Vacuum polarization for neutral particles in 2+1 dimensions

In 2+1 dimensions there exists a duality between a charged Dirac particle coupled minimally to a background vector potential and a neutral one coupled nonminimally to a background electromagnetic field strength. A constant uniform background electric current induces in the vacuum of the neutral particle a fermion current which is proportional to the background one. A background electromagnetic plane wave induces no current in the vacuum. For constant but nonuniform background electric charge, known results for charged particles can be translated to give the induced fermion number. Some new examples with infinite background electric charge are presented. The induced spin and total angular momentum are also discussed.Comment: REVTeX, 7 pages, no figur

Gamma-Ray Bursts are Produced Predominately in the Early Universe

It is known that some observed gamma-ray bursts (GRBs) are produced at cosmological distances and that the GRB production rate may follow the star formation rate. We model the BATSE-detected intensity distribution of long GRBs in order to determine their space density distribution and opening angle distribution. Our main results are: the lower and upper distance limits to the GRB production are z 0.24 and >10, respectively; the GRB opening angle follows an exponential distribution and the mean opening angle is about 0.03 radians; and the peak luminosity appears to be a better standard candle than the total energy of a GRB.Comment: 12 pages, 2 figur

A proposal for highly tunable optical parametric oscillation in silicon micro-resonators

We propose a novel scheme for continuous-wave pumped optical parametric oscillation (OPO) inside silicon micro-resonators. The proposed scheme not only requires a relative low lasing threshold, but also exhibits extremely broad tunability extending from the telecom band to mid infrared

Time evolution, cyclic solutions and geometric phases for general spin in an arbitrarily varying magnetic field

A neutral particle with general spin and magnetic moment moving in an arbitrarily varying magnetic field is studied. The time evolution operator for the Schr\"odinger equation can be obtained if one can find a unit vector that satisfies the equation obeyed by the mean of the spin operator. There exist at least $2s+1$ cyclic solutions in any time interval. Some particular time interval may exist in which all solutions are cyclic. The nonadiabatic geometric phase for cyclic solutions generally contains extra terms in addition to the familiar one that is proportional to the solid angle subtended by the closed trace of the spin vector.Comment: revtex4, 8 pages, no figur

On the exceptional damage-tolerance of gradient metallic materials

An experimental study is described on the fracture toughness and micro-mechanisms associated with the initiation and propagation of cracks in metallic nickel containing marked gradients in grain size, ranging from ∼30 nm to ∼4 μm. Specifically, cracks are grown in a gradient structured (GS) nickel with grain-size gradient ranging from the coarse macro-scale to nano-scale (CG → NG) and vice versa (NG → CG), with the measured crack-resistance R-curves compared to the corresponding behavior in uniform nano-grained (NG) and coarse-grained (CG) materials. It is found that the gradient structures display a much-improved combination of high strength and toughness compared to uniform grain-sized materials. However, based on J-integral measurements in the gradient materials, the crack-initiation toughness is far higher for cracks grown in the direction of the coarse-to-nano grained gradient than vice versa, a result which we ascribe primarily to excessive crack-tip blunting in the coarse-grained microstructure. Both gradient structures, however, display marked rising R-curve behavior with exceptional crack-growth toughnesses exceeding 200 MPa.m½

Computing the lower and upper bounds of Laplace eigenvalue problem: by combining conforming and nonconforming finite element methods

This article is devoted to computing the lower and upper bounds of the Laplace eigenvalue problem. By using the special nonconforming finite elements, i.e., enriched Crouzeix-Raviart element and extension $Q_1^{\rm rot}$, we get the lower bound of the eigenvalue. Additionally, we also use conforming finite elements to do the postprocessing to get the upper bound of the eigenvalue. The postprocessing method need only to solve the corresponding source problems and a small eigenvalue problem if higher order postprocessing method is implemented. Thus, we can obtain the lower and upper bounds of the eigenvalues simultaneously by solving eigenvalue problem only once. Some numerical results are also presented to validate our theoretical analysis.Comment: 19 pages, 4 figure

Concerning the Motion and Orientation of Flux Transfer Events Produced by Component and Antiparallel Reconnection

We employ the Cooling et al. (2001) model to predict the location, orientation, motion, and signatures of flux transfer events (FTEs) generated at the solstices and equinoxes along extended subsolar component and high ]latitude antiparallel reconnection curves for typical solar wind plasma conditions and various interplanetary magnetic field (IMF) strengths and directions. In general, events generated by the two mechanisms maintain the strikingly different orientations they begin with as they move toward the terminator in opposite pairs of magnetopause quadrants. The curves along which events generated by component reconnection form bow toward the winter cusp. Events generated by antiparallel reconnection form on the equatorial magnetopause during intervals of strongly southward IMF orientation during the equinoxes, form in the winter hemisphere and only reach the dayside equatorial magnetopause during the solstices when the IMF strength is very large and the IMF points strongly southward, never reach the equatorial dayside magnetopause when the IMF has a substantial dawnward or duskward component, and never reach the equatorial flank magnetopause during intervals of northward and dawnward or duskward IMF orientation. Magnetosheath magnetic fields typically have strong components transverse to events generated by component reconnection but only weak components transverse to the axes of events generated by antiparallel reconnection. As a result, much stronger bipolar magnetic field signatures normal to the nominal magnetopause should accompany events generated by component reconnection. The results presented in this paper suggest that events generated by component reconnection predominate on the dayside equatorial and flank magnetopause for most solar wind conditions

TimeMachine: Timeline Generation for Knowledge-Base Entities

We present a method called TIMEMACHINE to generate a timeline of events and relations for entities in a knowledge base. For example for an actor, such a timeline should show the most important professional and personal milestones and relationships such as works, awards, collaborations, and family relationships. We develop three orthogonal timeline quality criteria that an ideal timeline should satisfy: (1) it shows events that are relevant to the entity; (2) it shows events that are temporally diverse, so they distribute along the time axis, avoiding visual crowding and allowing for easy user interaction, such as zooming in and out; and (3) it shows events that are content diverse, so they contain many different types of events (e.g., for an actor, it should show movies and marriages and awards, not just movies). We present an algorithm to generate such timelines for a given time period and screen size, based on submodular optimization and web-co-occurrence statistics with provable performance guarantees. A series of user studies using Mechanical Turk shows that all three quality criteria are crucial to produce quality timelines and that our algorithm significantly outperforms various baseline and state-of-the-art methods.Comment: To appear at ACM SIGKDD KDD'15. 12pp, 7 fig. With appendix. Demo and other info available at http://cs.stanford.edu/~althoff/timemachine

Ground-state fidelity of Luttinger liquids: A wave functional approach

We use a wave functional approach to calculate the fidelity of ground states in the Luttinger liquid universality class of one-dimensional gapless quantum many-body systems. The ground-state wave functionals are discussed using both the Schrodinger (functional differential equation) formulation and a path integral formulation. The fidelity between Luttinger liquids with Luttinger parameters K and K' is found to decay exponentially with system size, and to obey the symmetry F(K,K')=F(1/K,1/K') as a consequence of a duality in the bosonization description of Luttinger liquids.Comment: 13 pages, IOP single-column format. Sec. 3 expanded with discussion of short-distance cut-off. Some typos corrected. Ref. 44 in v2 is now footnote 2 (moved by copy editor). Published versio