A note on convexity of sections of quaternionic numerical range

The quaternionic numerical range of matrices over the ring of quaternions is not necessarily convex. We prove Toeplitz-Hausdorff like theorem, that is, for any given quaternionic matrix every section of its quaternionic numerical range is convex. We provide some additional equivalent conditions for the quaternionic numerical range of matrices over quaternions to be convex and prove some numerical radius inequalities

A Secure and Fair Resource Sharing Model for Community Clouds

Cloud computing has gained a lot of importance and has been one of the most discussed segment of today\u27s IT industry. As enterprises explore the idea of using clouds, concerns have emerged related to cloud security and standardization. This thesis explores whether the Community Cloud Deployment Model can provide solutions to some of the concerns associated with cloud computing. A secure framework based on trust negotiations for resource sharing within the community is developed as a means to provide standardization and security while building trust during resource sharing within the community. Additionally, a model for fair sharing of resources is developed which makes the resource availability and usage transparent to the community so that members can make informed decisions about their own resource requirements based on the resource usage and availability within the community. Furthermore, the fair-share model discusses methods that can be employed to address situations when the demand for a resource is higher than the resource availability in the resource pool. Various methods that include reduction in the requested amount of resource, early release of the resources and taxing members have been studied, Based on comparisons of these methods along with the advantages and disadvantages of each model outlined, a hybrid method that only taxes members for unused resources is developed. All these methods have been studied through simulations

Anomalous transport and phonon renormalization in a chain with transverse and longitudinal vibrations

We study thermal transport in a chain of coupled atoms, which can vibrate in longitudinal as well as transverse directions. The particles interact through anharmonic potentials upto cubic order. The problem is treated quantum mechanically. We first calculate the phonon frequencies self-consistently taking into account the anharmonic interactions. We show that for all the modes, frequencies must have linear dispersion with wave-vector $q$ for small $q$ irrespective of their bare dispersions. We then calculate the phonon relaxation rates $\Gamma_i(q)$, where $i$ is the polarization index of the mode, in a self-consistent approximation based on second order perturbation diagrams. We find that the relaxation rate for the longitudinal phonon, $\Gamma_x(q) \propto q^{3/2}$, while that for the transverse phonon $\Gamma_y(q) \propto q^2$. The consequence of these results on the thermal conductivity $\kappa(N)$ of a chain of $N$ particles is that $\kappa(N) \propto N^{1/2}$

Cold reaction valleys in the radioactive decay of superheavy {286}^112, {292}^114 and {296}^116 nuclei

Cold reaction valleys in the radioactive decay of superheavy nuclei {286}^112, {292}^114 and {296}^116 are studied taking Coulomb and Proximity Potential as the interacting barrier. It is found that in addition to alpha particle, 8^Be, 14^C, 28^Mg, 34^Si, 50^Ca, etc. are optimal cases of cluster radioactivity since they lie in the cold valleys. Two other regions of deep minima centered on 208^Pb and 132^Sn are also found. Within our Coulomb and Proximity Potential Model half-life times and other characteristics such as barrier penetrability, decay constant for clusters ranging from alpha particle to 68^Ni are calculated. The computed alpha half-lives match with the values calculated using Viola--Seaborg--Sobiczewski systematics. The clusters 8^Be and 14^C are found to be most probable for emission with T_1/2 < 1030s. The alpha-decay chains of the three superheavy nuclei are also studied. The computed alpha decay half-lives are compared with the values predicted by Generalized Liquid Drop Model and they are found to match reasonably well.Comment: 21 pages, 6 figure

Quantum entanglement and Hawking temperature

The thermodynamic entropy of an isolated system is given by its von Neumann entropy. Over the last few years, there is an intense activity to understand thermodynamic entropy from the principles of quantum mechanics. More specifically, is there a relation between the (von Neumann) entropy of entanglement between a system and some (separate) environment is related to the thermodynamic entropy? It is difficult to obtain the relation for many body systems, hence, most of the work in the literature has focused on small number systems. In this work, we consider black-holes --- that are simple yet macroscopic systems --- and show that a direct connection could not be made between the entropy of entanglement and the Hawking temperature. In this work, within the adiabatic approximation, we explicitly show that the Hawking temperature is indeed given by the rate of change of the entropy of entanglement across a black hole's horizon with regard to the system energy. This is yet another numerical evidence to understand the key features of black hole thermodynamics from the viewpoint of quantum information theory.Comment: 10 pages, 5 figures (To appear in Eur. Phys. J. C

Systematic study of heavy cluster emission from {210-226}^Ra isotopes

The half lives for various clusters lying in the cold reaction valleys of {210-226}^Ra isotopes are computed using our Coulomb and proximity potential model (CPPM). The computed half lives of 4^He and 14^C clusters from {210-226}^Ra isotopes are in good agreement with experimental data. Half lives are also computed using the Universal formula for cluster decay (UNIV) of Poenaru et al., and are found to be in agreement with CPPM values. Our study reveals the role of doubly magic 208^Pb daughter in cluster decay process. Geiger - Nuttall plots for all clusters up to 62^Fe are studied and are found to be linear with different slopes and intercepts. {12,14}^C emission from 220^Ra; 14^C emission from {222,224}^Ra; 14^C and 20^O emission from 226^Ra are found to be most favourable for measurement and this observation will serve as a guide to the future experiments.Comment: 22 pages, 6 figures; Nuclear Physics A (2012

Fine structure in the {\alpha}-decay of odd-even nuclei

Systematic study on {\alpha}-decay fine structure is presented for the first time in the case of odd-even nuclei in the range 83 \leq Z \leq 101. The model used for the study is the recently proposed Coulomb and proximity potential model for deformed nuclei (CPPMDN), which employs deformed Coulomb potential, deformed two term proximity potential and centrifugal potential. The computed partial half lives, total half lives and branching ratios are compared with experimental data and are in good agreement. The standard deviation of partial half-life is 1.08 and that for branching ratio is 1.21. Our formalism is also successful in predicting angular momentum hindered and structure hindered transitions. The present study reveals that CPPMDN is a unified theory which is successful in explaining alpha decay from ground and isomeric state; and alpha fine structure of even-even, even-odd and odd-even nuclei. Our study relights that the differences in the parent and daughter surfaces or the changes in the deformation parameters as well as the shell structure of the parent and daughter nuclei, influences the alpha decay probability.Comment: 35 pages, 5 figure