Related papers: Phase model expectation values and the 2-Toda hier…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
The pion wave function is discussed in the light of the recent CLEO data on the pion gamma transition form factor. It turns out that the wave function is close to the asymptotic form whereas wave functions strongly concentrated in the…
A model of phase transitions with coupling between the order parameter and its gradient is proposed. It is shown, that this nonlinear model is suitable for the description of phase transitions accompanied by the formation of spatially…
We use a smoothed version of the explicit formula to find an approximation to the Riemann zeta function as a product over its nontrivial zeros multiplied by a product over the primes. We model the first product by characteristic polynomials…
We give the details of the calculation of the spectral functions of the 1D Hubbard model using the spin-charge factorized wave-function for several versions of the U -> +\infty limit. The spectral functions are expressed as a convolution of…
It is proved that the action for nonlinear Beltrami equation (quasiclassical dbar-problem) evaluated on its solution gives a tau-function for dispersionless KP hierarchy. Infinitesimal transformations of tau-function corresponding to…
We consider a spatial functional linear regression, where a scalar response is related to a square integrable spatial functional process. We use a smoothing spline estimator for the functional slope parameter and establish a finite sample…
The construction of a multiresolution analysis starts with specification of a scale function. The Fourier transform of this function is defined by an infinite product. The convergence of this product is usually discussed in the context of…
Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may…
The structure function of a scalar $\theta({\bf x},t)$, passively advected in a two-dimensional turbulent flow ${\bf u}({\bf x},t)$, is discussed by means of the fractal dimension $\delta^{(1)}_g$ of the passive scalar graph. A relation…
Using a Jacobi-Trudi-type identity, we show that the scalar product of a general state and a Bethe eigenstate in a finite-length XXZ spin-1/2 chain is (a restriction of) a KP tau function. This leads to a correspondence between the…
A class of Aubry-Andr\'e-Harper models of spin-orbit coupled electrons exhibits a topological phase diagram where two regions belonging to the same phase are split up by a multicritical point. The critical lines which meet at this point…
Self-regulatory models are common in nature, as described e.g. in (\cite{mur}), (\cite{ha}) and (\cite{Gb}).\\ Let us consider a system made up of a number of glands as a motivation. Each gland secretes a hormone that allows secretion in…
These lectures focus on bifurcation analysis as a tool for studying phase transitions that occur in models of liquid-crystalline systems. We show how this approach bridges the gap between the phenomenological Landau theory and the --- often…
In this paper we present numerical analysis of the phase transition of the area-interaction model, which is a standard model of Statistical Mechanics. The theoretical results are based on a recent paper by Dereudre \& Houdebert…
We consider multi-variable sigma function of a genus $g$ hyperelliptic curve as a function of two group of variables -jacobian variables and parameters of the curve. In the theta-functional representation of sigma-function, the second group…
Our previous work on a hidden integrable structure of the melting crystal model (the U(1) Nekrasov function) is extended to a modified crystal model. As in the previous case, "shift symmetries" of a quantum torus algebra plays a central…
This work deals with the evaluation of the flow curve of colloidal systems that develop fluid phases with different mechanical properties, namely shear-banding fluids. The problem involved is that, as different fluid phases coexist in the…
The stability properties of one-dimensional radiative shocks with a power-law cooling function of the form $\Lambda \propto \rho^2T^\alpha$ are the main subject of this work. The linear analysis originally presented by Chevalier & Imamura,…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…