Instabilities in the circulation of a pulse in a ring of excitable cardiac tissue are analyzed using two different formulations: (1) a reaction-diffusion partial differential equation (PDE) model for cardiac electrical activity using the Beeler-Reuter equations to represent ionic currents in the cardiac cells; (2) a neutral delay-differential equation that we propose as a model for the PDE. Stability analysis and numerical simulation of the delay equation agree with results from simulations of the PDE model.

We argue that percolation provides a unified theory for the geometry of fault patterns and the spatial distribution of earthquakes. We analyze the structure of fracture patterns in heterogeneous rocks and find that, at large length scales, they are percolation fractals with a fractal dimension D≃1.9 and 2.5, in 2D and 3D, respectively. A model is proposed that can predict these results. Three-dimensional fractal analysis of spatial distribution of earthquake hypocenters yields a fractal dimension of about 1.8, the same as that of the backbone of 3D percolation clusters.

We report here on a numerical model allowing direct numerical simulations of magnetohydrodynamic fluctuations advected by the expanding solar wind. We show that the expansion of the plasma delays and possibly freezes the turbulent evolution, but that it also triggers the nonlinear evolution of otherwise stable (Alfvén) waves, which can thus release their energy in the wind.

An unknown quantum state ‖φ〉 can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical Einstein-Podolsky-Rosen (EPR) correlations. To do so the sender, ‘‘Alice,’’ and the receiver, ‘‘Bob,’’ must prearrange the sharing of an EPR-correlated pair of particles. Alice makes a joint measurement on her EPR particle and the unknown quantum system, and sends Bob the classical result of this measurement. Knowing this, Bob can convert the state of his EPR particle into an exact replica of the unknown state ‖φ〉 which Alice destroyed.

Solutions to the time-dependent Schrödinger equation for a particle in a spatially uniform time-dependent field and some potentials of arbitrary form are proved to be like the time-independent eigenfunctions for an identical static potential. The field phase modulates the wave function and translates its envelope. This work applies directly to constant, linear, and parabolic static potentials and is self-consistent. Results for the modulation by a time-dependent field of the current through a rectangular barrier are relevant to the traversal time for tunneling and associated device limitations.

The conformal invariant charcter of n-multicomponent integrable systems is described from the point of veiw of the response to the curvature of the two-dimensional space. The ν×ν dressed-charge matrix, which determines the dimensions of the primary fields, is shown to be a representation of the momentum Fourier components of the diagonal generators of ν independent Kac-Moody algebras in the basis of the ground state and gapless excitations of momentum k→$0^{\pm }$. The dynamical decoupling which occurs in these systems is characterized in terms of the conductivities associated with the diagonal generators.

We study 4D simplicial quantum gravity in the dynamical triangulation approach with a nontrivial class of measures. We find that the measure contribution plays an important role, influencing the phase diagram and the nature of the (possible) critical theory. We discuss how the lattice theory could be used to fix the quantum measure in a nonambiguous way.

We present a model of chaotic inflation driven by the superpartner of the right-handed neutrino (N${\mathrm{̃}}_{\mathit{R}}$). This model gives the correct magnitude of the density perturbation observed by the Cosmic Background Explorer satellite with a right-handed neutrino mass ≃${10}^{13}$ GeV, which is also preferred by the Mikheyev-Smirnov-Wolfenstein solution to the solar neutrino problem. The reheating process is the dacay of the coherently oscillating N${\mathrm{̃}}_{\mathit{R}}$. This decay process also generates lepton asymmetry via CP violation, which will be converted to baryon asymmetry thanks to the electroweak anomaly. This model can incorporate the τ-neutrino mass ≃10 eV.

We have constructed a quantum field theory for the self-dual Yang-Mills system in terms of the group-valued fields J^. They satisfy exchange algebras, of which the structure matrices R^ satisfy Yang-Baxter equations. We show that the fields J^ form noncommutative vector spaces of a local quantum group and their products at short distances have nontrivial critical exponents. We obtain the quantum Hamiltonian and equations of motion; identify the generators for their symmetries; and construct the affine-Lie-algebra currents, Virasoro-algebra fields, and hierarchies of linear and nonlinear systems.

We compute the radiation of lepton pairs by the quarks during a central collision between gold nuclei at energy of the Brookhaven Relativistic Heavy Ion Collider (√s =200A GeV) within the parton cascade model. The distribution of radiated pairs evolves smoothly from the initial Drell-Yan type reactions all the way towards equilibrium radiation. Contributions from reactions involving secondary partons dominate the Drell-Yan yield by at least a factor of 5 even at an invariant mass of 8 GeV. Therefore, experiments can test the evolution of partons towards thermal equilibrium at these energies.

We present Z distributions for fragments with 1≤Z≤12 from central collisions of ${}_{}{}^{40}{}_{}{}^{}$ Ar${+}^{45}$Sc at incident energies ranging from 35 to 115 MeV/nucleon. We find that the Z distributions can be described by a power law or an exponential and steepen with increasing incident energy. Over the range of incident energies studied, the average number of intermediate mass fragments decreases while the average number of particles increases. When combined with previous results for the charge distributions, a minimum is observed in the extracted power-law parameter.

The classical three-body problem of the helium atom is numerically studied. For most initial conditions, orbits show chaotic transients until one of the electrons always escapes to infinity, leading to autoionization. For the remaining parts of initial conditions, several types of stable quasiperiodic motions (on tori) are found, which have a finite measure in the phase space. This discovery enables us to treat semiclassically a strongly correlated electronic system.

The stabilization method is used to calculate the density of resonance states and when applied to isolated resonances yields a most simple method for extracting the resonance energy and width.

A method for calculating total cross sections without formally including nonelastic channels is presented. The idea is to use a one channel T-matrix variational principle with a complex correlation function. The derived T matrix is therefore not unitary: Elastic scattering is calculated from ‖T${\mathrm{\Vert }}^2$, but total scattering is derived from the imaginary part of T using the optical theorem. The method is applied to the spherically symmetric model of electron-hydrogen scattering. No spurious structure arises; results for ${\mathrm{\sigma }}_{\mathrm{el}}$ and ${\mathrm{\sigma }}_{\mathrm{total}}$ are in excellent agreement with calculations of Callaway and Oza. The method has wide potential applicability.

The effects of internal noise on chaotic and periodic dynamics of a chemical system are investigated. Calculations are carried out for a mesoscopic model of the Williamowski-Rössler reaction, a mass-action model that displays deterministic chemical chaos. The model incorporates internal fluctuations that arise from the reactive and diffusion processes in the system. The character of noisy dynamics is analyzed and questions related to the validity of deterministic models in the chaotic regime are discussed. The interplay among spatial degrees of freedom, system size, and internal fluctuations are studied for this chaotic dynamical system.

We have constructed a large database of 171 first-principles total energy calculations of aluminum structures with coordination number ranging from 0 to 12 and nearest neighbor distance from 2.0 to 5.7 Å. These calculations throw quantitative light on the nature of metallic bonding. We have tested a large range of ‘‘glue’’ models with this database: none gives a rms error less than 0.10 eV per atom. We attribute this minimum error to bonding effects beyond the glue formalism, and as such it sets the ultimate reliability of any glue scheme.

The geometric and electronic structure of a ${\mathrm{C}}_{60}$ molecular layer on the Au(001) surfaces was studied by scanning tunneling microscopy and spectroscopy. The interaction between the substrate and overlayer is strong enough that the ${\mathrm{C}}_{60}$ monolayer is commensurate and uniaxially stressed along the 〈110〉 direction. As a result of stress the charge density around the ${\mathrm{C}}_{60}$ molecule appears to be deformed. Charge transfer was observed in ultraviolte photoemission spectroscopy and scanning tunneling spectroscopy, revealing the adsorption mechanism of the ${\mathrm{C}}_{60}$ molecule on this substrate.

We have performed quantum Monte Carlo calculations on atomic metallic hydrogen at zero temperature and constant volume (${\mathit{r}}_{\mathit{s}}$=1.31) for protons rigidly fixed to lattice sites and for protons having zero point motion. By studying a variety of crystal structures including bcc, simple cubic, simple hexagonal, diamond, and β-Sn, we show that low-coordination structures, especially diamond, are energetically favored for a range of pressures around 3.0 Mbars. Our results show that it is essential to treat the electrons beyond the local density approximation and protons beyond the harmonic approximation to predict the correct ground state structure.

We study the late-stage growth of order in the XY model with conserved order parameter in three dimensions using a Langevin formalism. At zero temperature topological defects (vortices) effect the growth law and make it difficult to reach the scaling regime. With the introduction of noise the dislocations get annealed and standard scaling of the correlation function is recovered. The domain size grows with time as ${\mathit{t}}^{1/4}$ in agtreement with a recent renormalization group calculation. Predictions for multiscaling behavior are inconsistent with our numerical data.

Molecular dynamics is used to model the friction between two ordered monolayers of alkane chains six units long bound at their ends to two rigid substrates. Depending on the interfacial interaction strength, energy dissipation occurs by a discontinuous ‘‘plucking’’ mechanism and a continuous viscous mechanism. The plucking mechanism follows a simple thermal activation model, while for the viscous mechanism, friction force is enhanced at the rotator transition temperature of the films.