Search results for " diffusion"
showing 10 items of 521 documents
Wait-and-switch stochastic model of the non-Debye relaxation. Derivation of the Burr survival probability
2006
Abstract Stochastic mechanism of relaxation, in which a dipole waits until a favourable condition for reorientation exists, is discussed. Assuming that an imposed direction of a dipole moment may be changed when a migrating defect reaches the dipole, we present a mathematically rigorous scheme relating the local random characteristics of a macroscopic system to its effective relaxation behaviour. We derive a relaxation function (the Burr survival probability) that is characterized by the stretched exponential or the power-law behaviour.
Structure and dynamics of yukawa systems
1993
Abstract Results of molecular dynamics simulations modelling two component charge stabilized colloidal particles interacting via a Yukawa potential are presented. After cooling, the systems freeze into either substitutionally disordered imperfect crystals or into glasslike states. This freezing is characterized by the divergence of a suitable correlation time due to loss of ergodicity. Describing the structure by bond correlation functions, local orientational ordering is observed in the glassy states which is not present in the liquid. In the liquid the diffusion constant obeys an Arrhenius law. As can be deduced from the van Hove functions, in the crystal the particles only oscillate arou…
Thermodynamic approach to vortex production and diffusion in inhomogeneous superfluid turbulence
2014
In this paper, we use a non-equilibrium thermodynamic framework to generalize a previous nonlocal model of counterflow superfluid turbulence to incorporate some new coupled terms which may be relevant in the evolution of inhomogeneous vortex tangles. The theory chooses as fundamental fields the energy density, the heat flux, and the averaged vortex line length per unit volume. The constitutive quantities are assumed to depend on the fundamental fields and on their first spatial derivatives, allowing us to describe thermal dissipation, vortex diffusion and a new contribution to vortex formation. The restrictions on the constitutive relations are deduced from the entropy principle, using the …
Escape Times in Fluctuating Metastable Potential and Acceleration of Diffusion in Periodic Fluctuating Potentials
2004
The problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered. For the overdamped Brownian particle moving in a piecewise linear dichotomously fluctuating metastable potential we obtain the mean first-passage time (MFPT) as a function of the potential parameters, the noise intensity and the mean rate of switchings of the dichotomous noise. We find noise enhanced stability (NES) phenomenon in the system investigated and the parameter region of the fluctuating potential where the effect can be observed. For the diffusion of the overdamped Brownian particle in a fast fluctuating symmetric periodic potential w…
Oxygen Consuming Regions in EMT60/Ro Multicellular Tumour Spheroids Determined by Nonlinear Regression Analysis of Experimental PO2 Profiles
1987
Malignant cells can be studied in vitro, in a tumour-like microenvironment, by growing multicellular tumour spheroids in culture (Sutherland, McCredie and Inch, 1971). Franko and Sutherland (1979) utilized diffusion theory to explain the viable rim thicknesses of spheroids measured histologically. Without PO2 profiles, however, an unequivocal interpretation of their results was not possible. Systematic studies of the PO2 profiles in spheroids have since been made with oxygen microelectrodes by several groups (Carlsson et al., 1979; Kaufman et al., 1981; Mueller-Klieser and Sutherland, 1982a,b). Based on these measurements, new analyses utilizing diffusion theory are being developed to chara…
Anomalous diffusion and nonlinear relaxation phenomena in stochastic models of interdisciplinary physics
2020
The study of nonlinear dynamical systems in the presence of both Gaussian and non-Gaussian noise sources is the topic of this research work. In particular, after shortly present new theoretical results for statistical characteristics in the framework of Markovian theory, we analyse four different physical systems in the presence of Levy noise source. (a) The residence time problem of a particle subject to a non-Gaussian noise source in arbitrary potential profile was analyzed and the exact analytical results for the statistical characteristics of the residence time for anomalous diffusion in the form of Levy flights in fully unstable potential profile was obtained. Noise enhanced stability …
Spread of franchising: a multinational comparison based on the notions of innovation diffusion
1998
Investigates the globalization of franchising through a discussion of the literature on innovation diffusion. Proceeds then to evaluate the globalization of format franchising in 31 countries, drawing data from Arthur Andersen’s multi‐national study. Finds that the USA has the greatest number of franchisors and franchisees, Japan seems to have a different franchise structure when compared to the other countries studied, and Israel is a franchising novice. Presents a number of tables, accompanied by notes of caution on analysing the statistics. Mentions briefly some examples of franchises. Refers the findings back to the literature review to assess how well they match the theoretical descrip…
Island Diffusion on Metal fcc (100) Surfaces
1999
We present Monte Carlo simulations for the size and temperature dependence of the diffusion coefficient of adatom islands on the Cu(100) surface. We show that the scaling exponent for the size dependence is not a constant but a decreasing function of the island size and approaches unity for very large islands. This is due to a crossover from periphery dominated mass transport to a regime where vacancies diffuse inside the island. The effective scaling exponents are in good agreement with theory and experiments.
Bridging scales with thermodynamics: from nano to macro
2014
We have recently developed a method to calculate thermodynamic properties of macroscopic systems by extrapolating properties of systems of molecular dimensions. Appropriate scaling laws for small systems were derived using the method for small systems thermodynamics of Hill, considering surface and nook energies in small systems of varying sizes. Given certain conditions, Hill's method provides the same systematic basis for small systems as conventional thermodynamics does for large systems. We show how the method can be used to compute thermodynamic data for the macroscopic limit from knowledge of fluctuations in the small system. The rapid and precise method offers an alternative to curre…
Epitaxial growth of molybdenum on TiO2(110)
2003
Abstract Molybdenum was deposited on blue (i.e. non-stoichiometric) TiO2(1 1 0) surface using a very low deposition rate (less than 0.05 eqML min−1). The resulting deposit was investigated by means of X-ray photoelectron diffraction (XPD), LEED and XPS. Just after deposition, the film is mainly constituted of metallic molybdenum, contains oxygen homogeneously dispersed through the whole deposit and the broad features detected in XPD scans are interpreted as a coarse epitaxy between TiO2(1 1 0) surface and the (0 0 1) face of bcc molybdenum. The orientation relationship is: Mo(1 0 0)[0 0 1]//TiO2(1 1 0)[0 0 1]. After annealing the deposit at 673 K, XPD scans become sharper and epitaxy is ach…