Abstract:
The pair interaction between magnetic flux lines in a semi-infinite slab of an anisotropic type-II superconductor in an external field is derived in the London limit. The case where the applied field is normal to the superconductor/vacuum interface is considered. The presence of stray fields near the surface leads to an additional contribution to the repulsive interaction between flux lines that vanishes exponentially with the distance from the interface. The pair interaction is used to obtain the continuum elastic energy of a distorted semi-infinite flux-line array. The presence of the superconductor/vacuum interface yields surface contributions to the compressional and tilt elastic constants.

Abstract:
The fabrication of artificial pinning structures allows a new generation of experiments which can probe the properties of vortex arrays by forcing them to flow in confined geometries. We discuss the theoretical analysis of such experiments in both flux liquids and flux solids, focusing on the Corbino disk geometry. In the liquid, these experiments can probe the critical behavior near a continuous liquid-glass transition. In the solid, they probe directly the onset of plasticity.

Abstract:
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.

Abstract:
We review in these notes the dynamics of extended condensed matter systesm, such as vortex lattices in type-II superconductors and charge density waves in anisotropic metals, driven over quenched disorder. We focus in particular on the case of strong disorder, where topological defects are generated in the driven lattice. In this case the repsonse is plastic and the depinning transition may become discontinuous and hysteretic.

Abstract:
Using tools of nonequilibirum mechanics, we study a model of self-propelled hard rods on a substrate in two dimensions to quantify the interplay of self-propulsion and excluded-volume effects. We derive of a Smoluchowski equation for the configurational probability density of self-propelled rods that contains several modifications as compared to the familiar Smoluchowski equation for thermal rods. As a side-product of our work, we also present a purely dynamical derivation of the Onsager form of the mean field excluded volume interaction among thermal hard rods.

Abstract:
We generalize our previous work on the phase stability and hydrodynamic of polar liquid crystals possessing local uniaxial $C_{\infty v}$-symmetry to biaxial systems exhibiting local $C_{2v}$-symmetry. Our work is motivated by the recently discovered examples of thermotropic biaxial nematic liquid crystals comprising bent-core mesogens, whose molecular structure is characterized by a non-polar body axis $({\bf{n}})$ as well as a polar axis $({\bf{p}})$ along the bisector of the bent mesogenic core which is coincident with a large, transverse dipole moment. The free energy for this system differs from that of biaxial nematic liquid crystals in that it contains terms violating the ${\bf{p}}\to -{\bf{p}}$ symmetry. We show that, in spite of a general splay instability associated with these parity-odd terms, a uniform polarized biaxial state can be stable in a range of parameters. We then derive the hydrodynamic equations of the system, via the Poisson-bracket formalism, in the polarized state and comment on the structure of the corresponding linear hydrodynamic modes. In our Poisson-bracket derivation, we also compute the flow-alignment parameters along the three symmetry axes in terms of microscopic parameters associated with the molecular geometry of the constituent biaxial mesogens.

Abstract:
Motivated by recent simulations and by experiments on aggregation of gliding bacteria, we study a model of the collective dynamics of self-propelled hard rods on a substrate in two dimensions. The rods have finite size, interact via excluded volume and their dynamics is overdamped by the interaction with the substrate. Starting from a microscopic model with non-thermal noise sources, a continuum description of the system is derived. The hydrodynamic equations are then used to characterize the possible steady states of the systems and their stability as a function of the particles packing fraction and the speed of self propulsion.

Abstract:
We study mode-locking in disordered media as a boundary-value problem. Focusing on the simplest class of mode-locking models which consists of a single driven overdamped degree-of-freedom, we develop an analytical method to obtain the shape of the Arnol'd tongues in the regime of low ac-driving amplitude or high ac-driving frequency. The method is exact for a scalloped pinning potential and easily adapted to other pinning potentials. It is complementary to the analysis based on the well-known Shapiro's argument that holds in the perturbative regime of large driving amplitudes or low driving frequency, where the effect of pinning is weak.

Abstract:
We study the spatio-temporal dynamics of a model of polar active fluid in two dimensions. The system exhibits a transition from an isotropic to a polarized state as a function of density. The uniform polarized state is, however, unstable above a critical value of activity. Upon increasing activity, the active fluids displays increasingly complex patterns, including traveling bands, traveling vortices and chaotic behavior. The advection arising from the particles self-propulsion and unique to polar fluids yields qualitatively new behavior as compared to that obtain in active nematic, with traveling-wave structures. We show that the nonlinear hydrodynamic equations can be mapped onto a simplified diffusion-reaction-convection model, highlighting the connection between the complex dynamics of active system and that of excitable systems.

Abstract:
We consider the hydrodynamic theory of an active fluid of self-propelled particles with nematic aligning interactions. This class of materials has polar symmetry at the microscopic level, but forms macrostates of nematic symmetry. We highlight three key features of the dynamics. First, as in polar active fluids, the control parameter for the order-disorder transition, namely the density, is dynamically convected by active currents, resulting in a generic, model independent dynamical self-regulation that destabilizes the uniform nematic state near the mean-field transition. Secondly, curvature driven currents render the system unstable deep in the nematic state, as found previously. Finally, and unique to self-propelled nematics, nematic order induces local polar order that in turn leads to the growth of density fluctuations. We propose this as a possible mechanism for the smectic order of polar clusters seen in numerical simulations.