence of weak solutions to functional equations. We describe the geometric framework, highlight several examples and describe how two well-known proofs fit with our setting. The first one is a re-interpretation of the classical

    更新日期:2020-10-30
  • The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states
    Nonlinearity (IF 1.505) Pub Date : 2020-10-22
    Grégory Dumont and Pierre Gabriel

    Neural network dynamics emerge from the interaction of spiking cells. One way to formulate the problem is through a theoretical framework inspired by ideas coming from statistical physics, the so-called mean-field theory. In this document, we investigate different issues related to the mean-field description of an excitatory network made up of leaky integrate-and-fire neurons. The description is written

    更新日期:2020-10-30
  • Semiclassical states for Choquard type equations with critical growth: critical frequency case
    Nonlinearity (IF 1.505) Pub Date : 2020-10-22
    Yanheng Ding, Fashun Gao and Minbo Yang

    In this paper we are interested in the existence of semiclassical states for the Choquard type equation ##IMG## [http://ej.iop.org/images/0951-7715/33/12/6695/nonaba88dieqn1.gif] {$-{\varepsilon }^{2}{\Delta}u+V\left(x\right)u=\left({\int }_{{\mathbb{R}}^{N}}\frac{G\left(u\left(y\right)\right)}{{\vert x-y\vert }^{\mu }}\mathrm{d}y\right)g\left(u\right)\text{in}\;{\mathbb{R}}^{N},$} where 0 < μ < N

    更新日期:2020-10-30
  • Existence of stationary stochastic Burgers evolutions on R 2 and R 3
    Nonlinearity (IF 1.505) Pub Date : 2020-10-22
    Alexander Dunlap

    We prove that the stochastic Burgers equation on R d , d < 4, forced by gradient noise that is white in time and smooth in space, admits spacetime-stationary solutions. These solutions are thus the gradients of solutions to the KPZ equation on R d with stationary gradients. The proof works by proving tightness of the time-averaged laws of the solutions in an appropriate weighted space.

    更新日期:2020-10-30
  • Nonradial solutions of nonlinear scalar field equations
    Nonlinearity (IF 1.505) Pub Date : 2020-10-22
    Jarosław Mederski

    We prove new results concerning the nonlinear scalar field equation ##IMG## [http://ej.iop.org/images/0951-7715/33/12/6349/nonaba889ieqn567.gif] {\begin{equation}\quad \quad \quad \quad \quad \begin{cases}-{\Delta}u=g\left(u\right)\quad \hfill & \quad \text{in}\;\;{\mathbb{R}}^{N},\enspace N{\geqslant}3,\hfill \\ u\in {H}^{1}\left({\mathbb{R}}^{N}\right)\quad \hfill & \hfill \end{cases}\end{equation}}

    更新日期:2020-10-30
  • Numerical computations of geometric ergodicity for stochastic dynamics
    Nonlinearity (IF 1.505) Pub Date : 2020-10-22
    Yao Li and Shirou Wang

    A probabilistic approach to compute the geometric convergence rate of a stochastic process is introduced in this paper. The goal is to quantitatively compute both the upper and lower bounds for rate of the exponential convergence to the stationary distribution of a stochastic dynamical system. By applying the coupling method, we derive an algorithm which does not rely on the discretization of the infinitesimal

    更新日期:2020-10-30
  • Hölder regularity and exponential decay of correlations for a class of piecewise partially hyperbolic maps
    Nonlinearity (IF 1.505) Pub Date : 2020-10-21
    Rafael A Bilbao, Ricardo Bioni and Rafael Lucena

    We consider a class of endomorphisms which contains a set of piecewise partially hyperbolic skew-products with a non-uniformly expanding base map. The aimed transformation preserves a foliation which is almost everywhere uniformly contracted with possible discontinuity sets, which are parallel to the contracting direction. We prove that the associated transfer operator, acting on suitable anisotropic

    更新日期:2020-10-30
  • On stationary solutions and inviscid limits for generalized Constantin–Lax–Majda equation with O (1) forcing
    Nonlinearity (IF 1.505) Pub Date : 2020-10-21
    In-Jee Jeong and Sun-Chul Kim

    The generalized Constantin–Lax–Majda (gCLM) equation was introduced to model the competing effects of advection and vortex stretching in hydrodynamics. Recent investigations revealed possible connections with the two-dimensional turbulence. With this connection in mind, we consider the steady problem for the viscous gCLM equations on ##IMG## [http://ej.iop.org/images/0951-7715/33/12/6662/nonaba93eieqn1

    更新日期:2020-10-30
  • Alsedà–Misiurewicz systems with place-dependent probabilities
    Nonlinearity (IF 1.505) Pub Date : 2020-10-11
    Klaudiusz Czudek

    We consider systems of two specific piecewise linear homeomorphisms of the unit interval, so called Alsedà–Misiurewicz systems, and investigate the basic properties of Markov chains which arise when these two transformations are applied randomly with probabilities depending on the point of the interval. Though this iterated function system is not contracting in average and known methods do not apply

    更新日期:2020-10-12
  • Topological Hausdorff dimension of fractal squares and its application to Lipschitz classification
    Nonlinearity (IF 1.505) Pub Date : 2020-10-11
    Ji-hua Ma and Yan-fang Zhang

    We calculate topological Hausdorff dimensions of a class of fractal squares by constructing certain self-similar curves. Examples include some generalized Sierpiński carpets, which have the same Hausdorff dimensions but different topological Hausdorff dimensions. Applications are given to the study of Lipschitz equivalence of fractal squares.

    更新日期:2020-10-12
  • Non-regular g -measures and variable length memory chains
    Nonlinearity (IF 1.505) Pub Date : 2020-10-08
    Ricardo F Ferreira, Sandro Gallo and Frédéric Paccaut

    It is well-known that there always exists at least one stationary measure compatible with a continuous g -function g . Here we prove that if the set of discontinuities of a g -function g has null measure under a candidate measure obtained by some asymptotic procedure, then this candidate measure is compatible with g . We explore several implications of this result, and discuss comparisons with the

    更新日期:2020-10-12
  • Fourier approximation of the statistical properties of Anosov maps on tori
    Nonlinearity (IF 1.505) Pub Date : 2020-10-07
    Harry Crimmins and Gary Froyland

    We study the stability of statistical properties of Anosov maps on tori by examining the stability of the spectrum of an analytically twisted Perron–Frobenius operator on the anisotropic Banach spaces of Gouëzel and Liverani (2006 Ergod. Theor. Dyn. Syst. 26 189–217). By extending our previous work in Crimmins and Froyland (2019 Ann. Henri Poincaré 20 3113–3161), we obtain the stability of various

    更新日期:2020-10-08
  • Nonlinear perturbations of evolution systems in scales of Banach spaces
    Nonlinearity (IF 1.505) Pub Date : 2020-10-07
    Martin Friesen and Oleksandr Kutoviy

    A variant of the abstract Cauchy–Kovalevskaya theorem is considered. We prove existence and uniqueness of classical solutions to the nonlinear, non-autonomous initial value problem ##IMG## [http://ej.iop.org/images/0951-7715/33/11/6134/nonab9dc9ieqn1.gif] {$\frac{\mathrm{d}u\left(t\right)}{\mathrm{d}t}=A\left(t\right)u\left(t\right)+B\left(u\left(t\right),t\right),\enspace u\left(0\right)=x$} in a

    更新日期:2020-10-08
  • Computability at zero temperature
    Nonlinearity (IF 1.505) Pub Date : 2020-10-07
    Michael Burr and Christian Wolf

    We investigate the computability of thermodynamic invariants at zero temperature for one-dimensional subshifts of finite type. In particular, we prove that the residual entropy (i.e., the joint ground state entropy) is an upper semi-computable function on the space of continuous potentials, but it is not computable. Next, we consider locally constant potentials for which the zero-temperature measure

    更新日期:2020-10-08
  • On the smallness condition in linear inviscid damping: monotonicity and resonance chains
    Nonlinearity (IF 1.505) Pub Date : 2020-10-07
    Yu Deng and Christian Zillinger

    We consider the effects of mixing by smooth bilipschitz shear flows in the linearized Euler equations on ##IMG## [http://ej.iop.org/images/0951-7715/33/11/6176/nonaba236ieqn1.gif] {${\mathbb{T}}_{L}{\times}\mathbb{R}$} . Here, we construct a model which is closely related to a small high frequency perturbation around Couette flow, which exhibits linear inviscid damping for L sufficiently small, but

    更新日期:2020-10-08
  • Completely degenerate responsive tori in Hamiltonian systems
    Nonlinearity (IF 1.505) Pub Date : 2020-10-07
    Wen Si and Yingfei Yi

    We consider the existence of responsive tori for the completely degenerate Hamiltonian system with the following Hamiltonian ##IMG## [http://ej.iop.org/images/0951-7715/33/11/6072/nonaba093ieqn1.gif] {$H\left(\theta ,I,x,y,{\epsilon}\right)=\langle \omega ,I\rangle +\lambda \frac{{x}^{n}}{n}+\frac{{y}^{m}}{m}+{\epsilon}P\left(\theta ,x,y,{\epsilon}\right),\enspace \left(\theta ,I,x,y\right)\in {\m

    更新日期:2020-10-08
  • Numerical simulations for the energy-supercritical nonlinear wave equation
    Nonlinearity (IF 1.505) Pub Date : 2020-10-07
    Jason Murphy and Yanzhi Zhang

    We carry out numerical simulations of the defocusing energy-supercritical nonlinear wave equation for a range of spherically-symmetric initial conditions. We demonstrate numerically that the critical Sobolev norm of solutions remains bounded in time. This lends support to conditional scattering results that have been recently established for nonlinear wave equations.

    更新日期:2020-10-08
  • Global existence and blow-up of solutions to a nonlocal Kirchhoff diffusion problem
    Nonlinearity (IF 1.505) Pub Date : 2020-10-07
    Hang Ding and Jun Zhou

    In this paper, we revisit the following nonlocal Kirchhoff diffusion problem:∂tu+M([u]s2)LKu=|u|p−2u,inΩ×R+,u(x,t)=0,in(RN\Ω)×R+,u(x,0)=u0(x),inΩ,where ##IMG## [http://ej.iop.org/images/0951-7715/33/11/6099/nonab9f84ieqn2.gif] {${\Omega}\subset {\mathbb{R}}^{N}$} is a bounded domain with Lipschitz boundary, [ u ] s is the Gagliardo seminorm of u , 0 < s < min{1, N /2}, ##IMG## [http://ej.iop.org/i

    更新日期:2020-10-08
  • Energy asymptotics of a Dirichlet to Neumann problem related to water waves
    Nonlinearity (IF 1.505) Pub Date : 2020-10-06
    Pietro Miraglio and Enrico Valdinoci

    We consider a Dirichlet to Neumann operator ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5997/nonab9dcbieqn1.gif] {${\mathcal{L}}_{a}$} arising in a model for water waves, with a nonlocal parameter a ∈ (−1, 1). We deduce the expression of the operator in terms of the Fourier transform, highlighting a local behaviour for small frequencies and a nonlocal behaviour for large frequencies. We further

    更新日期:2020-10-07
  • On the directional derivative of the Hausdorff dimension of quadratic polynomial Julia sets at 1/4
    Nonlinearity (IF 1.505) Pub Date : 2020-10-06
    Ludwik Jaksztas

    Let d ( ɛ ) and ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5919/nonab9a1aieqn1.gif] {$\mathcal{D}\left(\delta \right)$} denote the Hausdorff dimension of the Julia sets of the polynomials p ɛ ( z ) = z 2 + 1/4 + ɛ and f δ ( z ) = (1 + δ ) z + z 2 respectively. In this paper we will study the directional derivative of the functions d ( ɛ ) and ##IMG## [http://ej.iop.org/images/0951-7715/33/1

    更新日期:2020-10-07
  • Linear relations for Laurent polynomials and lattice equations
    Nonlinearity (IF 1.505) Pub Date : 2020-10-06
    Andrew N W Hone and Joe Pallister

    A recurrence relation is said to have the Laurent property if all of its iterates are Laurent polynomials in the initial values with integer coefficients. Recurrences with this property appear in diverse areas of mathematics and physics, ranging from Lie theory and supersymmetric gauge theories to Teichmüller theory and dimer models. In many cases where such recurrences appear, there is a common structural

    更新日期:2020-10-07
  • Synchronization of Kuramoto oscillators in dense networks
    Nonlinearity (IF 1.505) Pub Date : 2020-10-04
    Jianfeng Lu and Stefan Steinerberger

    We study synchronization properties of systems of Kuramoto oscillators. The problem can also be understood as a question about the properties of an energy landscape created by a graph. More formally, let G = ( V , E ) be a connected graph and ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5905/nonab9baaieqn1.gif] {${\left({a}_{ij}\right)}_{i,j=1}^{n}$} denotes its adjacency matrix. Let the function

    更新日期:2020-10-05
  • Crossing periodic orbits of nonsmooth Liénard systems and applications
    Nonlinearity (IF 1.505) Pub Date : 2020-10-04
    Tao Li, Hebai Chen and Xingwu Chen

    Continuing the investigation for the number of crossing periodic orbits of nonsmooth Liénard systems in (2008 Nonlinearity 21 2121–42) for the case of a unique equilibrium, in this paper we allow the considered system to have one or multiple equilibria. By constructing two control functions that are decreasing in a much narrower interval than the one used in the above work in the estimate of divergence

    更新日期:2020-10-05
  • Asymptotic analysis of selection-mutation models in the presence of multiple fitness peaks
    Nonlinearity (IF 1.505) Pub Date : 2020-10-04
    Tommaso Lorenzi and Camille Pouchol

    We study the long-time behaviour of phenotype-structured models describing the evolutionary dynamics of asexual populations whose phenotypic fitness landscape is characterised by multiple peaks. First we consider the case where phenotypic changes do not occur, and then we include the effect of heritable phenotypic changes. In the former case the model is formulated as an integrodifferential equation

    更新日期:2020-10-05
  • On omega limiting sets of infinite dimensional Volterra operators
    Nonlinearity (IF 1.505) Pub Date : 2020-09-30
    Farrukh Mukhamedov, Otabek Khakimov and Ahmad Fadillah Embong

    In the present paper, we are aiming to study limiting behaviour of infinite dimensional Volterra operators. We introduce two classes ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5875/nonab9a1cieqn1.gif] {${\tilde {\mathcal{V}}}^{+}$} and ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5875/nonab9a1cieqn2.gif] {${\tilde {\mathcal{V}}}^{-}$} of infinite dimensional Volterra operators. For operators

    更新日期:2020-10-02
  • Large deviations for denominators of continued fractions
    Nonlinearity (IF 1.505) Pub Date : 2020-09-30
    Hiroki Takahasi

    We give exponential upper bounds on the probability with which the denominator of the n th convergent in the regular continued fraction expansion stays away from the mean ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5861/nonab9a1dieqn1.gif] {$\frac{n{\pi }^{2}}{12\enspace \mathrm{log}\enspace 2}$} . The exponential rate is best possible, given by an analytic function related to the dimension spectrum

    更新日期:2020-10-02
  • Dynamics of a chemostat with periodic nutrient supply and delay in the growth
    Nonlinearity (IF 1.505) Pub Date : 2020-09-30
    Pablo Amster, Gonzalo Robledo and Daniel Sepúlveda

    This paper introduces a new consideration in the well known chemostat model of a one-species with a periodic input of single nutrient with period ω , which is described by a system of differential delay equations. The delay represents the interval time between the consumption of nutrient and its metabolization by the microbial species. We obtain a necessary and sufficient condition ensuring the existence

    更新日期:2020-10-02
  • A proof of unlimited multistability for phosphorylation cycles
    Nonlinearity (IF 1.505) Pub Date : 2020-09-29
    Elisenda Feliu, Alan D Rendall and Carsten Wiuf

    The multiple futile cycle is a phosphorylation system in which a molecular substrate might be phosphorylated sequentially n times by means of an enzymatic mechanism. The system has been studied mathematically using reaction network theory and ordinary differential equations. It is known that the system might have at least as many as ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5629/nonab9a1eieqn1

    更新日期:2020-09-30
  • Schmidt’s game and nonuniformly expanding interval maps
    Nonlinearity (IF 1.505) Pub Date : 2020-09-29
    Jason Duvall

    We study a class of nonuniformly expanding interval maps with a neutral fixed point at 0, a class that includes Manneville–Pomeau maps. We prove that the set of points whose forward orbits miss an interval with left endpoint 0 is strong winning for Schmidt’s game. Strong winning sets are dense, have full Hausdorff dimension, and satisfy a countable intersection property. Similar results were known

    更新日期:2020-09-30
  • Variance reduction for effective energies of random lattices in the Thomas–Fermi–von Weizsäcker model
    Nonlinearity (IF 1.505) Pub Date : 2020-09-29
    Julian Fischer and Michael Kniely

    In the computation of the material properties of random alloys, the method of ‘special quasirandom structures’ attempts to approximate the properties of the alloy on a finite volume with higher accuracy by replicating certain statistics of the random atomic lattice in the finite volume as accurately as possible. In the present work, we provide a rigorous justification for a variant of this method in

    更新日期:2020-09-30
  • Micropolar meets Newtonian in 3D. The Rayleigh–Bénard problem for large Prandtl numbers
    Nonlinearity (IF 1.505) Pub Date : 2020-09-29
    Piotr Kalita and Grzegorz Łukaszewicz

    We consider the Rayleigh–Bénard problem for the three-dimensional Boussinesq system for the micropolar fluid. We introduce the notion of the multivalued eventual semiflow and prove the existence of the two-space global attractor ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5686/nonab9729ieqn1.gif] {${\mathcal{A}}^{K}$} corresponding to weak solutions, for every micropolar parameter K ⩾ 0 denoting

    更新日期:2020-09-30
  • Transfer operator approach to ray-tracing in circular domains
    Nonlinearity (IF 1.505) Pub Date : 2020-09-29
    J Slipantschuk, M Richter, D J Chappell, G Tanner, W Just and O F Bandtlow

    The computation of wave-energy distributions in the mid-to-high frequency regime can be reduced to ray-tracing calculations. Solving the ray-tracing problem in terms of an operator equation for the energy density leads to an inhomogeneous equation which involves a Perron–Frobenius operator defined on a suitable Sobolev space. Even for fairly simple geometries, let alone realistic scenarios such as

    更新日期:2020-09-30
  • On the determination of ischemic regions in the monodomain model of cardiac electrophysiology from boundary measurements
    Nonlinearity (IF 1.505) Pub Date : 2020-09-29
    Elena Beretta, Cecilia Cavaterra and Luca Ratti

    In this paper we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the model we determine an asymptotic expansion of the perturbed potential due to the presence of small conductivity inhomogeneities (modelling small ischemic regions in the cardiac tissue) and use it to detect the anomalies from partial boundary measurements. This is done by determining

    更新日期:2020-09-30
  • Stationary shock-like transition fronts in dispersive systems
    Nonlinearity (IF 1.505) Pub Date : 2020-09-21
    Sergey Gavrilyuk, Boniface Nkonga, Keh-Ming Shyue and Lev Truskinovsky

    We show that, contrary to popular belief, lower order dispersive regularization of hyperbolic systems does not exclude the development of the localized shock-like transition fronts. To guide the numerical search of such solutions, we generalize Rankine–Hugoniot relations to cover the case of higher order dispersive discontinuities and study their properties in an idealized case of a transition between

    更新日期:2020-09-22
  • Homogenization of biomechanical models of plant tissues with randomly distributed cells
    Nonlinearity (IF 1.505) Pub Date : 2020-09-17
    Andrey Piatnitski and Mariya Ptashnyk

    In this paper homogenization of a mathematical model for biomechanics of a plant tissue with randomly distributed cells is considered. Mechanical properties of a plant tissue are modelled by a strongly coupled system of reaction-diffusion-convection equations for chemical processes in plant cells and cell walls, the equations of poroelasticity for elastic deformations of plant cell walls and middle

    更新日期:2020-09-20
  • Mean convergence for intermediately trimmed Birkhoff sums of observables with regularly varying tails
    Nonlinearity (IF 1.505) Pub Date : 2020-09-17
    Marc Kesseböhmer and Tanja I Schindler

    On a measure theoretical dynamical system with spectral gap property we consider non-integrable observables with regularly varying tails. Under a mild mixing condition we show that the appropriately normed and trimmed sum process of these observables then converges in mean. This result is new also for the special case of i.i.d. random variables and contrasts the general case where mean convergence

    更新日期:2020-09-20
  • No solitary waves in 2D gravity and capillary waves in deep water
    Nonlinearity (IF 1.505) Pub Date : 2020-09-15
    Mihaela Ifrim and Daniel Tataru

    A fundamental question in the study of water waves is the existence and stability of solitary waves. Solitary waves have been proved to exist and have been studied in many interesting situations, and often arise from the balance of different forces/factors influencing the fluid dynamics, e.g. gravity, surface tension or the fluid bottom. However, the existence of solitary waves has remained an open

    更新日期:2020-09-16
  • Well-posedness of the nonlinear Schrödinger equation on the half-plane
    Nonlinearity (IF 1.505) Pub Date : 2020-09-15
    A Alexandrou Himonas and Dionyssios Mantzavinos

    The initial-boundary value problem (ibvp) for the nonlinear Schrödinger (NLS) equation on the half-plane with nonzero boundary data is studied by advancing a novel approach recently developed for the well-posedness of the cubic NLS equation on the half-line, which takes advantage of the solution formula produced via the unified transform of Fokas for the associated linear ibvp. For initial data in

    更新日期:2020-09-16
  • Madelung transform and probability densities in hybrid quantum–classical dynamics
    Nonlinearity (IF 1.505) Pub Date : 2020-09-03
    François Gay-Balmaz and Cesare Tronci

    This paper extends the Madelung–Bohm formulation of quantum mechanics to describe the time-reversible interaction of classical and quantum systems. The symplectic geometry of the Madelung transform leads to identifying hybrid quantum–classical Lagrangian paths extending the Bohmian trajectories from standard quantum theory. As the classical symplectic form is no longer preserved, the nontrivial evolution

    更新日期:2020-09-05
  • On moving hypersurfaces and the discontinuous ODE-system associated with two-phase flows
    Nonlinearity (IF 1.505) Pub Date : 2020-09-03
    Dieter Bothe

    We consider the initial value problem ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5425/nonab987dieqn1.gif] {$\dot {x}\left(t\right)=v\left(t,x\left(t\right)\right)\;\text{for}\,\;t\in \left(a,b\right),x\left({t}_{0}\right)={x}_{0}$} which determines the pathlines of a two-phase flow, i.e. v = v ( t , x ) is a given velocity field of the type ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5425/nonab987dieqn2

    更新日期:2020-09-05
  • Dimension of Gibbs measures with infinite entropy
    Nonlinearity (IF 1.505) Pub Date : 2020-09-03
    Felipe Pérez Pereira

    We study the Hausdorff dimension of Gibbs measures with infinite entropy with respect to maps of the interval with countably many branches. We show that under simple conditions, such measures are symbolic-exact dimensional, and provide an almost sure value for the symbolic dimension. We also show that the lower local dimension dimension is almost surely equal to zero, while the upper local dimension

    更新日期:2020-09-05
  • A sufficient and necessary condition of PS-ergodicity of periodic measures and generated ergodic upper expectations
    Nonlinearity (IF 1.505) Pub Date : 2020-09-03
    Chunrong Feng, Baoyou Qu and Huaizhong Zhao

    This paper contains two parts. In the first part, we study the ergodicity of periodic measures of random dynamical systems on a separable Banach space. We obtain that the periodic measure of the continuous time skew-product dynamical system generated by a random periodic path is ergodic if and only if the underlying noise metric dynamical system at discrete time of integral multiples of the period

    更新日期:2020-09-05
  • Local well-posedness of the topological Euler alignment models of collective behavior
    Nonlinearity (IF 1.505) Pub Date : 2020-09-02
    David N Reynolds and Roman Shvydkoy

    In this paper we address the problem of well-posedness of multi-dimensional topological Euler-alignment models introduced by Roman and Tadmor (2018 arXiv:1806.01371). The main result demonstrates local existence and uniqueness of classical solutions in class ( ρ , u ) ∈ H m + α × H m +1 on the periodic domain ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5176/nonab9497ieqn1.gif] {${\mathbb{T}}^{n}$}

    更新日期:2020-09-03
  • Global regularity for solutions of the three dimensional Navier–Stokes equation with almost two dimensional initial data
    Nonlinearity (IF 1.505) Pub Date : 2020-09-02
    Evan Miller

    In this paper, we will prove a new result that guarantees the global existence of solutions to the Navier–Stokes equation in three dimensions when the initial data is sufficiently close to being two dimensional. This result interpolates between the global existence of smooth solutions for the two dimensional Navier–Stokes equation with arbitrarily large initial data, and the global existence of smooth

    更新日期:2020-09-03
  • Vortex lattice solutions of the ZHK Chern–Simons equations
    Nonlinearity (IF 1.505) Pub Date : 2020-09-02
    K Rajaratnam and I M Sigal

    We consider the non-relativistic Chern–Simons equations proposed by Zhang, Hansen and Kivelson as the mean field theory of the fractional Hall effect. We prove the existence of the vortex lattice solutions (i.e. solution with lattice symmetry and with topological degree one per lattice cell) similar to the Abrikosov solutions of superconductivity. We derive an asymptotic expression for the energy per

    更新日期:2020-09-03
  • Large time asymptotics for the cylindrical Korteweg–de Vries equation. I.
    Nonlinearity (IF 1.505) Pub Date : 2020-09-02
    A Its and V Sukhanov

    This paper is the first part of our study the asymptotic behavior of the solutions of the cylindrical Korteweg–de Vries equation (cKdV). In this first part, we consider the solutions from Schwarz’s class and calculate the large time asymptotics using the method based on the asymptotic solution of the associated direct scattering problem. This approach was first suggested, in the cases of usual KdV

    更新日期:2020-09-03
  • Construction of nonlinear lattice with potential symmetry for smooth propagation of discrete breather
    Nonlinearity (IF 1.505) Pub Date : 2020-08-26
    Yusuke Doi and Kazuyuki Yoshimura

    We construct a nonlinear lattice that has a particular symmetry in its potential function consisting of long-range pairwise interactions. The symmetry enhances smooth propagation of discrete breathers, and it is defined by an invariance of the potential function with respect to a map acting on the complex normal mode coordinates. Condition of the symmetry is given by a set of algebraic equations with

    更新日期:2020-08-27
  • Boundary-layer profile of a singularly perturbed nonlocal semi-linear problem arising in chemotaxis
    Nonlinearity (IF 1.505) Pub Date : 2020-08-26
    Chiun-Chang Lee, Zhi-An Wang and Wen Yang

    This paper is concerned with the stationary problem of an aero-taxis system with physical boundary conditions proposed by Tuval et al (2005 Proc. Natl Acad. Sci . 102 2277–82) to describe the boundary layer formation in the air–fluid interface in any dimensions. By considering a special case where fluid is free, the stationary problem is essentially reduced to a singularly perturbed nonlocal semi-linear

    更新日期:2020-08-27
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