The long time behavior of the velocity autocorrelation function in a plasma

The utilization of the Landau-Placzek method results in a velocity autocorrelation function for a one component plasma having oscillatory behavior (at the plasma frequency) in addition to the t^?(d/2) (d = dimension) behavior previously found in neutral gas systems.     

The curve of ``Prym canonical' Gauss divisors on a Prym theta divisor

The Gauss linear system on the theta divisor of the Jacobian of a nonhyperelliptic curve has two striking properties:

1) the branch divisor of the Gauss map on the theta divisor is dual to the canonical model of the curve;

2) those divisors in the Gauss system parametrized by the canonical curve are reducible.

In contrast, Beauville and Debarre prove on a general Prym theta divisor of dimension all Gauss divisors are irreducible and normal. One is led to ask whether properties 1) and 2) may characterize the Gauss system of the theta divisor of a Jacobian. Since for a Prym theta divisor, the most distinguished curve in the Gauss system is the Prym canonical curve, the natural analog of the canonical curve for a Jacobian, in the present paper we analyze whether the analogs of properties 1) or 2) can ever hold for the Prym canonical curve. We note that both those properties would imply that the general Prym canonical Gauss divisor would be nonnormal. Then we find an explicit geometric model for the Prym canonical Gauss divisors and prove the following results using Beauville's singularities criterion for special subvarieties of Prym varieties:

Theorem. For all smooth doubly covered nonhyperelliptic curves of genus , the general Prym canonical Gauss divisor is normal and irreducible.

Corollary. For all smooth doubly covered nonhyperelliptic curves of genus , the Prym canonical curve is not dual to the branch divisor of the Gauss map.

     

Phosphorus intercalation of halloysite nanotubes for enhanced fire properties of polyamide 6

The fire performance of polyamide 6 (PA6) blended with phenyl phosphonic acid functionalized halloysite nanotubes (PPA‐HNTs) is evaluated in order to determine if there is any fire performance gains over the unmodified composite. In the continuing search for safe halogen‐free fire retardants for polymers, and the desire to more fully capture the advantages of nano‐materials, this research seeks to utilize any synergy which might result in improved fire performance of PA6, via the known advantages offered by nano particles and phosphorus‐based compounds. HNTs offer the ability for functionalization by exchange at their hydroxyl sites, while PPA can readily attach at these sites because of its acidity. In this context, the nanotubes act as a carrier for the acid within the polyamide polymeric matrix because it is readily intercalated and functionalized with the acid. The intercalated nano particles are added to the polyamide via melt extrusion and then analyzed using thermal analysis and cone calorimetry. The key finding from this work is that functionalization of HNTs with PPA, followed by blending into PA6 results in a significant improvement in fire performance by altering the combustion dynamics of the polymer. This work proposes a new synergistic fire retardant system for polyamides utilising relatively safe and inexpensive components. More broadly, the concept of using a carrier such as HNTs, which is so easily functionalized, can be applied to other thermoplastic materials, and other additives, for improvements in material properties other than fire. Copyright © 2012 John Wiley & Sons, Ltd.     

Search for octupole deformation in neutron-rich Xe isotopes

A search for octupole deformation in neutron-rich Xe isotopes has been conducted through prompt gammaray spectroscopy of secondary fragments produced in the spontaneous fission of²⁴⁸Cm. The spectrometer consisted of the Eurogam 1 array and a set of 5 LEPS detectors. Level schemes were constructed for Xe isotopes with mass number ranging from 140 to 144 and excited states for^143,144Xe nuclei were observed for the first time. None of the level schemes exhibit an alternating parity quasimolecular band, a feature usually expected in nuclei in which octupole correlation effects are strong enough to produce stable octupole deformation. For several isotopes, structures observed in the level schemes are consistent with an octupole softness of the nuclei.     

Dual behavior of excess electrons in rutile TiO2

The behavior of electrons in the conduction band of TiO₂ and other transition‐metal oxides is key to the many applications of these materials. Experiments seem to produce conflicting results: optical and spin‐resonance techniques reveal strongly localized small polarons, while electrical measurements show high mobilities that can only be explained by delocalized free electrons. By means of hybrid functional calculations we resolve this apparent contradiction and show that small polarons can actually coexist with delocalized electrons in the conduction band of TiO₂, the former being energetically only slightly more favorable. We also find that small polarons can form complexes with oxygen vacancies and ionized shallow‐donor impurities, explaining the rich spectrum of Ti³⁺ species observed in electron spin resonance experiments. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A splitting criterion for an isolated singularity at x = 0 in a family of even hypersurfaces

Assume given a family of even local analytic hypersurfaces, whose central fiber has an isolated singularity at x =?0 which is not an ordinary double point. We prove that if the family is sufficiently general, for instance if the general fiber is smooth and the general singular fiber has only ordinary double points, then the singularity at x = 0 “splits in codimension one”, i.e., the local discriminant divisor has an irreducible component, over which a general fiber has more than one singularity specializing to the original one. As a corollary, we deduce the result by Grushevsky and Salvati Manni (Singularities of the theta divisor at points of order two, IMRN, 2007, Proposition 8) that on a principally polarized abelian variety (A, Θ) with dim(A) = g ≥ 4, a singularity of even multiplicity on Θ, isolated or not, at a point of order two and not an ordinary double point, must be a limit of two distinct ordinary double points {x, ?x} on nearby theta divisors.     

Bi2223带材临界电流沿长度方向的统计分布

本文采用四引线法测量了Bi2223带材临界电流沿长度方向的分布,采用正态分布、对数正态分布、威布尔分布和最小极值分布对临界电流分布进行了拟合检验,确定了临界电流的最优统计分布模型.     

Limits on equal energy back-to-backγ-rays in252Cf decay

A search has been made for coincident, equal-energy, 180° correlatedγ-rays from²⁵²Cf fission decay. Theseγ-rays may arise if new neutral particles are produced in fission, and if they decay byγ-emission. The fraction of fissions which give rise to particles at rest with masses between 1.4 and 2.0 MeV, which then decay into twoγ-rays in a time ? 10^?19s, is less than 8 × 10^?7 at the 95% confidence level.     

Solutions to the Navier-Stokes Equations Describing Local Flows of Stratified and Compressible Fluids

A family of exact solutions of the Navier-Stokes equations is used to describe local flows of incompressible stratified and compressible fluids. For some of the flows, the coefficient of viscosity can depend on the temperature. An example of an incompressible stratified flow for which the analysis is applicable is the sheared swirling flow that is produced between two parallel plates that translate with different velocities and rotate with different angular velocities about different, but parallel, axes. The fluid may be stratified in the direction normal to the plates. These generalized von Karman flows are relevant to the study of strong local atmospheric disturbances, such as might be produced by the passage of a tornado. Also, when the coefficient of viscosity depends on the temperature, they can be used to analyze the flow of molten metals between surfaces that are in relative motion. An example of a compressible flow for which the analysis is applicable is that produced by a plane shock wave as it traverses a layer where the fluid is sheared in a direction normal to the shock.     

Approximate solutions of the Liouville equation. IV. The two-body additive approximation

The two-body additive approximation on the time-dependent Liouville distribution, first introduced in part I of this series, is put into the conventional form of a self-contained kinetic equation for the doublet distribution. From this point of view the approximation consists in truncating the BBGKY chain by expressing the triplet distribution as a functional of lower distributions at the same value of the time variable. To accomplish this, it is necessary to study two associated purely spatial integral equations. The doublet kinetic equation can then be written in terms of solutions of these integral equations and comparison with conventional methods of truncating the BBGKY chain can then be made. For the purpose of comparison a method of truncating the chain based on the Kirkwood superposition approximation is introduced and discussed briefly. The momentum structure of the resulting doublet kinetic equation is similar, but the nonlocality in space of our truncation introduces distinct differences in the spatial structure. The inconsistency between conventional truncations and the exact initial conditions used for the calculation of time-dependent correlation functions is pointed out. This inconsistency is not shared by the two-body additive approximation.