Bistability for asymmetric discrete random walks

We show that asymmetric time-continuous discrete random walks can display bistability for equal values of Jauslin's shifting parameters. The bistability becomes more pronounced at increased asymmetry parameterComment: Follow-up note to hep-th/9411026[PRE 51, 5112 (May 95)], one fig. include

Supersymmetry of FRW barotropic cosmologies

Barotropic FRW cosmologies are presented from the standpoint of nonrelativistic supersymmetry. First, we reduce the barotropic FRW system of differential equations to simple harmonic oscillator differential equations. Employing the factorization procedure, the solutions of the latter equations are divided into the two classes of bosonic (nonsingular) and fermionic (singular) cosmological solutions. We next introduce a coupling parameter denoted by K between the two classes of solutions and obtain barotropic cosmologies with dissipative features acting on the scale factors and spatial curvature of the universe. The K-extended FRW equations in comoving time are presented in explicit form in the low coupling regime. The standard barotropic FRW cosmologies correspond to the dissipationless limit K =0Comment: 6 page

Supersymmetric free-damped oscillators: Adaptive observer estimation of the Riccati parameter

A supersymmetric class of free damped oscillators with three parameters has been obtained in 1998 by Rosu and Reyes through the factorization of the Newton equation. The supplementary parameter is the integration constant of the general Riccati solution. The estimation of the latter parameter is performed here by employing the recent adaptive observer scheme of Besancon et al., but applied in a nonstandard form in which a time-varying quantity containing the unknown Riccati parameter is estimated first. Results of computer simulations are presented to illustrate the good feasibility of this approach for a case in which the estimation is not easily accomplished by other meansComment: 8 pages, 6 figure

Barotropic FRW cosmologies with a Dirac-like parameter

Using the known connection between Schroedinger-like equations and Dirac-like equations in the supersymmetric context, we discuss an extension of FRW barotropic cosmologies in which a Dirac mass-like parameter is introduced. New Hubble cosmological parameters H_K(eta) depending on the Dirac-like parameter are plotted and compared with the standard Hubble case H_0(eta). The new H_K(eta) are complex quantities. The imaginary part is a supersymmetric way of introducing dissipation and instabilities in the barotropic FRW hydrodynamicsComment: 7 pages, 4 figures, accepted at MPL

Classical harmonic oscillator with Dirac-like parameters and possible applications

We obtain a class of parametric oscillation modes that we call K-modes with damping and absorption that are connected to the classical harmonic oscillator modes through the "supersymmetric" one-dimensional matrix procedure similar to relationships of the same type between Dirac and Schroedinger equations in particle physics. When a single coupling parameter, denoted by K, is used, it characterizes both the damping and the dissipative features of these modes. Generalizations to several K parameters are also possible and lead to analytical results. If the problem is passed to the physical optics (and/or acoustics) context by switching from the oscillator equation to the corresponding Helmholtz equation, one may hope to detect the K-modes as waveguide modes of specially designed waveguides and/or cavitiesComment: 14 pages, 9 figures, revised, accepted at J. Phys.

Riccati nonhermiticity with application to the Morse potential

A supersymmetric one-dimensional matrix procedure similar to relationships of the same type between Dirac and Schrodinger equations in particle physics is described at the general level. By this means we are able to introduce a nonhermitic Hamiltonian having the imaginary part proportional to the solution of a Riccati equation of the Witten type. The procedure is applied to the exactly solvable Morse potential introducing in this way the corresponding nonhermitic Morse problem. A possible application is to molecular diffraction in evanescent waves over nanostructured surfacesComment: 8 pages, 4 figure