Synthesis and Crystal Structure of New Indium Iodate (K<Subscript>0.6</Subscript>Na<Subscript>0.4</Subscript>Ba)In[IO<Subscript>3</Subscript>]<Subscript>6</Subscript>

Crystals of new indium iodate (K_0.6Na_0.4Ba)In[IO₃]₆ were prepared by the hydrothermal synthesis. The unit-cell parameters are a = 11.3984(3) Å, с = 11.3817(3) Å, sp. gr. R3?. The chemical formula of the compound was derived from the structure determination and refinement with anisotropic displacement parameters to R = 0.0284. In the structure the InO₆ octahedra share vertices with six umbrella-like [IO₃]–groups typical of iodates and form isolated 3?-symmetric charged \(\rm{In[IO_{3}]_6^{3-}}\) clusters. Large Ba, K, and Na cations occupy a common site on a threefold axis due to the isomorphous substitution and compensate the charge of the clusters. The new structure extends the family of the recently discovered alkali-metal and barium iodates containing Ti and Zr atoms in octahedral sites. The iodate K₂Ge[IO₃]₆ containing Ge atoms in the centers of octahedra is the parent compound of this structural family.     

Σ-Definability in Hereditarily Finite Superstructures and Computable Analysis

We construct a computable real function not Σ-definable in hereditarily finite superstructures over the extensions with decidable theory of the reals.     

Static Charge Susceptibility in the <Emphasis Type="Italic">t-J-V</Emphasis> Model

We describe the static charge susceptibility and correlation function of the charge density in the twodimensional t-J-V model based on the method of equations of motion for the relaxation functions of the Hubbard operators. We obtain the dependence of the susceptibility and correlation function on the hole concentration and temperature. Charge density waves can develop if the intersite Coulomb interaction is sufficiently strong.     

Electroosmosis modulated peristaltic biorheological flow through an asymmetric microchannel: mathematical model

A theoretical study is presented of peristaltic hydrodynamics of an aqueous electrolytic non-Newtonian Jeffrey bio-rheological fluid through an asymmetric microchannel under an applied axial electric field. An analytical approach is adopted to obtain the closed form solution for velocity, volumetric flow, pressure difference and stream function. The analysis is also restricted under the low Reynolds number assumption (Stokes flow) and lubrication theory approximations (large wavelength). Small ionic Peclét number and Debye–Hückel linearization (i.e. wall zeta potential ≤ 25 mV) are also considered to simplify the Nernst–Planck and Poisson–Boltzmann equations. Streamline plots are also presented for the different electro-osmotic parameter, varying magnitudes of the electric field (both aiding and opposing cases) and for different values of the ratio of relaxation to retardation time parameter. Comparisons are also included between the Newtonian and general non-Newtonian Jeffrey fluid cases. The results presented here may be of fundamental interest towards designing lab-on-a-chip devices for flow mixing, cell manipulation, micro-scale pumps etc. Trapping is shown to be more sensitive to an electric field (aiding, opposing and neutral) rather than the electro-osmotic parameter and viscoelastic relaxation to retardation ratio parameter. The results may also help towards the design of organ-on-a-chip like devices for better drug design.     

A Framework for Characterizing Structural Uncertainty in Large-Eddy Simulation Closures

Motivated by the sizable increase of available computing resources, large-eddy simulation of complex turbulent flow is becoming increasingly popular. The underlying filtering operation of this approach enables to represent only large-scale motions. However, the small-scale fluctuations and their effects on the resolved flow field require additional modeling. As a consequence, the assumptions made in the closure formulations become potential sources of incertitude that can impact the quantities of interest. The objective of this work is to introduce a framework for the systematic estimation of structural uncertainty in large-eddy simulation closures. In particular, the methodology proposed is independent of the initial model form, computationally efficient, and suitable to general flow solvers. The approach is based on introducing controlled perturbations to the turbulent stress tensor in terms of magnitude, shape and orientation, such that propagation of their effects can be assessed. The framework is rigorously described, and physically plausible bounds for the perturbations are proposed. As a means to test its performance, a comprehensive set of numerical experiments are reported for which physical interpretation of the deviations in the quantities of interest are discussed.     

Statistical Model of the Explosive Fragmentation of a Ring

A model of the explosive fragmentation of a thin ring is developed which takes into account the statistical dispersion of the relative fracture deformation along the length of the ring. A formula is proposed for calculating the velocity of the boundary of the region near a plastic rupture in which the plastic flow of the ring material ceases. Methods for the numerical and analytical calculation of the average number of fragments of the ring are developed. The calculation results are compared with available experimental data.