Gibbsianness of fermion random point fields

We consider fermion (or determinantal) random point fields on Euclidean space ℝ^d. Given a bounded, translation invariant, and positive definite integral operator J on L²(ℝ^d), we introduce a determinantal interaction for a system of particles moving on ℝ^d as follows: the n points located at x₁,· · ·,x_n ∈ ℝ^d have the potential energy given by where j(x−y) is the integral kernel function of the operator J. We show that the Gibbsian specification for this interaction is well-defined. When J is of finite range in addition, and for d≥2 if the intensity is small enough, we show that the fermion random point field corresponding to the operator J(I+J)⁻¹ is a Gibbs measure admitted to the specification.     

Processus de diffusion associe a certains modeles d'Ising a spins continus

Sans résumé     

Restoration of Gibbsianness for projected and FKG renormalized measures

We restore part of the thermodynamic formalism for some renormalized measures that are known to be non-Gibbsian. We determine a necessary and sufficient condition for consistency with a specification that is quasilocal only in a fixed direction. This condition is then applied to models with FKG monotonicity and to models with appropriate directional continuity rates, in particular to (noisy) decimations or projections of the Ising model. In this way we establish: (i) the validity of the second part of the variational principle for projected and FKG block-renormalized measures, and (ii) the almost quasilocality of FKG block-renormalized + and – measures.     

Floquet operators without singular continuous spectrum

Let U be a unitary operator defined on a infinite-dimensional separable complex Hilbert space H. Assume there exists a self-adjoint operator A on H such that

U^∗AU−A?cI+K     

Coagulation, diffusion and the continuous Smoluchowski equation

The Smoluchowski equations are a system of partial differential equations modelling the diffusion and binary coagulation of a large collection of tiny particles. The mass parameter may be indexed either by positive integers or by positive reals, these corresponding to the discrete or the continuous form of the equations. For dimension d≥3, we derive the continuous Smoluchowski PDE as a kinetic limit of a microscopic model of Brownian particles liable to coalesce, using a method similar to that used to derive the discrete form of the equations in [A. Hammond, F. Rezakhanlou, The kinetic limit of a system of coagulating Brownian particles, Arch. Ration. Mech. Anal. 185 (2007) 1–67]. The principal innovation is a correlation-type bound on particle locations that permits the derivation in the continuous context while simplifying the arguments of the cited work. We also comment on the scaling satisfied by the continuous Smoluchowski PDE, and its potential implications for blow-up of solutions of the equations.     

Topological pressure of continuous flows without fixed points

In this paper, we give the equivalent definitions of topological pressure for flows by using spanning sets, weakly spanning sets, strongly separated sets and tracing sets, respectively. We get an inequality between the topological pressures of Lipschitz conjugate flows, and prove that the topological pressure of expansive flows with tracing property can be described by its periodic orbits.     

Saddle-point optimality criteria of continuous time programming without differentiability

Saddle-point optimality criteria of Kuhn-Tucker and Fritz Johns are established in the case of continuous time programming problems. The functions involved are not assumed to be differentiable. In the process, an important theorem of the alternative is also proven.     

Energy estimates for continuous and discretized electro-reaction–diffusion systems

We consider electro-reaction–diffusion systems consisting of continuity equations for a finite number of species coupled with a Poisson equation. We take into account heterostructures, anisotropic materials and rather general statistic relations.     

A microbial continuous culture system with diffusion and diversified growth

A reaction-diffusion model is presented to describe the microbial continuous culture with diversified growth. The existence of nonnegative solutions and attractors for the system is obtained, the stability of steady states and the steady state bifurcation are studied under three growth conditions. In the case of no growth inhibition or only product inhibition, the system admits one positive constant steady state which is stable; in the case of growth inhibition only by substrate, the system can have two positive constant steady states, explicit conditions of the stability and the steady state bifurcation are also determined. In addition, numerical simulations are given to exhibit the theoretical results.     

Traveling wave fronts of delayed non-local diffusion systems without quasimonotonicity

This paper is concerned with the existence of traveling wave fronts for delayed non-local diffusion systems without quasimonotonicity, which can not be answered by the known results. By using exponential order, upper-lower solutions and Schauder's fixed point theorem, we reduce the existence of monotone traveling wave fronts to the existence of upper-lower solutions without the requirement of monotonicity. To illustrate our results, we establish the existence of traveling wave fronts for two examples which are the delayed non-local diffusion version of the Nicholson's blowflies equation and the Belousov-Zhabotinskii model. These results imply that the traveling wave fronts of the delayed non-local diffusion systems without quasimonotonicity are persistent if the delay is small.     

Optimal equipment replacement without paradoxes: A continuous analysis

Combining known continuous- and discrete-time models of equipment replacement, we show that the optimal equipment lifetime is shorter when the embodied technological change is more intense. The paper has been inspired by a paradox in the equipment replacement raised by Cheevaprawatdomrong and Smith in Oper. Res. Lett. 31 (2003).     

Simulation of the continuous time random walk of the space-fractional diffusion equations

In this article, we discuss the solution of the space-fractional diffusion equation with and without central linear drift in the Fourier domain and show the strong connection between it and the α$\alpha$-stable Lévy distribution, 0<α<2$0<\alpha <2$. We use some relevant transformations of the independent variables x$x$ and t$t$, to find the solution of the space-fractional diffusion equation with central linear drift which is a special form of the space-fractional Fokker–Planck equation which is useful in studying the dynamic behaviour of stochastic differential equations driven by the non-Gaussian (Lévy) noises. We simulate the continuous time random walk of these models by using the Monte Carlo method.     

Heat transfer and turbulent diffusion in one-dimensional hydrodynamics without pressure

A one-dimensional transient non-linear problem of continuum mechanics is considered, the possibility of an accurate analytic solution of which is later based on a general local analysis of singular solutions known as the Painlevé test. For one-dimensional non-linear hydrodynamic models without pressure, with the transfer of a passive impunity, which generalizes the well-known Burgers' model, it is shown that it is possible to reduce the problem to linear problems when the kinetic coefficients (viscosity and thermal conductivity) are equal. Using examples of their accurate solutions, the high sensitivity of the structure of shock waves with impurity fronts to the satisfaction of the law of conservation of impurity in the models is demonstrated. When it is satisfied, each steady propagating shock wave with a viscous structure of the velocity field is accompanied by an impurity soliton. When several such shock waves merge (the accurately solved problem), concentration of the impurity in one overall soliton occurs. It is shown that, when the action of time-dependent Gaussian random forces is taken into account, an additional diffusive spreading of the perturbations, with a time-dependent diffusion coefficient, is superimposed on the linearized viscous behaviour of the main models.     

Local and global strong solutions to continuous coagulation-fragmentation equations with diffusion

We consider the diffusive continuous coagulation-fragmentation equations with and without scattering and show that they admit unique strong solutions for a large class of initial values. If the latter values are small with respect to a suitable norm, we provide sufficient conditions for global-in-time existence in the absence of fragmentation.