Billiards correlation functions

We discuss various experiments on the time decay of velocity autocorrelation functions in billiards. We perform new experiments and find results which are compatible with an exponential mixing hypothesis, first put forward by [FM]: they do not seem compatible with the stretched exponentials believed, in spite of [FM], to describe the mixing. The analysis led us to several byproducts: we obtain information about the normal diffusive nature of the motion and we consider the probability distribution of the number of collisions in time $t_m$ (as t_m\to\io) finding a strong dependence on some geometric characteristics of the locus of the billiards obstacles.Comment: 25 pages, 27 figures, POSTSCRIPT, not encoded, 730K. Keywords: Billiards, correlation functions, velocity autocorrelation, diffusion coefficients, Lorentz model, mixing, ergodic theory, chaos, Lyapunov exponents, numerical experiment

Metastability and Avalanches in a Nonequilibrium Ferromagnetic System

We present preliminary results on the metastable behavior of a nonequilibrium ferromagnetic system. The metastable state mean lifetime is a non-monotonous function of temperature; it shows a maximum at certain non-zero temperature which depends on the strengh of the nonequilibrium perturbation. This is in contrast with the equilibrium case in which lifetime increases monotonously as the temperature is decreasesed. We also report on avalanches during the decay from the metastable state. Assuming both free boundaries and nonequilibrium impurities, the avalanches exhibit power-law size and lifetime distributions. Such scale free behavior is very sensible. The chances are that our observations may be observable in real (i.e. impure) ferromagnetic nanoparticles.Comment: 6 pages, 4 figures, to be published in 2002 Granada Seminar Proceeding

Stability results for 2D Navier-Stokes equations with unbounded delay

Some results related to 2D Navier-Stokes equations when the external force contains hereditary characteristics involving unbounded delays are analyzed. First, the existence and uniqueness of solutions is proved by Galerkin approximations and the energy method. The existence of stationary solution is then established by means of the Lax-Milgram theorem and the Schauder fixed point theorem. The local stability analysis of stationary solutions is studied by several different methods: the classical Lyapunov function method, the Razumikhin-Lyapunov technique and by constructing appropriate Lyapunov functionals. Finally, we also verify the polynomial stability of the stationary solution in a particular case of unbounded variable delay. Exponential stability in this infinite delay setting remains as an open problem.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalJunta de AndalucíaNational Science Foundation of ChinaScience and Technology Commission of Shanghai MunicipalityShanghai Leading Academic Discipline Projec

Time-dependent attractors for non-autonomous nonlocal reaction-diffusion equations

In this paper, the existence and uniqueness of weak and strong solutions for a non-autonomous nonlocal reaction-diffusion equation is proved. Next, the existence of minimal pullback attractors in the L2 -norm in the frameworks of universes of fixed bounded sets and those given by a tempered growth condition, and some relationships between them are established. Finally, we prove the existence of minimal pullback attractors in the H1-norm and study relationships among these new families and those given previously in the L2 - context. The results are also new in the autonomous framework in order to ensure the existence of global compact attractors, as a particular case.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalJunta de Andalucí

Robustness of time-dependent attractors in H1-norm for nonlocal problems

In this paper, the existence of regular pullback attractors as well as their upper semicontinuous behaviour in H1-norm are analysed for a parameterized family of non-autonomous nonlocal reaction-diffusion equations without uniqueness, improving previous results [Nonlinear Dyn. 84 (2016), 35–50].Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalJunta de Andalucí

Sol-gel incorporation of organometallic compounds into silica: useful precursors to metallic nanostructured materials

Indexación: Web of Science; ScieloLa inclusión del MLN organometálica = HOC 6 H 4 CH 2 CN • Mo (CO) 5 (6) en sílice amorfa con los precursores TEOS gelificante y N 3 P 3 {NH [CH 2 ] 3 Si [OEt] 3 } 6 permitirse los geles (MLN) ( SiO 2 ) n . Los nanocompuestos híbridos inorgánicos-orgánicos se piroliza bajo aire a 800 º C para dar óxidos nanoestructurados metálicos y / o pirofosfatos de metal (fosfatos) incluidos en las matrices de sílice. La morfología de los nanocompuestos monolíticas exhiben una fuerte dependencia con el precursor del gel utilizado es principalmente laminar para aquellos preparados utilizando N 3 P 3 {NH [CH 2 ] 3 Si [OEt] 3 } como gelificante. Las imágenes de TEM muestran la forma y tamaño diferentes, tales como nanopartículas circulares, nanocables y aglomerados en algunos casos con tamaños de 20 nm para las nanoestructuras circulares y de diámetro aproximadamente 25 nm para los nanocables.Inclusion of the organometallic MLn = [HOC5H4N•Cp2TiCl][PF6] (1), HOC5H4N-W(CO)5 (2), HOC5H4N•Mo(CO)5 (3), [HOC6H4CH2CN•Cp2TiCl][PF6] (4), HOC6H4CH2CN•W(CO)5 (5) and HOC6H4CH2CN•Mo(CO)5 (6) into amorphous silica using the gelator precursor TEOS and N3P3{NH[CH2]3Si[OEt]3}6 afford the gels (MLn)(SiO2)n. The inorganic-organic hybrid nanocomposites were pyrolyzed under air at 800°C to give nanostructured metal oxides and/or metal pyrophosphates (phosphates) included in the silica matrices. The morphology of the monolithic nanocomposites exhibited a strong dependence on the gel precursor used being mainly laminar for those prepared using N3P3{NH[CH2]3Si[OEt]3} as gelator. TEM images show different shape and size such as circular nanoparticles, nanocables and agglomerates in some cases with sizes of 20 nm for the circular nanostructures, and diameter about 25 nm for the nanocables.http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0717-97072012000200021&nrm=is