Related papers: Collective Description in FELWI
Dynamical behaviors of complex interacting systems, including brain activities, financial price movements, and physical collective phenomena, are associated with underlying interactions between the system's components. The issue of…
We first present a general method for extracting collective variables out of non-relativistic fermions by extending the gauge theory of collective coordinates to fermionic systems. We then apply the method to a system of non-interacting…
We investigate a model for collective behaviour with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure solutions (defined via mass transport) on sphere, as well as investigate the mean-field particle…
We here discuss the outcome of an hypothetic experiments of populations dynamics, where a set of independent realizations is made available. The importance of ensemble average is clarified with reference to the registered time evolution of…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
Collective excitations in fermionic systems play a crucial role in determining their physical properties. An important challenge is to develop efficient theoretical approaches for describing these excitations and their coupling to fermionic…
A multicanonical formalism is introduced to describe statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales, where the hierarchical structure is described as a set of nested "internal heat reservoirs"…
We analyze the stability of Maxwell equations in bounded domains taking into account electric and magnetization effects. Well-posedness of the model is obtained by means of semigroup theory. A passitivity assumption guarantees the…
For a multi-component system, general formulas are derived for the dimension of a coexisting region in the phase diagram in various state spaces.
In this communication, the derivation of the Boltzmann-Gibbs and the Maxwellian distributions is presented from a geometrical point of view under the hypothesis of equiprobability. It is shown that both distributions can be obtained by…
We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by…
The emerging collective motions of swarms of interacting agents are a subject of great interest in application areas ranging from biology to physics and robotics. In this paper, we conduct a careful analysis of the collective dynamics of a…
We consider principal properties of various wave regimes in two selected excitable systems with linear cross-diffusion in one spatial dimension observed at different parameter values. This includes fixed-shape propagating waves, envelope…
Particular solutions of the Benney equations are constructed. Their properties are discussed.
We propose a (time) multiscale method for the coarse-grained analysis of self--propelled particle models of swarms comprising a mixture of `na\"{i}ve' and `informed' individuals, used to address questions related to collective motion and…
Extencion of Krein's special method for solving of integral equation to that method for solving of systems of integral equations is established. Generalizations of formulae for solution of integral equations are obtained. The result…
A mathematical framework for the physics of nonequilibrium phenomena is gradually being developed. This review is meant to shed light on some aspects of Response Theory, on the theory of Fluctuation Relations, on the so-called "t-mixing"…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
The dispersive approach to QCD is briefly overviewed and its application to the assessment of hadronic contributions to electroweak observables is discussed.
It is shown in linear approximation that in the case of one-dimensional problem of transverse electron waves in a half-infinite slab of homogeneous Maxwellian collisionless plasma with the given boundary field frequency two wave branches of…