Speaker
Umberto Marini Bettolo Marconi

Description By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on the evolution of the one particle phase space distribution, f(r,v,t), rather than on the evolution of the average particle density, which features in dynamic density functional theory often employed to describe colloidal systems. In order to describe with sufficient accuracy the fluid structure at length scales comparable with the size of the particles we shall resort to methods similar to those of density functional theory (DFT) employed in the study of equilibrium and non equilibrium properties. In the case of hard-core fluids, DFT and its dynamical extension give excellent results and can be extended to more realistic fluids by using the van der Waals picture of decomposing the total inter-particle potential into a short-range repulsive potential and a long-range attractive potential tail. The first is treated by means of a reference hard-sphere system whilst the second is considered within the random phase approximation (RPA). A simple analysis of the equations is used to derive explicit expressions both for equilibrium thermodynamic quantities, such as pressure, compressibility etc., and for non equilibrium transport coefficients. In the second part of our presentation we shall introduce a a multicomponent extension of our theory and describe miscible and immiscible liquid mixtures under inhomogeneous, non steady conditions typical of confined fluid flows. We first derive from a microscopic level the evolution equations of the phase space distribution function of each component in terms of a set of self consistent fields, representing both body forces and viscous forces. Secondly, we solve numerically the resulting governing equations by means of the Lattice Boltzmann method whose implementation contains novel features with respect to existing approaches. Our model incorporates hydrodynamic flow, diffusion, surface tension,and the possibility for global and local viscosity variations. We validate our model by studying the bulk viscosity dependence of the mixture on concentration, packing fraction and size ratio. Finally we consider inhomogeneous systems and study the dynamics of mixtures in slits of molecular thickness and relate structural and flow properties.

Speaker
Reinhard Illner

Description Many processes in cell biology are driven by interactions between protein compounds and the DNA; because of the microscopic scales, the activation or deactivation of genes by such compounds are best described by random processes. I will begin by showing an example of such a process which gives rise to a random evolution known as a "transcriptional-translational oscillator (TTO)." It will be explained how TTOs can possibly interact to explain the origin of circadian rhythms in organisms. In a highly oscillatory regime TTO models turn (formally and rigorously) into ordinary dynamical systems, and there the oscillatory behaviour is easily seen to be the result of a Hopf bifurcation. This high oscillatory limit is a second level of description and is common in the math biology literature. Kolmogorov master equations for the original random evolution are the most complete level of description, and they allow (in principle) computing probabilities to find the system in a certain state at a certain time. These master equations are the third level of description, and they provide a link to kinetic theory, as they are simply linear kinetic equations. Close to the high frequency limit the random switchings in the DNA behaviour lead to inherent noise, and this noisy behaviour can be modelled via a diffusion approximation, derived from the Kolmogorov equations with the Chapman-Enskog expansion. This is the fourth and last level of description which will be shown.

Speaker
Francesco Zamponi

Description I will review the recent results that our group obtained on quantum optimization problems. These problems can be thought equivalently as 1) Hamiltonians describing the evolution of a quantum computer that attempts to solve complex optimization problems or 2) quantum spin glass Hamiltonians. Therefore, their analysis is relevant both for quantum computing and for the physics of quantum glasses. I will show that their spectrum can be extremely complex, being characterized by quantum glass transitions, and a continuum of level crossings. I will try to discuss the problem of localization in these models.

Speaker
Dan Gauthier

Description There is great current interest in investigating the dynamics of networks consisting of a large number of nodes and links, yet it is difficult to purposefully construct a network where the experimentalist has full control over the node and link properties and the network topology. In this talk, we describe our recent work on using field-programmable gate arrays (FPGAs) as an experimental tool for studying dynamics of large networks. A FPGA consists of a large number of programmable logic elements (>10,000) that perform user-controllable Boolean operations whose output can be wired in a flexible manner to the other elements. We will give several examples of the types of behaviors observed in this system, starting with the observation of chaos in a three-node autonomous time-delay network similar to that previously observed by our group using discrete electronic logic gates [1,2]. Other examples include: a true random number generator realized using a moderate-size autonomous network with 10's of nodes; cluster-synchronization in large networks where the nodes display excitable behavior; phase-transition behavior in autonomous and clocked Kauffman NK networks; and Kuramoto-like networks composed of coupled phase oscillators. [1] R. Zhang, H.L.D. de S. Cavalcante, Z. Gao, D.J. Gauthier, J.E.S. Socolar, M.M. Adams, and D.P. Lathrop, `Boolean chaos,' Phys. Rev. E, 80, 045202(R) (2009). [2] H. L. D. de S. Cavalcante, D. J. Gauthier, J. E. S. Socolar, and R. Zhang, `On the Origin of Chaos in Autonomous Boolean Networks,' Philos. Trans. Royal Soc. A, 368, 495 (2010).

Description

Reunión anual de la red Ibersinc

Organizers
Red Ibersinc