On Estimation of Fully Entangled Fraction

We study the fully entangled fraction (FEF) of arbitrary mixed states. New upper bounds of FEF are derived. These upper bounds make complements on the estimation of the value of FEF. For weakly mixed quantum states, an upper bound is shown to be very tight to the exact value of FEF.Comment: 8 pages, 2 figure

First-principles study of iron oxyfluorides and lithiation of FeOF

First-principles studies of iron oxyfluorides in the FeF[subscript 2] rutile framework (FeO[subscript x]F[subscript 2−x], 0≤x≤1) are performed using density functional theory (DFT) in the general gradient approximation (GGA) with a Hubbard U correction. Studies of O/F orderings reveal FeOF to be particularly stable compared to other FeO[subscript x]F[subscript 2−x] (x≠1) structures, where FeF[subscript 2]-FeOF mixing is not energetically favored. The band gap of FeF[subscript 2] is found to decrease as oxygen is substituted into its structure. The GGA + U electronic structure evolves from that of a Mott-Hubbard insulator (x=0) to a charge transfer semiconductor (x=1). Lithiation studies reveal that lithiation sites offering mixed O/F environments are the most stable. An insertion voltage plateau up to Li[subscript 0.5]FeOF on lithiation is found, in agreement with recent Li-ion battery experiments. The energetics of further lithiation with respect to conversion scenarios are discussed.United States. Dept. of Energy. Office of Basic Energy Sciences (Northeastern Center for Chemical Energy Storage Award DE-SC0001294

Physical electrostatics of small field emitter arrays/clusters

This paper improves understanding of electrostatic influences on apex field enhancement factors (AFEFs) for small field emitter arrays. Using the "floating sphere at emitter-plate potential" (FSEPP) model, it re-examines the electrostatics and mathematics of three simple systems of identical post-like emitters. For the isolated emitter, various approaches are noted. On need consider only the effects of sphere charges and (for separated emitters) image charges. For the 2-emitter system, formulas are found for "charge-blunting" and "neighbour-field" effects, for widely spaced and "sufficiently closely spaced" emitters. Mutual charge-blunting is always dominant, with a related (negative) fractional AFEF-change {\delta}_two. For sufficiently small emitter spacing c, |{\delta}_two| varies as 1/c; for large spacing, |{\delta}_two| decreases as 1/c^3. In a 3-emitter linear array, differential charge-blunting and differential neighbor-field effects occur, but the former are dominant, and cause the "exposed" outer emitters to have higher AFEF ({\gamma}_0) than the central emitter ({\gamma}_1). Formulas are found for the exposure ratio {\Xi}={\gamma}_0/{\gamma}_1, for large and for sufficiently small separations. The FSEPP model for an isolated emitter has accuracy around 30%. Line-charge models (LCMs) are an alternative, but an apparent difficulty with recent LCM models is identified. Better descriptions of array electrostatics may involve developing good fitting equations for AFEFs derived from accurate numerical solution of Laplace's equation, perhaps with equation form(s) guided qualitatively by FSEPP-model results. In existing fitting formulas, the AFEF-reduction decreases exponentially as c increases, which differs from FSEPP-model formulas. FSEPP models might provide a useful guide to the qualitative behaviour of small field emitter clusters larger than those investigated.Comment: 34 pages, including 3 figures, with an extra 7 pages of Supplementary Material (giving details of algebraic analysis); v3 is slightly revised version, submitted after reviewin

The reentry hypothesis: The putative interaction of the frontal eye field, ventrolateral prefrontal cortex, and areas V4, IT for attention and eye movement

Attention is known to play a key role in perception, including action selection, object recognition and memory. Despite findings revealing competitive interactions among cell populations, attention remains difficult to explain. The central purpose of this paper is to link up a large number of findings in a single computational approach. Our simulation results suggest that attention can be well explained on a network level involving many areas of the brain. We argue that attention is an emergent phenomenon that arises from reentry and competitive interactions. We hypothesize that guided visual search requires the usage of an object-specific template in prefrontal cortex to sensitize V4 and IT cells whose preferred stimuli match the target template. This induces a feature-specific bias and provides guidance for eye movements. Prior to an eye movement, a spatially organized reentry from occulomotor centers, specifically the movement cells of the frontal eye field, occurs and modulates the gain of V4 and IT cells. The processes involved are elucidated by quantitatively comparing the time course of simulated neural activity with experimental data. Using visual search tasks as an example, we provide clear and empirically testable predictions for the participation of IT, V4 and the frontal eye field in attention. Finally, we explain a possible physiological mechanism that can lead to non-flat search slopes as the result of a slow, parallel discrimination process

Interplay between morphological and shielding effects in field emission via Schwarz-Christoffel transformation

It is well known that sufficiently strong electrostatic fields are able to change the morphology of Large Area Field Emitters (LAFEs). This phenomenon affects the electrostatic interactions between adjacent sites on a LAFE during field emission and may lead to several consequences, such as: the emitter's degradation, diffusion of absorbed particles on the emitter's surface, deflection due to electrostatic forces and mechanical stress. These consequences are undesirable for technological applications, since they may significantly affect the macroscopic current density on the LAFE. Despite the technological importance, these processes are not completely understood yet. Moreover, the electrostatic effects due to the proximity between emitters on a LAFE may compete with the morphological ones. The balance between these effects may lead to a non trivial behavior in the apex-Field Enhancement Factor (FEF). The present work intends to study the interplay between proximity and morphological effects by studying a model amenable for an analytical treatment. In order to do that, a conducting system under an external electrostatic field, with a profile limited by two mirror-reflected triangular protrusions on an infinite line, is considered. The FEF near the apex of each emitter is obtained as a function of their shape and the distance between them via a Schwarz-Christoffel transformation. Our results suggest that a tradeoff between morphological and proximity effects on a LAFE may provide an explanation for the observed reduction of the local FEF and its variation at small distances between the emitter sites.Comment: 8 pages, 7 figures, published versio