Hetero-phase fluctuations in the pre-melting region in ionic crystals

The theory of the pre-melting phenomena in ionic crystals on the basis of the concept of the hetero phase fluctuation has been applied to KCl and AgCl crystal. The large scale molecular dynamics simulations (MD) in KCl and AgCl crystals are also performed to examine the ionic configuration in premelting region in the vicinity of their melting points. The size of the liquid like clusters are estimated by the theory and MD. The structural features of liquid like clusters are discussed by MD results using the Lindemann instability condition. The ionic conductivities in the pre-melting region are also discussed on the same theoretical basis.     

Extended Hubbard model with renormalized Wannier wave functions in the correlated state: beyond the parametrized models

The method used earlier for analysis of correlated nanoscopic systems is extended to infinite (periodic) s-band-like systems described by the Hubbard model. The optimized single-particle Wannier wave functions contained in the parameters of the extended Hubbard model (in the nearest-neghbor hopping (-t), in the magnitude of the intraatomic interaction U, and in other parameters) are determined explicitly in the correlated state for the electronic systems of various symmetries and dimensions: Hubbard chain, square and triangular planar lattices, and the three cubic lattices (SC, BCC, FCC). In effect, the evolution of the electronic properties as a function of interatomic distance R is obtained. The model parameters in most cases do not scale linearly with the lattice spacing and hence, their solution as a function of microscopic parameters reflects only qualitatively the system evolution. Also, the atomic energy changes with R and therefore should be included in the model analysis. The solutions in one dimension (D = 1) can be analyzed both rigorously (by making use of the Lieb–Wu solution) and compared with the approximate Gutzwiller treatments. In higher dimensions (D = 2 and 3) only the latter approach is possible to implement within the scheme. The renormalized single particle wave functions are almost independent of the choice of the scheme selected to diagonalize the Hamiltonian in the Fock space in D = 1 case. For dimensions D > 1 the qualitative behavior is independent of the structure considered. The wave-function size increases above the Mott-Hubbard localization threshold and gradually reaches the atomic limit value. The method can be extended to other approximation schemes, as stressed at the end.     

On the molecular origin of the sensitivity to impact of cyclic nitramines

Nitramine explosives can combine relative insensitivity to initiation and great energy content. In this work, based on a previous approach developed for nitroaromatic explosives, we propose four mathematical models to correlate impact sensitivity, given by the h₅₀ value, to molecular charge properties. Fourteen cyclic nitramines were studied using Density Functional Theory (DFT). Six molecules of the set have measured h₅₀ values, which were used to evaluate the sensitivity models. Converged DFT charge densities of the molecules were partitioned and analyzed according to the distributed multipole analysis (DMA) atom-centered method. The sensitivity models were based on the DMA electric multipole values. The electron withdrawing role of the nitro group and the strong polarization of the charges of the nitrogen atom in the amine group were clearly identified. The influence of the electronic properties on the sensitivity of the explosives was characterized by including in the sensitivity models the charge values of the nitro or the nitramine groups and electron delocalization, the latter quantified by the DMA quadrupole values of the ring atoms. Inclusion of electron delocalization effects can improve the prediction of h₅₀ values for two out of the five strained-ring nitramines in the set. The charge values of the nitramine groups are the most important molecular property affecting the impact sensitivity. The h₅₀ values of eight nitramine explosives of the set not available experimentally were computed.     

Relations between kinetic parameters of different column models for liquid chromatography applying core-shell particles

This article presents analytical solutions of the general rate model (GRM), the lumped kinetic model (LKM), and the simpler equilibrium dispersive model (EDM) for core-shell particles and linear adsorption isotherms. The solutions in the Laplace domain are applied to derive analytical expressions for the temporal moments of these models. The results provide relations between the model specific kinetic parameters by matching one or more of the temporal moments. Several case studies are considered for illustration. The results show that simpler models are in many cases as good as the most detailed GRM if their kinetic parameters fulfill the matching relations. Thus, it is possible to reliably predict elution profiles using the simpler models. The derived analytical expressions can also be utilized to efficiently estimate model parameters from experimentally observed elution profiles to further optimize core-shell particles and to identify suitable column sizes and operating conditions.     

Early Universe in Scalar-Tensor Theory

We consider the flat Robertson–Walker model in scalar-tensor theory proposed by Lau and Prokhovnik. In this model, the field equations are solved by using “gamma-law” form of equation of state p=(γ−1)ρ, where the adiabatic parameter ‘gamma’ (γ) varies continuously as the universe expands. Our aim is to study how the adiabatic parameter γ should vary so that in the course of its evolution the universe goes through a transition from an inflationary to a radiation-dominated phase. A unified one parameter function of γ has been considered to describe the two early phases of evolution of universe. The solutions show the power-law expansion and cosmological constant is found to be positive and decreasing function of cosmic time. The solutions are compatible with the Dirac’s large number hypothesis. The deceleration parameter has been presented in a unified manner in terms of scale factor, which describes the inflation of the model. The nature of singularity and the physical properties have been discussed in details.     

Bianchi Type <Emphasis Type="Italic">VI</Emphasis><Subscript>0</Subscript> Magnetized Barotropic Bulk Viscous Fluid Massive String Universe in General Relativity

A model of a cloud formed by massive strings is studied in the context of the usual general relativity. This model is used as a source of Bianchi type VI ₀ massive with magnetic field and bulk viscosity. To get a determinate model, we assume that the expansion (θ) in the model is proportional to the shear (σ) and also the fluid obeys the barotropic equation of state. The behaviour of the models from physical and geometrical aspects in presence and absence of magnetic field and bulk viscosity is discussed.     

Speeds of sound and isothermal compressibility of ternary liquid systems: Application of Flory’s statistical theory and hard sphere models

Speeds of sound and densities of three ternary liquid systems namely, toluene + n-heptane + n-hexane (I), cyclohexane + n-heptane + n-hexane (II) and n-hexane + n-heptane + n-decane (III) have been measured as a function of the composition at 298.15 K at atmospheric pressure. The experimental isothermal compressibility has been evaluated from measured values of speeds of sound and density. The isothermal compressibility of these mixtures has also been computed theoretically using different models for hard sphere equations of state and Flory’s statistical theory. Computed values of isothermal compressibility have been compared with experimental findings. A satisfactory agreement has been observed. The superiority of Flory’s statistical theory has been established quite reasonably over hard sphere models.      

Reflection positivity and Levin–Wen models

We give a transparent algebraic formulation of our pictorial approach to the reflection positivity (RP), that we introduced in a previous paper. We apply this quantization to the $2+1$ Levin–Wen model to obtain $1+1$ anyonic/quantum spin chain theory on the boundary, possibly entangled in the bulk. The reflection positivity property has played a central role in both mathematics and physics, as well as providing a crucial link between the two subjects. In a previous paper we gave a new geometric approach to understanding reflection positivity in terms of pictures. Here we give a transparent algebraic formulation of our pictorial approach. We use insights from this translation to establish the reflection positivity property for the fashionable Levin–Wen models with respect both to vacuum and to bulk excitations. We believe these methods will be useful for understanding a variety of other problems.     

Dynamic Behaviour in Microcompartments

Compartmentalisation is recognised to be a primary step for the assembly of non-living matter towards the construction of life-like microensembles. To date, a host of hollow microcompartments with various functionalities have been widely developed. Within this respect, given that dynamic behaviour is one of the fundamental features to distinguish living ensembles from those that are non-living, the design and construction of microcompartments with various dynamic behaviours are attracting considerable interest from a wide range of research communities. Significantly, the created dynamic microcompartments could also be widely used as chassis for further bottom-up design towards building protocell models by integrating and booting up necessary biological information. Herein, strategies to install the various motility behaviours into microcompartments, including haptotaxis, chemotaxis and gravitaxis, are summarized in the anticipation of inspiring more designs towards creating various advanced active microcompartments, and contributing new techniques to the ultimate goal of constructing a basic living unit entirely from non-living components.