Kinematic theory of diffraction by matter of any kind and the theory of liquids

An expression for the intensity function scattered coherently by an arbitrarily distorted lattice has been derived which degenerates under well-defined conditions to the well-known formulae valid for crystals, liquids and gases or amorphous substances. A new method for the analysis of the radial distribution function (RDF) of simple liquids has been suggested. RDF curves for liquid argon near the triple point have been analysed to obtain the distance statistics of neighbours and their coordination numbers. Using the first-neighbour statistics an expression for the partition function for matter of any kind and, in particular, for simple liquids has been deduced.     

Patterned Silk Film Scaffolds for Aligned Lamellar Bone Tissue Engineering

The alignment and osteogenic differentiation of MSCs on patterned silk films (PF) is investigated as a bottom‐up approach toward engineering bone lamellae. Screening PF with various groove dimensions shows that cell alignment is mediated by both the pattern width and depth. MSCs are differentiated in osteogenic medium for four weeks on flat films and on the PF that produce the best alignment. The PF support osteogenic differentiation while also inducing lamellar alignment of cells and matrix deposition. A secondary alignment effect is noted on the PF where a new layer of aligned cells grows over the first layer, but rotated obliquely to the underlying pattern. This layering and rotation of the MSCs resembles the cellular organization observed in native lamellar bone.

     

Minimal length in quantum mechanics and non-Hermitian Hamiltonian systems

Deformations of the canonical commutation relations lead to non-Hermitian momentum and position operators and therefore almost inevitably to non-Hermitian Hamiltonians. We demonstrate that such type of deformed quantum mechanical systems may be treated in a similar framework as quasi/pseudo and/or -symmetric systems, which have recently attracted much attention. For a newly proposed deformation of exponential type we compute the minimal uncertainty and minimal length, which are essential in almost all approaches to quantum gravity.     

Bound for entropy and viscosity ratio of strange quark matter

High energy density (?) and temperature (T) links general relativity and hydrodynamics leading to a lower bound for the ratio of shear viscosity (η) and entropy density (s  ). We get the interesting result that the bound is saturated in the simple model for quark matter that we use for strange stars at the surface for T∼80 MeV$T\sim 80\text{MeV}$. At this T   we have the possibility of cosmic separation of phases. At the surface of the star where the pressure is zero—the density ? has a fixed value for all stars of various masses with correspondingly varying central energy density ?c${\mathrm{?}}_c$. Inside the star where this density is higher, the ratio of η/s$\eta /s$ is larger and are like the known results found for perturbative QCD. This serves as a check of our calculation. The deconfined quarks at the surface of the strange star at T=80 MeV$T=80\text{MeV}$ seem to constitute the most perfect interacting fluid permitted by nature.     

On a transformation and re-transformation technique for constructing an affine equivariant multivariate median

An affine equivariant version of multivariate median is introduced. The proposed median is easy to compute and has some appealing geometric features that are related to the configuration of a multivariate data cloud. The transformation and re-transformation approach used in the construction of the median has some fundamental connection with the data driven co-ordinate system considered by Chaudhuri and Sengupta (1993, Journal of the American Statistical Association). Large sample statistical properties of the median are discussed and finite sample performance is investigated using Monte Carlo simulations.

     

A new look at the harmonic oscillator problem in a finite-dimensional Hilbert space

In this Letter some basic properties of a truncated oscillator are studied. By using finite-dimensional representation matrices of the truncated oscillator we construct new parasupersymmetric schemes and remark on their relevance to the transition operators of the non-interacting N-level system endowed with bosonic modes.     

Nonet symmetry,anomalous Ward identities and meson-gluonium mixing

TheSU(3) flavour structure of ι(1460) is exploited to seek consistency between vector meson dominance and anomalous Ward identities. Our analysis shows that a minimum of 10 to 20% breaking in nonet symmetry is necessary to get an overall fit with the radiative rates of low-lying η and η′.