In this note we study a minimization problem for a vector of measures subject to a prescribed interaction matrix in the presence of external potentials. The conductors are allowed to have zero distance from each other but the external potentials satisfy a growth condition near the common points. We then specialize the setting to a specific problem on the real line which arises in the study of c...

We derive the first nontrivial rigorous bounds on the mean distance between nearest neighbors l in ergodic, isotropic packings of hard D-dimensional spheres that depend on the packing fraction and nearest-neighbor distribution function. Several interesting implications of these bounds for equilibrium as well as nonequilibrium ensembles are explored. For an equilibrium ensemble, we find accurate...

We consider a peer-to-peer electricity market, where agents hold private information that they might not want to share. The problem is modeled as noncooperative communication game, which takes the form of Generalized Nash Equilibrium Problem, determine their randomized reports share with other market players, while anticipating equilibrium. In each agent decides on deterministic and random part...

We consider the statistical mechanics of interfering transmissions in a wireless communications protocol. In this case, a connection between two nodes requires all other nodes within communication distance of the given two nodes to remain quiet on the given channel. This leads to an interesting problem of dimers on a lattice, with a restriction that no two dimers can overlap or be nearest neigh...

We consider the effect of global repulsive coupling on an ensemble of identical excitable elements. An increase of the coupling strength destabilizes the synchronous equilibrium and replaces it with many attracting oscillatory states, created in the transcritical heteroclinic bifurcation. The period of oscillations is inversely proportional to the distance from the critical parameter value. If ...

This paper studies the stability of a finite local public goods economy in horizontal differentiation, where a jurisdiction’s choice of the public good is given by an exogenous decision scheme. In this paper, we characterize the class of decision schemes that ensure the existence of an equilibrium with free mobility (that we call Tiebout equilibrium) for monotone distribution of players. This c...

In this paper, by using Bregman’s technique, we introduce and study the hybrid proximal-point methods for finding a common element of the set of solutions to a system of generalized equilibrium Problems and zeros of a finite family of maximal monotone operators in reflexive Banach spaces. Strong convergence results of the proposed hybrid proximal-point algorithms are also established under some...

Coulomb cluster of dust particles in an RF helium plasma under cryogenic environment is observed experimentally. Background neutral temperature is controlled by cryogenic liquid such as liquid helium or liquid nitrogen. Dust dynamics in a sheath is studied. A dust injected into a sheath moves toward an equilibrium position where the sheath electric force balances with the gravitational force. D...

The equilibrium measure of a compact plane set gives the steady state distribution of charges on the conductor. We show that certain moments of this equilibrium measure, when taken about the electrostatic centroid and depending only on the real coordinate, are extremal for an interval centered at the origin. This has consequences for means of zeros of polynomials, and for means of critical poin...

Blasting is essential for breaking hard rock in opencast mines and tunneling projects. It creates an adverse impact on flyrock. Thus, it to forecast flyrock minimize the environmental effects. The objective of this study forecast/estimate amount produced during blasting by applying three creative composite intelligent models: equilibrium optimizer-coupled extreme learning machine (EO-ELM), part...