Decay in Time for a One-Dimensional Two-Component Plasma

The motion of a collisionless plasma is described by the Vlasov-Poisson system, or in the presence of large velocities, the relativistic Vlasov-Poisson system. Both systems are considered in one space and one momentum dimension, with two species of oppositely charged particles. A new identity is derived for both systems and is used to study the behavior of solutions for large times.Comment: 17 pages, no figure

Large Time Behavior of the Relativistic Vlasov Maxwell System in Low Space Dimension

When particle speeds are large the motion of a collisionless plasma is modeled by the relativistic Vlasov Maxwell system. Large time behavior of solutions which depend on one position variable and two momentum variables is considered. In the case of a single species of charge it is shown that there are solutions for which the charge density does not decay in time. This is in marked contrast to results for the non-relativistic Vlasov Poisson system in one space dimension. The case when two oppositely charged species are present and the net total charge is zero is also considered. In this case, it is shown that the support in the first component of momentum can grow at most like t to the three-fourths power.Comment: 22 pages, no figure

Thermodynamic Analysis of Interacting Nucleic Acid Strands

Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for single-stranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium base-pairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality

Gas permeable vs gas impermeable contact lenses and their compared effects on the cornea

A study was completed comparing the differences in effect of gas permeable contact lenses (Polycon) vs gas impermeable contact lenses (PMMA). Eleven subjects were chosen, each of whom were to wear a Polycon lens on one eye and a PMMA lens on the other eye. Keratometric findings, refraction, visual acuity, edema and the endothelial mosaic were measured at varying stages of wear. It was shown that there was significantly less edema with the Polycon lens. Also it was found that the slides taken of endothelial cells could not be read as well when the eye photographed was wearing a PMMA lens (as opposed .to the Polycon lens). It therefore appears that more corneal change is taking place when a PMMA lens is worn: than when a Polycon lens is worn

Odd permutations are nicer than even ones

International audienceWe give simple combinatorial proofs of some formulas for the number of factorizations of permutations in S n as a product of two n-cycles, or of an n-cycle and an (n−1)-cycle. ... The parameter number of cycles plays a central role in the algebraic theory of the symmetric group, however there are very few results giving a relationship between the number of cycles of two permutations and that of their product. ... The first results on the subject go back to Ore, Bertram, Stanley (see [13], [1] and [15]), who proved some existence theorems. These results allowed to obtain ..

Time Decay for solutions to One-Dimensional Two-Component Plasma Equations

We represent three generations of students: Bob Glassey, Walter's student finishing at Brown in 1972, Jack Schaeffer, Bob's student finishing at Indiana University in 1983, and Steve Pankavich, Jack's student finishing at Carnegie Mellon in 2005. We have all thrived professionally from our association with Walter and are delighted to dedicate this note to him on the occasion of his 70th birthday. The problem we study concerns the asymptotic behavior of solutions to Vlasov equations, an area to which Walter has contributed greatly.Comment: 7 page