Related papers: Scaling behaviour of two-dimensional polygon model…
We discuss the scaling behaviour of different fermion actions in dynamical simulations of the 2-dimensional massive Schwinger model. We have chosen Wilson, hypercube, twisted mass and overlap fermion actions. As physical observables, the…
I consider ageing behaviour in two exactly solvable reaction-diffusion systems. Ageing exponents and scaling functions are determined. I discuss in particular a case in which the equality of two critical exponents, known from systems with…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
The supersymmetric intertwining relations with second order supercharges allow to investigate new two-dimensional model which is not amenable to standard separation of variables. The corresponding potential being the two-dimensional…
We study two simple modifications of self-avoiding polygons. Osculating polygons are a super-set in which we allow the perimeter of the polygon to touch at a vertex. Neighbour-avoiding polygons are only allowed to have nearest neighbour…
Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…
We construct new solvable rational and trigonometric spin models with near-neighbors interactions by an extension of the Dunkl operator formalism. In the trigonometric case we obtain a finite number of energy levels in the center of mass…
We introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For…
We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously has been found for short-range interactions, this leads to a singular…
We derive the dominant asymptotic form and the order of the correction terms of the finite-perimeter partition function of self-avoiding polygons on the square lattice, which are weighted according to their area A as q^A, in the inflated…
We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution…
We study surface growth models exhibiting anomalous scaling of the local surface fluctuations. An analytical approach to determine the local scaling exponents of continuum growth models is proposed. The method allows to predict when a…
We propose the notion of $E_{2}$-quasi-exact solvability and apply this idea to find explicit solutions to the eigenvalue problem for a non-Hermitian Hamiltonian system depending on two parameters. The model considered reduces to the…
We study a large class of models with an arbitrary (finite) number of degrees of freedom, described by Hamiltonians which are polynomial in bosonic creation and annihilation operators, and including as particular cases n-th harmonic…
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…
In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…
We introduce an algebraic multiscale method for two--dimensional problems. The method uses the generalized multiscale finite element method based on the quadrilateral nonconforming finite element spaces. Differently from the…
There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…
The solution of some equations involving functional derivatives is given as a series indexed by planar binary trees. The terms of the series are given by an explicit recursive formula. Some algebraic properties of these series are…