Comparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations

This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree $p$. Such nonlinear terms have an on-line complexity of $\mathcal{O}(k^{p+1})$, where $k$ is the dimension of POD basis, and therefore is independent of full space dimension. However it is efficient only for quadratic nonlinear terms since for higher nonlinearities standard POD proves to be less time consuming once the POD basis dimension $k$ is increased. Numerical experiments are carried out with a two dimensional shallow water equation (SWE) test problem to compare the performance of tensorial POD, standard POD, and POD/Discrete Empirical Interpolation Method (DEIM). Numerical results show that tensorial POD decreases by $76\times$ times the computational cost of the on-line stage of standard POD for configurations using more than $300,000$ model variables. The tensorial POD SWE model was only $2-8\times$ slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM shallow water equation model to compute its off-line stage faster than the standard and tensorial POD approaches.Comment: 23 pages, 8 figures, 5 table

Collective Oscillations of an Imbalanced Fermi Gas: Axial Compression Modes and Polaron Effective Mass

We investigate the low-lying compression modes of a unitary Fermi gas with imbalanced spin populations. For low polarization, the strong coupling between the two spin components leads to a hydrodynamic behavior of the cloud. For large population imbalance we observe a decoupling of the oscillations of the two spin components, giving access to the effective mass of the Fermi polaron, a quasi-particle composed of an impurity dressed by particle-hole pair excitations in a surrounding Fermi sea. We find $m^*/m=1.17(10)$, in agreement with the most recent theoretical predictions.Comment: 4 pages, 4 figures, submitted to PR

Dynamics and Thermodynamics of the Low-Temperature Strongly Interacting Bose Gas

We measure the zero-temperature equation of state of a homogeneous Bose gas of $^7$Li atoms by analyzing the \emph{in-situ} density distributions of trapped samples. For increasing repulsive interactions our data shows a clear departure from mean-field theory and provides a quantitative test of the many-body corrections first predicted in 1957 by Lee, Huang and Yang. We further probe the dynamic response of the Bose gas to a varying interaction strength and compare it to simple theoretical models. We deduce a lower bound for the value of the universal constant $\xi>0.44(8)$ that would characterize the universal Bose gas at the unitary limit

The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions

Interacting fermions are ubiquitous in nature and understanding their thermodynamics is an important problem. We measure the equation of state of a two-component ultracold Fermi gas for a wide range of interaction strengths at low temperature. A detailed comparison with theories including Monte-Carlo calculations and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids is presented. The low-temperature phase diagram of the spin imbalanced gas reveals Fermi liquid behavior of the partially polarized normal phase for all but the weakest interactions. Our results provide a benchmark for many-body theories and are relevant to other fermionic systems such as the crust of neutron stars.Comment: 28 pages, 7 figure

The equation of state of ultracold Bose and Fermi gases: a few examples

We describe a powerful method for determining the equation of state of an ultracold gas from in situ images. The method provides a measurement of the local pressure of an harmonically trapped gas and we give several applications to Bose and Fermi gases. We obtain the grand-canonical equation of state of a spin-balanced Fermi gas with resonant interactions as a function of temperature. We compare our equation of state with an equation of state measured by the Tokyo group, that reveals a significant difference in the high-temperature regime. The normal phase, at low temperature, is well described by a Landau Fermi liquid model, and we observe a clear thermodynamic signature of the superfluid transition. In a second part we apply the same procedure to Bose gases. From a single image of a quasi ideal Bose gas we determine the equation of state from the classical to the condensed regime. Finally the method is applied to a Bose gas in a 3D optical lattice in the Mott insulator regime. Our equation of state directly reveals the Mott insulator behavior and is suited to investigate finite-temperature effects.Comment: 14 pages, 6 figure

Metastability in spin polarised Fermi gases and quasiparticle decays

We investigate the metastability associated with the first order transition from normal to superfluid phases in the phase diagram of two-component polarised Fermi gases.We begin by detailing the dominant decay processes of single quasiparticles.Having determined the momentum thresholds of each process and calculated their rates, we apply this understanding to a Fermi sea of polarons by linking its metastability to the stability of individual polarons, and predicting a region of metastability for the normal partially polarised phase. In the limit of a single impurity, this region extends from the interaction strength at which a polarised phase of molecules becomes the groundstate, to the one at which the single quasiparticle groundstate changes character from polaronic to molecular. Our argument in terms of a Fermi sea of polarons naturally suggests their use as an experimental probe. We propose experiments to observe the threshold of the predicted region of metastability, the interaction strength at which the quasiparticle groundstate changes character, and the decay rate of polarons

Changing the mind: hypnosis and diabetes

[Excerpt] Diabetes, although a physiological disorder suffers the impact of negative psychological stresses through the dysfunctional activation of the autonomic nervous and endocrine systems. In fact, a variety of psychological variables have been found to be important in the metabolic control and management of diabetic patients, particularly regarding adherence to self-care behaviors and medication. Lifestyle therapy is the cornerstone of diabetes treatment and, therefore, any intervention that is able to achieve the control of glycaemia, prevent micro and macro complications of diabetes, improve patient’s quality of life and decrease diabetes risk factors is certainly welcome. [...](undefined)info:eu-repo/semantics/publishedVersio

Gastrointestinal colonization by KPC-producing Klebsiella pneumoniae following hospital discharge: duration of carriage and risk factors for persistent carriage

AbstractThe natural history of KPC-producing Klebsiella pneumoniae (KPC KP) carriage is unknown. We aimed to examine the duration of KPC KP carriage following hospital discharge and to study the risk factors for persistent carriage. A cohort of 125 KPC KP carriers was followed monthly for between 3 and 6 months after discharge from an acute-care hospital. Rectal swabs and data were collected at baseline and at each visit. KPC KP was detected by culture and direct blaKPC PCR. Acquisition time was regarded as the earliest date of KPC KP isolation. Resolution of carriage was defined as a negative KPC KP test in at least two consecutive samples. Analyses were separated for recent (<4 months) (REC, 75 patients) and remote (≥4 months) (REM, 50 patients) acquisition groups. Risk factors for persistent carriage were examined by survival analyses for the REC group and by prevalence methods for the REM group. The mean age of patients was 67.5 years and 49.6% were male. Forty-six (61%) patients in the REC group and 14 (28%) in the REM group were persistent carriers (p < 0.001). A significant risk factor for persistent carriage identified in both the REC and REM groups was the presence of any catheter (p < 0.05). Unique risk factor groups included long-term care facility (LTCF) residence (p < 0.01) and a low functional status as measured by the Barthel’s index (p < 0.05) in the REC group and high Charlson’s score in the REM group (p < 0.05). Out of the entire 100 patients who had at least one negative sample, only 65 remained negative on subsequent cultures. In conclusion, persistent carriage of KPC KP is associated with catheter use and a low functional status; it is more common in patients with recent acquisition and is related to LTCF stay. A single negative KPC KP test is insufficient to exclude persistent carriage