The case of a domain wall of finite thickness is examined by use of two different expressions for the energy-stress tensor of domain walls but no symmetry condition. It is found that the equations of general relativity show that such walls cannot be in static equilibrium, and further even nonequilibrium walls can be consistent with Einstein’s equations only under very special circumstances.

The organization, encoding, and hierarchical construction of a generic chaotic attractor is presented. A systematic calculation of the multifractal properties is accomplished, and an understanding of the spectrum of singularities is reported. In general we expect nontrivial phase transitions in the thermodynamic formalism of strange attractors.

The detailed dependence of the smallest nonzero eigenvalue of a bistable periodic Fokker-Planck equation on the external-noise correlation time is determined for the first time numerically to tie down contrasting theoretical predictions. The isospectrality with the Fokker-Planck equation for the metastable system defined by inversion of the bistable potential is proved analytically. This amounts to a generalized supersymmetric transformation between the corresponding non-Hermitean Hamiltonian operators.

We have conducted an experiment to detect a composition-dependent force with range λ between 10 m and 1 km, and find a statistically significant effect. If interpreted as arising from a new force, this result and other recent measurementes would be consistent in strength only if the coupling were predominantly to nuclear isospin.

We extend Einstein’s field equations and Hilbert’s action for gravity to the hyperspace of dimension ${\mathrm{N}}^2$ that is built out of N-component spinors in the way that four-dimensional time-space is built out of two-component ones. The hypergravitational field equation is of differential order N in a chronometric tensor with N indices. The natural spin structures of the unitary groups U(N) define Einstein-type cosmologies, static, U(N)-invariant, and closed, that satisfy the extended equations with neither dust nor cosmological constant, except for N=2 which requires both.

For a slowly time-dependent Hamiltonian system exhibiting motion which ergodically covers the energy surface, the phase-space volume enclosed inside this surface is an adiabatic invariant. In this paper the scaling of the error in the adiabatic approximation is investigated for this situation via numerical experiments on chaotic billiard systems. It is found that the scaling depends on the long-time behavior of correlations in the chaotic system.

We point out that, on very general grounds, experiments with directionally collimated beams (of neutrons or other particles) incident on passive targets cannot distinguish between their coherent wave-packet structure and the incoherent mixing due, for example, to multiple emitters or to interactions with other particles in the source.

This paper considers the three-dimensional inverse scattering problem for the wave equation with variable velocity. A possible solution is presented in terms of equations whose self-consistent solution determines the velocity from scattering data. These self-consistent equations are (1) the wave equation in integral form, (2) a linear integral equation which relates the wave field and scattering data, and (3) a novel formula for the velocity in terms of the wave field.

We present a forecasting technique for chaotic data. After embedding a time series in a state space using delay coordinates, we ‘‘learn’’ the induced nonlinear mapping using local approximation. This allows us to make short-term predictions of the future behavior of a time series, using information based only on past values. We present an error estimate for this technique, and demonstrate its effectiveness by applying it to several examples, including data from the Mackey-Glass delay differential equation, Rayleigh-Benard convection, and Taylor-Couette flow.

Results from two recent ‘‘fifth-force’’ experiments disagree when analyzed in terms of a single baryonic interaction. We consider an interaction coupling to ${\mathrm{q}}_5$=B cos${\mathrm{\theta }}_5$+L sin${\mathrm{\theta }}_5$ where ${\mathrm{\theta }}_5$ has a value that could explain our null Cu-Be data while preserving Thieberger’s positive Cu-${\mathrm{H}}_2$O result. (B and L are baryon and lepton number, respectively.) We present new Al-Be data that rule out this possibility except for a narrow region around ${\mathrm{\theta }}_5$≊-63° (${\mathrm{q}}_5$∝${\mathrm{I}}_3$, the third component of isospin), where the ${\mathrm{q}}_5$ of terrestrial sources vanishes.

The formation of fractal patterns during an amorphous structural transition in Ni-Mo thin films after 200-keV xenon-ion irradiation is presented. The dimension of the ion-induced fractals is 1.72±0.07. The fractal patterns, together with other microscopic features, are described and characterized. Our results are compared to the cluster-diffusion-limited-aggregation model. The growth habit is attributed to long-range correlation which occurs at a critical condition during the amorphous-crystal transition.

It is argued that the global, uniform semiclassical approximation to quantization afforded by a coherent-state approach is well suited for an analysis of classically chaotic systems. Special attention is given to the interpolating action which incorporates in a single expression the classical action for each and every contributing classical trajectory. Approximate expressions for the configuration-space propagator are presented for small, intermediate, and large propagation times.

We have carried out a direct free-fall experiment to measure the differential acceleration between two different materials (copper and uranium) falling in the Earth’s gravitational field. The differential acceleration was measured to be less than 5 parts in ${10}^{10}$ of the normal gravitational acceleration. This null result puts new limits on the strength and range of the proposed fifth force.

We report that dc-excited discharges in gases that display current oscillations which develop into deterministically chaotic behavior. A period-doubling route to chaos characteristic of 1D maps is established for sealed discharges in Plücker’s tubes containing helium. Besides this we report the observation of a scenario showing properties analogous to those of the 2D map of Hénon. Clear sequences of period doublings are also reported for flowing discharges.

We propose that space-time at the smallest scales is in reality a causal set: a locally finite set of elements endowed with a partial order corresponding to the macroscopic relation that defines past and future. We explore how a Lorentzian manifold can approximate a causal set, noting in particular that the thereby defined effective dimensionality of a given causal set can vary with length scale. Finally, we speculate briefly on the quantum dynamics of causal sets, indicating why an appropriate choice of action can reproduce general relativity in the classical limit.

It is shown that the Fokker-Wheeler-Feynman model of a system of massive, charged particles interacting via forces of electromagnetic origin can be rewritten to yield a physically acceptable relativistic many-particle Lagrangean. Contrary to the postulates of Wheeler and Feynman, the model satisfies causality and can be generalized to include arbitrary forces. It also allows a simple description of radiation reaction and, as well, may provide the basis for any comparable modeling of other systems.

We show that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point. Flicker noise, or 1/f noise, can be identified with the dynamics of the critical state. This picture also yields insight into the origin of fractal objects.

Recently, Berry recognized that topological phase factors may arise when a quantum mechanical system is adiabatically transported around a closed circuit. We have measured Berry’s topological phases by polarized-neutron spin rotation in a helical magnetic field. Berry’s law is thus verified for fermions.

It is pointed out that for the pulsed rotators the classical resonance-overlapping criterion for the onset of chaotic motion implies the existence of avoided crossings among an arbitrarily large number of quantum levels at the classical limit ħ small, nħ=A close to a classical resonance.

The spectrum of excitations of a spin-(1/2 Heisenberg chain in the region of anisotropy 1>Δ>0 (where the model is critical and has no bound states) exhibits a ‘‘tower structure’’ in the energy-momentum plane as predicted by the hypothesis of conformal invariance. For a given magnetization the apices of the towers are located on a parabola. The spectrum shows remarkable degeneracies at some discrete values of Δ given by the Tutte-Behara numbers.