Critical temperature and Ginzburg-Landau equation for a trapped Fermi gas

We discuss a superfluid phase transition in a trapped neutral-atom Fermi gas. We consider the case where the critical temperature greatly exceeds the spacing between the trap levels and derive the corresponding Ginzburg-Landau equation. The latter turns out to be analogous to the equation for the condensate wave function in a trapped Bose gas. The analysis of its solution provides us with the value of the critical temperature $T_{c}$ and with the spatial and temperature dependence of the order parameter in the vicinity of the phase transition point.Comment: 6 pages, 1 figure, REVTeX. The figure improved. Misprints corrected. More discussion adde

Macroscopic Quantum Tunneling of a Bose Condensate

We study, by means of a variational method, the stability of a condensate in a magnetically trapped atomic Bose gas with a negative scattering length and find that the condensate is unstable in general. However, for temperatures sufficiently close to the critical temperature the condensate turns out to be metastable. For that case we determine in the usual WKB approximation the decay rate of the condensate due to macroscopic quantum fluctuations. When appropriate, we also calculate the decay rate due to thermal fluctuations. An important feature of our approach is that (nonsingular) phase fluctuations of the condensate are taken into account exactly.Comment: Invited paper for the Journal of Statistical Physic

Influence of nearly resonant light on the scattering length in low-temperature atomic gases

We develop the idea of manipulating the scattering length $a$ in low-temperature atomic gases by using nearly resonant light. As found, if the incident light is close to resonance with one of the bound $p$ levels of electronically excited molecule, then virtual radiative transitions of a pair of interacting atoms to this level can significantly change the value and even reverse the sign of $a$. The decay of the gas due to photon recoil, resulting from the scattering of light by single atoms, and due to photoassociation can be minimized by selecting the frequency detuning and the Rabi frequency. Our calculations show the feasibility of optical manipulations of trapped Bose condensates through a light-induced change in the mean field interaction between atoms, which is illustrated for $^7$Li.Comment: 12 pages, 1 Postscript figur

Feynman scaling violation on baryon spectra in pp collisions at LHC and cosmic ray energies

A significant asymmetry in baryon/antibaryon yields in the central region of high energy collisions is observed when the initial state has non-zero baryon charge. This asymmetry is connected with the possibility of baryon charge diffusion in rapidity space. Such a diffusion should decrease the baryon charge in the fragmentation region and translate into the corresponding decrease of the multiplicity of leading baryons. As a result, a new mechanism for Feynman scaling violation in the fragmentation region is obtained. Another numerically more significant reason for the Feynman scaling violation comes from the fact that the average number of cutted Pomerons increases with initial energy. We present the quantitative predictions of the Quark-Gluon String Model (QGSM) for the Feynman scaling violation at LHC energies and at even higher energies that can be important for cosmic ray physics.Comment: 21 pages, 11 figures, and 1 table. arXiv admin note: substantial text overlap with arXiv:1107.1615, arXiv:1007.320

Effect of quantum group invariance on trapped Fermi gases

We study the properties of a thermodynamic system having the symmetry of a quantum group and interacting with a harmonic potential. We calculate the dependence of the chemical potential, heat capacity and spatial distribution of the gas on the quantum group parameter $q$ and the number of spatial dimensions $D$. In addition, we consider a fourth-order interaction in the quantum group fields $\Psi$, and calculate the ground state energy up to first order.Comment: LaTeX file, 20 pages, four figures, uses epsf.sty, packaged as a single tar.gz uuencoded fil

Predictive modeling of die filling of the pharmaceutical granules using the flexible neural tree

In this work, a computational intelligence (CI) technique named flexible neural tree (FNT) was developed to predict die filling performance of pharmaceutical granules and to identify significant die filling process variables. FNT resembles feedforward neural network, which creates a tree-like structure by using genetic programming. To improve accuracy, FNT parameters were optimized by using differential evolution algorithm. The performance of the FNT-based CI model was evaluated and compared with other CI techniques: multilayer perceptron, Gaussian process regression, and reduced error pruning tree. The accuracy of the CI model was evaluated experimentally using die filling as a case study. The die filling experiments were performed using a model shoe system and three different grades of microcrystalline cellulose (MCC) powders (MCC PH 101, MCC PH 102, and MCC DG). The feed powders were roll-compacted and milled into granules. The granules were then sieved into samples of various size classes. The mass of granules deposited into the die at different shoe speeds was measured. From these experiments, a dataset consisting true density, mean diameter (d50), granule size, and shoe speed as the inputs and the deposited mass as the output was generated. Cross-validation (CV) methods such as 10FCV and 5x2FCV were applied to develop and to validate the predictive models. It was found that the FNT-based CI model (for both CV methods) performed much better than other CI models. Additionally, it was observed that process variables such as the granule size and the shoe speed had a higher impact on the predictability than that of the powder property such as d50. Furthermore, validation of model prediction with experimental data showed that the die filling behavior of coarse granules could be better predicted than that of fine granules

Edge-variational Graph Convolutional Networks for Uncertainty-aware Disease Prediction

There is a rising need for computational models that can complementarily leverage data of different modalities while investigating associations between subjects for population-based disease analysis. Despite the success of convolutional neural networks in representation learning for imaging data, it is still a very challenging task. In this paper, we propose a generalizable framework that can automatically integrate imaging data with non-imaging data in populations for uncertainty-aware disease prediction. At its core is a learnable adaptive population graph with variational edges, which we mathematically prove that it is optimizable in conjunction with graph convolutional neural networks. To estimate the predictive uncertainty related to the graph topology, we propose the novel concept of Monte-Carlo edge dropout. Experimental results on four databases show that our method can consistently and significantly improve the diagnostic accuracy for Autism spectrum disorder, Alzheimer's disease, and ocular diseases, indicating its generalizability in leveraging multimodal data for computer-aided diagnosis.Comment: Accepted to MICCAI 202

Implementation of seven echocardiographic parameters of myocardial asynchrony to improve the long-term response rate of cardiac resynchronization therapy (CRT)

<p>Abstract</p> <p>Background</p> <p>Cardiac resynchronization Therapy (CRT) is an effective therapy for chronic heart failure with beneficial hemodynamic effects leading to a reduction of morbidity and mortality. The responder rates, however, are low. There are various and contentious echocardiographic parameters of myocardial asynchrony. Patient selection by echocardiographic assessment of asynchrony is thought to improve responder rates.</p> <p>Methods</p> <p>In this small single-center pilot-study, seven established parameters of myocardial asynchrony were used to select patients for CRT: (1) interventricular electromechanical delay (IMD, cut-off ≥ 40 ms), (2) Septal-to-posterior wall motion delay (SPWMD, ≥ 130 ms), (3) maximal difference in time-to-peak velocities between any two of twelve LV segments (Ts-12 ≥ 104 ms), (4) standard deviation of time to peak myocardial velocities (Ts-12-SD, ≥ 34.4 ms), (5) difference between the septal and basal time-to-peak velocity (TDId, ≥ 60 ms), (6) left ventricular electromechanical delay (LVEMD, > 140 ms) and (7) delayed longitudinal contraction (DLC, > 2 segments).</p> <p>16 chronic heart failure patients (NYHA III–IV, LVEF < 0.35, QRS ≥ 120 ms) at least two out of seven parameters of myocardial asynchrony received cardiac resynchronization therapy (CRT-ICD). Follow-up echo examination was after 6 months. The control group was a historic group of CRT patients (n = 38) who had not been screened for echocardiographic signs of myocardial asynchrony prior to device implantation.</p> <p>Results</p> <p>Based on reverse remodeling (relative reduction of LVESV > 15%, relative increase of LVEF > 25%), the responder rate to CRT was 81.2% in patients selected for CRT according to our protocol as compared to 47.4% in the control group (p = 0.04). At baseline, there were on average 4.1 ± 1.6 positive parameters of asynchrony (follow-up: 3.7 [± 1.6] parameters positive, p = 0.52). Only the LVEMD decreased significantly after CRT (p = 0.027). The remaining parameters showed a non-significant trend towards reduction of myocardial asynchrony.</p> <p>Conclusion</p> <p>The implementation of different markers of asynchrony in the selection process for CRT improves the hemodynamic response rate to CRT.</p

Nature of Phase Transitions of Superconducting Wire Networks in a Magnetic Field

We study $I$-$V$ characteristics of periodic square Nb wire networks as a function of temperature in a transverse magnetic field, with a focus on three fillings 2/5, 1/2, and 0.618 that represent very different levels of incommensurability. For all three fillings, a scaling behavior of $I$-$V$ characteristics is found, suggesting a finite temperature continuous superconducting phase transition. The low-temperature $I$-$V$ characteristics are found to have an exponential form, indicative of the domain-wall excitations.Comment: 5 pages, also available at http://www.neci.nj.nec.com/homepages/tang.htm