In this article a nonnegative blind source separation technique, known as nonnegative matrix factorization, is applied to microdiffraction data in order to extract characteristic patterns and to determine their spatial distribution in tissue typing problems occurring in bone-tissue engineering. In contrast to other blind source separation methods, nonnegative matrix factorization only requires nonnegative constraints on the extracted sources and corresponding weights, which makes it suitable for the analysis of data occurring in a variety of applications. In particular, here nonnegative matrix factorization is hierarchically applied to two-dimensional meshes of X-ray diffraction data measured in bone samples with implanted tissue. Such data are characterized by nonnegative profiles and their analysis provides significant information about the structure of possibly new deposited bone tissue. A simulation and real data studies show that the proposed method is able to retrieve the patterns of interest and to provide a reliable and accurate segmentation of the given X-ray diffraction data.

The non-equilibrium structural and dynamical properties of semiflexible polymers confined to two dimensions are investigated by molecular dynamics simulations. Three different scenarios are considered: the force-extension relation of tethered polymers, the relaxation of an initially stretched semiflexible polymer, and semiflexible polymers under shear flow. We find quantitative agreement with theoretical predictions for the force-extension relation and the time dependence of the entropically contracting polymer. The semiflexible polymers under shear flow exhibit significant conformational changes at large shear rates, where less stiff polymers are extended by the flow, whereas rather stiff polymers are contracted. In addition, the polymers are aligned by the flow, thereby the two-dimensional semiflexible polymers behave similarly to flexible polymers in three dimensions. The tumbling times display a power-law dependence at high shear rate rates with an exponent comparable to the one of flexible polymers in three-dimensional systems.

Phase separation in a complex fluid with lamellar order has been studied in the case of cold thermal fronts propagating diffusively from external walls. The velocity hydrodynamic modes are taken into account by coupling the convection-diffusion equation for the order parameter to a generalized Navier-Stokes equation. The dynamical equations are simulated by implementing a hybrid method based on a lattice Boltzmann algorithm coupled to finite difference schemes. Simulations show that the ordering process occurs with morphologies depending on the speed of the thermal fronts or, equivalently, on the value of the thermal conductivity xi. At large values of xi, as in instantaneous quenching, the system is frozen in entangled configurations at high viscosity while it consists of grains with well-ordered lamellae at low viscosity. By decreasing the value of xi, a regime with very ordered lamellae parallel to the thermal fronts is found. At very low values of xi the preferred orientation is perpendicular to the walls in d = 2, while perpendicular order is lost moving far from the walls in d = 3.

Purpose - The purpose of this paper is to present numerical results about phase separation of binary fluid mixtures quenched by contact with cold walls. Design/methodology/approach - The thermal phase separation is simulated by using a hybrid lattice Boltzmann method that solves the continuity and the Navier-Stokes equations. The equations for energy and concentration are solved by using a finite-difference scheme. This approach provides a complete description of the thermo-hydrodynamic effects in the mixture. Findings - A rich variety of domain patterns are found depending on the viscosity and on the heat conductivity of the mixture. Ordered lamellar structures are observed at high viscosity while domains rounded in shape dominate the phase separation at low viscosity, where two scales characterize the growth of domains. Research limitations/implications - The present approach provides a numerical method that can be extended to other systems such as liquid-vapor or lamellar systems. Moreover, a three-dimensional study can give a complete picture of thermo-hydrodynamic effects. Originality/value - This paper provides a consistent thermodynamic theoretical framework for a binary fluid mixture and a numerically stable method to simulate them.