The Path Integral for 1+1-dimensional QCD

We derive a path integral expression for the transition amplitude in 1+1-dimensional QCD starting from canonically quantized QCD. Gauge fixing after quantization leads to a formulation in terms of gauge invariant but curvilinear variables. Remainders of the curved space are Jacobians, an effective potential, and sign factors just as for the problem of a particle in a box. Based on this result we derive a Faddeev-Popov like expression for the transition amplitude avoiding standard infinities that are caused by integrations over gauge equivalent configurations.Comment: 16 pages, LaTeX, 3 PostScript figures, uses epsf.st

Inducing or suppressing the anisotropy in multilayers based on CoFeB

Controlling the uniaxial magnetic anisotropy is of practical interest to a wide variety of applications. We study Co$_{40}$Fe$_{40}$B$_{20}$ single films grown on various crystalline orientations of LiNbO$_3$ substrates and on oxidized silicon. We identify the annealing conditions that are appropriate to induce or suppress uniaxial anisotropy. Anisotropy fields can be increased by annealing up to 11 mT when using substrates with anisotropic surfaces. They can be decreased to below 1 mT when using isotropic surfaces. In the first case, the observed increase of the anisotropy originates from the biaxial strain in the film caused by the anisotropic thermal contraction of the substrate when back at room temperature after strain relaxation during annealing. In the second case, anisotropy is progressively removed by applying successive orthogonal fields that are assumed to progressively suppress any chemical ordering within the magnetic film. The method can be applied to CoFeB/Ru/CoFeB synthetic antiferromagnets but the tuning of the anisotropy comes with a decrease of the interlayer exchange coupling and a drastic change of the exchange stiffness

LINVIEW: Incremental View Maintenance for Complex Analytical Queries

Many analytics tasks and machine learning problems can be naturally expressed by iterative linear algebra programs. In this paper, we study the incremental view maintenance problem for such complex analytical queries. We develop a framework, called LINVIEW, for capturing deltas of linear algebra programs and understanding their computational cost. Linear algebra operations tend to cause an avalanche effect where even very local changes to the input matrices spread out and infect all of the intermediate results and the final view, causing incremental view maintenance to lose its performance benefit over re-evaluation. We develop techniques based on matrix factorizations to contain such epidemics of change. As a consequence, our techniques make incremental view maintenance of linear algebra practical and usually substantially cheaper than re-evaluation. We show, both analytically and experimentally, the usefulness of these techniques when applied to standard analytics tasks. Our evaluation demonstrates the efficiency of LINVIEW in generating parallel incremental programs that outperform re-evaluation techniques by more than an order of magnitude.Comment: 14 pages, SIGMO

Implementation of the Backlund transformations for the Ablowitz-Ladik hierarchy

The derivation of the Backlund transformations (BTs) is a standard problem of the theory of the integrable systems. Here, I discuss the equations describing the BTs for the Ablowitz-Ladik hierarchy (ALH), which have been already obtained by several authors. The main aim of this work is to solve these equations. This can be done in the framework of the so-called functional representation of the ALH, when an infinite number of the evolutionary equations are replaced, using the Miwa's shifts, with a few equations linking tau-functions with different arguments. It is shown that starting from these equations it is possible to obtain explicit solutions of the BT equations. In other words, the main result of this work is a presentation of the discrete BTs as a superposition of an infinite number of evolutionary flows of the hierarchy. These results are used to derive the superposition formulae for the BTs as well as pure soliton solutions.Comment: 20 page

The influence of anesthetics, neurotransmitters and antibiotics on the relaxation processes in lipid membranes

In the proximity of melting transitions of artificial and biological membranes fluctuations in enthalpy, area, volume and concentration are enhanced. This results in domain formation, changes of the elastic constants, changes in permeability and slowing down of relaxation processes. In this study we used pressure perturbation calorimetry to investigate the relaxation time scale after a jump into the melting transition regime of artificial lipid membranes. This time corresponds to the characteristic rate of domain growth. The studies were performed on single-component large unilamellar and multilamellar vesicle systems with and without the addition of small molecules such as general anesthetics, neurotransmitters and antibiotics. These drugs interact with membranes and affect melting points and profiles. In all systems we found that heat capacity and relaxation times are related to each other in a simple manner. The maximum relaxation time depends on the cooperativity of the heat capacity profile and decreases with a broadening of the transition. For this reason the influence of a drug on the time scale of domain formation processes can be understood on the basis of their influence on the heat capacity profile. This allows estimations of the time scale of domain formation processes in biological membranes.Comment: 12 pages, 6 figure

Characterization of a Combined CARS and Interferometric Rayleigh Scattering System

This paper describes the characterization of a combined Coherent anti-Stokes Raman Spectroscopy and Interferometric Rayleigh Scattering (CARS-IRS) system by reporting the accuracy and precision of the measurements of temperature, species mole fraction of N2, O2, and H2, and two-components of velocity. A near-adiabatic H2-air Hencken burner flame was used to provide known properties for measurements made with the system. The measurement system is also demonstrated in a small-scale Mach 1.6 H2-air combustion-heated supersonic jet with a co-flow of H2. The system is found to have a precision that is sufficient to resolve fluctuations of flow properties in the mixing layer of the jet

Statistical Mechanics of Kinks in (1+1)-Dimensions: Numerical Simulations and Double Gaussian Approximation

We investigate the thermal equilibrium properties of kinks in a classical \F^4 field theory in $1+1$ dimensions. From large scale Langevin simulations we identify the temperature below which a dilute gas description of kinks is valid. The standard dilute gas/WKB description is shown to be remarkably accurate below this temperature. At higher, ``intermediate'' temperatures, where kinks still exist, this description breaks down. By introducing a double Gaussian variational ansatz for the eigenfunctions of the statistical transfer operator for the system, we are able to study this region analytically. In particular, our predictions for the number of kinks and the correlation length are in agreement with the simulations. The double Gaussian prediction for the characteristic temperature at which the kink description ultimately breaks down is also in accord with the simulations. We also analytically calculate the internal energy and demonstrate that the peak in the specific heat near the kink characteristic temperature is indeed due to kinks. In the neighborhood of this temperature there appears to be an intricate energy sharing mechanism operating between nonlinear phonons and kinks.Comment: 28 pages (8 Figures not included, hard-copies available), Latex, LA-UR-93-276

Diffusion controlled initial recombination

This work addresses nucleation rates in systems with strong initial recombination. Initial (or `geminate') recombination is a process where a dissociated structure (anion, vortex, kink etc.) recombines with its twin brother (cation, anti-vortex, anti-kink) generated in the same nucleation event. Initial recombination is important if there is an asymptotically vanishing interaction force instead of a generic saddle-type activation barrier. At low temperatures, initial recombination strongly dominates homogeneous recombination. In a first part, we discuss the effect in one-, two-, and three-dimensional diffusion controlled systems with spherical symmetry. Since there is no well-defined saddle, we introduce a threshold which is to some extent arbitrary but which is restricted by physically reasonable conditions. We show that the dependence of the nucleation rate on the specific choice of this threshold is strongest for one-dimensional systems and decreases in higher dimensions. We discuss also the influence of a weak driving force and show that the transport current is directly determined by the imbalance of the activation rate in the direction of the field and the rate against this direction. In a second part, we apply the results to the overdamped sine-Gordon system at equilibrium. It turns out that diffusive initial recombination is the essential mechanism which governs the equilibrium kink nucleation rate. We emphasize analogies between the single particle problem with initial recombination and the multi-dimensional kink-antikink nucleation problem.Comment: LaTeX, 11 pages, 1 ps-figures Extended versio

Magnetic domain size tuning in asymmetric Pd/Co/W/Pd multilayers with perpendicular magnetic anisotropy

CAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIORFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOMagnetic multilayers presenting perpendicular magnetic anisotropy (PMA) have great potential for technological applications. On the path to develop further magnetic devices, one can adjust the physical properties of multilayered thin films by modifying their interfaces, thus determining the magnetic domain type, chirality, and size. Here, we demonstrate the tailoring of the domain pattern by tuning the perpendicular anisotropy, the saturation magnetization, and the interfacial Dzyaloshinskii-Moriya interaction (iDMI) in Pd/Co/Pd multilayers with the insertion of an ultrathin tungsten layer at the top interface. The average domain size decreases around 60% when a 0.2 nm thick W layer is added to the Co/Pd interface. Magnetic force microscopy images and micromagnetic simulations were contrasted to elucidate the mechanisms that determine the domain textures and sizes. Our results indicate that both iDMI and PMA can be tuned by carefully changing the interfaces of originally symmetric multilayers, leading to magnetic domain patterns promising for high density magnetic memories.1151816CAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIORFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIORFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO0012012/51198-22017/10581-1309354/2015-3302950/2017-6436573/2018-

High-Dimensional Feature Selection by Feature-Wise Kernelized Lasso

The goal of supervised feature selection is to find a subset of input features that are responsible for predicting output values. The least absolute shrinkage and selection operator (Lasso) allows computationally efficient feature selection based on linear dependency between input features and output values. In this paper, we consider a feature-wise kernelized Lasso for capturing non-linear input-output dependency. We first show that, with particular choices of kernel functions, non-redundant features with strong statistical dependence on output values can be found in terms of kernel-based independence measures. We then show that the globally optimal solution can be efficiently computed; this makes the approach scalable to high-dimensional problems. The effectiveness of the proposed method is demonstrated through feature selection experiments with thousands of features.Comment: 18 page