相关论文: Exactly solvable models through the generalized em…

After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of…

We suggest a natural approach that leads to a modification of classical quasispecies models and incorporates the possibility of population extinction in addition to growth. The resulting modified models are called open. Their essential…

We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial…

The Lotka-Volterra (LV) model is a simple, robust, and versatile model used to describe large interacting systems such as food webs or microbiomes. The model consists of $n$ coupled differential equations linking the abundances of $n$…

Reaction-diffusion equations are treated on infinite networks using semigroup methods. To blend high fidelity local analysis with coarse remote modeling, initial data and solutions come from a uniformly closed algebra generated by functions…

Q-conditional (nonclassical) symmetries of the known three-component reaction-diffusion system [K. Aoki et al Theor. Pop. Biol. 50(1) (1996)] modeling interaction between farmers and hunter-gatherers are constructed for the first time. A…

An infinite number of solvable Hamiltonians, including the transverse Ising chain, the XY chain with an external field, the cluster model with next-nearest-neighbor x-x interactions, or with next-nearest-neighbor z-z interactions, and other…

We review the construction of exactly solvable lattice models whose continuum limits are $N=2$ supersymmetric models. Both critical and off-critical models are discussed. The approach we take is to first find lattice models with natural…

This paper concerns the modeling and numerical simulation of the process of speciation. In particular, given conditions for which one or more speciation events within an ecosystem occur, our aim is to develop the necessary modeling and…

Phenotypically structured equations arise in population biology to describe the interaction of species with their environment that brings the nutrients. This interaction usually leads to selection of the fittest individuals. Models used in…

In this work, we introduce long range version of the extended Hubbard model. The system is defined on a non-uniform lattice. We show that the system is integrable. The ground state, the ground state energies, the energy spectrum are also…

Parametrized polynomial ordinary differential equation systems are broadly used for modeling, specially in the study of biochemical reaction networks under the assumption of mass-action kinetics. Understanding the qualitative behavior of…

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…

The study of interactions between multiple species in an ecosystem is an active and impactful direction of inquiry. This is true in particular for fragile systems in which even small perturbations of their functional parameters can produce…

We consider systems of weakly interacting fermions on a lattice. The corresponding free fermionic system is assumed to have a ground state separated by a gap from the rest of the spectrum. We prove that, if both the interaction and the free…

We propose the deterministic rate equation of three-species in the reaction - diffusion system. For this case, our purpose is to carry out the decay process in our three-species reaction-diffusion model of the form $A+B+C\to D$. The…

First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit (but still…

In the context of unitary evolution of a generic quantum system interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus, we adduce a general theoretical…

The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…

We introduce a formalism modelling communication of distributed agents strictly in continuous-time. Within this framework, we study the problem of synthesising local strategies for individual agents such that a specified set of goal states…