Large-scale lattice Boltzmann simulations of complex fluids: advances through the advent of computational grids

During the last two years the RealityGrid project has allowed us to be one of the few scientific groups involved in the development of computational grids. Since smoothly working production grids are not yet available, we have been able to substantially influence the direction of software development and grid deployment within the project. In this paper we review our results from large scale three-dimensional lattice Boltzmann simulations performed over the last two years. We describe how the proactive use of computational steering and advanced job migration and visualization techniques enabled us to do our scientific work more efficiently. The projects reported on in this paper are studies of complex fluid flows under shear or in porous media, as well as large-scale parameter searches, and studies of the self-organisation of liquid cubic mesophases. Movies are available at http://www.ica1.uni-stuttgart.de/~jens/pub/05/05-PhilTransReview.htmlComment: 18 pages, 9 figures, 4 movies available, accepted for publication in Phil. Trans. R. Soc. London Series

Production of cold molecules via magnetically tunable Feshbach resonances

Magnetically tunable Feshbach resonances were employed to associate cold diatomic molecules in a series of experiments involving both atomic Bose as well as two spin component Fermi gases. This review illustrates theoretical concepts of both the particular nature of the highly excited Feshbach molecules produced and the techniques for their association from unbound atom pairs. Coupled channels theory provides the rigorous formulation of the microscopic physics of Feshbach resonances in cold gases. Concepts of dressed versus bare energy states, universal properties of Feshbach molecules, as well as the classification in terms of entrance- and closed-channel dominated resonances are introduced on the basis of practical two-channel approaches. Their significance is illustrated for several experimental observations, such as binding energies and lifetimes with respect to collisional relaxation. Molecular association and dissociation are discussed in the context of techniques involving linear magnetic field sweeps in cold Bose and Fermi gases as well as pulse sequences leading to Ramsey-type interference fringes. Their descriptions in terms of Landau-Zener, two-level mean field as well as beyond mean field approaches are reviewed in detail, including the associated ranges of validity.Comment: 50 pages, 26 figures, to be published in Reviews of Modern Physics, final version with updated reference

Theory of ultracold Fermi gases

The physics of quantum degenerate Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions which play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems interactions are characterized by a single parameter, the s-wave scattering length, whose value can be tuned using an external magnetic field near a Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, of the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to non-perturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare the theoretical predictions with the available experimental results.Comment: Revised and abridged version accepted for publication in Rev. Mod. Phys.: 63 pages, 36 figure

On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients

We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique. We transform the two-dimensional two coupled variable coefficients nonlinear Schr\"{o}dinger equations into Manakov equation with a constraint that connects diffraction and gain parameters with nonlinearity parameter. We investigate the characteristics of the constructed vector rogue wave solutions with four different forms of diffraction parameters. We report some interesting patterns that occur in the rogue wave structures. Further, we construct vector dark rogue wave solutions of the two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients and report some novel characteristics that we observe in the vector dark rogue wave solutions.Comment: Accepted for publication in The European Physical Journal

A Monte Carlo approach to statics and dynamics of quantum fluids

The main objective of the thesis is to study static and/or dynamic properties of a set of quantum fluids by means of quantum Monte Carlo techniques, mainly using the path integral formalism to obtain results both at zero temperature and finite temperature. First, we present briefly some of the more important quantum Monte Carlo methods, and introduce the Path Integral Monte Carlo (PIMC) method, which has been used during all this thesis, as well as the Path Integral Ground State (PIGS), which is an extension of the first at ground state. After introducing the basic formalism, we comment on the approximations needed and provide a comparison between different actions. We also comment on parallelization schemes and advanced sampling techniques. The first results shown in this thesis are for the phase diagram of a one-dimensional Coulomb gas, which have been obtained using the PIMC method. The phase diagram have been constructed mainly by calculating energetic and structural properties. The obtained results extend previous knowledge of different phases in the one-dimensional Coulomb gas at zero temperature. Our results show the existence of a quantum Wigner crystal regime and a Ideal Fermi gas regime at low temperatures. As temperature increases, we reach a classic Wigner crystal regime and a classical gas. In the following chapter we show the results of a quasi-one-dimensional para-H2. The aim of this work is to see how the quasi-one-dimensionality affects the Luttinger parameter when comparing it with the pure one-dimensional case. This is done at zero temperature using PIGS. As para-hydrogen is an important candidate to superfluidity, the main idea behind study a quasi-one-dimensional system is to reduce dimensionality in order to soften intermolecular interaction. For that, we try different external potentials to control the opening of the system in two dimensions. Despite an increase in the Luttinger parameter in the various quasi-one-dimensional cases, it still does not reach the values displaying superfluidity. The next work shown in the thesis is our extensive study of the dynamic structure factor for the 4He. Using Path Integral Monte Carlo, we compute the intermediate scattering function at different temperatures and perform an inversion in order to gain access at the dynamics of the system. Despite the ill-posed problem of this inversion, we obtain results in a qualitative agreement with the experiments and prove that our method of inversion, despite having to yield with inversion problems achieves to obtain better numerical results for 4He at finite temperature than the ones previously reported. In this sense, we provide comparisons with the Maximum Entropy method and with experimental results. The study at different temperatures shows us the dissappearance of the roton peak when we cross T=2.17K from the superfluid regime to the normal fluid. We also observe a kink in the momentum distribution at the superfluid regime that dissappears at higher temperatures, for which does not exist an explanation in the theory. In the final chapter of the thesis we provide a method to sample complex-time correlation functions whose aim is to obtain better dynamic structure factor functions than the ones obtained via pure imaginary-time correlation functions. This model has already been tested for single-particle systems. Our aim is to test it for multi-particle systems, and to see if we can still recover good results at a reasonable high complex-time when the number of particles is closer to the typical simulation values of real systems. We tested it with particles interacting with an harmonic potential. Despite an increased variance compared with the one-particle case, we obtain good results that allow us to obtain the dynamic structure factor. Comparing the results with ones obtained at pure-imaginary time, we show how the complex-time inversion is superior and provides results closer to the exact ones.L'objectiu principal d'aquesta tesi es l'estudi de propietats estàtiques i dinàmiques de diferents fluids quàntics utilitzant tècniques de Monte Carlo quàntiques, principalment emprant el formalisme de path integrals per obtenir resultats tan a temperatura zero com a temperatura finita. Primer de tot, presentem els mètodes de Monte Carlo quàntics més importants, i introduïm el mètode de Path Integral Monte Carlo (PIMC), que fem servir al llarg de tota la tesi, i el mètode de Path Integral Ground State (PIGS), que es una extensió del primer però a temperatura zero. Després d'introduir el formalisme bàsic, comentem les diferents aproximacions necessàries i aportem una comparació entre elles. També expliquem un possible mètode de paral·lelització i tècniques de mostreig avançat. Els primers resultats que mostrem en aquesta tesi son pel diagrama de fases d'un gas de Coulomb unidimensional, que hem obtingut emprant PIMC. Hem construït el diagrama de fases mitjançant el càlcul de propietats energètiques i estructurals. Els nostres resultats amplien estudis previs que s'havien realitzat pel mateix sistema a temperatura zero. Els nostres resultats mostren l'existència d'un règim de cristall de Wigner quàntic i un d'un gas de Fermi ideal a temperatures baixes. Incrementant la temperatura obtenim un cristall de Wigner clàssic i un gas clàssic. En el següent capítol ensenyem els resultats per un sistema quasi-unidimensional de parahidrogen. L'objectiu d'aquest estudi es veure si la quasi-unidimensionalitat afecta al paràmetre de Luttinger quan el comparem pel cas purament unidimensional. Això ho fem a temperatura zero utilitzant PIGS. Sent el parahidrogen un fort candidat a ser superfluid, la idea principal es veure si reduint la dimensionalitat del sistema podem alleugerir suficient la interacció intermolecular. Per fer-ho, provem diferents potencials externs per controlar l'obertura del sistema en dues de les dimensions. Tot i l'increment del paràmetre de Luttinger respecte al cas unidimensional, aquest no arriba als valors esperats per mostrar superfluïdesa. El següents resultats són del nostre estudi sobre el factor d'estructura dinàmic per 4He. Utilitzant PIMC, calculem la funció de dispersió a diferents temperatures i fem una inversió per tal d'accedir a les propietats dinàmiques del sistema. Tot i la naturalesa de problema mal posat d'aquesta inversió, obtenim resultats qualitativament bons en comparació amb els experimentals, i provem que el nostre mètode d'inversió obté resultats superiors per 4He a temperatura finita que els obtinguts prèviament utilitzant altres mètodes. En aquest sentit, aportem una comparació amb el mètode de màxima entropia i amb resultats experimentals. L'estudi a diferents temperatures ens deixa veure la desaparició del pic del rotó quan creuem T=2.17K des de el règim superfluid al fluid normal. També observem una curvatura estranya en la distribució de moments en el règim de superfluïdesa que desapareix a temperatures més elevades, i pel qual no existeix cap explicació teòrica. Finalment, mostrem un mètode per calcular funcions de correlació en temps complex, l'objectiu del qual es obtenir factors d'estructura dinàmic superiors als obtinguts en temps purament imaginari. Aquest model ha sigut provat amb èxit en sistemes d'una sola partícula. El nostre objectiu es veure si obtenim resultats bons en sistemes amb més partícules, i si el temps complex màxim al que podem accedir no es redueix amb aquest increment. Tot i l'increment en la variança, obtenim bons resultats pel factor dinàmic i, comparant-los amb els obtinguts amb temps imaginari, podem veure com el temps complex ofereix resultats més pròxims als exactes

Proceedings for the ICASE Workshop on Heterogeneous Boundary Conditions

Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposition can be made based on many different criteria, and the choice of interface of internal boundary conditions are numerous. The various regions under study may have different dynamical balances, indicating that different physical processes are dominating the flow in these regions. This conference was called in recognition of the need to more clearly define the nature of these complex problems. This proceedings is a collection of the presentations and the discussion groups

On metrics of curvature 1 with four conic singularities on tori and on the sphere

We discuss conformal metrics of curvature 1 on tori and on the sphere, with four conic singularities whose angles are multiples of pi/2. Besides some general results we study in detail the family of such symmetric metrics on the sphere, with angles (pi/2,3pi/2,pi/2,3pi/2).Comment: 25 pages, 5 figure