Bragg Spectroscopy of Cold Atomic Fermi Gases

We propose a Bragg spectroscopy experiment to measure the onset of superfluid pairing in ultracold trapped Fermi gases. In particular, we study two component Fermi gases in the weak coupling BCS and BEC limits as well as in the strong coupling unitarity limit. The low temperature Bragg spectrum exhibits a gap directly related to the pair-breaking energy. Furthermore, the Bragg spectrum has a large maximum just below the critical temperature when the gas is superfluid in the BCS limit. In the unitarity regime, we show how the pseudogap in the normal phase leads to a significant suppression of the low frequency Bragg spectrum.Comment: 8 pages, 9 figures. Typos corrected. Reference update

Centralized content delivery infrastructure exploiting resource pools : performance models and asymptotics

textWe consider a centralized content delivery infrastructure where a large number of storage-intensive files are replicated across several collocated servers. To achieve scalable delays in file downloads under stochastic loads, we allow multiple servers to work together as a pooled resource to meet individual download requests. In such systems basic questions include: How and where to replicate files? How significant are the gains of resource pooling over policies which use single server per request? What are the tradeoffs among conflicting metrics such as delays, reliability and recovery costs, and power? How robust is performance to heterogeneity and choice of fairness criterion? In this thesis we provide a simple performance model for large systems towards addressing these basic questions. For large systems where the overall system load is proportional to the number of servers, we establish scaling laws among delays, system load, number of file replicas, demand heterogeneity, power, and network capacity.Electrical and Computer Engineerin

Particle Filtering for Large Dimensional State Spaces with Multimodal Observation Likelihoods

We study efficient importance sampling techniques for particle filtering (PF) when either (a) the observation likelihood (OL) is frequently multimodal or heavy-tailed, or (b) the state space dimension is large or both. When the OL is multimodal, but the state transition pdf (STP) is narrow enough, the optimal importance density is usually unimodal. Under this assumption, many techniques have been proposed. But when the STP is broad, this assumption does not hold. We study how existing techniques can be generalized to situations where the optimal importance density is multimodal, but is unimodal conditioned on a part of the state vector. Sufficient conditions to test for the unimodality of this conditional posterior are derived. The number of particles, N, to accurately track using a PF increases with state space dimension, thus making any regular PF impractical for large dimensional tracking problems. We propose a solution that partially addresses this problem. An important class of large dimensional problems with multimodal OL is tracking spatially varying physical quantities such as temperature or pressure in a large area using a network of sensors which may be nonlinear and/or may have non-negligible failure probabilities.Comment: To appear in IEEE Trans. Signal Processin

Harnessing entropy to enhance toughness in reversibly crosslinked polymer networks

Reversible crosslinking is a design paradigm for polymeric materials, wherein they are microscopically reinforced with chemical species that form transient crosslinks between the polymer chains. Besides the potential for self-healing, recent experimental work suggests that freely diffusing reversible crosslinks in polymer networks, such as gels, can enhance the toughness of the material without substantial change in elasticity. This presents the opportunity for making highly elastic materials that can be strained to a large extent before rupturing. Here, we employ Gaussian chain theory, molecular simulation, and polymer self-consistent field theory for networks to construct an equilibrium picture for how reversible crosslinks can toughen a polymer network without affecting its linear elasticity. Maximisation of polymer entropy drives the reversible crosslinks to bind preferentially near the permanent crosslinks in the network, leading to local molecular reinforcement without significant alteration of the network topology. In equilibrium conditions, permanent crosslinks share effectively the load with neighbouring reversible crosslinks, forming multi-functional crosslink points. The network is thereby globally toughened, while the linear elasticity is left largely unaltered. Practical guidelines are proposed to optimise this design in experiment, along with a discussion of key kinetic and timescale considerations

Simultaneous Exoplanet Characterization and deep wide-field imaging with a diffractive pupil telescope

High-precision astrometry can identify exoplanets and measure their orbits and masses, while coronagraphic imaging enables detailed characterization of their physical properties and atmospheric compositions through spectroscopy. In a previous paper, we showed that a diffractive pupil telescope (DPT) in space can enable sub-microarcsecond accuracy astrometric measurements from wide-field images by creating faint but sharp diffraction spikes around the bright target star. The DPT allows simultaneous astrometric measurement and coronagraphic imaging, and we discuss and quantify in this paper the scientific benefits of this combination for exoplanet science investigations: identification of exoplanets with increased sensitivity and robustness, and ability to measure planetary masses to high accuracy. We show how using both measurements to identify planets and measure their masses offers greater sensitivity and provides more reliable measurements than possible with separate missions, and therefore results in a large gain in mission efficiency. The combined measurements reliably identify potentially habitable planets in multiple systems with a few observations, while astrometry or imaging alone would require many measurements over a long time baseline. In addition, the combined measurement allows direct determination of stellar masses to percent-level accuracy, using planets as test particles. We also show that the DPT maintains the full sensitivity of the telescope for deep wide-field imaging, and is therefore compatible with simultaneous scientific observations unrelated to exoplanets. We conclude that astrometry, coronagraphy, and deep wide-field imaging can be performed simultaneously on a single telescope without significant negative impact on the performance of any of the three techniques.Comment: 15 pages, 6 figures. This second paper, following the paper describing the diffractive pupil telescope (DPT) astrometric technique, shows how simultaneous astrometry and coronagraphy observations, enabled by the DPT concept, constrain the orbital parameters and mass of exoplanet