相关论文: Variational approach for a class of cooperative sy…

We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…

Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions…

Recent work draws attention to community-community encounters ("coalescence") as likely an important factor shaping natural ecosystems. This work builds on MacArthur's classic model of competitive coexistence to investigate such…

We consider a nonlinear wave equation with nonconstant coefficients. In particular, the coefficient in front of the second order space derivative is degenerate. We give the blow-up behavior and the regularity of the blow-up set. Partial…

We study the reaction-diffusion system, its stationary solutions, the behavior of the system near them and discuss similarities and differences for different boundary conditions.

We study a fuzzy Boltzmann equation, where particles interact via delocalised collisions, in contrast to classical Boltzmann equations. We discuss the existence and uniqueness of solutions and provide a natural variational characterisation…

Collective phenomena in strongly nonequilibrium systems interacting with electromagnetic field are considered. Such systems are described by complicated nonlinear differential or integro-differential equations. The aim of this review is to…

In this paper, we discuss the existence and uniqueness of coexistence states for a class of non-local elliptic system. This problem models the behaviour of a bacteria and a living nutrient, whose diffusion depends on the population of the…

We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase-space, in order to theoretically study the dynamics of quantum accelerator modes. In the simplest case, this involves determining…

We propose an information-theoretic quantifier for the advantage gained from cooperation that captures the degree of dependency between subsystems of a global system. The quantifier is distinct from measures of multipartite correlations…

Nonclassicality cannot be a single-observable property since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior from the joint measurement of…

A class of nonlinear viscous transport equations describing aggregation phenomena in biology is considered. Optimal conditions on an interaction potential are obtained which lead either to the existence or to the nonexistence of…

Experimentally, certain degrees of freedom may appear classical because their quantum fluctuations are smaller than the experimental error associated with measuring them. An approximation to a fully quantum theory is described in which the…

Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence…

We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…

We deal with existence and non-existence of non-negative entire solutions that blow-up at infinity for a quasilinear problem depending on a non-negative real parameter. Our main objectives in this paper are to provide far more general…

The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…

Models and simulations of collective behaviours are often based on considering them as assumed by interactive particle systems. The focus is then on behavioural and interaction rules by using approaches based on artificial agents designed…

Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough…

Cointegration is an important topic for time-series, and describes a relationship between two series in which a linear combination is stationary. Classically, the test for cointegration is based on a two stage process in which first the…