The Two-Point Function and the Effective Magnetic Field in Diluted Ising Models on the Cayley Tree

Some results on the two-point function and on the analytic structure of the momenta of the effective fugacity at the origin for a class of diluted ferromagnetic Ising models on the Cayley tree are presented.Comment: 22 page

Spontaneous rotating vortex rings in a parametrically driven polariton fluid

We present the theoretical prediction of spontaneous rotating vortex rings in a parametrically driven quantum fluid of polaritons -- coherent superpositions of coupled quantum well excitons and microcavity photons. These rings arise not only in the absence of any rotating drive, but also in the absence of a trapping potential, in a model known to map quantitatively to experiments. We begin by proposing a novel parametric pumping scheme for polaritons, with circular symmetry and radial currents, and characterize the resulting nonequilibrium condensate. We show that the system is unstable to spontaneous breaking of circular symmetry via a modulational instability, following which a vortex ring with large net angular momentum emerges, rotating in one of two topologically distinct states. Such rings are robust and carry distinctive experimental signatures, and so they could find applications in the new generation of polaritonic devices.Comment: 6 pages, 4 figure

Contractile stresses in cohesive cell layers on finite-thickness substrates

Using a minimal model of cells or cohesive cell layers as continuum active elastic media, we examine the effect of substrate thickness and stiffness on traction forces exerted by strongly adhering cells. We obtain a simple expression for the length scale controlling the spatial variation of stresses in terms of cell and substrate parameters that describes the crossover between the thin and thick substrate limits. Our model is an important step towards a unified theoretical description of the dependence of traction forces on cell or colony size, acto-myosin contractility, substrate depth and stiffness, and strength of focal adhesions, and makes experimentally testable predictions.Comment: 5 pages, 3 figure

Nematic and Polar order in Active Filament Solutions

Using a microscopic model of interacting polar biofilaments and motor proteins, we characterize the phase diagram of both homogeneous and inhomogeneous states in terms of experimental parameters. The polarity of motor clusters is key in determining the organization of the filaments in homogeneous isotropic, polarized and nematic states, while motor-induced bundling yields spatially inhomogeneous structures.Comment: 4 pages. 3 figure

Pattern formation in self-propelled particles with density-dependent motility

We study the behaviour of interacting self-propelled particles, whose self-propulsion speed decreases with their local density. By combining direct simulations of the microscopic model with an analysis of the hydrodynamic equations obtained by explicitly coarse graining the model, we show that interactions lead generically to the formation of a host of patterns, including moving clumps, active lanes and asters. This general mechanism could explain many of the patterns seen in recent experiments and simulations

Translational Correlations in the Vortex Array at the Surface of a Type-II Superconductor

We discuss the statistical mechanics of magnetic flux lines in a finite-thickness slab of type-II superconductor. The long wavelength properties of a flux-line liquid in a slab geometry are described by a hydrodynamic free energy that incorporates the boundary conditions on the flux lines at the sample's surface as a surface contribution to the free energy. Bulk and surface weak disorder are modeled via Gaussian impurity potentials. This free energy is used to evaluate the two-dimensional structure factor of the flux-line tips at the sample surface. We find that surface interaction always dominates in determining the decay of translational correlations in the asymptotic long-wavelength limit. On the other hand, such large length scales have not been probed by the decoration experiments. Our results indicate that the translational correlations extracted from the analysis of the Bitter patterns are indeed representative of behavior of flux lines in the bulk.Comment: 23 pages, 1 figure (not included), harvmac.tex macro needed (e-mail requests to [email protected] SU-CM-92-01

Models of plastic depinning of driven disordered systems

Two classes of models of driven disordered systems that exhibit history-dependent dynamics are discussed. The first class incorporates local inertia in the dynamics via nonmonotonic stress transfer between adjacent degrees of freedom. The second class allows for proliferation of topological defects due to the interplay of strong disorder and drive. In mean field theory both models exhibit a tricritical point as a function of disorder strength. At weak disorder depinning is continuous and the sliding state is unique. At strong disorder depinning is discontinuous and hysteretic.Comment: 3 figures, invited talk at StatPhys 2

Spin-charge gauge approach to metal-insulator crossover and transport properties in High-Tc_c cuprates

The spin-charge gauge approach to consider the metal-insulator crossover (MIC) and other anomalous transport properties in High-T$_c$ cuprates is briefly reviewed. A U(1) field gauging the global charge symmetry and an SU(2) field gauging the global spin-rotational symmetry are introduced to study the two-dimensional $t-J$ model in the limit $t\gg J$. The MIC as a clue to the understanding of the ``pseudogap'' (PG) phase, is attributed to the competition between the short-range antiferromagnetic order and dissipative motion of charge carriers coupled to the slave-particle gauge field. The composite particle formed by binding the charge carrier (holon) and spin excitation (spinon) via the slave particle gauge field exhibits a number of peculiar properties, and the calculated results are in good agreement with experimental data for both PG and ``strange metal'' phases. Connections to other gauge field approaches in studying the strong correlation problem are also briefly outlined.Comment: 32 pages, to appear in the special issue on "Correlated Electrons" of J. Phys.: Condens. Mat

Stellar density profile and mass of the Milky Way Bulge from VVV data

We present the first stellar density profile of the Milky Way bulge reaching latitude $b=0^\circ$. It is derived by counting red clump stars within the colour\--magnitude diagram constructed with the new PSF-fitting photometry from VISTA Variables in the V\'\i a L\'actea (VVV) survey data. The new stellar density map covers the area between $|l|\leq 10^\circ$ and $|b|\leq 4.5^\circ$ with unprecedented accuracy, allowing to establish a direct link between the stellar kinematics from the Giraffe Inner Bulge Spectroscopic Survey (GIBS) and the stellar mass density distribution. In particular, the location of the central velocity dispersion peak from GIBS matches a high overdensity in the VVV star count map. By scaling the total luminosity function (LF) obtained from all VVV fields to the LF from Zoccali et al.(2003), we obtain the first fully empirical estimate of the mass in stars and remnants of the Galactic bulge. The Milky Way bulge stellar mass within ($|b|<9.5^\circ$, $|l|<10^\circ$) is $2.0\pm0.3\times 10^{10}M_{\odot}$.Comment: 4 pages, 5 figures, accepted for publication on A&