Tests of local realism and their applications aim for very high confidence in their results even in the presence of potentially adversarial effects. For this purpose, one can measure a quantity that reflects the amoun...
Tests of local realism and their applications aim for very high confidence in their results even in the presence of potentially adversarial effects. For this purpose, one can measure a quantity that reflects the amount of violation of local realism and determine a bound on the probability, according to local realism, of obtaining a violation at least that observed. In general, it is difficult to obtain sufficiently robust and small bounds. Here we describe an efficient protocol for computing such bounds from any set of Bell inequalities for any number of parties, measurement settings, or outcomes. The protocol can be applied to tests of other properties (such as entanglement or dimensionality) that are witnessed by linear inequalities.
The purpose of this paper is to prove the existence of a spatially periodic weak solution to the steady compressible isentropic MHD equations in R3 for any specific heat ratio γ〉 1. The proof is based on the weighte...
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The purpose of this paper is to prove the existence of a spatially periodic weak solution to the steady compressible isentropic MHD equations in R3 for any specific heat ratio γ〉 1. The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method of weak convergence. According to the author＇s knowledge, it is the first result that treats in three dimensions the existence of weak solutions to the steady compressible MHD equations with γ〉1.
The ocean and the atmosphere, and hence the climate, are governed at large scale by interactions between pressure gradient and Coriolis and buoyancy forces. This leads to a quasigeostrophic balance in which, in a two-...
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The ocean and the atmosphere, and hence the climate, are governed at large scale by interactions between pressure gradient and Coriolis and buoyancy forces. This leads to a quasigeostrophic balance in which, in a two-dimensional-like fashion, the energy injected by solar radiation, winds, or tides goes to large scales in what is known as an inverse cascade. Yet, except for Ekman friction, energy dissipation and turbulent mixing occur at a small scale implying the formation of such scales associated with breaking of geostrophic dynamics through wave-eddy interactions or frontogenesis, in opposition to the inverse cascade. Can it be both at the same time? We exemplify here this dual behavior of energy with the help of three-dimensional direct numerical simulations of rotating stratified Boussinesq turbulence. We show that efficient small-scale mixing and large-scale coherence develop simultaneously in such geophysical and astrophysical flows, both with constant flux as required by theoretical arguments, thereby clearly resolving the aforementioned contradiction.
作者：
S. TorquatoY. JiaoDepartment of Chemistry
Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA. torquato@princeton.edu
We study the effect of dimensionality on the percolation threshold ηc of identical overlapping nonspherical convex hyperparticles in d-dimensional Euclidean space Rd. This is done by formulating a scaling relation f...
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We study the effect of dimensionality on the percolation threshold ηc of identical overlapping nonspherical convex hyperparticles in d-dimensional Euclidean space Rd. This is done by formulating a scaling relation for ηc that is based on a rigorous lower bound [Torquato, J. Chem. Phys. 136, 054106 (2012)] and a conjecture that hyperspheres provide the highest threshold, for any d, among all convex hyperparticle shapes (that are not a trivial affine transformation of a hypersphere). This scaling relation also exploits the recently discovered principle that low-dimensional continuum percolation behavior encodes high-dimensional information. We derive an explicit formula for the exclusion volume vex of a hyperparticle of arbitrary shape in terms of its d-dimensional volume v, surface area s, and radius of mean curvature R¯ (or, equivalently, mean width). These basic geometrical properties are computed for a wide variety of nonspherical hyperparticle shapes with random orientations across all dimensions, including, among other shapes, various polygons for d=2, Platonic solids, spherocylinders, parallepipeds, and zero-volume plates for d=3 and their appropriate generalizations for d≥4. Using this information, we compute the lower bound and scaling relation for ηc for this comprehensive set of continuum percolation models across dimensions. We demonstrate that the scaling relation provides accurate upper-bound estimates of the threshold ηc across dimensions and becomes increasingly accurate as the space dimension increases.
The effect of initial longitudinal velocity of the tunnelled electron on the non-sequential double ionization （NSDI） process in an elliptically polarized laser field is studied by a semiclassical model. We find that...
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The effect of initial longitudinal velocity of the tunnelled electron on the non-sequential double ionization （NSDI） process in an elliptically polarized laser field is studied by a semiclassical model. We find that the non-zero initial longitudinal velocity has a suppressing effect on single-return collision （SRC） events in the double ionization process, more specifically, it results in an obvious reduction in the center part of the correlation momentum distributions in the direction of the major polarization axis （z axis） and makes the distribution of single-return collision in the minor polarization axis （x axis） become narrower.
Dislocation motion governs the strength and ductility of metals, and the Peierls stress (σp) quantifies dislocation mobility. σp measurements carry substantial uncertainty in face-centered cubic (fcc) metals, and σ...
Dislocation motion governs the strength and ductility of metals, and the Peierls stress (σp) quantifies dislocation mobility. σp measurements carry substantial uncertainty in face-centered cubic (fcc) metals, and σp values can differ by up to two orders of magnitude. We perform first-principles simulations based on orbital-free density functional theory (OFDFT) to calculate the most accurate currently possible σp for the motion of 12〈110〉111 dislocations in fcc Al. We predict the σps of screw and edge dislocations (dissociated in their equilibrium state) to be 1.9×10−4G and 4.9×10−5G, respectively (G is the shear modulus). These values fall within the range of measurements from mechanical deformation tests (10−4–10−5G). OFDFT also finds a new metastable structure for a screw dislocation not seen in earlier simulations, in which a dislocation core on the glide plane does not dissociate into partials. The corresponding σp for this undissociated dislocation is predicted to be 1.1×10−2G, which agrees with typical Bordoni peak measurements (10−2–10−3G). The calculated σps for dissociated and undissociated screw dislocations differ by two orders of magnitude. The presence of undissociated, as well as dissociated, screw dislocations may resolve the decades-long mystery in fcc metals regarding the two orders of magnitude discrepancy in σp measurements.
The low energy electron impact cross sections of helium from some low excited states are calculated in the R-matrix method. The convergences of the cross sections are checked systematically by using 5 sets of high qua...
The low energy electron impact cross sections of helium from some low excited states are calculated in the R-matrix method. The convergences of the cross sections are checked systematically by using 5 sets of high quality target states; i.e., 5, 11, 19, 29 and 39 physical target states.
The first fully nonlinear numerical simulations of colliding charged black holes in D=4 Einstein-Maxwell theory were recently reported [Zilhão et al., Phys. Rev. D 85, 124062 (2012)]. These collisions were perfor...
The first fully nonlinear numerical simulations of colliding charged black holes in D=4 Einstein-Maxwell theory were recently reported [Zilhão et al., Phys. Rev. D 85, 124062 (2012)]. These collisions were performed for black holes with equal charge-to-mass ratio, for which initial data can be found in closed analytic form. Here we generalize the study of collisions of charged black holes to the case of unequal charge-to-mass ratios. We focus on oppositely charged black holes, as to maximize acceleration-dependent effects. As |Q|/M increases from 0 to 0.99, we observe that the gravitational radiation emitted increases by a factor of ∼2.7; the electromagnetic radiation emission becomes dominant for |Q|/M≳0.37 and at |Q|/M=0.99 is larger, by a factor of ∼5.8, than its gravitational counterpart. We observe that these numerical results exhibit a precise and simple scaling with the charge. Furthermore, we show that the results from the numerical simulations are qualitatively captured by a simple analytic model that computes the electromagnetic dipolar radiation and the gravitational quadrupolar radiation of two nonrelativistic interacting particles in Minkowski spacetime.
To alleviate the congestion caused by rapid growth in demand for mobile data, ISPs have begun encouraging users to offload some of their traffic onto a supplementary, better quality network technology, e.g., offloadin...
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ISBN:
(纸本)9781467359443
To alleviate the congestion caused by rapid growth in demand for mobile data, ISPs have begun encouraging users to offload some of their traffic onto a supplementary, better quality network technology, e.g., offloading from 3G or 4G to WiFi and femtocells. With the growing popularity of such offerings, a deeper understanding of the underlying economic principles and their impact on technology adoption is necessary. To this end, we develop a model for user adoption of a base wireless technology and a bundle of the base plus a supplementary technology. In our model, individual users make their adoption decisions based on several factors, including the technologies' intrinsic qualities, throughput degradation due to congestion externalities from other subscribers, and the flat access rates that an ISP charges. We study the adoption dynamics and show that they converge to a unique equilibrium for a given set of exogenously determined system parameters. In particular, we characterize the occurrence of interesting adoption behaviors, including a possible decrease in the adoption of the supplementary technology as its coverage increases. Similar behaviors occur at an ISP's profit-maximizing prices and the optimal coverage area for the supplementary technology. To account for the potential benefits from offloading in practice, we collect 3G and WiFi usage and location data from twenty mobile users. We then use this data to numerically investigate the profit-maximizing adoption levels when an ISP accounts for its cost of deploying the supplemental technology and savings from offloading traffic onto this technology.
The momentum spectrum of multiphoton-created electrons in the presence of a a static potential well as well as an alternating field is found to be related to the electron energy levels in the potential well and the en...
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The momentum spectrum of multiphoton-created electrons in the presence of a a static potential well as well as an alternating field is found to be related to the electron energy levels in the potential well and the energy of the photons. A simple relation among three energies, the created electron energy associated with the momentum distribution, the level energy of the electron bound state, and the photon energy, is obtained. Pair production can be significantly enhanced by this two-field configuration. In this case, the depth of the static potential well and the frequency of the alternating field also need not be supercritical.
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