Hidden Variables or Positive Probabilities?

Despite claims that Bell's inequalities are based on the Einstein locality condition, or equivalent, all derivations make an identical mathematical assumption: that local hidden-variable theories produce a set of positive-definite probabilities for detecting a particle with a given spin orientation. The standard argument is that because quantum mechanics assumes that particles are emitted in a superposition of states the theory cannot produce such a set of probabilities. We examine a paper by Eberhard, and several similar papers, which claim to show that a generalized Bell inequality, the CHSH inequality, can be derived solely on the basis of the locality condition, without recourse to hidden variables. We point out that these authors nonetheless assumes a set of positive-definite probabilities, which supports the claim that hidden variables or "locality" is not at issue here, positive-definite probabilities are. We demonstrate that quantum mechanics does predict a set of probabilities that violate the CHSH inequality; however these probabilities are not positive-definite. Nevertheless, they are physically meaningful in that they give the usual quantum-mechanical predictions in physical situations. We discuss in what sense our results are related to the Wigner distribution.Comment: 19 pages, 2 ps files This is a second replacement. In this version we include an analysis of yet another version of Bell's theorem which has been brought to our attention. We also discuss in what sense our results are related to the Wigner distributio

Lattice-Boltzmann Method for Non-Newtonian Fluid Flows

We study an ad hoc extension of the Lattice-Boltzmann method that allows the simulation of non-Newtonian fluids described by generalized Newtonian models. We extensively test the accuracy of the method for the case of shear-thinning and shear-thickening truncated power-law fluids in the parallel plate geometry, and show that the relative error compared to analytical solutions decays approximately linear with the lattice resolution. Finally, we also tested the method in the reentrant-flow geometry, in which the shear-rate is no-longer a scalar and the presence of two singular points requires high accuracy in order to obtain satisfactory resolution in the local stress near these points. In this geometry, we also found excellent agreement with the solutions obtained by standard finite-element methods, and the agreement improves with higher lattice resolution

Simulating Three-Dimensional Hydrodynamics on a Cellular-Automata Machine

We demonstrate how three-dimensional fluid flow simulations can be carried out on the Cellular Automata Machine 8 (CAM-8), a special-purpose computer for cellular-automata computations. The principal algorithmic innovation is the use of a lattice-gas model with a 16-bit collision operator that is specially adapted to the machine architecture. It is shown how the collision rules can be optimized to obtain a low viscosity of the fluid. Predictions of the viscosity based on a Boltzmann approximation agree well with measurements of the viscosity made on CAM-8. Several test simulations of flows in simple geometries -- channels, pipes, and a cubic array of spheres -- are carried out. Measurements of average flux in these geometries compare well with theoretical predictions.Comment: 19 pages, REVTeX and epsf macros require

A Phase Space Approach to Gravitational Enropy

We examine the definition S = ln Omega as a candidate "gravitational entropy" function. We calculate its behavior for gravitationl and density perturbations in closed, open and flat cosmologies and find that in all cases it increases monotonically. Using the formalism to calculate the gravitational entropy produced during inflation gives the canonical answer. We compare the behavior of S with the behavior of the square of the Weyl tensor. Applying the formalism to black holes has proven more problematical.Comment: Talk delivered at South African Relativistic Cosmology Symposium, Feb 1999. Some new results over Rothman and Anninos 97. To appear in GRG, 17 page

Interface Roughening in a Hydrodynamic Lattice-Gas Model with Surfactant

Using a hydrodynamic lattice-gas model, we study interface growth in a binary fluid with various concentrations of surfactant. We find that the interface is smoothed by small concentrations of surfactant, while microemulsion droplets form for large surfactant concentrations. To assist in determining the stability limits of the interface, we calculate the change in the roughness and growth exponents $\alpha$ and $\beta$ as a function of surfactant concentration along the interface.Comment: 4 pages with 4 embedded ps figures. Requires psfig.tex. Will appear in PRL 14 Oct 199

Super-resolution provided by the arbitrarily strong superlinearity of the blackbody radiation

Blackbody radiation is a fundamental phenomenon in nature, and its explanation by Planck marks a cornerstone in the history of Physics. In this theoretical work, we show that the spectral radiance given by Planck's law is strongly superlinear with temperature, with an arbitrarily large local exponent for decreasing wavelengths. From that scaling analysis, we propose a new concept of super-resolved detection and imaging: if a focused beam of energy is scanned over an object that absorbs and linearly converts that energy into heat, a highly nonlinear thermal radiation response is generated, and its point spread function can be made arbitrarily smaller than the excitation beam focus. Based on a few practical scenarios, we propose to extend the notion of super-resolution beyond its current niche in microscopy to various kinds of excitation beams, a wide range of spatial scales, and a broader diversity of target objects

Far Infrared and Submillimeter Emission from Galactic and Extragalactic Photo-Dissociation Regions

Photodissociation Region (PDR) models are computed over a wide range of physical conditions, from those appropriate to giant molecular clouds illuminated by the interstellar radiation field to the conditions experienced by circumstellar disks very close to hot massive stars. These models use the most up-to-date values of atomic and molecular data, the most current chemical rate coefficients, and the newest grain photoelectric heating rates which include treatments of small grains and large molecules. In addition, we examine the effects of metallicity and cloud extinction on the predicted line intensities. Results are presented for PDR models with densities over the range n=10^1-10^7 cm^-3 and for incident far-ultraviolet radiation fields over the range G_0=10^-0.5-10^6.5, for metallicities Z=1 and 0.1 times the local Galactic value, and for a range of PDR cloud sizes. We present line strength and/or line ratio plots for a variety of useful PDR diagnostics: [C II] 158 micron, [O I] 63 and 145 micron, [C I] 370 and 609 micron, CO J=1-0, J=2-1, J=3-2, J=6-5 and J=15-14, as well as the strength of the far-infrared continuum. These plots will be useful for the interpretation of Galactic and extragalactic far infrared and submillimeter spectra observable with ISO, SOFIA, SWAS, FIRST and other orbital and suborbital platforms. As examples, we apply our results to ISO and ground based observations of M82, NGC 278, and the Large Magellenic Cloud.Comment: 54 pages, 20 figures, accepted for publication in The Astrophysical Journa