Mutual diffusion in dense supercritical fluids

An expression for the mutual diffusion coefficient of a dense binary system of hard spheres, derived by using the Percus-Yevick approximation for the contact radial distribution function, together with Thorne's extension of the Enskog theory, is used to study the variation of the mutual diffusion coefficient with pressure, composition and ratio of the molecular diameters. Applications are made to real systems.     

Opinion dynamics in networks with heterogeneous confidence and influence

We propose a discrete-time model of opinion dynamics. The neighborhood relationship is decided by confidence radius and influence radius of each agent. We investigate the influence of heterogeneity in confidence/influence distribution on the behavior of the network. The simulations suggest that the heterogeneity of single confidence or influence networks can promote the opinions to achieve consensus. It is shown that the heterogeneous influence radius systems converge in fewer time steps and more often in finite time than the heterogeneous confidence radius systems. We find that heterogeneity does not always promote consensus, and there is an optimal heterogeneity so that the relative size of the largest consensus cluster reaches maximum in heterogeneous confidence and influence networks.     

A mesoscopic thermomechanically coupled model for thin-film shape-memory alloys by dimension reduction and scale transition

We design a new mesoscopic thin-film model for shape-memory materials which takes into account thermomechanical effects. Starting from a microscopic thermodynamical bulk model, we guide the reader through a suitable dimension reduction procedure followed by a scale transition valid for specimen large in area up to a limiting model which describes microstructure by means of parametrized measures. All our models obey the second law of thermodynamics and possess suitable weak solutions. This is shown for the resulting thin-film models by making the procedure described above mathematically rigorous. The main emphasis is, thus, put on modeling and mathematical treatment of joint interactions of mechanical and thermal effects accompanying phase transitions and on reduction in specimen dimensions and transition of material scales.     

Some combinatorial aspects of discrete non-linear population dynamics

Motivated by issues arising in population dynamics, we consider the problem of iterating a given analytic function a number of times. We use the celebrated technique known as Carleman linearization that turns (for a certain class of functions) this problem into simply taking the power of a real number. We expand this method, showing in particular that it can be used for population models with immigration, and we also apply it to the famous logistic map. We also are able to give a number of results for the invariant density of this map, some being related to the Carleman linearization.     

Dynamical instability of laminated plates with external cutout

A method to study dynamical instability and non-linear parametric vibrations of symmetrically laminated plates of complex shapes and having different cutouts is proposed. The first-order shear deformation theory (FSDT) and the classical plate theory (CPT) are used to formulate a mathematical statement of the given problem. The presence of cutouts essentially complicates the solution of buckling problem, since the stress field is non-uniform. At first, a plane stress analysis is carried out using the variational Ritz method and the R-functions theory. The obtained results are applied to investigate buckling and parametric vibrations of laminated plates. The developed method uses the R-functions theory, and it may be directly employed to study laminated plates of arbitrary forms and different boundary conditions. Besides, the proposed method is numerical-analytical, what greatly facilitates a solution of similar-like non-linear problems. In order to show the advantage of the developed approach, instability zones and response curves for the layered cross- and angle-ply plates with external cutouts are constructed and discussed.     

Spin and orbital angular momenta defined for electromagnetic fields in planar anisotropic media

The spin and orbital angular momenta (S and L) of the radiation fields were defined newly to satisfy the duality transformation and to hold for planar anisotropic media, by introducing an entirely new vector potential. Some features of them are discussed in connection with the anisotropy in the permittivity and permeability of a medium.     

Dual-fibre stretcher and coma as tools for independent 2nd and 3rd order tunable dispersion compensation in a fibre-based ‘scan-free’ time domain optical coherence tomography system

Dispersion compensation up to the third order is experimentally demonstrated by using a dual-fibre stretcher combined with the coma of an imaging lens, in a fibre-based scan-free time domain optical coherence tomography system, leading to an axial resolution of less than 3 μm.     

Stability and bifurcation analysis in the delay-coupled van der Pol oscillators

In this paper, the dynamics of a system of two van der Pol equations with a finite delay are investigated. We show that there exist the stability switches and a sequence of Hopf bifurcations occur at the zero equilibrium when the delay varies. Using the theory of normal form and the center manifold theorem, the explicit expression for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived.     

Synthesis of cobalt doped silica thin film for low temperature optical gas sensor

A modified sol–gel method was used to prepare cobalt doped silica thin film with a cobalt content of 10, 20 and 30 mol% (10Co, 20Co and 30Co). The prepared films were annealed at different temperatures in the range 400–1,000 °C, and their structural evolution examined. The mixed valence cobalt oxide, Co₃O₄, crystallizes only in the sample with the higher cobalt content, while cobalt silicate is the only crystalline phase detected in the sample 10Co and 20Co. Both the cobalt content and the temperature of heat treatment resulted to affect the nature of cobalt species dispersed in the silica matrix. The 30Co was selected for further investigations by FTIR spectroscopy to follow the structural evolution of 30Co film as function of the temperature and UV–Vis to get information on the cobalt valence state. The optical gas-sensing properties of 30Co films, containing Co₃O₄ as the major cobalt phase, were studied through the measuring of the film transmittance in dry air and in presence of dry air containing variable concentrations of polluting gases, CO and NO₂. The 30Co samples resulted to be highly sensitive to CO at room temperature. An explanation for the CO sensing characteristics, at low temperature, was proposed by referring to the physisorption-related mechanics of CO.