In nonlinear matrix models, strong Allee effects typically arise when the fundamental bifurcation of positive equilibria from the extinction equilibrium at r=1 (or R0=1) is backward. This occurs when positive feedback (component Allee) effects are dominant at low densities and negative feedback effects are dominant at high densities. This scenario allows population survival when r (or equivalen...

We develop a new perturbative method for studying any steady states of quantum impurities, in or out of equilibrium. We show that steady-state averages are completely fixed by basic properties of the steady-state (Hershfield's) density matrix along with dynamical "impurity conditions." This gives the full perturbative expansion without Feynman diagrams (matrix products instead are used), and "r...

We study an evolutionary language game that describes how signals become associated with meaning. In our context, a language, L, is described by two matrices: the P matrix contains the probabilities that for a speaker certain objects are associated with certain signals, while the Q matrix contains the probabilities that for a listener certain signals are associated with certain objects. We defi...

Introduction: Molecular interactions between glycosaminoglycans (GAGs) affect the behavior of extracellular matrix in health and disease. However, their heterogeneous composition, distribution, and physical-chemical properties complicate their characterization in situ. Here we present a new approach to measuring intermolecular electrostatic repulsive forces between GAGs (and between other matri...

There is a classical technique for determining the equilibrium probabilities of M/G/1 type Markov chains. After transforming the equilibrium balance equations of the chain, one obtains an equivalent system of equations in analytic functions to be solved. This method requires nding all singularities of a given matrix function in the unit disk and then using them to obtain a set of linear equatio...

We consider the Laplacian of a finite network as a kernel on the vertex set. The properties of this kernel allow us to assign to every proper set an equilibrium measure and a capacity. So, we can build a discrete Potential Theory with respect to the Laplacian kernel on networks. We aim here at showing how equilibrium measures can be used to obtain simple expressions for both Poisson and Green k...

The R-matrix method is used to study electron collisions with the BeH molecular ion. The diatomic version of the UK Molecular R-matrix codes is used and a configuration-interaction calculation is first performed for the BeH target to obtain its potential energy curves for 19 lowest singlet and triplet states. Scattering calculations are then done to yield excitation and rotational excitation cr...

The second entropy theory for nonequilibrium thermodynamics is extended to the nonlinear regime and to systems of mixed parity (even and odd functions of molecular velocities). The steady state phase space probability density is given for systems of mixed parity. The nonlinear transport matrix is obtained and it is shown to yield the analog of the linear Onsager-Casimir reciprocal relations. It...

The spectral fluctuations of quantum (or wave) systems with a chaotic classical (or ray) limit are mostly universal and faithful to random-matrix theory. Taking up ideas of Pechukas and Yukawa we show that equilibrium statistical mechanics for the fictitious gas of particles associated with the parametric motion of levels yields spectral fluctuations of the random-matrix type. Previously known ...

We consider the two matrix model with an even quartic potential W (y) = y/4+αy/2 and an even polynomial potential V (x). The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices M1. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and ...