Equilibrium properties of a multi-component ionic mixture: I. Sum rules for correlation functions

Equilibrium statistical methods are used to derive sum rules for two- and three-particle correlation functions of a multi-component ionic mixture. Some of these rules are general consequences of the electrostatic character of the interaction, whereas others depend on specific thermodynamic properties of the system. The first group of rules follows from the BBGKY hierarchy and a clustering hypothesis for Ursell functions. The sum rules of the second group are obtained by describing the system with the help of a restricted grand-canonical ensemble in which the particle numbers of the various components in the mixture fluctuate under the condition that the total charge in the system remains constant.     

Fluctuation problem in electromagnetic cascades. II

The fluctuation problem in electromagnetic cascades is examined in the light of the new approach to Cascade Theory. The moments of the number distribution of electrons produced in the entire shower (corresponding to infinite thickness) are obtained explicitly by a direct evaluation of inversion integrals. In particular, it is shown that the mean number of electrons that are produced in the shower for an energy greater thanE is found to be proportional toE ₀/E, whileE ₀ is the energy of the primary electron. In view of this result, it has been found possible to evaluate the higher moments of the number distribution explicitly.     

多元混合气体中非线性声衰减的数值模拟

采用直接模拟蒙特卡罗方法(DSMC)对多元混合气体中的非线性声衰减进行数值模拟,提出了一种不依赖于经验参数的声衰减的理论预测模型。通过DSMC数值模拟方法获得了包括氮气、氧气、二氧化碳、甲烷和水蒸气在内的多种多元混合气体的声衰减谱,研究的声波频率范围从8MHz到232MHz。与弛豫衰减的DL模型和经典衰减的Stokes-Kirchhoff公式的结果比较表明,该模型的声衰减预测结果与之相符,其预测精度取决于对产生声衰减的分子碰撞过程的正确认识。另外数值模拟结果还表明,不同频率声波的声衰减对包含不同气体成分的混合气体特征不同,这将使得开发能够定量的检测不同环境和过程中的气体成分的智能声气体传感器成为可能。     

Numerical simulation of nonlinear acoustic attenuation of multi-component gas mixture

The direct simulation Monte Carlo （DSMC） method was introduced to model the acoustic propagation in multi-component gas mixtures. And a theoretical predictive model of acoustic attenuation was proposed, which does not rely on experiential parameters. The acoustic attenuation spectra of various multi-component gas mixtures, consisting of nitrogen, oxygen, carbon dioxide, methane and water, were estimated by the DSMC method. The sound frequency range of interest is from 8 MHz to 232 MHz. Compared with the result of the relaxation attenuation based on the DL model plus that of the classical attenuation calculated by the Stokes-Kirchhoff formula, the estimations of acoustic attenuation of our model agreed with them. The precision of the model depends upon the understanding of the physical mechanism of molecule collision from which the attenuation arises. In addition, the result of our model shows that the characters of the frequency-dependent acoustic attenuation rely on the composition of the gas mixtures. And this could lead to the development of smart acoustic gas sensors capable of quantitatively determining gas composition in various environments and processes.     

Investigating magnetorheological properties of a mixture of two types of carbonyl iron powders suspended in an ionic liquid

In this work, properties of a magnetorheological (MR) fluid, prepared by dispersing a mixture of two types of carbonyl iron powders (CIPs) of different sizes, in an ionic liquid (N,N-diethyl-N-methyl-N-(2-methoxyethyl) ammonium tetrafluoroborate) that is stable from 9 °C to ca. 300 °C, have been investigated. At first, the random packing density of the mixture was computed as function of mixing ratio of CIP, in order to find out the tendency of the variation. Next, several mixtures, all having the same weight, were prepared at various mixing ratios and dispersed in the ionic liquid, in order to experimentally find the most suitable mixing ratio of CIP. Then, the magnetic clusters of the synthesized MR fluids were observed by using a digital microscope equipped with two permanent magnets, whereas the MR properties were investigated by using a rotation viscometer equipped with a solenoid coil. The experimental results pointed out that the MR fluid with 60 wt% fraction of large particles exhibited the highest MR response.     

Theoretical investigation of imidazolium based ionic liquid/alcohol mixture: a molecular dynamic simulation

In this work, molecular dynamic simulation of the mixture of imidazolium based ionic liquids with alcohols is implemented in order to investigate mixing excess properties and some structural and physical properties of the mixture. Excess volumes and enthalpies are evaluated for 11 different mole fractions of ionic liquids at each 0.1, in the range of 0 to 1. Radial distribution function, cohesive energy density, potential of mean force, solvation energy, and diffusion coefficient are reported and analysed. The effects of the cationic alkyl chain length, in comparison with changes of the anions, on these properties are reported. Results reveal that the methanol molecule participates with its hydrophilic characteristics in the mixing process and tends to aggregate around anion part of the ionic liquids, especially in the case of Cl.     

Equilibrium properties of ferrocolloids

We consider a thermodynamic model of a stable macroscopically homogeneous ferrocolloid containing identical spherical particles with permanent moments suspended in a non-dissociated liquid on the basis of the hard sphere perturbation theory. Magnetostatic properties and the phase diagram of the ferrocolloid are shown to agree very well with experimental evidence. Dipole interparticle interactions result in an effective attraction between the particles which increase, as the strength of an externally applied magnetic field grows, favours the phase separation and cause a reduction in the coefficient of mutual Brownian diffusion of the particles.     

Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles

We apply Lieb–Robinson bounds for multi-commutators we recently derived (Bru and de Siqueira Pedra, Lieb–Robinson bounds for multi-commutators and applications to response theory, 2015) to study the (possibly non-linear) response of interacting fermions at thermal equilibrium to perturbations of the external electromagnetic field. This analysis leads to an extension of the results for quasi-free fermions of (Bru et al. Commun Pure Appl Math 68(6):964–1013, 2015; Bru et al. J Math Phys 56:051901-1–051901-51, 2015) to fermion systems on the lattice with short-range interactions. More precisely, we investigate entropy production and charge transport properties of non-autonomous C*-dynamical systems associated with interacting lattice fermions within bounded static potentials and in presence of an electric field that is time and space dependent. We verify the 1st law of thermodynamics for the heat production of the system under consideration. In linear response theory, the latter is related with Ohm and Joule’s laws. These laws are proven here to hold at the microscopic scale, uniformly with respect to the size of the (microscopic) region where the electric field is applied. An important outcome is the extension of the notion of conductivity measures to interacting fermions.     

Ronchi test formulae : 1. Theory

The Ronchi test of the quality of optical systems and components is very widely used but is usually regarded as a qualitative test. In an attempt to make this very simple technique at least semi-quantitative, we have derived easy to use analytical formulae for some basic but important types of aberration. A companion paper will describe their implementation and their experimental verification.     

On the nonequilibrium statistical mechanics of a binary mixture. II. The transport coefficients

This paper is devoted to the study of the hydrodynamic stage of a two-component dense fluid. Starting from the BBGKY hierarchy obtained earlier, we first derive the expressions for the generalized fluxes. We proceed to set up the generalized kinetic equations, using Bogoliubov's functional assumption. Then we solve these equations by means of a Chapman-Enskog method. The generalized expressions for the transport coefficients are thus obtained. All our results are independent of the existence of density expansions of the relevant quantities.     

Exothermic effects during sintering of a mixture of nickel and aluminum powders. II

When a mixture of nickel and aluminum powders is sintered there is an exothermic effect which involves a rise of several hundred degrees in the temperature of the compact in a few seconds. The magnitude and nature of the exothermic effect depend on the aluminum content of the mixture, the degree of dispersion of the powders, and the initial porosity of the specimens. The temperature at which the exothermic effect begins moves towards lower temperatures with increase in the degree of dispersion, with increase in the concentration of aluminum in the mixture, and with decrease in the porosity. The magnitude of the heat effect increases with increase in the aluminum content.It is shown that the exothermic effect in the sintering process arises mainly from decomposition of the liquid phase and crystallization of chemical compounds with large heats of formation. A definite role is played by the metallothermic reduction of nickel oxide by aluminum present in the liquid phase and by the formation of intermetallic compounds at the boundaries of dissimilar particles of powder during sintering in the solid phase.     

Thermal stability of microstructures and mechanical properties in a Fe-based Fe-Cr-Mn-Cu-Mo multi-component alloy

A Fe-based multi-component alloy, 60Fe-12Cr-10Mn-15Cu-3Mo, was designed and fabricated for nuclear applications in the present study. The crystal structure of the alloy is a ～85% body – and 15% face–centered cubic. A detailed microstructure analysis indicated that Cu segregated in the alloy to form Cu-rich precipitates, and the Cu precipitates grew during high temperature annealing at up to 773?K. The high temperature tensile test of the alloys showed that both the yield stress and tensile strength of the 60Fe-12Cr-10Mn-15Cu-3Mo were greater than those of typical austenitic and ferritic stainless steels at 773?K. The Vickers microhardness of the designed alloy did not change after high temperature annealing for 1?h at up to 1073?K. The results indicated that the designed alloy has the potential to be used for high temperature applications.     

Dielectric properties of a mixture of dipolar hard spheres

A theory for the dielectric constant, ε, of a fluid mixture of dipolar hard spheres is formulated by generalizing the methods developed by Ramshaw and Wertheim for the pure fluid case. The resulting expression for ε depends on the pair distribution functions, g _αβ(r ₁, θ₁, r ₂, θ₂) for a dipolar mixture. Due to the unavailability of exact representations for these dipolar pair distribution functions, the results of the mean spherical approximation are employed in the formalism developed. Numerical results are given for ε as calculated from the pair distribution functions for a spherical volume of macroscopic dimensions. The compositional dependence of the ε obtained in this way for a specific mixture is compared with the corresponding properties of the well established theories of Clausius-Mossotti-Debye and Onsager. In addition, the relative importance of the dipole moment and size of the hard sphere parameters in determining ε for a dipolar mixture (the correlative behaviour of which is described by the mean spherical approximation) is evaluated. It is found that the differences in hard core diameters can be largely ignored, in that ε for an ‘effective’ single component fluid can be given to within 2–5 per cent relative error (at worst) of the mean spherical approximation's result. Such an ‘effective pure fluid’ is described as having the same polarization content as the actual mixture being considered. Thereby, the properties of the effective fluid are determined by the quantity y = 4πβ(m ₁ ² ρ₁ + m ₂ ² ρ₂)/9 where m_i and ρ _i are the dipole moment and number density of component i in the binary mixture, with β = (kT)^-1.     

Fluctuation properties of states in26Al

The fluctuation properties of the energy levels of²⁶Al from the ground state to excitation energies of about 8 MeV have been examined. Several statistics have been employed, and particular attention has been given to the suitability of these statistics for small sample sizes. The results show, for a variety of states, behavior intermediate between GOE and Poisson but apparently favoring GOE. The results are consistent with the fluctuations' being independent of isospin.     

Development of a perturbed hard-sphere equation of state for pure and mixture of ionic liquids

A perturbed hard-sphere equation of state (PHS EOS) was previously proposed to present the volumetric properties of ionic liquids by employing a variable parameter β being a function of acentric factor to justify the range of vdW dispersion forces (M. M. Papari, J. Moghadasi, S. M. Hosseini, F. Akbari, J. Mol. Liq. 158 (2011) 57–60). The main aim of the present study is to revise an attractive part of the preceding EOS by re-evaluating the above-mentioned variable parameter as well as the repulsive term. Two temperature-dependent parameters appearing in the revisited EOS have been determined from the corresponding states correlations using the interfacial properties of ILs, i.e., surface tension and liquid density, both at room temperature. The revisited EOS has been employed to model the volumetric properties of ionic liquids (ILs). The predictive power of the proposed model has been assessed by comparing the results obtained with 2189 experimental data points related to 24 ILs over a broad range of pressures and temperatures. The overall average absolute deviation (AAD) of the calculated densities from literature data was found to be 0.62 %. Furthermore, the revisited PHS EOS has been employed to model the volumetric properties of 23 mixtures including IL + IL and IL+ solvent over the vast range of temperatures. From 1580 data points of the binary mixtures of interest, the AAD of the correlated densities from the measurements was found to be 0.47 %.     

Structural properties of ionic liquids

Two types of ionic liquids are considered: molten salts and aqueous solutions of strong electrolytes. It is shown that in both cases, modern theoretical methods are capable of making definite predictions about the spatial correlations between the ions themselves and between the ions and water molecules. It is further shown that the technique of neutron diffraction as applied to isotopically enriched samples allows, for the first time, detailed comparisons to be made between theory and experiment. The results of these comparisons are discussed and areas in which the theory is in urgent need of revision are identified.     

Repeller structure in a hierarchical model. II. Metric properties

We study the renormalization dynamics deriving from a hierarchical tight-binding Schrödinger equation. In the Part I of this work we analyzed the topological structure of the recurrent set-a chaotic repeller- and its relation with the spectral problem. In this part we turn our attention to the metric properties of the repeller. We first study periodic orbits and their bifurcation unfolding, and we organize them on a binary tree. We then apply a thermodynamic formalism which provides a complete characterization of the scaling properties of the energy spectrum. The distributionf() of local dimensions is determined by computing both a generalized -function through the periodic orbits and the bandwidths of periodic approximants of the Schrödinger operator. When the growth rateR of the potential is smaller than 1, we find evidence of a phase transition, implying that two different classes of states coexist in the spectrum. The asymptotic behavior of the Lebesgue measure of the spectrum is also studied. A linear scaling of to 0 is observed forR 1_–, while forR > 1, the measure of the periodic approximants goes to 0 as R^–h with the hierarchical orderh. Finally, we show that the localized state, present for R<1, is characterized by a superexponential scaling of the bandwidth.     

Equilibrium properties of fast-rotating headed nuclei

We report on calculations of the equilibrium deformation in excited heated rotating nuclei. At A ～ 150–200 and temperature t > t_c ≈ 1.2 MeV the shell effects turn out to be small to compete with the variations of the liquid drop component of the energy. The transition from the shape of a “cool” nucleus to that of a “hot” nucleus takes place at t_c and in deformed nuclei resembles a phase transition. The stiffness parameter with respect to shape variations at t_c is anomalously low.     

Correlation effects in tracer diffusion and ionic conductivity. II

In this paper it is shown that the physical or conductivity correlation factor can be simply and directly expressed in terms of the well-known tracer correlation factor and a new two particle correlation factor. A Monte Carlo calculation of these correlation factors was performed to illustrate the use of the expression. The physics of the two-particle correlation factor are discussed.