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The large-N limit of the two-dimensional non-local U$(N)$ Yang-Mills theory on an orientable and non-orientable surface with boundaries is studied. For the case which the holonomies of the gauge group on the boundaries are near the…
We model the flow of a bi-viscous non-Newtonian fluid in a porous medium by a square lattice where the links obey a piece-wise linear constitutive equation. We find numerically that the flow regime where the network transitions from all…
We study numerically and analytically the behavior of classical Yang-Mills color fields in a random one-dimensional potential described by the Anderson model with disorder. Above a certain threshold the nonlinear interactions of Yang-Mills…
The quantum-mechanical collapse (alias fall onto the center of particles attracted by potential -1/r^2), or "quantum anomaly", is a well-known issue in the quantum theory. We demonstrate that the mean-field repulsive nonlinearity prevents…
We extend our earlier work on anomalies in the space of coupling constants to four-dimensional gauge theories. Pure Yang-Mills theory (without matter) with a simple and simply connected gauge group has a mixed anomaly between its one-form…
Phase separation of sequence-disordered liquid crystalline polymers, a promising class of technological and biological relevance, is studied by field theory, and thermodynamic mechanisms responsible for orientational ordering observed in…
The focusing cubic nonlinear Schr\"odinger equation in two dimensions admits vortex solitons, standing wave solutions with spatial structure, Qm(r,theta) = e^{i m theta} Rm(r). In the case of spin m = 1, we prove there exists a class of…
We report extensive simulation studies of phase behaviour in single component systems of particles interacting via a core-softened interparticle potential. Two recently proposed examples of such potentials are considered; one in which the…
We deal with the large time behavior for a porous medium equation posed in nonhomogeneous media with singular critical density $$ |x|^{-2}\partial_tu(x,t)=\Delta u^m(x,t), \quad (x,t)\in \real^N\times(0,\infty), \ m\geq1, $$ posed in…
We review the role of dual pairs in mechanics and use them to derive particle-like solutions to regularized incompressible fluid systems. In our case we have a dual pair resulting from the action of diffeomorphisms on point particles…
The molecular motion in heterogeneous media displays anomalous diffusion by the mean-squared displacement $\langle X^2(t) \rangle = 2 D t^\alpha$. Motivated by experiments reporting populations of the anomalous diffusion parameters $\alpha$…
A colloidal monolayer embedded in the bulk of a fluid experiences a "compressible", long-range hydrodynamic interaction which, far from boundaries, leads to a breakdown of Fick's law above a well defined length scale, showing up as…
In a recent comment, M. Kosterlitz described how the discrepancy about the lack of broken translational symmetry in two dimensions - doubting the existence of 2D crystals - and the first computer simulations foretelling 2D crystals at least…
We present a numerical study on an interacting monomer-dimer model with nearest neighbor repulsion on a square lattice, which possesses two symmetric absorbing states. The model is observed to exhibit two nearby continuous transitions: the…
We consider certain two-dimensional systems with self--dual points including uniform and disordered $q$-state Potts models. For systems with continuous energy density (such as the disordered versions) it is established that the self--dual…
The impact of polymer-polymer interactions of various types on the thermodynamics, structure, and accommodation of topological constraints is addressed for systems comprising many directed polymers in two spatial dimensions. The approach is…
The large-N limit of the expectation values of the Wilson loops corresponding to two-dimensional U(N) Yang-Mills and generalized Yang-Mills theories on a sphere are studied. The behavior of the expectation values of the Wilson loops both…
In this paper, we discuss a new nonlinear phenomenon. We find that in $n\geq 2$ space dimensions, there exists two indexes $p$ and $q$ such that the cauchy problems for the nonlinear wave equations {equation} \label{0.1} \Box u(t,x) =…
Changing the interactions between particles in an ensemble-by varying the temperature or pressure, for example-can lead to phase transitions whose critical behaviour depends on the collective nature of the many-body system. Despite the…
We study diffusion of colloids on a fluid-fluid interface using particle simulations and fluctuating hydrodynamics. Diffusion on a two-dimensional interface with three-dimensional hydrodynamics is known to be anomalous, with the collective…