A model for interacting instabilities and texture dynamics of patterns

A simple model to study interacting instabilities and textures of resulting patterns for thermal convection is presented. The model consisting of twelve-mode dynamical system derived for periodic square lattice describes convective patterns in the form of stripes and patchwork quilt. The interaction between stationary zig-zag stripes and standing patchwork quilt pattern leads to spatiotemporal patterns of twisted patchwork quilt. Textures of these patterns, which depend strongly on Prandtl number, are investigated numerically using the model. The model also shows an interesting possibility of a multicritical point, where stability boundaries of four different structures meet.Comment: 4 pages including 4 figures, page width revise

Hydrodynamics of thermal granular convection

A hydrodynamic theory is formulated for buoyancy-driven ("thermal") granular convection, recently predicted in molecular dynamic simulations and observed in experiment. The limit of a dilute flow is considered. The problem is fully described by three scaled parameters. The convection occurs via a supercritical bifurcation, the inelasticity of the collisions being the control parameter. The theory is expected to be valid for small Knudsen numbers and nearly elastic grain collisions.Comment: 4 pages, 4 EPS figures, some details adde

Wavy stripes and squares in zero P number convection

A simple model to explain numerically observed behaviour of chaotically varying stripes and square patterns in zero Prandtl number convection in Boussinesq fluid is presented. The nonlinear interaction of mutually perpendicular sets of wavy rolls, via higher mode, may lead to a competition between the two sets of wavy rolls. The appearance of square patterns is due to the secondary forward Hopf bifurcation of a set of wavy rolls.Comment: 8 pages and 3 figures, late

Onset of thermal convection in a horizontal layer of granular gas

The Navier-Stokes granular hydrodynamics is employed for determining the threshold of thermal convection in an infinite horizontal layer of granular gas. The dependence of the convection threshold, in terms of the inelasticity of particle collisions, on the Froude and Knudsen numbers is found. A simple necessary condition for convection is formulated in terms of the Schwarzschild's criterion, well-known in thermal convection of (compressible) classical fluids. The morphology of convection cells at the onset is determined. At large Froude numbers, the Froude number drops out of the problem. As the Froude number goes to zero, the convection instability turns into a recently discovered phase separation instability.Comment: 6 pages, 6 figures. An extended version. A simple and universal necessary criterion for convection presente

External Fluctuations in a Pattern-Forming Instability

The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the bifurcation point controlled by the intensity of the multiplicative noise. This shift takes place in the ordering direction (i.e. produces patterns), but its magnitude decreases with that of the noise correlation length. Analytical arguments are presented to explain these facts.Comment: 11 pages, Revtex, 10 Postscript figures added with psfig style (included). To appear in Physical Review

Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach

We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian with a competing long-range repulsive term in the presence of an external magnetic field. The model is analytically solved within the self consistent Hartree approximation for two different initial conditions: disordered or zero field cooled (ZFC), and fully magnetized or field cooled (FC). To test the predictions of the approximation we develop a suitable numerical scheme to ensure the isotropic nature of the interactions. Both the analytical approach and the numerical simulations of two-dimensional finite systems confirm a simple aging scenario at zero temperature and zero field. At zero temperature a critical field $h_c$ is found below which the initial conditions are relevant for the long time dynamics of the system. For $h < h_c$ a logarithmic growth of modulated domains is found in the numerical simulations but this behavior is not captured by the analytical approach which predicts a $t^1/2$ growth law at $T = 0$

N-myristoylated proteins, key components in intracellular signal transduction systems enabling rapid and flexible cell responses

N-myristoylation, one of the co- or post-translational modifications of proteins, has so far been regarded as necessary for anchoring of proteins to membranes. Recently, we have revealed that Nα-myristoylation of several brain proteins unambiguously regulates certain protein–protein interactions that may affect signaling pathways in brain. Comparison of the amino acid sequences of myristoylated proteins including those in other organs suggests that this regulation is involved in signaling pathways not only in brain but also in other organs. Thus, it has been shown that myristoylated proteins in cells regulate the signal transduction between membranes and cytoplasmic fractions. An algorithm we have developed to identify myristoylated proteins in cells predicts the presence of hundreds of myristoylated proteins. Interestingly, a large portion of the myristoylated proteins thought to take part in signal transduction between membranes and cytoplasmic fractions are included in the predicted myristoylated proteins. If the proteins functionally regulated by myristoylation, a posttranslational protein modification, were understood as cross-talk points within the intracellular signal transduction system, known signaling pathways could thus be linked to each other, and a novel map of this intracellular network could be constructed. On the basis of our recent results, this review will highlight the multifunctional aspects of protein N-myristoylation in brain

Spinor condensates and light scattering from Bose-Einstein condensates

These notes discuss two aspects of the physics of atomic Bose-Einstein condensates: optical properties and spinor condensates. The first topic includes light scattering experiments which probe the excitations of a condensate in both the free-particle and phonon regime. At higher light intensity, a new form of superradiance and phase-coherent matter wave amplification were observed. We also discuss properties of spinor condensates and describe studies of ground--state spin domain structures and dynamical studies which revealed metastable excited states and quantum tunneling.Comment: 58 pages, 33 figures, to appear in Proceedings of Les Houches 1999 Summer School, Session LXXI