Real null coframes in general relativity and GPS type coordinates

Based on work of Derrick, Coll, and Morales, we define a `symmetric' null coframe with {\it four real null covectors}. We show that this coframe is closely related to the GPS type coordinates recently introduced by Rovelli.Comment: Latex script, 9 pages, 4 figures; references added to work of Derrick, Coll, and Morales, 1 new figur

Global attractivity and permanence of a SVEIR epidemic model with pulse vaccination and time delay

AbstractIn this study, we propose a new SVEIR epidemic disease model with time delay, and analyze the dynamic behavior of the model under pulse vaccination. Pulse vaccination is an effective strategy for the elimination of infectious disease. Using the discrete dynamical system determined by the stroboscopic map, we obtain an ‘infection-free’ periodic solution. We also show that the ‘infection-free’ periodic solution is globally attractive when some parameters of the model under appropriate conditions. The permanence of the model is investigated analytically. Our results indicate that a large vaccination rate or a short pulse of vaccination or a long latent period is a sufficient condition for the extinction of the disease

Complex-valued Burgers and KdV-Burgers equations

Spatially periodic complex-valued solutions of the Burgers and KdV-Burgers equations are studied in this paper. It is shown that for any sufficiently large time T, there exists an explicit initial data such that its corresponding solution of the Burgers equation blows up at T. In addition, the global convergence and regularity of series solutions is established for initial data satisfying mild conditions

Density functional theory and demixing of binary hard rod-polymer mixtures

A density functional theory for a mixture of hard rods and polymers modeled as chains built of hard tangent spheres is proposed by combining the functional due to Yu and Wu for the polymer mixtures [J. Chem. Phys. {\bf 117}, 2368 (2002)] with the Schmidt's functional [Phys. Rev. E {\bf 63}, 50201 (2001)] for rod-sphere mixtures. As a simple application of the functional, the demixing transition into polymer-rich and rod-rich phases is examined. When the chain length increases, the phase boundary broadens and the critical packing fraction decreases. The shift of the critical point of a demixing transition is most noticeable for short chains.Comment: 4 pages,2 figures, in press, PR

Production of Secondaries in High Energy d+Au Collisions

In the framework of Quark-Gluon String Model we calculate the inclusive spectra of secondaries produced in d+Au collisions at intermediate (CERN SPS) and at much higher (RHIC) energies. The results of numerical calculations at intermediate energies are in reasonable agreement with the data. At RHIC energies numerically large inelastic screening corrections (percolation effects) should be accounted for in calculations. We extract these effects from the existing RHIC experimental data on minimum bias and central d+Au collisions. The predictions for p+Au interactions at LHC energy are also given.Comment: 18 pages and 10 figure

A toy model of fractal glioma development under RF electric field treatment

A toy model for glioma treatment by a radio frequency electric field is suggested. This low-intensity, intermediate-frequency alternating electric field is known as the tumor-treating-field (TTF). In the framework of this model the efficiency of this TTF is estimated, and the interplay between the TTF and the migration-proliferation dichotomy of cancer cells is considered. The model is based on a modification of a comb model for cancer cells, where the migration-proliferation dichotomy becomes naturally apparent. Considering glioma cancer as a fractal dielectric composite of cancer cells and normal tissue cells, a new effective mechanism of glioma treatment is suggested in the form of a giant enhancement of the TTF. This leads to the irreversible electroporation that may be an effective non-invasive method of treating brain cancer.Comment: Submitted for publication in European Physical Journal

Self-induced and induced transparencies of two-dimensional and three- dimensional superlattices

The phenomenon of transparency in two-dimensional and three-dimensional superlattices is analyzed on the basis of the Boltzmann equation with a collision term encompassing three distinct scattering mechanisms (elastic, inelastic and electron-electron) in terms of three corresponding distinct relaxation times. On this basis, we show that electron heating in the plane perpendicular to the current direction drastically changes the conditions for the occurrence of self-induced transparency in the superlattice. In particular, it leads to an additional modulation of the current amplitudes excited by an applied biharmonic electric field with harmonic components polarized in orthogonal directions. Furthermore, we show that self-induced transparency and dynamic localization are different phenomena with different physical origins, displaced in time from each other, and, in general, they arise at different electric fields.Comment: to appear in Physical Review