Finite temperature effects in light scattering off Cooper-paired Fermi atoms

We study stimulated light scattering off a superfluid Fermi gas of atoms at finite temperature. We derive response function that takes into account vertex correction due to final state interactions; and analyze finite temperature effects on collective and quasiparticle excitations of a uniform superfluid Fermi gas. Light polarization is shown to play an important role in excitations. Our results suggest that it is possible to excite Bogoliubov-Anderson phonon at a large scattering length by light scattering.Comment: 18 pages, 4 figures, Accepted in J. Phys. B: At. Mol. & Opt. Phy

Linear systems with adiabatic fluctuations

We consider a dynamical system subjected to weak but adiabatically slow fluctuations of external origin. Based on the ``adiabatic following'' approximation we carry out an expansion in \alpha/|\mu|, where \alpha is the strength of fluctuations and 1/|\mu| refers to the time scale of evolution of the unperturbed system to obtain a linear differential equation for the average solution. The theory is applied to the problems of a damped harmonic oscillator and diffusion in a turbulent fluid. The result is the realization of `renormalized' diffusion constant or damping constant for the respective problems. The applicability of the method has been critically analyzed.Comment: Plain Latex, no figure, 21 page

Correlating contexts and NFR conflicts from event logs

In the design of autonomous systems, it is important to consider the preferences of the interested parties to improve the user experience. These preferences are often associated with the contexts in which each system is likely to operate. The operational behavior of a system must also meet various non-functional requirements (NFRs), which can present different levels of conflict depending on the operational context. This work aims to model correlations between the individual contexts and the consequent conflicts between NFRs. The proposed approach is based on analyzing the system event logs, tracing them back to the leaf elements at the specification level and providing a contextual explanation of the system’s behavior. The traced contexts and NFR conflicts are then mined to produce Context-Context and Context-NFR conflict sequential rules. The proposed Contextual Explainability (ConE) framework uses BERT-based pre-trained language models and sequential rule mining libraries for deriving the above correlations. Extensive evaluations are performed to compare the existing state-of-the-art approaches. The best-fit solutions are chosen to integrate within the ConE framework. Based on experiments, an accuracy of 80%, a precision of 90%, a recall of 97%, and an F1-score of 88% are recorded for the ConE framework on the sequential rules that were mined

Reinforcing age Hardenable Al-Cr Matrix Alloy In-Situ and by SiC/Al2O3

The achievable high ductility value of Al-Cr alloys (over 35% total elongation) has led to the attempt to produce in-situ composites with Al-Cr solid solution as the matrix phase and excess insoluble intermetallics CrAL as the reinforcing constituent.The alloy produced with 1.20 wt% Cr results in in-situ composites which gives a good combination of high tensile strength and ductility (approx. 30% elongation). Composites based on Al-Cr matrix alloy with SiC or A1,03 as the reinforcing phase showed that the increase in strength is quite considerable even at a relatively good ductility

Light scattering in Cooper-paired Fermi atoms

We present a detailed theoretical study of light scattering off superfluid trapped Fermi gas of atoms at zero temperature. We apply Nambu-Gorkov formalism of superconductivity to calculate the response function of superfluid gas due to stimulated light scattering taking into account the final state interactions. The polarization of light has been shown to play a significant role in response of Cooper-pairs in the presence of a magnetic field. Particularly important is a scheme of polarization-selective light scattering by either spin-component of the Cooper-pairs leading to the single-particle excitations of one spin-component only. These excitations have a threshold of $2\Delta$ where $\Delta$ is the superfluid gap energy. Furthermore, polarization-selective light scattering allows for unequal energy and momentum transfer to the two partner atoms of a Cooper-pair. In the regime of low energy ($<< 2\Delta$) and low momentum ($<2\Delta/(\hbar v_F)$, $v_F$ being the Fermi velocity) transfer, a small difference in momentum transfers to the two spin-components may be useful in exciting Bogoliubov-Anderson phonon mode. We present detailed results on the dynamic structure factor (DSF) deduced from the response function making use of generalized fluctuation-dissipation theorem. Model calculations using local density approximation for trapped superfluid Fermi gas shows that when the energy transfer is less than $2\Delta_0$, where $\Delta_0$ refers to the gap at the trap center, DSF as a function of energy transfer has reduced gradient compared to that of normal Fermi gas.Comment: single column, 26 pages, 10 figures; Title changed, discussion on experimental implication added in concluding section. Accepted for publication in J. Phys.

A Multi-objective Exploratory Procedure for Regression Model Selection

Variable selection is recognized as one of the most critical steps in statistical modeling. The problems encountered in engineering and social sciences are commonly characterized by over-abundance of explanatory variables, non-linearities and unknown interdependencies between the regressors. An added difficulty is that the analysts may have little or no prior knowledge on the relative importance of the variables. To provide a robust method for model selection, this paper introduces the Multi-objective Genetic Algorithm for Variable Selection (MOGA-VS) that provides the user with an optimal set of regression models for a given data-set. The algorithm considers the regression problem as a two objective task, and explores the Pareto-optimal (best subset) models by preferring those models over the other which have less number of regression coefficients and better goodness of fit. The model exploration can be performed based on in-sample or generalization error minimization. The model selection is proposed to be performed in two steps. First, we generate the frontier of Pareto-optimal regression models by eliminating the dominated models without any user intervention. Second, a decision making process is executed which allows the user to choose the most preferred model using visualisations and simple metrics. The method has been evaluated on a recently published real dataset on Communities and Crime within United States.Comment: in Journal of Computational and Graphical Statistics, Vol. 24, Iss. 1, 201

Entangling two Bose Einstein condensates in a double cavity system

We propose a scheme to transfer the quantum state of light fields to the collective density excitations of a Bose Einstein condensate (BEC) in a cavity. This scheme allows to entangle two BECs in a double cavity setup by transferring the quantum entanglement of two light fields produced from a nondegenerate parametric amplifier (NOPA) to the collective density excitations of the two BECs. An EPR state of the collective density excitations can be created by a judicious choice of the system parameters.Comment: 3 figure