Smooth Solution of the Compressible Navier–Stokes Equations in an Unbounded Domain with Inflow Boundary Condition

The barotropic compressible Navier–Stokes equations in an unbounded domain are studied. We prove the unique existence of the solution (u, p) of the system (1.1) in the Sobolev spaceH^{k + 3} × H^{k + 2}provided that the derivatives of the data of the problem are sufficiently small, wherek ≥ 0 is any integer. The proof follows from an analysis of the linearized problem, the solvability of the continuity equation, and the Schauder fixed point theory. Similar smoothness results are obtained for a linearized form of (1.1).     

On a possibility to find experimental evidence for the many-worlds interpretation of quantum mechanics

The many-worlds interpretation of quantum mechanics predicts the formation of distinct parallel worlds as a result, of a quantum mechanical measurement. Communication among these parallel worlds would experimentally rule out alternatives to this interpretation. A possible procedure for “interworld” exchange of information and energy, using only state of the art quantum optical equipement, is described. A single ion is isolated from its environment in an ion trap. Then a quantum mechanical measurement with two discrete outcomes is performed on another system, resulting in the formation of two parallel worlds. Depending on the outcome of this measurement the ion is excited from only one of the parallel worlds before the ion decoheres through its interaction with the environment. A detection of this excitation in the other parallel world is direct evidence for the many-worlds interpretation. This method could have important practical applications in physics and beyond.     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

FORECASTING MINERAL SUPPLY FROM MINERAL RENT DATA

An optimal control model of exhaustible resources is used to clarify the long run relationship between mineral rent and depletion cost at the industry level. A standard first order condition of the time rate of change of rents is reformulated to reveal that rent data may be used to help forecast the rise in extraction costs resulting from resource depletion. This application of the theory of exhaustible resources is illustrated using historical mineral industry rent and extraction cost data. A forecast of U.S. coal extraction costs, following the method proposed in this paper, suggests that future rates of extraction cost increases will be similar to rates experienced in the past.     

Investigation of the layer-by-layer transition near the bulk smectic-A-crystal-B transition in thick free-standing films

Highly sensitive optical reflectivity measurements are used to investigate the layer-by-layer transition in extremely thin and thick N-(4-n-hexyloxybenzylidene)-4-n-hexylaniline (6O.6) films. The simple power-law form, N=N ₀ t ^−1/3, for the penetration of the crystal-B order is found to describe the transitions only near the surface. A deviation from the power law is observed for the interior layers. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 4, 266–269 (25 February 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Hydroxyl ion conduction in ytterbium-doped strontium cerate at T<580 K in H2O/air atmosphere

Open circuit voltage (OCV) measurements in H₂O/air concentration cells at T<580 K using Yb-doped SrCeO₃ electrolyte indicate that under these conditions, protons are transported through the electrolyte as -ve ions, possibly as hydroxyl (OH⁻) ions. The H⁺ ionic transport, which is generally reported, becomes the dominant mode for H₂O/air concentration cells at temperatures greater than 750 K or when H₂O/air electrodes are replaced by H₂/Ar, and the anomalous OCV sign disappears. The combination of low temperature and the presence of hydrogen and oxygen as provided by the H₂O/air system appears to be necessary for the postulated hydroxyl ion electrode reactions to take place. In addition to OCV measurements, results from impedance spectroscopy are used to provide evidence in support of the suggested hydroxyl ion mode of protonic transport under the specified conditions. These findings are directly relevant in the development of novel humidity sensors in the temperature range 450–580K and is reported in a separate paper in this conference. Paper presented at the 3rd Euroconference on Solid State Ionics, Teulada, Sardinia, Italy, Sept. 15–22, 1996     

Experimental investigation and numerical simulation of the influence of resonator-length detuning on the output power,pulse duration and spectral width of a cw mode-locked picosecond optical parametric oscillator

We report on a cw mode-locked non-critically phase matched KTP optical parametric oscillator synchronously pumped by a picosecond Ti:Sapphire laser. High average signal output power of up to 950 mW over a large tuning range has been achieved. For this OPO the influence of resonator-length detuning on the output power, pulse duration and spectral bandwidth has been investigated. The measured data are in good agreement with the results of a numerical simulation using a split-step Fourier method which considers the group-velocity mismatch, the group-velocity dispersion and the self-phase modulation. The numerical simulation also describes the measured strong pump depletion and its influence on the OPO output and efficiency.     

The Hausdorff dimension of graphs of Weierstrass functions

The Weierstrass nowhere differentiable function, and functions constructed from similar infinite series, have been studied often as examples of functions whose graph is a fractal. Though there is a simple formula for the Hausdorff dimension of the graph which is widely accepted, it has not been rigorously proved to hold. We prove that if arbitrary phases are included in each term of the summation for the Weierstrass function, the Hausdorff dimension of the graph of the function has the conjectured value for almost every sequence of phases. The argument extends to a much wider class of Weierstrass-like functions.