The points which converge to ∞ under iteration of the maps z↦λ(z) for λ ∈ C/{0} are investigated. A complete classification such 'escaping points' is given: they organized in form differentiable curves called rays diffeomorphic open intervals, together with endpoints certain (but not all) these rays. Every escaping point either on a ray or endpoint (landing point) ray. This answers special case question Eremenko. combinatorics occurring rays, and them land at points, described exactly. It...

In this paper we discuss the connections between a Vlasov–Fokker–Planck equation and an underlying microscopic particle system, interpret those in context of GENERIC framework (Öttinger 2005 Beyond Equilibrium Thermodynamics (New York: Wiley-Interscience)). This interpretation provides (a) variational formulation for systems, (b) insight into origin formulation, (c) explanation origins conditions that places on its constitutive elements, notably so-called degeneracy or non-interaction...

In recent work [1] we uncovered intriguing connections between Otto's characterisation of diffusion as entropic gradient flow [16] on one hand and large-deviation principles describing the microscopic picture (Brownian motion) other. this paper, sketch connection, show how it generalises to a wider class systems, comment consequences implications. Specifically, connect macroscopic flows with large deviation principles, point out potential bigger emerging: indicate that in some non-...

We discuss a canonical structure that provides unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, and Macroscopic Fluctuation Theory (MFT). For chains, this theory involves non-linear relation between probability currents their conjugate forces. Within framework, we show how the forces can be split into two components, which are orthogonal to each other, in generalised sense. This splitting allows decomposition...

We analyse and interpret the effects of breaking detailed balance on convergence to equilibrium conservative interacting particle systems their hydrodynamic scaling limits. For finite particles, we review existing results showing that irreversible processes converge faster steady state than reversible ones. show how this behaviour appears in limit such processes, as described by macroscopic fluctuation theory, provide a quantitative expression for acceleration setting. give geometrical...

We propose three new discrete variational schemes that capture the conservative-dissipative structure of a generalized Kramers equation. The first two are single-step minimization schemes, whereas third one combines streaming and step. cost functionals in inspired by rate functional Freidlin-Wentzell theory large deviations for underlying stochastic system. prove all converge to solution Copyright © 2013 John Wiley & Sons, Ltd.

The Dean--Kawasaki model consists of a nonlinear stochastic partial differential equation featuring conservative, multiplicative, term with non-Lipschitz coefficient, driven by space-time white noise; this describes the evolution density function for system finitely many particles governed Langevin dynamics. Well-posedness is open except specific diffusive cases, corresponding to overdamped It was recently shown Lehmann, Konarovskyi, and von Renesse that no regular (nonatomic) solutions...

This paper deals with traveling wavefronts for temporally delayed, spatially discrete reaction-diffusion equations. Using a combination of the weighted energy method and Green function technique, we prove that all noncritical are globally exponentially stable, critical algebraically stable when initial perturbations around wavefront decay to zero near minus infinity regardless magnitude time delay.

We investigate the optical and thermal hysteresis of single-domain vanadium dioxide nanocrystals fabricated by ion beam synthesis in a fused silica matrix. The exhibit giant hysteresis, which permits to optically generate long-time stable supercooled metallic phase persistent down practically room temperature. Spatial patterns insulating feature large dielectric contrast, particular, for telecom wavelengths. utilize this contrast imprint reconfigurable photonic elements comprising...

Nonlinear diffusion $\partial_t \rho = \Delta(\Phi(\rho))$ is considered for a class of nonlinearities $\Phi$. It shown that suitable choices $\Phi$, an associated Lyapunov functional can be interpreted as thermodynamics entropy. This information used to derive metric, here called thermodynamic metric. The analysis confined nonlinear obtainable hydrodynamic limit zero range process. setting linked large deviation principle the underlying process and corresponding equation fluctuating...

We propose and implement a new concept for thermochromic plasmonic elements. It is based on vanadium dioxide (VO2) nanocrystals located in the near field of surface plasmon polaritons supported by an otherwise unstructured gold thin film. When VO2 undergoes metal-insulator phase transition, coupling conditions conversion light into propagating change markedly. In particular, we realize grating couplers with substantial switching contrast as well tunable Kretschmann configuration. The use...

The existence of travelling waves in an atomistic model for martensitic phase transitions is the focus this study. elastic energy assumed to be piecewise quadratic, with two wells representing stable phases. We develop a framework such that subsonic heteroclinic bi-infinite chain atoms can proved rigorously. key represent solution as sum (here explicitly given) profile and corrector $L^2(\mathbb{R})$. It demonstrated kinetic relation easily inferred from framework.

Abstract Gas Shielded Tungsten Arc Welding (GTAW) – a process well-known providing highest quality weld results joined though by lower performance. Metal (GMAW) is frequently chosen to increase productivity along with broadly accepted quality. Those industry segments, especially required produce high corrosion resistant surfacing e.g. applying nickel base filler materials, are regularly in consistent demand comply "zero defect" criteria. In this conjunction performance limitations overcome...

Purely dissipative evolution equations are often cast as gradient flow structures, z ̇=K(z)DS(z), where the variable of interest evolves towards maximum a functional S according to metric defined by an operator K. While follows immediately from physical considerations (e.g., thermodynamic entropy), K and associated geometry does not necessarily do so Wasserstein for diffusion). In this paper, we present variational statement in sense entropy production that directly delivers relationship...

Abstract Martensitic transformations with elasto-plastic effects caused by the formation of dislocations in a parent austenite phase are studied using phase-field description. The method presented this paper extends an existing microelastic model for simulation coherent martensitic taking into account dislocation dynamics. Computational results show difference between and partially transformation illuminate on final microstructure. Keywords: dislocationselasticitymodellingphase...

A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The strategy requires system be in local equilibrium and have Gaussian fluctuations but otherwise allowed undergo arbitrary out evolutions. This could potentially relevant for data obtained experimental applications. key idea that finite, yet large, systems formally obey partial differential equations gradient flow type satisfying...

The evolution of finitely many particles obeying Langevin dynamics is described by Dean–Kawasaki equations, a class stochastic equations featuring non-Lipschitz multiplicative noise in divergence form. We derive regularised model based on second order analysing system interacting via pairwise potential. Key tools our analysis are the propagation chaos and Simon's compactness criterion. we obtain small-noise perturbation undamped McKean–Vlasov equation. also provide high-probability result...

We consider the chemical reaction networks and study currents in these systems. Reviewing recent decomposition of rate functionals from large deviation theory for Markov processes, we adapt results networks. In particular, state a suitable generalisation orthogonality forces systems, derive an inequality that bounds free energy loss Fisher information by functional.