Related papers: A Calogero-Sutherland Type Model For Branched Poly…
Interactions between active particles may be non-reciprocal, breaking action-reaction symmetry and leading to novel physics not observed in equilibrium systems. The non-reciprocalCahn-Hilliard (NRCH) model is a phenomenological model that…
A nonlocal nonlinear Schr\"odinger equation with focusing nonlinearity is considered which has been derived as a continuum limit of the Calogero-Sutherland model in an integrable classical dynamical system. The equation is shown to stem…
We present a surprising redefinition of matrix fermions which brings the supercharges of the $\cal N$-extended supersymmetric $A_{n-1}$ Calogero model introduced in [1] to the standard form maximally cubic in the fermions. The complexity of…
We study phase transition behavior of the Heisenberg model on a distorted triangular lattice with competing interactions. The ground-state phase diagram indicates that underlying symmetry can be changed by tuning parameters. We focus on two…
The paper presents a model of lateral phase separation in a two component material surface. The resulting fourth order nonlinear PDE can be seen as a Cahn-Hilliard equation posed on a time-dependent surface. Only elementary tangential…
The celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. The…
We review some recent results on how PT-symmetry, that is a simultaneous time-reversal and parity transformation, can be used to construct new integrable models. Some complex valued multi-particle systems, such as deformations of the…
We propose a phenomenological form of the charged lepton mass matrix, which extends the idea of ``lopsided'' mass matrix in the literature. The features of the form are that both the 2-3 and 1-3 elements of the charged lepton mass matrix…
The phase structure of self-avoiding polymerized membranes is studied by extensive Hybrid Monte Carlo simulations. Several folding transitions from the flat to a collapsed state are found. Using a suitable order parameter and finite size…
Nonlinear integrable equations, such as the KdV equation, the Boussinesq equation and the KP equation, have the close relation with many-body problem. The solutions of such equations are the same as the restricted flows of the classical…
The critical behaviour of the $D=0$ matrix model with potential perturbed by nonlocal term generating touchings between random surfaces is studied. It is found that the phase diagram of the model has many features of the phase diagram of…
We investigate the matrix-model origin of the spherical sector of the rational Calogero model and its constants of motion. We develop a diagrammatic technique which allows us to find explicit expressions of the constants of motion and…
Two problems of the Standard Model, associated with the introduction of non-gauge interactions and with the introduction of an electromagnetic field as a linear combination of fields on which various gauge groups are implemented, are…
Many water soluble polymers are chemically modified versions of insoluble base materials such as cellulose. A Flory-Huggins model is solved to determine the effects of heterogeneity in modification on the solubility of such polymers. It is…
The {\sl dressed} Scattering matrix describing scattering of quasiparticles in various models with long-range interactions is evaluated by means of Korepin's method\upref vek1/. For models with ${1\over\sin^2(r)}$-interactions the S-matrix…
We present a theoretical model for predicting the phase behavior of polymer solutions in which phase separation competes with oligomerization. Specifically, we consider scenarios in which the assembly of polymer chains into stoichiometric…
In a previous paper (Corrigan-Sasaki), many remarkable properties of classical Calogero and Sutherland systems at equilibrium are reported. For example, the minimum energies, frequencies of small oscillations and the eigenvalues of Lax pair…
The charged fermion mass matrices are invariant under $U(1)^3$ symmetry linked to the fermion number transformation. Under the condition that the definition of this symmetry in arbitrary weak basis does not depend upon Higgs parameters such…
We propose and solve a simple model describing secondary structure formation in random hetero-polymers. It describes monomers with a combination of one-dimensional short-range interactions (representing steric forces and hydrogen bonds) and…
We study the conformational properties of complex Gaussian polymers containing $f_c$ linear branches and $f_r$ closed loops, periodically tethered at $n$ branching points to either a linear polymer backbone (generalized bottlebrush…