Violation of Kohler's rule by the magnetoresistance of a quasi-two-dimensional organic metal

The interlayer magnetoresistance of the quasi-two-dimensional metal $\alpha$-(BEDT-TTF)$_2$KHg(SCN)$_4$ is considered. In the temperature range from 0.5 to 10 K and for fields up to 10 tesla the magnetoresistance has a stronger temperature dependence than the zero-field resistance. Consequently Kohler's rule is not obeyed for any range of temperatures or fields. This means that the magnetoresistance cannot be described in terms of semiclassical transport on a single Fermi surface with a single scattering time. Possible explanations for the violations of Kohler's rule are considered, both within the framework of semi-classical transport theory and involving incoherent interlayer transport. The issues considered are similar to those raised by the magnetotransport of the cuprate superconductors.Comment: 5 pages, RevTeX + epsf, 2 figures. Slightly revised version to appear in Physical Review B, May 15, 199

Passive scalar convection in 2D long-range delta-correlated velocity field: Exact results

The letter presents new field-theoretical approach to 2D passive scalar problem. The Gaussian form of the distribution for the Lyapunov exponent is derived and its parameters are found explicitly.Comment: 11 pages, RevTex 3.0, IFUM-94/455/January-F

Triaxial Galaxies with Cusps

We have constructed fully self-consistent models of triaxial galaxies with central density cusps. The triaxial generalizations of Dehnen's spherical models are presented, which have densities that vary as 1/r^gamma near the center and 1/r^4 at large radii. We computed libraries of about 7000 orbits in each of two triaxial models with gamma=1 (weak cusp) and gamma=2 (strong cusp); these two models have density profiles similar to those of the core and power-law galaxies observed by HST. Both mass models have short-to-long axis ratios of 1:2 and are maximally triaxial. A large fraction of the orbits in both model potentials are stochastic, as evidenced by their non-zero Liapunov exponents. We show that most of the stochastic orbits in the strong- cusp potential diffuse relatively quickly through their allowed phase-space volumes, on time scales of 100 - 1000 dynamical times. Stochastic orbits in the weak-cusp potential diffuse more slowly, often retaining their box-like shapes for 1000 dynamical times or longer. Attempts to construct self- consistent solutions using just the regular orbits failed for both mass models. Quasi-equilibrium solutions that include the stochastic orbits exist for both models; however, real galaxies constructed in this way would evolve near the center due to the continued mixing of the stochastic orbits. We attempted to construct more nearly stationary models in which stochastic phase space was uniformly populated at low energies. These ``fully mixed'' solutions were found to exist only for the weak-cusp potential. No significant fraction of the mass could be placed on fully-mixed stochastic orbits in the strong-cusp model, demonstrating that strong triaxiality can be inconsistent with a high central density.Comment: 58 TEX pages, 14 PostScript figures, uses epsf.st

Permeability of self-affine rough fractures

The permeability of two-dimensional fractures with self-affine fractal roughness is studied via analytic arguments and numerical simulations. The limit where the roughness amplitude is small compared with average fracture aperture is analyzed by a perturbation method, while in the opposite case of narrow aperture, we use heuristic arguments based on lubrication theory. Numerical simulations, using the lattice Boltzmann method, are used to examine the complete range of aperture sizes, and confirm the analytic arguments.Comment: 11 pages, 9 figure

Intermittency and roughening in the failure of brittle heterogeneous materials

Stress enhancement in the vicinity of brittle cracks makes the macro-scale failure properties extremely sensitive to the micro-scale material disorder. Therefore: (i) Fracturing systems often display a jerky dynamics, so-called crackling noise, with seemingly random sudden energy release spanning over a broad range of scales, reminiscent of earthquakes; (ii) Fracture surfaces exhibit roughness at scales much larger than that of material micro-structure. Here, I provide a critical review of experiments and simulations performed in this context, highlighting the existence of universal scaling features, independent of both the material and the loading conditions, reminiscent of critical phenomena. I finally discuss recent stochastic descriptions of crack growth in brittle disordered media that seem to capture qualitatively - and sometimes quantitatively - these scaling features.Comment: 38 pages, invited review for J. Phys. D cluster issue on "Fracture: from the Atomic to the Geophysics Scale

Anatomy of quantum chaotic eigenstates

The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The levels of description are macroscopic (one wants to understand the quantum averages of smooth observables), and microscopic (one wants informations on maxima of eigenfunctions, "scars" of periodic orbits, structure of the nodal sets and domains, local correlations), and often focusses on statistical results. Various models of "random wavefunctions" have been introduced to understand these statistical properties, with usually good agreement with the numerical data. We also discuss some specific systems (like arithmetic ones) which depart from these random models.Comment: Corrected typos, added a few references and updated some result