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M. L. Glasser

Publications and source records attributed to M. L. Glasser.

44 records · Page 3Linked to original sources
arXiv2006

A non-linear equation from photopolymerization kinetics

In a medium where a photoreactive species produces N equally photoreactive radicals, by combining the Lambert-Beer law for the decay of light intensity, as a beam propagates into the medium, with the kinetic equation, one obtains a generalization of the Wegscheider equation from photobleaching theory. It is shown that this equation can be solved exactly, but implicitly, and can be reduced to a first order ordinary differential equation in a single reduced variable.

physics.chem-ph↗
arXiv2005

Solvable Sextic Equations

Criteria are given for determining whether an irreducible sextic equation with rational coefficients is algebraically solvable over the complex numbers.

math-ph↗
arXiv2003

On the entropy of spanning trees on a large triangular lattice

The double integral representing the entropy S_{tri} of spanning trees on a large triangular lattice is evaluated using two different methods, one algebraic and one graphical. Both methods lead to the same result S_{tri} = [1/(2 Pi)]^2 \int_0^{2 Pi} dθ\int_0^{2 Pi} dϕln [6-2 cos(θ) - 2 cos(ϕ) -2 cos(θ+ϕ)] = [3(\sqrt 3)/Pi](1 - 5^{-2} + 7^{-2} - 11^{-2} + 13^{-2} - ...)

cond-mat.stat-mech↗
arXiv2003

New exactly solvable periodic potentials for the Dirac equation

A new exactly solvable relativistic periodic potential is obtained by the periodic extension of a well-known transparent scalar potential. It is found that the energy band edges are determined by a transcendental equation which is very similar to the corresponding equation for the Dirac Kronig-Penney model. The solutions of the Dirac equation are expressed in terms of elementary functions.

quant-ph↗
arXiv2003

Supersymmetric manipulation of quasienergy states. Application to the Berry phase

Time-dependent supersymmetry allows one to delete quasienergy levels for time-periodic Hamiltonians and to create new ones. We illustrate this by examining an exactly solvable model related to the simple harmonic oscillator with a time-varying frequency. For an interesting nonharmonic example we present the change of the Berry phase due to a supersymmetry transformation.

quant-ph↗
arXiv2002

Enhanced cohesion of matter on a cylindrical surface

We evaluate the cohesive energies E$_b$ of four systems in which particles move on a cylindrical surface, at fixed distance R from the axis. We find quite nonuniversal dependences of E$_b$ on R. For the Coulomb binding problem, E$_b$ is a monotonically decreasing function of R. For three problems involving Lennard-Jones interactions, the behavior is nonmonotonic; E$_b$ is larger at R = $\infty$ than at R=0; the maximum binding corresponds to R $\sim 0.7 σ$ (the hard core parameter). Consequences of the enhanced binding are discussed.

cond-mat↗