Desenvolupament de codis numèrics per a la resolució de fluxos turbulents en ordinadors paral·lels emprant discretitzacions tipus symmetry-preserving

Projecte de recerca elaborat a partir d’una estada a la University of Groningen, Holanda, entre 2007 i 2009. La simulació directa de la turbulència (DNS) és una eina clau dins de la mecànica de fluids computacional. Per una banda permet conèixer millor la física de la turbulència i per l'altra els resultats obtinguts són claus per el desenvolupament dels models de turbulència. No obstant, el DNS no és una tècnica vàlida per a la gran majoria d'aplicacions industrials degut al elevats costos computacionals. Per tant, és necessari cert grau de modelització de la turbulència. En aquest context, s'han introduïts importants millores basades en la modelització del terme convectiu (no lineal) emprant symmetry-preserving regularizations. En tracta de modificar adequadament el terme convectiu a fi de reduir la producció d'escales més i més petites (vortex-stretching) tot mantenint tots els invariants de les equacions originals. Fins ara, aquest models s'han emprat amb èxit per nombres de Rayleigh (Ra) relativament elevats. En aquest punt, disposar de resultats DNS per a configuracions més complexes i nombres de Ra més elevats és clau. En aquest contexte, s'han dut a terme simulacions DNS en el supercomputador MareNostrum d'una Differentially Heated Cavity amb Ra=1e11 i Pr=0.71 durant el primer any dels dos que consta el projecte. A més a més, s'ha adaptat el codi a fi de poder simular el fluxe al voltant d'un cub sobre una pared amb Re=10000. Aquestes simulacions DNS són les més grans fetes fins ara per aquestes configuracions i la seva correcta modelització és un gran repte degut la complexitat dels fluxes. Aquestes noves simulacions DNS estan aportant nous coneixements a la física de la turbulència i aportant resultats indispensables per al progrés de les modelitzacións tipus symmetry-preserving regularization.

The equity core and the Lorenz-maximal allocations in the equal division core

In this paper, we characterize the non-emptiness of the equity core (Selten, 1978) and provide a method, easy to implement, for computing the Lorenz-maximal allocations in the equal division core (Dutta-Ray, 1991). Both results are based on a geometrical decomposition of the equity core as a finite union of polyhedrons. Keywords: Cooperative game, equity core, equal division core, Lorenz domination. JEL classification: C71

Reduction of symmetry in grandite solid solution

The results of a crystal structure refinement of an anisotropic grandite garnet specimen with composition Gro36-4 And63-6 are given. The structure obtained has orthorrombic symmetry (space group Fddd) and is compared with similar results obtained by other authors. In all cases the reduction of symmetry is due to the ordering of Fe3+ and Al in octahedral sites. Non cubic structures of grandites are discussed in connection with optical, morphological an grou-th features of these minerals.

Travelling-stripe forcing generates hexagonal patterns

We study the response of Turing stripe patterns to a simple spatiotemporal forcing. This forcing has the form of a traveling wave and is spatially resonant with the characteristic Turing wavelength. Experiments conducted with the photosensitive chlorine dioxide-iodine-malonic acid reaction reveal a striking symmetry-breaking phenomenon of the intrinsic striped patterns giving rise to hexagonal lattices for intermediate values of the forcing velocity. The phenomenon is understood in the framework of the corresponding amplitude equations, which unveils a complex scenario of dynamical behaviors.

Travelling-stripe forcing generates hexagonal patterns

We study the response of Turing stripe patterns to a simple spatiotemporal forcing. This forcing has the form of a traveling wave and is spatially resonant with the characteristic Turing wavelength. Experiments conducted with the photosensitive chlorine dioxide-iodine-malonic acid reaction reveal a striking symmetry-breaking phenomenon of the intrinsic striped patterns giving rise to hexagonal lattices for intermediate values of the forcing velocity. The phenomenon is understood in the framework of the corresponding amplitude equations, which unveils a complex scenario of dynamical behaviors.

Spontaneous mirror symmetry breaking in the limited enantioselective autocatalysis model: abyssal hydrotermal vents as scenario for the emergence of chirality in prebiotic chemistry

The emergence of chirality in enantioselective autocatalysis for compounds unable to transform according to the Frank-like reaction network is discussed with respect to the controversial limited enantioselectivity (LES) model composed of coupled enantioselective and non-enantioselective autocatalyses. The LES model cannot lead to spontaneous mirror symmetry breaking (SMSB) either in closed systems with a homogeneous temperature distribution or in closed systems with a stationary non-uniform temperature distribution. However, simulations of chemical kinetics in a two-compartment model demonstrate that SMSB may occur if both autocatalytic reactions are spatially separated at different temperatures in different compartments but coupled under the action of a continuous internal flow. In such conditions, the system can evolve, for certain reaction and system parameters, toward a chiral stationary state; that is, the system is able to reach a bifurcation point leading to SMSB. Numerical simulations in which reasonable chemical parameters have been used suggest that an ade- quate scenario for such a SMSB would be that of abyssal hydrothermal vents, by virtue of the typical temper- ature gradients found there and the role of inorganic solids mediating chemical reactions in an enzyme-like role. Key Words: Homochirality Prebiotic chemistry.

The equity core and the core

In this paper we study the equity core (Selten, 1978) and compare it with the core. A payo vector is in the equity core if no coalition can divide its value among its members proportionally to a given weight system and, in this way, give more to each member than the amount he or she receives in the payo vector. We show that the equity core is a compact extension of the core and that, for non-negative games, the intersection of all equity cores with respect to all weights coincides with the core of the game. Keywords: Cooperative game, equity core, equal division core, core. JEL classi cation: C71

A security layer for JXTA core protocols

JXTA define un conjunto de seis protocolos básicos especialmente adecuados para una computación ad hoc, permanente, multi-hop, peer-to-peer (P2P). Estos protocolos permiten que los iguales cooperen y formen grupos autónomos de pares. Este artículo presenta un método que proporciona servicios de seguridad en los protocolos básicos: protección de datos, autenticidad, integridad y no repudio. Los mecanismos que se presentan son totalmente distribuidos y basados ¿¿en un modelo puro peer-to-peer, que no requieren el arbitraje de un tercero de confianza o una relación de confianza establecida previamente entre pares, que es uno de los principales retos en este tipo de entornos.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schr odinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schrödinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Consistency and the core of multi-sided assignment markets

[cat] En aquest treball es demostra que en el domini dels jocs d’assignació equilibrats multisectorials (Quint, 1991), el core és l’única solució no buida que satisfà derived consistency i projection consistency. També es caracteritza el core en tota la classe dels jocs d’assignació multisectorials amb els axiomes de singleness best, individual antimonotonicity i derived consistency. Com a casos particulars, s’obtenen dues noves axiomàtiques del core per als jocs d’assignació bilaterals (Shapley and Shubik, 1972).

Consistency and the core of multi-sided assignment markets

[cat] En aquest treball es demostra que en el domini dels jocs d’assignació equilibrats multisectorials (Quint, 1991), el core és l’única solució no buida que satisfà derived consistency i projection consistency. També es caracteritza el core en tota la classe dels jocs d’assignació multisectorials amb els axiomes de singleness best, individual antimonotonicity i derived consistency. Com a casos particulars, s’obtenen dues noves axiomàtiques del core per als jocs d’assignació bilaterals (Shapley and Shubik, 1972).

BioSuper: A web tool for the superimposition of biomolecules and assemblies with rotational symmetry

Background Most of the proteins in the Protein Data Bank (PDB) are oligomeric complexes consisting of two or more subunits that associate by rotational or helical symmetries. Despite the myriad of superimposition tools in the literature, we could not find any able to account for rotational symmetry and display the graphical results in the web browser. Results BioSuper is a free web server that superimposes and calculates the root mean square deviation (RMSD) of protein complexes displaying rotational symmetry. To the best of our knowledge, BioSuper is the first tool of its kind that provides immediate interactive visualization of the graphical results in the browser, biomolecule generator capabilities, different levels of atom selection, sequence-dependent and structure-based superimposition types, and is the only web tool that takes into account the equivalence of atoms in side chains displaying symmetry ambiguity. BioSuper uses ICM program functionality as a core for the superimpositions and displays the results as text, HTML tables and 3D interactive molecular objects that can be visualized in the browser or in Android and iOS platforms with a free plugin. Conclusions BioSuper is a fast and functional tool that allows for pairwise superimposition of proteins and assemblies displaying rotational symmetry. The web server was created after our own frustration when attempting to superimpose flexible oligomers. We strongly believe that its user-friendly and functional design will be of great interest for structural and computational biologists who need to superimpose oligomeric proteins (or any protein). BioSuper web server is freely available to all users at http://ablab.ucsd.edu/BioSuper webcite.