[en] We study the response of one- and two-dimensional excitable media to external spatiotemporal noise in terms of synchronization. The media are modeled by a finite-size lattice of locally coupled nonidentical units of the FitzHugh-Nagumo type driven by additive noise. We show that at nonzero noise level the behavior of the system becomes extremely ordered which is manifested by entrainment of the mean frequencies and by stochastic phase locking of distant oscillators in the lattice. (c) 1999 The American Physical Society

[en] We generalize lattice models of brittle fracture to arbitrary nonlinear force laws and study the existence of arrested semi-infinite cracks. Unlike what is seen in the discontinuous case studied to date, the range in driving displacement for which these arrested cracks exist is very small. Also, our results indicate that small changes in the vicinity of the crack tip can have an extremely large effect on arrested cracks. Finally, we briefly discuss the possible relevance of our findings to recent experiments. (c) 1999 The American Physical Society

[en] The shock-induced α(bcc)→ var-epsilon(hcp) transition in iron begins at 13 GPa on the Hugoniot. In the two-phase region above 13 GPa, the Hugoniot lies well above the equilibrium surface defined by G_α=G_var-epsilon, with G the Gibbs free energy. Also, the phase transition relaxation time τ is uncertain, with estimates ranging from <50 ns to ∼180 ns. Here we present an extensive study of these important aspects, metastability and dynamics, of the α-var-epsilon transition in iron. Our primary theoretical tools are (a) accurate theoretically based free energies for α and var-epsilon phases of iron and (b) accurate calculations of the wave evolution following planar impacts. We define metastable surfaces for forward and reverse transitions by the condition that the thermodynamic driving force G_α-G_var-epsilon is just balanced by an opposing force resulting from elastic stresses, and we calibrate the forward surface from the Hugoniot and the reverse surface from the phase interface reflection feature of shock profiles. These metastable surfaces, corresponding to α↔ var-epsilon transitions proceeding at a rate of tens of nanoseconds, are in remarkable agreement with quasistatic diamond cell measurements. When the relaxation time τ is calibrated from the rise time of the P2 wave, our calculated wave profiles are in good agreement with VISAR data. The overall comparison of theory and experiment indicates that (a) τ depends on shock strength and is approximately 60→12 ns for shocks of 17→30 GPa, and (b) while τ expresses linear irreversible-thermodynamic relaxation, some nonlinear relaxation must also be present in the shock process in iron. copyright 1997 The American Physical Society

[en] Statistical mechanics of the discrete nonlinear Schroedinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T=∞ , we identify a phase transition through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breatherlike localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes. (c) 2000 The American Physical Society

[en] A lattice-Boltzmann method has been developed to incorporate solid-fluid boundary conditions on length scales less than the grid spacing. By introducing a continuous parameter, specified at each node and representing the fluid volume fraction associated with that node, we obtain second-order accuracy for boundaries at arbitrary positions and orientations with respect to the grid. The method does not require surface normals, and can therefore be applied to irregular geometries such as porous media. The new rules conserve mass and momentum, and reduce to the link bounce-back rule at aligned interfaces. (c) 2000 The American Physical Society

[en] We have studied the dispersion of long wavelength longitudinal phonons in silicon and germanium using ultrasonic techniques. For long wavelengths, the acoustic phonon dispersion relation is of the form ω(k)≅ck-γk³ , where c is the speed of sound and γ measures the lowest-order phonon dispersion. By sending an ultrasonic pulse of length a few hundred angstroms into a crystal and measuring the change of the pulse shape with propagation distance, we are able to determine the parameter γ . The results are compared with lattice dynamics models. (c) 2000 The American Physical Society

[en] Under quite general conditions, we prove that for classical many-body lattice Hamiltonians in one dimension (1D) total momentum conservation implies anomalous conductivity in the sense of the divergence of the Kubo expression for the coefficient of thermal conductivity, κ . Our results provide rigorous confirmation and explanation of many of the existing ''surprising'' numerical studies of anomalous conductivity in 1D classical lattices, including the celebrated Fermi-Pasta-Ulam problem. (c) 2000 The American Physical Society

[en] The existence of anharmonic localization of lattice vibrations in a perfect three-dimensional diatomic ionic crystal is established for the rigid-ion model by molecular dynamics simulations. For a realistic set of NaI potential parameters, an intrinsic localized gap mode vibrating in the [111] direction is observed for fcc and zinc-blende lattices. An axial elastic distortion is an integral feature of this mode which forms more readily for the zinc blende than for the fcc structure. Molecular dynamics simulations verify that in each structure this localized mode may be stable for at least 200 cycles. copyright 1997 The American Physical Society

[en] Time-resolved x-ray diffraction with picosecond temporal resolution is used to observe scattering from impulsively generated coherent acoustic phonons in laser-excited InSb crystals. The observed frequencies and damping rates are in agreement with a model based on dynamical diffraction theory coupled to analytic solutions for the laser-induced strain profile. The results are consistent with a 12 ps thermal electron-acoustic phonon coupling time together with an instantaneous component from the deformation-potential interaction. Above a critical laser fluence, we show that the first step in the transition to a disordered state is the excitation of large amplitude, coherent atomic motion. (c) 1999 The American Physical Society

[en] Lattice Green close-quote s functions are used to investigate localized rotating modes recently exhibited in some nonlinear lattices. For a one-dimensional lattice, analytical expressions of the solution are obtained, first in the rotating-wave approximation and then by including higher-order terms. Numerical simulations confirm the validity of these solutions. The method is not restricted to one-dimensional lattices. copyright 1997 The American Physical Society