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Some gravitational consequences of certain extensions of Einstein's general theory of relativity are discussed. These theories are not alternative theories of gravity in the usual sense. It is assumed that general relativity is the appropriate description of all gravitational phenomena which were observed to date.
We derive a relationship for the electric field dependent ionic conductivity in terms of fluctuations of time integrated microscopic variables. We demonstrate this formalism with molecular dynamics simulations of solutions of differing ionic strength with implicit solvent conditions and molten salts. These calculations are aided by a novel nonequilibrium statistical reweighting scheme that allows for the conductivity to be computed as a continuous function of the applied field. In strong electrolytes, we find the fluctuations of the ionic current are Gaussian, and subsequently, the conductivity is constant with applied field. In weaker electrolytes and molten salts, we find the fluctuations of the ionic current are strongly non-Gaussian, and the conductivity increases with applied field. Furthermore, this nonlinear behavior, known phenomenologically for dilute electrolytes as the Onsager-Wien effect, is general and results from the suppression of ionic correlations at large applied fields, as we elucidate through both dynamic and static correlations within nonequilibrium steady states.
We describe two relatively simple reductions to order 6 for the planar general three-body problem. We also show that this reduction leads to the distinction between two types of periodic solutions: absolute or relative periodic solutions. An algorithm for obtaining relative periodic solutions using heliocentric coordinates is then described. It is concluded from the periodicity conditions that relative periodic solutions must form families with a single parameter. Finally, two such families have been obtained numerically and are described in some detail.
The inverse factorial series expansion for the ratio of products of gamma functions whose arguments are linear functions of the variable is found. A recurrence relation for the coefficients in terms of the Nørlund–Bernoulli polynomials is provided, and the half-plane of convergence is determined. The results obtained naturally supplement a number of previous investigations of the gamma ratios, which began in the 1930-ies. The expansion obtained in this paper plays a crucial role in the study of the behavior of the delta-neutral Fox’s H-function in the neighborhood of its finite singular point. A particular case of the inverse factorial series expansion is used in deriving a possibly new identity for the Nørlund–Bernoulli polynomials.
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An improved method for transforming radar-observed reflectivities Ze into rain rate R is presented. The method is based on a formulation of a Ze-R function constrained such that (1) the radar-retrieved pdf of R and all of its moments are identical to those determined from the gauges over a sufficiently large domain, and (2) the fraction of the time that it is raining above a low but still has an accurately measurable rain intensity is identical for both the radar and for simultaneous measurements of collocated gauges on average. Data measured by a 1.65-deg beamwidth C-band radar and 22 gauges located in the vicinity of Darwin, Australia, are used. The resultant Ze-R functions show a strong range dependence, especially for the rain regimes characterized by strong reflectivity gradients and substantial attenuation. The application of these novel Ze-R functions to the radar data produces excellent matches to the gauge measurements without any systematic bias.
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The dispersion characteristics of small signal electrohydrodynamic space charge and polarization waves in continuously and discretely stratified liquids are developed. The liquids, modeled as incompressible, inviscid, and perfectly insulating have distributions of mass density, charge density, permittivity, and electric field. A general set of relations for perturbation field and flow variables defined for a prototype layer are used to describe the dynamics of many superposed planar layers. It is shown that the general relations can be used to represent systems of coupled layers which approximate continuous distributions by a series of step functions. Specific examples of weak gradient and exponential distributions are presented showing that the solution found directly from the distributed theory is approached by the system of coupled layers, if the limit is taken in which the number of layers become large while each layer thickness approaches zero.
A reciprocity theorem is presented that relates the short-circuit current of a device, induced by a carrier generation source, to the minority-carrier Fermi level in the dark. The basic relation is general under low injection. It holds for three-dimensional devices with position dependent parameters (energy gap, electron affinity, mobility, etc.), and for transient or steady-state conditions. This theorem allows calculation of the internal quantum efficiency of a solar cell by using the analysis of the device in the dark. Other applications could involve measurements of various device parameters, interfacial surface recombination velocity at a polcrystalline silicon emitter contact, for rexample, by using steady-state or transient photon or mass-particle radiation.
We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of discretized Laplacian operators to allow for polynomially improved scaling in truncation errors and improved scaling for state preparation relative to general purpose quantum algorithms for solving linear differential equations. Relative to classical algorithms for simulating the D-dimensional wave equation, our quantum algorithm achieves exponential space savings and achieves a speedup which is polynomial for fixed D and exponential in D. Furthermore, we also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell's equations.
Using concepts of (C,A)-invariant and unobservability (complementary observability) subspaces, a geometric formulation of the failure detection and identification filter problem is stated. Using these geometric concepts, it is shown that it is possible to design a causal linear time-invariant processor that can be used to detect and uniquely identify a component failure in a linear time-invariant system, assuming: (1) The components can fail simultaneously, and (2) The components can fail only one at a time. In addition, a geometric formulation of Beard's failure detection filter problem is stated. This new formulation completely clarifies of output separability and mutual detectability introduced by Beard and also exploits the dual relationship between a restricted version of the failure detection and identification problem and the control decoupling problem. Moreover, the frequency domain interpretation of the results is used to relate the concepts of failure sensitive observers with the generalized parity relations introduced by Chow. This interpretation unifies the various failure detection and identification concepts and design procedures.
It is shown how the genus per unit volume of isodensity surfaces in general nonlinear universes is related to the entire hierarchy of correlation functions. The general relation between the correlation function, the probability distribution of densities at several points, and the probability distributions of density and its derivatives at a point are given. Formulas for the area and genus per unit volume of isodensity surfaces are presented. As an application, after first reviewing the case of Gaussian fields, analytic results are reported for one particular example of a thoroughly nonlinear universe, Mandelbrot's Rayleigh-Levy random-walk fractal. While this fractal bears little resemblance to the real universe of galaxies, it possesses the singular and theoretically interesting property that in it cluster-cluster correlations are identically equal to galaxy-galaxy correlations to all orders.
The relation of the pilot to the aircraft in general aviation is considered. The human component is analyzed, along with general aviation facilities. The man-machine interface, and the man-environment interface are discussed.
Experimental strain measurements have been made at the highly strained regions on notched plate specimens that were made of Hastelloy X. Tests were performed at temperatures up to 1,600 F. Variable load patterns were chosen so as to produce plastic and creep strains. Were appropriate, notch root stresses were experimentally estimated by subjecting a smooth specimen to the measured notch root strains. The results of three analysis techniques are presented and compared to the experimental data. The most accurate results were obtained from an analysis procedure that used a smooth specimen and the Neuber relation to simulate the notch root stress-strain response. When a generalized constitutive relation was used with the Neuber relation, good results were also obtained, however, these results were not as accurate as those obtained when the smooth specimen was used directly. Finally, a general finite element program, ANYSIS, was used which resulted in acceptable solutions, but, these were the least accurate predictions.
Two sets of coupled-mode equations for multiwaveguide systems are derived using a generalized reciprocity relation; one set for a lossless system, and the other for a general lossy or lossless system. The second set of equations also reduces to those of the first set in the lossless case under the condition that the transverse field components are chosen to be real. Analytical relations between the coupling coefficients are shown and applied to the coupling of mode equations. It is shown analytically that these results satisfy exactly both the reciprocity theorem and power conservation. New orthogonal relations between the supermodes are derived in matrix form, with the overlap integrals taken into account.
This paper is concerned with the bounds and approximations that are found in the original derivation of the fourth-power scaling of shock waves in solids [D. Grady, Appl. Phys. Lett. 38, 825 (1981)]. The analysis is focused on the framework of the derivation and is independent of constitutive assumption, such as visco-plastic behavior. Results include an upper bound for the shock pressure and a restriction on the range of power coefficient for materials having a power-type function for the shock velocity–particle velocity relation. Relaxation of this restriction is proposed based on the idea that the rise time along the Rayleigh line is strain dependent. The idea led to the application of the Onsager relation to strain rate calculation that in turn resulted in a quadratic function for the strain rate–shock pressure relation. The fourth-power relation is obtained by generalizing the Onsager relation through the introduction of a quadratic dissipative potential in analogy to Rayleigh's dissipative potential.
The International DORIS Service (IDS) was created in 2003 under the umbrella of the International Association of Geodesy (IAG) to foster scientific research related to the French DORIS tracking system and to deliver scientific products, mostly related to the International Earth rotation and Reference systems Service (IERS). We first present some general background related to the DORIS system (current and planned satellites, current tracking network and expected evolution) and to the general IDS organization (from Data Centers, Analysis Centers and Combination Center). Then, we discuss some of the steps recently taken to prepare the IDS submission to ITRF2013 (combined weekly time series based on individual solutions from several Analysis Centers). In particular, recent results obtained from the Analysis Centers and the Combination Center show that improvements can still be made when updating physical models of some DORIS satellites, such as Envisat, Cryosat-2 or Jason-2. The DORIS contribution to ITRF2013 should also benefit from the larger number of ground observations collected by the last generation of DGXX receivers (first instrument being onboard Jason-2 satellite). In particular for polar motion, sub-millarcsecond accuracy seems now to be achievable. Weekly station positioning internal consistency also seems to be improved with a larger DORIS constellation.
We find that different asymptotic measurements in quantum field theory can be related to one another through new versions of crossing symmetry. Assuming analyticity, we conjecture generalized crossing relations for multi-particle processes and the corresponding paths of analytic continuation. We prove them to all multiplicity at tree-level in quantum field theory and string theory. We illustrate how to practically perform analytic continuations on loop-level examples using different methods, including unitarity cuts and differential equations. We study the extent to which anomalous thresholds away from the usual physical region can cause an analytic obstruction to crossing when massless particles are involved. In an appendix, we review and streamline historical proofs of four-particle crossing symmetry in gapped theories.