A study on Quantization Dimension in complete metric spaces

The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a complete metric space. This generalizes the known results on quantization dimension of self-similar measures in the Euclidean space to a complete metric space. In the last part, continuity of quantization dimension is discussed

Metastable states and information propagation in a 1D array of locally-coupled bistable cells

We study the effect of metastable states on the relaxation process (and hence information propagation) in locally coupled and boundary-driven structures. We first give a general argument to show that metastable states are inevitable even in the simplest of structures, a wire. At finite temperatures, the relaxation mechanism is a thermally assisted random walk. The time required to reach the ground state and its life time are determined by the coupling parameters. These time scales are studied in a model based on an array of quantum dots.Comment: Accepted for publication in Journal of Applied Physic

Studies in Chlorination : Part I - Magnesite

Preparation of anhydrous magnesium chloride by dehydration from hydrated magnesium chloride is not straight forward after dihydrate stage due to hydrolysis. Magnesium oxide and oxy-chloride contaminate the final product in uncertain amounts

Some recent developments in quantization of fractal measures

We give an overview on the quantization problem for fractal measures, including some related results and methods which have been developed in the last decades. Based on the work of Graf and Luschgy, we propose a three-step procedure to estimate the quantization errors. We survey some recent progress, which makes use of this procedure, including the quantization for self-affine measures, Markov-type measures on graph-directed fractals, and product measures on multiscale Moran sets. Several open problems are mentioned.Comment: 13 page

Problem samofokusiranja i poprečne stabilnosti u magnetiziranoj plazmi s ionskom strujom

Self-focusing in a magnetized plasma consisting of cold electrons and ions has been studied in a situation when ions have a streaming velocity and the external magnetic field is at an angle µ with the streaming direction. By the use of a modified scaling, we have deduced an analogue of a non-linear Schrodinger equation involving only the space variables, which actually controls the transversal stability of the system, thus signaling the possibility of self-focusing. The various situations arising due to the variation of the propagation angle µ and the streaming velocity u0 are discussed in detail for the specific cases of D2 and N2 ions.Proučavamo samofokusiranje u magnetiziranoj plazmi koja se sastoji of hladnih elektrona i iona u uvjetima kada ioni struje a magnetsko je polje pod nekim kutom prema smjeru njihovog strujanja. Primjenom modificirane promjene mjera, izveli smo jednadžbu koja je analogna Schrodingerovoj jednadžbi s prostornim varijablama koja opisuje poprečnu stabilnost sustava i tako najavljuje mogućnost samofokusiranja. Raspravljaju se podrobno razni uvjeti koji nastaju zbog promjena smjera strujanja iona (kuta θ) i brzine strujanja (u0) za posebne slučajeve D2 i N2 iona

Linearno i nelinearno sirenje ionsko-zvučnih valova u plazmi u posudi koja sadrži i negativne ione

Linear and nonlinear propagation of ion-acoustic waves are theoretically investigated in a multicomponent plasma consisting of electrons, positive ions and negative ions bounded in a cylindrical waveguide. The stability of the ion-acoustic wave is discussed taking into account the role of finite geometry and the concentration of negative ions of the plasma. The effect of nonlinearity on the ion-acoustic wave is investigated through the derivation of the effective potential (Sagdeev potential) and the results are discussed graphically with the variation of ion-streaming and the geometry of the bounded plasma.Teorijski istražujemo linearno i nelinearno širenje ionsko-zvučnih valova u višekomponentnoj plazmi koja se sastoji od elektrona, te pozitivnih i negativnih iona i nalazi se u valjkastom valovodu. Raspravljamo stabilnost ionsko-zvučnih valova uzimajućci u obzir utjecaj ograničenog prostora i koncentracije negativnih iona u plazmi. Istražujemo učinke nelinearnosti na ionsko-zvučni val putem izvođenja efektivnog (Sagdeevog) potencijala a ishodi numeričkih računa predočuju se grafički za različita strujanja iona i oblike valovoda

Sunyaev-Zel'dovich Effects from Quasars in Galaxies and Groups

The energy fed by active galactic nuclei to the surrounding diffuse baryons changes their amount, temperature, and distribution; so in groups and in member galaxies it affects the X-ray luminosity and also the Sunyaev-Zel'dovich effect. Here we compute how the latter is enhanced by the transient blastwave driven by an active quasar, and is depressed when the equilibrium is recovered with a depleted density. We constrain such depressions and enhancements with the masses of relic black holes in galaxies and the X-ray luminosities in groups. We discuss how all these linked observables can tell the quasar contribution to the thermal history of the baryons pervading galaxies and groups.Comment: 4 pages, 3 figures, uses REVTeX4 and emulateapj.cls. Accepted by ApJ

Thermodynamics of Photon Gas with an Invariant Energy Scale

Quantum Gravity framework motivates us to find new theories in which an observer independent finite energy upper bound (preferably Planck Energy) exists. We have studied the modifications in the thermodynamical properties of a photon gas in such a scenario where we have an invariant energy scale. We show that the density of states and the entropy in such a framework are less than the corresponding quantities in Einstein's Special Relativity (SR) theory. This result can be interpreted as a consequence of the deformed Lorentz symmetry present in the particular model we have considered.Comment: 17 pages, 3 figure files, some addition in text as well as in references, the scaling of figures have been modifie