Yukawa couplings and proton decay in SUSY models

We discuss proton decay induced by dimension--5 operators in supersymmetric models containing extra hypercharge-1/3 color-triplets. We derive a general formula relating dimension-5 operator to the color-triplet mass matrix. We show that certain zeros in the triplet mass-matrix together with some triplet coupling selection rules can lead to elimination of dimension-5 operators. We apply this mechanism to SU(5) and flipped SU(5) theories with extended Higgs sectors.Comment: 6 pages, uses JHEP.cls, talk given at the Trieste Meeting of the TMR Network on Physics Beyond the Standard Model, 24-27 February 1999, Trieste, Italy (to appear in the proceedings

Invalidation of the Kelvin Force in Ferrofluids

Direct and unambiguous experimental evidence for the magnetic force density being of the form $M\nabla B$ in a certain geometry - rather than being the Kelvin force $M\nabla H$ - is provided for the first time. (M is the magnetization, H the field, and B the flux density.)Comment: 4 pages, 4 figure

Carbon dioxide catastrophes: Past and future menace

Carbon dioxide is important in its role as coupler of the terrestrial biosphere to inorganic chemical processes and as the principal greenhouse gas controlling Earth's surface temperature. The hypothesis that atmospheric CO2 levels have diminished with time, with the resulting cooling effect offsetting an increase in the solar constant, seems firmly established, and it is shown that feedback mechanisms exist which can maintain the terrestrial surface in a relatively narrow temperature range over geological time. Of the factors involved in such CO2 variation, the oceanic reservoir appears the most important. Surface waters are probably in approximate equilibrium with regard to CO2 exchange with the ambient atmosphere in most regions, but data from deep-ocean water sampling indicates that such waters are somewhat undersaturated in the sense that they would tend to absorb CO2 from the atmosphere if brought to the surface without change in composition or temperature. If major impacts into the ocean can result in loss of a substantial portion of the atmospheric CO2 reservoir, then any such future event could imperil the continuation of most higher forms of life on Earth. The most likely candidate for an inverse Nyos global event in previous Earth history is the Cretaceous-Tertiary terminal extinction event. The Cretaceous was characterized by warm, equable temperatures presumably indicative of relatively high CO2 levels and an intense greenhouse heating. Cooling of the oceans in absence of massive transfer of CO2 to the oceanic reservoir in itself would promote a condition of CO2 undersaturation in abyssal waters, and this is made even more extreme by the pattern of ocean water circulation. It is possible to envision a situation in which deep ocean waters were at least occasionally profoundly undersaturated with regard to CO2. Turnover of a major fraction of such an ocean would then remove, on a very short time scale, as much as 90 percent of the atmospheric CO2 inventory

Visual identification by signature tracking

We propose a new camera-based biometric: visual signature identification. We discuss the importance of the parameterization of the signatures in order to achieve good classification results, independently of variations in the position of the camera with respect to the writing surface. We show that affine arc-length parameterization performs better than conventional time and Euclidean arc-length ones. We find that the system verification performance is better than 4 percent error on skilled forgeries and 1 percent error on random forgeries, and that its recognition performance is better than 1 percent error rate, comparable to the best camera-based biometrics

Scaling properties of energy spreading in nonlinear Hamiltonian two-dimensional lattices

In nonlinear disordered Hamiltonian lattices, where there are no propagating phonons, the spreading of energy is of subdiffusive nature. Recently, the universality class of the subdiffusive spreading according to the nonlinear diffusion equation (NDE) has been suggested and checked for one-dimensional lattices. Here, we apply this approach to two-dimensional strongly nonlinear lattices and find a nice agreement of the scaling predicted from the NDE with the spreading results from extensive numerical studies. Moreover, we show that the scaling works also for regular lattices with strongly nonlinear coupling, for which the scaling exponent is estimated analytically. This shows that the process of chaotic diffusion in such lattices does not require disorder.Comment: 7 pages, 7 figure

The Maximal Positively Invariant Set: Polynomial Setting

This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating that the related preimage map preserves basic semialgebraic structure. In fact, this property propagates to underlying set--dynamics induced by the associated restricted preimage map in general and to its maximal trajectory in particular. The finite time convergence of the corresponding maximal trajectory to the maximal positively invariant set is verified under reasonably mild conditions. The analysis is complemented with a discussion of computational aspects and a prototype implementation based on existing toolboxes for polynomial optimization