Dynamical cluster-decay model for hot and rotating light-mass nuclear systems, applied to low-energy 32^{32}S + 24^{24}Mg →56\to ^{56}Ni reaction

The dynamical cluster-decay model (DCM) is developed further for the decay of hot and rotating compound nuclei (CN) formed in light heavy-ion reactions. The model is worked out in terms of only one parameter, namely the neck-length parameter, which is related to the total kinetic energy TKE(T) or effective Q-value $Q_{eff}(T)$ at temperature T of the hot CN, defined in terms of the both the light-particles (LP), with $A \leq$ 4, Z $\leq$ 2, as well as the complex intermediate mass fragments (IMF), with $4 2$, is considered as the dynamical collective mass motion of preformed clusters through the barrier. Within the same dynamical model treatment, the LPs are shown to have different characteristics as compared to the IMFs. The systematic variation of the LP emission cross section $\sigma_{LP}$, and IMF emission cross section $\sigma_{IMF}$, calculated on the present DCM match exactly the statistical fission model predictions. It is for the first time that a non-statistical dynamical description is developed for the emission of light-particles from the hot and rotating CN. The model is applied to the decay of $^{56}$Ni formed in the $^{32}$S + $^{24}$Mg reaction at two incident energies E$_{c.m.}$ = 51.6 and 60.5 MeV. Both the IMFs and average $\bar{TKE}$ spectra are found to compare reasonably nicely with the experimental data, favoring asymmetric mass distributions. The LPs emission cross section is shown to depend strongly on the type of emitted particles and their multiplicities

Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity

We develop a strong-coupling ($t \ll U$) expansion technique for calculating the density profile for bosonic atoms trapped in an optical lattice with an overall harmonic trap at finite temperature and finite on site interaction in the presence of superfluid regions. Our results match well with quantum Monte Carlo simulations at finite temperature. We also show that the superfluid order parameter never vanishes in the trap due to proximity effect. Our calculations for the scaled density in the vacuum to superfluid transition agree well with the experimental data for appropriate temperatures. We present calculations for the entropy per particle as a function of temperature which can be used to calibrate the temperature in experiments. We also discuss issues connected with the demonstration of universal quantum critical scaling in the experiments.Comment: 11 pages, 9 figure

Shell closure effects studied via cluster decay in heavy nuclei

The effects of shell closure in nuclei via the cluster decay is studied. In this context, we have made use of the Preformed Cluster Model ($PCM$) of Gupta and collaborators based on the Quantum Mechanical Fragmentation Theory. The key point in the cluster radioactivity is that it involves the interplay of close shell effects of parent and daughter. Small half life for a parent indicates shell stabilized daughter and long half life indicates the stability of the parent against the decay. In the cluster decay of trans lead nuclei observed so far, the end product is doubly magic lead or its neighbors. With this in our mind we have extended the idea of cluster radioactivity. We investigated decay of different nuclei where Zirconium is always taken as a daughter nucleus, which is very well known deformed nucleus. The branching ratio of cluster decay and $\alpha$-decay is also studied for various nuclei, leading to magic or almost doubly magic daughter nuclei. The calculated cluster decay half-life are in well agreement with the observed data. First time a possibility of cluster decay in $^{218}U$ nucleus is predicted

Profitable Scheduling on Multiple Speed-Scalable Processors

We present a new online algorithm for profit-oriented scheduling on multiple speed-scalable processors. Moreover, we provide a tight analysis of the algorithm's competitiveness. Our results generalize and improve upon work by \textcite{Chan:2010}, which considers a single speed-scalable processor. Using significantly different techniques, we can not only extend their model to multiprocessors but also prove an enhanced and tight competitive ratio for our algorithm. In our scheduling problem, jobs arrive over time and are preemptable. They have different workloads, values, and deadlines. The scheduler may decide not to finish a job but instead to suffer a loss equaling the job's value. However, to process a job's workload until its deadline the scheduler must invest a certain amount of energy. The cost of a schedule is the sum of lost values and invested energy. In order to finish a job the scheduler has to determine which processors to use and set their speeds accordingly. A processor's energy consumption is power \Power{s} integrated over time, where \Power{s}=s^{\alpha} is the power consumption when running at speed $s$. Since we consider the online variant of the problem, the scheduler has no knowledge about future jobs. This problem was introduced by \textcite{Chan:2010} for the case of a single processor. They presented an online algorithm which is $\alpha^{\alpha}+2e\alpha$-competitive. We provide an online algorithm for the case of multiple processors with an improved competitive ratio of $\alpha^{\alpha}$.Comment: Extended abstract submitted to STACS 201

Obtaining pressure versus concentration phase diagrams in spin systems from Monte Carlo simulations

We propose an efficient procedure for determining phase diagrams of systems that are described by spin models. It consists of combining cluster algorithms with the method proposed by Sauerwein and de Oliveira where the grand canonical potential is obtained directly from the Monte Carlo simulation, without the necessity of performing numerical integrations. The cluster algorithm presented in this paper eliminates metastability in first order phase transitions allowing us to locate precisely the first-order transitions lines. We also produce a different technique for calculating the thermodynamic limit of quantities such as the magnetization whose infinite volume limit is not straightforward in first order phase transitions. As an application, we study the Andelman model for Langmuir monolayers made of chiral molecules that is equivalent to the Blume-Emery-Griffiths spin-1 model. We have obtained the phase diagrams in the case where the intermolecular forces favor interactions between enantiomers of the same type (homochiral interactions). In particular, we have determined diagrams in the surface pressure versus concentration plane which are more relevant from the experimental point of view and less usual in numerical studies