Analysis of thermodynamic identities for materials under extreme compression

Some basic relationships for materials under extreme compression are analyzed with the help of the calculus of indeterminates. The analysis presented here provides an understanding of the origin of identities and constraints at infinite pressure which are satisfied by all physically acceptable equations of state. These identities involve the bulk modulus and its pressure derivatives, the Grüneisen parameter and its volume derivatives, the thermal expansivity, and the Anderson-Grüneisen parameter. The identity for the third-order Grüneisen parameter in terms of the pressure derivatives of the bulk modulus at extreme compression is valid even if the free-volume parameter changes with pressure.     

Apatite type lanthanum silicate and composite anode half cells

Apatite type rare earth silicates are being extensively studied as electrolyte material for intermediate temperature solid oxide fuel cells (SOFC). In this paper we presents results on synthesis of Al and/or Fe-doped ATLS, the design of compatible anode materials, thermal expansion properties and co-sintering of half-cells from expansion matched materials using the advanced pulsed electric current sintering (PECS) technique. The issues related to the co-sintering of half cells have been addressed successfully by the combined use of nano powders and PECS.     

High-temperature electrical properties of magnesiowustite Mg1 − xFexO and spinel Fe3 − x − yMgxCryO4 ceramics

Phase relationships, thermal expansion and electrical properties of Mg_1 − xFe_xO (x = 0.1-0.45) cubic solid solutions and Fe_{3 − x − y}Mg_xCr_yO_4 ± δ (x = 0.7-0.95; y = 0 or 0.5) spinels were studied at 300-1770 K in the oxygen partial pressure range from 10 Pa to 21 kPa. Increasing iron content enlarges the spinel phase stability domain at reduced oxygen pressures and elevated temperatures. The total conductivity of the spinel ceramics is predominantly n-type electronic and is essentially p(O₂)-independent within the stability domain. The computer simulations using molecular dynamics technique confirmed that overall level of ion diffusion remains low even at high temperatures close to the melting point. Temperature dependencies of the total conductivity in air exhibit a complex behavior associated with changing the dominant defect-chemistry mechanism from prevailing formation of the interstitial cations above 1370-1470 K to the generation of cation vacancies at lower temperatures, and with kinetically frozen cation redistribution in spinel lattice below 700-800 K. The average thermal expansion coefficients of the spinel ceramics calculated from dilatometric data in air vary in the range (9.6-10.0) × 10^− 6 K^− 1 at 300-500 K and (13.2-16.1) × 10^− 6 K^− 1 at 1050-1370 K. Mg_1 − xFe_xO solid solutions undergo partial decomposition on heating under oxidizing and mildly reducing conditions, resulting in the segregation of spinel phase and conductivity decrease.     

Obtaining certificates for complete synchronisation of coupled oscillators

In this paper, we provide a novel reformulation of sufficient conditions that guarantee global complete synchronisation of coupled identical oscillators to make them computationally implementable. To this end, we use semidefinite programming techniques. For the first time, we can efficiently search for and obtain certificates for synchronisability and, additionally, also optimise associated cost functions. In this paper, a Lyapunov-like function (certificate) is used to certify that all trajectories of a networked system consisting of coupled dynamical systems will eventually converge towards a common one, which implies synchronisation. Moreover, we establish new conditions for complete synchronisation, which are based on the so called Bendixson’s Criterion for higher dimensional systems. This leads to major improvements on the lower bound of the coupling constant that guarantees global complete synchronisation. Importantly, the certificates are obtained by analysing the connection network and the model representing an individual system only. In order to illustrate the strength of our method we apply it to a system of coupled identical Lorenz oscillators and to coupled van der Pol oscillators.     

随机对流扩散方程的数值仿真

本文针对对流一扩散随机过程在随机输入（即随机输运和源项）,作用下进行数值仿真。我们先将对流扩散随机微分方程中的随机函数采用有限项截断的多项式浑沌展开（Polynomial Chaos Expansion）展开,再由Galerkin映射法得到求解浑沌展开系数的确定性方程组。这是一个在物理空间包含多尺度解的大方程组。为此我...     

The nucleon wave function at the origin

We calculate the next-to-leading order perturbative corrections to the SVZ sum rules for the coupling fN$f_N$, the nucleon leading twist wave function at the origin. The results are compared to the established Ioffe sum rules and also to lattice QCD simulations.     

Evidence for shape coexistence at medium spin in Rb

Four previously known rotational bands in ⁷⁶Rb have been extended to moderate spins using the Gammasphere and Microball γ ray and charged particle detector arrays and the ⁴⁰Ca(⁴⁰Ca, 3pn) reaction at a beam energy of 165 MeV. The properties of two of the negative-parity bands can only readily be interpreted in terms of the highly successful Cranked Nilsson-Strutinsky model calculations if they have the same configuration in terms of the number of g9/2 particles, but they result from different nuclear shapes (one near-oblate and the other near-prolate). These data appear to constitute a unique example of shape coexisting structures at medium spins.     

The Pietra term structures of financial assets

This paper explores an elemental connection between call options-the most commonly tradable financial derivatives, implied volatility term structures-critical “market information” emanating from call-option prices, and the Pietra index-a quantitative economic measure of societal egalitarianism. Our study: (i) unveils an intrinsic “Pietra structure” of call-option prices; (ii) introduces the notion of the “Pietra term structures” of financial assets; (iii) describes the probabilistic meaning of the Pietra term structures; (iv) establishes an explicit nonlinear one-to-one mapping between the Pietra term structures and the implied volatility term structures of financial assets. The results presented in this paper provide a deep insight into the econophysics of call options and implied volatility term structures.     

A holomorphic and background independent partition function for matrix models and topological strings

We study various properties of a nonperturbative partition function which can be associated with any spectral curve. When the spectral curve arises from a matrix model, this nonperturbative partition function is given by a sum of matrix integrals over all possible filling fractions, and includes all the multi-instanton corrections to the perturbative 1/N$1/N$ expansion. We show that the nonperturbative partition function, which is manifestly holomorphic, is also modular and background independent: it transforms as the partition function of a twisted fermion on the spectral curve. Therefore, modularity is restored by nonperturbative corrections. We also show that this nonperturbative partition function obeys the Hirota equation and provides a natural nonperturbative completion for topological string theory on local Calabi–Yau 3-folds.