In this paper, we define energy-momentum density as a product of the complex vector electromagnetic field and its complex conjugate. We derive an equation for the spacetime derivative of the energy-momentum density. We show that the scalar and vector parts of this equation are the differential conservation laws for energy and momentum, and the imaginary vector part is a relation for the curl of...

A. B. Balantekin, J. H. de Jesus, and Y. Pehlivan Department of Physics, University of Wisconsin Madison, Wisconsin 53706 USA (Dated: February 20, 2007) We apply the algebraic Bethe ansatz technique to the nuclear pairing problem with orbit dependent coupling constants and degenerate single particle energy levels. We find the exact energies and eigenstates. We show that for a given shell, there...

in this paper, a rectangular sandwich plate with a constrained layer and an electrorheological (er) fluid core is investigated. the rectangular plate is covered an er fluid core and a constraining layer to improve the stability of the system. the two outer layers of the sandwich structure are elastic. the viscoelastic materials express the middle layer behavior under electric field and small st...

The loop equations for a chain of hermitian random matrices are computed explicitely, including the 1/N2 corrections. To leading order, the master loop equation reduces to an algebraic equation, whose solution can be written in terms of geometric properties of the underlying algebraic curve. In particular we compute the free energy, the resolvents, the 2-loop functions and some mixed one loop f...

We perform a study of cosmic evolution with an equation of state parameter ω(t) = ω0 + ω1(tḢ/H) by selecting a phenomenological Λ model of the form, Λ̇ ∼ H. This simple proposition explains both linearly expanding and inflationary Universes with a single set of equations. We notice that the inflation leads to a scaling in the equation of state parameter, ω(t), and hence in equation of state. In ...

We study the spectrum of the Salpeter Hamiltonian H = β √ m2 + p2 +V (r), where V (r) is an attractive central potential in three dimensions. If V (r) is a convex transformation of the Coulomb potential −1/r and a concave transformation of the harmonic-oscillator potential r, then upper and lower bounds on the discrete eigenvalues of H can be constructed, which may all be expressed in the form ...

We obtain a dispersive long-time decay in weighted energy norms for solutions to the 1D wave equation with generic potential. The decay extends the results obtained by Murata for the 1D Schrödinger equation.

The acceleration of the expansion of the universe has deep implications for structure formation, the composition of the universe, and its fate. Roughly 70% of the energy density is in a dark energy, whose nature remains unknown. Mapping the expansion history through supernovae, mapping the geometry of the universe and formation of structure through redshift surveys, and mapping the distance to ...

We establish a new and intriguing connection between the FokkerPlanck equation with gradient drift term and an associated free energy functional. Namely, we demonstrate that such a Fokker-Planck equation may be interpreted as a gradient flux, or a steepest descent, of a free energy functional with respect to a certain metric. This is accomplished through the construction of a time-discrete iter...