Variable-step variable-order 3-stage Hermite-Birkhoff-Obrechkoff DDE solver of order 4 to 14

This article presents a solver for delay differential equations (DDEs) called HBO414DDE based on a hybrid variable-step variable-order 3-stage Hermite-Birkhoff-Obrechkoff ODE solver of order 4 to 14. The current version of our method solves DDEs with state dependent, non-vanishing, small, vanishing and asymptotically vanishing delays, except neutral type and initial value DDEs. Delayed values are computed using Hermite interpolation, small delays are dealt with by extrapolation, and discontinuities are located by a bisection method. HBO414DDE was tested on several problems and results were compared with those of known solvers like SYSDEL and the recent Matlab DDE solver ddesd and statistics show that it gives, most of the time, a smaller relative error than the other solvers for the same number of function evaluations.     

A system-theoretic model for cooperation, interaction and allocation

A system-theoretic approach to cooperation, interaction and allocation is presented that simplifies, unifies and extends the results on classical cooperative games and their generalizations. In particular, a general Weber theory of linear values is obtained and a new theory for local cooperation and general interaction indices is established. The model is dynamic and based on the notion of states of cooperation that change under actions of agents. Careful distinction between “local” states of cooperation and general “system” states leads to a notion of entropy for arbitrary non-negative and efficient allocations and thus to a new information-theoretic criterion for fairness of allocation mechanisms. Shapley allocations, for instance, are exhibited as arising from random walks with maximal entropy. For a large class of cooperation systems, a characterization of game symmetries in terms of λ-values is given. A concept for cores and Weber sets is proposed and it is shown that a Weber set of a game with selection structure always contains the core.     

Theory of fractional order in generalized thermoelectric MHD

A new mathematical model of thermoelectric MHD theory has been constructed in the context of a new consideration of heat conduction with fractional orders. This model is applied to Stokes’ first problem for a conducting fluid with heat sources. Laplace transforms and state-space techniques [1] will be used to obtain the general solution for any set of boundary conditions. According to the numerical results and its graphs, conclusion about the new theory has been constructed. Some comparisons have been shown in figures to estimate the effects of the fractional order parameters on all the studied fields.     

Transport Properties and Phase Behaviour in Binary and Ternary Ionic Liquid Electrolyte Systems of Interest in Lithium Batteries

A binary ionic liquid (IL) system based on a common cation, N‐methyl‐N‐propylpyrrolidinium (C₃mpyr⁺), and either bis(trifluoromethanesulfonyl)imide (NTf₂^?) or bis(fluorosulfonyl) imide (FSI^?) as the anion is explored over its entire composition range. Phase behavior, determined by DSC, shows the presence of a eutectic temperature at 247 K and composition around an anion ratio of 2:1 (FSI^?:NTf₂^?) with the phase diagram for this system proposed (under the thermal conditions used). Importantly for electrochemical devices, the single phase melting transition at the eutectic is well below ambient temperatures (247 K). To investigate the effect of such anion mixing on the lithium ion speciation, conductivity and PFG–NMR diffusion measurements were performed in both the binary IL system as well as the Li‐NTf₂‐containing ternary system. The addition of the lithium salt to the mixed IL system resulted in a decrease in conductivity, as is commonly observed in the single‐component IL systems. For a fixed lithium salt composition, both conductivity and ion diffusion have linear behaviour as a function of the anion ratio, however, the rate of change of the diffusion coefficient seems greater in the presence of lithium. From the application point of view, the addition of the FSI^? to the NTf₂^? IL results in a considerable increase in lithium ion diffusivity at room temperature and no evidence of additional complex ion behaviour.     

Analysis of strong and strong periodic detectability of bounded labeled Petri nets

Detectability describes the property of a system to uniquely determine, after a finite number of observations, the current and the subsequent states. Different notions of detectability have been proposed in the literature. In this paper, we formalize and analyze strong detectability and strong periodic detectability for systems that are modeled as labeled Petri nets with partial observation on their transitions. We provide three new approaches for the verification of such detectability properties using three different structures. The computational complexity of the proposed approaches is analyzed and the three methods are compared. The main feature of all the three approaches is that they do not require the calculation of the entire reachability space or the construction of an observer. As a result, they have lower computational complexity than other methods in the literature.     

Stability of MgAl 2 O 4 Under High-Pressure Conditions

A theoretical investigation of the MgAl 2 O 4 crystal response to high-pressure conditions has been carried out to determine its stability against decomposition towards MgO and f -Al 2 O 3 , and towards recently observed orthorhombic phases. We have evaluated total energy versus volume curves using the density functional formalism under the non-local B3LYP approximation, as implemented in the CRYSTAL package. Numerical and analytical fittings have been carried out to determine the equilibrium unit cell geometry and equation of state parameters for all the structures and compounds involved in the phase diagram. The macroscopic compressibility of the spinel phase is interpreted considering the compressibility of its elementary MgO 4 and AlO 6 coordination polyhedra, and implications to understand the phase stability are suggested.     

Phase transitions and equations of state at multimegabar pressures

Abstract

Review of phase transitions and equations of state at multimegabar pressures (100–300 GPa) is presented. Energy dispersive x-ray diffraction techniques in conjunction with synchrotron radiation sources are used. Besides several transition metals, Pt to 282 GPa, Re to 251 GPa, W to 209 GPa, and Fe to 255 GPa, the special focus is on Group IVA elements and isoelectronic III-V compounds. At high pressure, the isoelectronic materials are isostructural and exhibit similar equation of state.     

恒虚警率采样粒子滤波技术及其应用研究

粒子滤波是一种基于蒙特卡洛思想的非线性、非高斯滤波器,其一般采用重要性采样进行粒子采样。但重要性采样容易出现粒子退化现象。解决粒子样本退化问题一般采用重采样。重采样虽然解决了样本的退化问题,同时又引入了采样贫瘠问题。本文根据海洋混响的统计特性和混响中目标的恒虚警率检测原理,提出了恒虚警率采样粒子滤波技术,恒虚警率采样粒子滤波技术使采样粒子尽可能集中在目标附近,有效地描述目标后验概率,降低了粒子数,减小了计算量。本文将此技术应用到海洋混响中的声纳目标跟踪中,既解决了传统卡尔曼滤波在声纳目标跟踪中的非线性、非高斯问题,又解决了粒子滤波的粒子退化及采样贫瘠问题。文中对高分辨率声纳目标数据进行了滤波跟踪,结果验证了本文方法的有效性。     

d = 3 anisotropic and d = 2 tJ models: phase diagrams, thermodynamic properties, and chemical potential shift

The anisotropic d=3 tJ model is studied by renormalization-group theory, yielding the evolution of the system as interplane coupling is varied from the isotropic three-dimensional to quasi-two-dimensional regimes. Finite-temperature phase diagrams, chemical potential shifts, and in-plane and interplane kinetic energies and antiferromagnetic correlations are calculated for the entire range of electron densities. We find that the novel τ phase, seen in earlier studies of the isotropic d=3 tJ model, persists even for strong anisotropy. While the τ phase appears at low temperatures at 30–35% hole doping away from 〈 n_i〉=1, at smaller hole dopings we see a complex lamellar structure of antiferromagnetic and disordered regions, with a suppressed chemical potential shift, a possible marker of incommensurate ordering in the form of microscopic stripes. An investigation of the renormalization-group flows for the isotropic two-dimensional tJ model also shows a clear pre-signature of the τ phase, which in fact appears with finite transition temperatures upon addition of the smallest interplane coupling.