Theory of the Normal/Superfluid interface in population imbalanced Fermi gases

We present a series of theoretical studies of the boundary between a superfluid and normal region in a partially polarized gas of strongly interacting fermions. We present mean-field estimates of the surface energy in this boundary as a function of temperature and scattering length. We discuss the structure of the domain wall, and use a previously introduced phenomonological model to study its influence on experimental observables. Our microscopic mean-field calculations are not consistent with the magnitude of the surface tension found from our phenomonological modelling of data from the Rice experiments. We conclude that one must search for novel mechanisms to explain the experiments.Comment: 15 pages, 9 figures (13 subfigures) -- v2: minor change

High Throughput VLSI Architecture for Soft-Output MIMO Detection Based on A Greedy Graph Algorithm

Maximum-likelihood (ML) decoding is a very computational- intensive task for multiple-input multiple-output (MIMO) wireless channel detection. This paper presents a new graph based algorithm to achieve near ML performance for soft MIMO detection. Instead of using the traditional tree search based structure, we represent the search space of the MIMO signals with a directed graph and a greedy algorithm is ap- plied to compute the a posteriori probability (APP) for each transmitted bit. The proposed detector has two advantages: 1) it keeps a fixed throughput and has a regular and parallel datapath structure which makes it amenable to high speed VLSI implementation, and 2) it attempts to maximize the a posteriori probability by making the locally optimum choice at each stage with the hope of finding the global minimum Euclidean distance for every transmitted bit x_k element of {-1, +1}. Compared to the soft K-best detector, the proposed solution significantly reduces the complexity because sorting is not required, while still maintaining good bit error rate (BER) performance. The proposed greedy detection algorithm has been designed and synthesized for a 4 x 4 16-QAM MIMO system in a TSMC 65 nm CMOS technology. The detector achieves a maximum throughput of 600 Mbps with a 0.79 mm2 core area.Nokia CorporationNational Science Foundatio

Chiral Logs in Quenched QCD

The quenched chiral logs are examined on a $16^3 \times 28$ lattice with Iwasaki gauge action and overlap fermions. The pion decay constant $f_{\pi}$ is used to set the lattice spacing, $a = 0.200(3) {\rm fm}$. With pion mass as low as $\sim 180 {\rm MeV}$, we see the quenched chiral logs clearly in $m_{\pi}^2/m$ and $f_P$, the pseudoscalar decay constant. We analyze the data to determine how low the pion mass needs to be in order for the quenched one-loop chiral perturbation theory ($\chi$PT) to apply. With the constrained curve-fitting method, we are able to extract the quenched chiral log parameter $\delta$ together with other low-energy parameters. Only for $m_{\pi} \leq 300 {\rm MeV}$ do we obtain a consistent and stable fit with a constant $\delta$ which we determine to be 0.24(3)(4) (at the chiral scale $\Lambda_{\chi}=0.8 {\rm GeV}$). By comparing to the $12^3 \times 28$ lattice, we estimate the finite volume effect to be about 2.7% for the smallest pion mass. We also fitted the pion mass to the form for the re-summed cactus diagrams and found that its applicable region is extended farther than the range for the one-loop formula, perhaps up to $m_{\pi} \sim 500-600$ MeV. The scale independent $\delta$ is determined to be 0.20(3) in this case. We study the quenched non-analytic terms in the nucleon mass and find that the coefficient $C_{1/2}$ in the nucleon mass is consistent with the prediction of one-loop $\chi$PT\@. We also obtain the low energy constant $L_5$ from $f_{\pi}$. We conclude from this study that it is imperative to cover only the range of data with the pion mass less than $\sim 300 {\rm MeV}$ in order to examine the chiral behavior of the hadron masses and decay constants in quenched QCD and match them with quenched one-loop $\chi$PT\@.Comment: 37 pages and 24 figures, pion masses are fitted to the form for the re-summed cactus diagrams, figures added, to appear in PR

Bayesian Quality-Diversity approaches for constrained optimization problems with mixed continuous, discrete and categorical variables

Complex engineering design problems, such as those involved in aerospace, civil, or energy engineering, require the use of numerically costly simulation codes in order to predict the behavior and performance of the system to be designed. To perform the design of the systems, these codes are often embedded into an optimization process to provide the best design while satisfying the design constraints. Recently, new approaches, called Quality-Diversity, have been proposed in order to enhance the exploration of the design space and to provide a set of optimal diversified solutions with respect to some feature functions. These functions are interesting to assess trade-offs. Furthermore, complex engineering design problems often involve mixed continuous, discrete, and categorical design variables allowing to take into account technological choices in the optimization problem. In this paper, a new Quality-Diversity methodology based on mixed continuous, discrete and categorical Bayesian optimization strategy is proposed. This approach allows to reduce the computational cost with respect to classical Quality - Diversity approaches while dealing with discrete choices and constraints. The performance of the proposed method is assessed on a benchmark of analytical problems as well as on an industrial design optimization problem dealing with aerospace systems

Gaussian mixture model for robust design optimization of planar steel frames

A new method is presented for an application of the Gaussian mixture model (GMM) to a multi-objective robust design optimization (RDO) of planar steel frame structures under aleatory (stochastic) uncertainty in material properties, external loads, and discrete design variables. Uncertainty in the discrete design variables is modeled in the wide range between the smallest and largest values in the catalog of the cross-sectional areas. A weighted sum of Gaussians is statistically trained based on the sampled training data to capture an underlying joint probability distribution function (PDF) of random input variables and the corresponding structural response. A simple regression function for predicting the structural response can be found by extracting the information from a conditional PDF, which is directly derived from the captured joint PDF. A multi-objective RDO problem is formulated with three objective functions, namely, the total mass of the structure, and the mean and variance values of the maximum inter-story drift under some constraints on design strength and serviceability requirements. The optimization problem is solved using a multi-objective genetic algorithm utilizing the trained GMM for calculating the statistical values of objective and constraint functions to obtain Pareto-optimal solutions. Since the three objective functions are highly conflicting, the best trade-off solution is desired and found from the obtained Pareto-optimal solutions by performing fuzzy-based compromise programming. The robustness and feasibility of the proposed method for finding the RDO of planar steel frame structures with discrete variables are demonstrated through two design examples