Out of equilibrium dynamics of a Quantum Heisenberg Spin Glass

We study the out of equilibrium dynamics of the infinite range quantum Heisenberg spin glass model coupled to a thermal relaxation bath. The SU(2) spin algebra is generalized to SU(N) and we analyse the large-N limit. The model displays a dynamical phase transition between a paramagnetic and a glassy phase. In the latter, the system remains out of equilibrium and displays an aging phenomenon, which we characterize using both analytical and numerical methods. In the aging regime, the quantum fluctuation-dissipation relation is violated and replaced at very long time by its classical generalization, as in models involving simple spin algebras studied previously. We also discuss the effect of a finite coupling to the relaxation baths and their possible forms. This work completes and justifies previous studies on this model using a static approach.Comment: Minor change

Simulation of pore-scale flow using finite element-methods

I present a new finite element (FE) simulation method to simulate pore-scale flow. Within the pore-space, I solve a simplified form of the incompressible Navier-Stoke’s equation, yielding the velocity field in a two-step solution approach. First, Poisson’s equation is solved with homogeneous boundary conditions, and then the pore pressure is computed and the velocity field obtained for no slip conditions at the grain boundaries. From the computed velocity field I estimate the effective permeability of porous media samples characterized by thin section micrographs, micro-CT scans and synthetically generated grain packings. This two-step process is much simpler than solving the full Navier Stokes equation and therefore provides the opportunity to study pore geometries with hundreds of thousands of pores in a computationally more cost effective manner than solving the full Navier-Stoke’s equation. My numerical model is verified with an analytical solution and validated on samples whose permeabilities and porosities had been measured in laboratory experiments (Akanji and Matthai, 2010). Comparisons were also made with Stokes solver, published experimental, approximate and exact permeability data. Starting with a numerically constructed synthetic grain packings, I also investigated the extent to which the details of pore micro-structure affect the hydraulic permeability (Garcia et al., 2009). I then estimate the hydraulic anisotropy of unconsolidated granular packings. With the future aim to simulate multiphase flow within the pore-space, I also compute the radii and derive capillary pressure from the Young-Laplace equation (Akanji and Matthai,2010

4D electron imaging: principles and perspectives

In this perspective we highlight developments and concepts in the field of 4D electron imaging. With spatial and temporal resolutions reaching the picometer and femtosecond, respectively, the field is now embracing ultrafast electron diffraction, crystallography and microscopy. Here, we overview the principles involved in the direct visualization of structural dynamics with applications in chemistry, materials science and biology. The examples include the studies of complex isolated chemical reactions, phase transitions and cellular structures. We conclude with an outlook on the potential of the approach and with some questions that may define new frontiers of research

From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond

The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observations in the twentieth century. The connection between the two areas was first observed through Montgomery's work on the pair correlation of zeros of the Riemann zeta function. As its generalizations and consequences have motivated much of the following work, and to this day remains one of the most important outstanding conjectures in the field, it occupies a central role in our discussion below. We describe some of the many techniques and results from the past sixty years, especially the important roles played by numerical and experimental investigations, that led to the discovery of the connections and progress towards understanding the behaviors. In our survey of these two areas, we describe the common mathematics that explains the remarkable universality. We conclude with some thoughts on what might lie ahead in the pair correlation of zeros of the zeta function, and other similar quantities.Comment: Version 1.1, 50 pages, 6 figures. To appear in "Open Problems in Mathematics", Editors John Nash and Michael Th. Rassias. arXiv admin note: text overlap with arXiv:0909.491

A quantum mechanical NMR simulation algorithm for protein-scale spin systems

Nuclear magnetic resonance spectroscopy is one of the few remaining areas of physical chemistry for which polynomially scaling simulation methods have not so far been available. Here, we report such a method and illustrate its performance by simulating common 2D and 3D liquid state NMR experiments (including accurate description of spin relaxation processes) on isotopically enriched human ubiquitin - a protein containing over a thousand nuclear spins forming an irregular polycyclic three-dimensional coupling lattice. The algorithm uses careful tailoring of the density operator space to only include nuclear spin states that are populated to a significant extent. The reduced state space is generated by analyzing spin connectivity and decoherence properties: rapidly relaxing states as well as correlations between topologically remote spins are dropped from the basis set. In the examples provided, the resulting reduction in the quantum mechanical simulation time is by many orders of magnitude.Comment: Submitted for publicatio

An automated archival VLA transients survey

In this paper we present the results of a survey for radio transients using data obtained from the Very Large Array archive. We have reduced, using a pipeline procedure, 5037 observations of the most common pointings - i.e. the calibrator fields. These fields typically contain a relatively bright point source and are used to calibrate `target' observations: they are therefore rarely imaged themselves. The observations used span a time range ~ 1984 - 2008 and consist of eight different pointings, three different frequencies (8.4, 4.8 and 1.4 GHz) and have a total observing time of 435 hours. We have searched for transient and variable radio sources within these observations using components from the prototype LOFAR transient detection system. In this paper we present the methodology for reducing large volumes of Very Large Array data; and we also present a brief overview of the prototype LOFAR transient detection algorithms. No radio transients were detected in this survey, therefore we place an upper limit on the snapshot rate of GHz frequency transients > 8.0 mJy to rho less than or equal to 0.032 deg^-2 that have typical timescales 4.3 to 45.3 days. We compare and contrast our upper limit with the snapshot rates - derived from either detections or non-detections of transient and variable radio sources - reported in the literature. When compared with the current Log N - Log S distribution formed from previous surveys, we show that our upper limit is consistent with the observed population. Current and future radio transient surveys will hopefully further constrain these statistics, and potentially discover dominant transient source populations. In this paper we also briefly explore the current transient commissioning observations with LOFAR, and the impact they will make on the field.Comment: Accepted for publication in MNRA

Weakly Supervised Object Localization with Multi-fold Multiple Instance Learning

Object category localization is a challenging problem in computer vision. Standard supervised training requires bounding box annotations of object instances. This time-consuming annotation process is sidestepped in weakly supervised learning. In this case, the supervised information is restricted to binary labels that indicate the absence/presence of object instances in the image, without their locations. We follow a multiple-instance learning approach that iteratively trains the detector and infers the object locations in the positive training images. Our main contribution is a multi-fold multiple instance learning procedure, which prevents training from prematurely locking onto erroneous object locations. This procedure is particularly important when using high-dimensional representations, such as Fisher vectors and convolutional neural network features. We also propose a window refinement method, which improves the localization accuracy by incorporating an objectness prior. We present a detailed experimental evaluation using the PASCAL VOC 2007 dataset, which verifies the effectiveness of our approach.Comment: To appear in IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI