Efficient Algorithm on a Non-staggered Mesh for Simulating Rayleigh-Benard Convection in a Box

An efficient semi-implicit second-order-accurate finite-difference method is described for studying incompressible Rayleigh-Benard convection in a box, with sidewalls that are periodic, thermally insulated, or thermally conducting. Operator-splitting and a projection method reduce the algorithm at each time step to the solution of four Helmholtz equations and one Poisson equation, and these are are solved by fast direct methods. The method is numerically stable even though all field values are placed on a single non-staggered mesh commensurate with the boundaries. The efficiency and accuracy of the method are characterized for several representative convection problems.Comment: REVTeX, 30 pages, 5 figure

Convective Motion in a Vibrated Granular Layer

Experimental results are presented for a vertically shaken granular layer. In the range of accelerations explored, the layer develops a convective motion in the form of one or more rolls. The velocity of the grains near the wall has been measured. It grows linearly with the acceleration, then the growing rate slows down. A rescaling with the amplitude of the wall velocity and the height of the granular layer makes all data collapse in a single curve. This can provide insights on the mechanism driving the motion.Comment: 10 pages, 5 figures submitted to Phys. Rev. Let

Kinetics of Ordering in Fluctuation-Driven First-Order Transitions: Simulations and Dynamical Renormalization

Many systems where interactions compete with each other or with constraints are well described by a model first introduced by Brazovskii. Such systems include block copolymers, alloys with modulated phases, Rayleigh-Benard Cells and type-I superconductors. The hallmark of this model is that the fluctuation spectrum is isotropic and has a minimum at a nonzero wave vector represented by the surface of a d-dimensional hyper-sphere. It was shown by Brazovskii that the fluctuations change the free energy structure from a $\phi ^{4}$ to a $\phi ^{6}$ form with the disordered state metastable for all quench depths. The transition from the disordered to the periodic, lamellar structure changes from second order to first order and suggests that the dynamics is governed by nucleation. Using numerical simulations we have confirmed that the equilibrium free energy function is indeed of a $\phi ^{6}$ form. A study of the dynamics, however, shows that, following a deep quench, the dynamics is described by unstable growth rather than nucleation. A dynamical calculation, based on a generalization of the Brazovskii calculations shows that the disordered state can remain unstable for a long time following the quench.Comment: 18 pages, 15 figures submitted to PR

Noise sensitivity of sub- and supercritically bifurcating patterns with group velocities close to the convective-absolute instability

The influence of small additive noise on structure formation near a forwards and near an inverted bifurcation as described by a cubic and quintic Ginzburg Landau amplitude equation, respectively, is studied numerically for group velocities in the vicinity of the convective-absolute instability where the deterministic front dynamics would empty the system.Comment: 16 pages, 7 Postscript figure

Selfsimilar Domain Growth, Localized Structures and Labyrinthine Patterns in Vectorial Kerr Resonators

We study domain growth in a nonlinear optical system useful to explore different scenarios that might occur in systems which do not relax to thermodynamic equilibrium. Domains correspond to equivalent states of different circular polarization of light. We describe three dynamical regimes: a coarsening regime in which dynamical scaling holds with a growth law dictated by curvature effects, a regime in which localized structures form, and a regime in which polarization domain walls are modulationally unstable and the system freezes in a labyrinthine pattern.Comment: 13 pages, 6 figure

Inflammation decreases keratin level in ulcerative colitis; inadequate restoration associates with increased risk of colitis-associated cancer

Background Keratins are intermediate filament (IF) proteins, which form part of the epithelial cytoskeleton and which have been implicated pathology of inflammatory bowel diseases (IBD). Methods In this study biopsies were obtained from IBD patients grouped by disease duration and subtype into eight categories based on cancer risk and inflammatory status: quiescent recent onset (<5 years) UC (ROUC); UC with primary sclerosing cholangitis; quiescent long-standing pancolitis (20–40 years) (LSPC); active colitis and non-inflamed proximal colonic mucosa; pancolitis with dysplasia-both dysplastic lesions (DT) and distal rectal mucosa (DR); control group without pathology. Alterations in IF protein composition across the groups were determined by quantitative proteomics. Key protein changes were validated by western immunoblotting and immunohistochemical analysis. Result Acute inflammation resulted in reduced K8, K18, K19 and VIM (all p<0.05) compared to controls and non inflamed mucosa; reduced levels of if– associated proteins were also seen in DT and DR. Increased levels of keratins in LSPC was noted relative to controls or ROUC (K8, K18, K19 and VIM, p<0.05). Multiple K8 forms were noted on immunoblotting, with K8 phosphorylation reduced in progressive disease along with an increase in VIM:K8 ratio. K8 levels and phosphorylation are reduced in acute inflammation but appear restored or elevated in subjects with clinical and endoscopic remission (LSPC) but not apparent in subjects with elevated risk of cancer. Conclusions These data suggest that keratin regulation in remission may influence subsequent cancer risk

Heat kernel regularization of the effective action for stochastic reaction-diffusion equations

The presence of fluctuations and non-linear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise. We calculate the one-loop {\emph{effective action}} and its ultraviolet scale dependent divergences. We show that for white noise a polynomial reaction-diffusion equation is one-loop {\emph{finite}} in $d=0$ and $d=1$, and is one-loop renormalizable in $d=2$ and $d=3$ space dimensions. We obtain the one-loop renormalization group equations and find they run with scale only in $d=2$.Comment: 21 pages, uses ReV-TeX 3.

From Gapped Excitons to Gapless Triplons in One Dimension

Often, exotic phases appear in the phase diagrams between conventional phases. Their elementary excitations are of particular interest. Here, we consider the example of the ionic Hubbard model in one dimension. This model is a band insulator (BI) for weak interaction and a Mott insulator (MI) for strong interaction. Inbetween, a spontaneously dimerized insulator (SDI) occurs which is governed by energetically low-lying charge and spin degrees of freedom. Applying a systematically controlled version of the continuous unitary transformations (CUTs) we are able to determine the dispersions of the elementary charge and spin excitations and of their most relevant bound states on equal footing. The key idea is to start from an externally dimerized system using the relative weak interdimer coupling as small expansion parameter which finally is set to unity to recover the original model.Comment: 18 pages, 10 figure

Dynamics of fluctuations in a fluid below the onset of Rayleigh-B\'enard convection

We present experimental data and their theoretical interpretation for the decay rates of temperature fluctuations in a thin layer of a fluid heated from below and confined between parallel horizontal plates. The measurements were made with the mean temperature of the layer corresponding to the critical isochore of sulfur hexafluoride above but near the critical point where fluctuations are exceptionally strong. They cover a wide range of temperature gradients below the onset of Rayleigh-B\'enard convection, and span wave numbers on both sides of the critical value for this onset. The decay rates were determined from experimental shadowgraph images of the fluctuations at several camera exposure times. We present a theoretical expression for an exposure-time-dependent structure factor which is needed for the data analysis. As the onset of convection is approached, the data reveal the critical slowing-down associated with the bifurcation. Theoretical predictions for the decay rates as a function of the wave number and temperature gradient are presented and compared with the experimental data. Quantitative agreement is obtained if allowance is made for some uncertainty in the small spacing between the plates, and when an empirical estimate is employed for the influence of symmetric deviations from the Oberbeck-Boussinesq approximation which are to be expected in a fluid with its density at the mean temperature located on the critical isochore.Comment: 13 pages, 10 figures, 52 reference

Colossal dielectric constants in transition-metal oxides

Many transition-metal oxides show very large ("colossal") magnitudes of the dielectric constant and thus have immense potential for applications in modern microelectronics and for the development of new capacitance-based energy-storage devices. In the present work, we thoroughly discuss the mechanisms that can lead to colossal values of the dielectric constant, especially emphasising effects generated by external and internal interfaces, including electronic phase separation. In addition, we provide a detailed overview and discussion of the dielectric properties of CaCu3Ti4O12 and related systems, which is today's most investigated material with colossal dielectric constant. Also a variety of further transition-metal oxides with large dielectric constants are treated in detail, among them the system La2-xSrxNiO4 where electronic phase separation may play a role in the generation of a colossal dielectric constant.Comment: 31 pages, 18 figures, submitted to Eur. Phys. J. for publication in the Special Topics volume "Cooperative Phenomena in Solids: Metal-Insulator Transitions and Ordering of Microscopic Degrees of Freedom