Search results for "equation"
showing 10 items of 4219 documents
Diffusion and Migration
2003
The sections in this article are Introduction Fundamental Concepts Diffusion–migration Flux Equations Poisson Equation and the LEN Assumption Continuity Equation Ohm's Law and Migrational Transport Numbers Diffusion-conduction Flux Equation Diffusion Boundary Layer Faraday's Law and Integral Transport Numbers Nernst Equation and Concentration Overpotential Steady State Current–voltage Curves of Systems with One Active Species Integration of the Transport Equations Solutions of Homovalent Ions, |zi | =z Binary Electrolyte Solutions Ternary Electrolyte Solutions. The Supporting Electrolyte Weak Binary Electrolyte Steady State Current–overpotential Curves in the Presence of Supporting Electrol…
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…
Probabilistic response of linear structures equipped with nonlinear damper devices (PIS method)
2008
Passive control introducing energy absorbing devices into the structure has received considerable attention in recent years. Unfortunately the constitutive law of viscous fluid dampers is highly nonlinear, and even supposing that the structure behaves linearly, the whole system has inherent nonlinear properties. Usually the analysis is performed by a stochastic linearization technique (SLT) determining a linear system equivalent to the nonlinear one, in a statistical sense. In this paper the effect of the non-Gaussianity of the response due to the inherent nonlinearity of the damper device will be studied in detail via the Path Integral Solution (PIS) method. A systematic study is conducted…
On the application of the extended Fujita-Nishioka equation to polysubstitued system. A kinetic study of the rearrangement of several poly-substitued…
2005
Abstract The rearrangement rates of several di-, tri-, tetra- or penta-substituted Z -arylhydrazones of 3-benzoyl-5-phenyl-1,2,4-oxadiazole ( 1a – 18a ) into the relevant 2-aryl-4-benzoylamino-5-phenyl-1,2,3-triazoles ( 1b – 18b ) have been determined in 1:1 (v:v) dioxane/water in a wide range of p S + (3.80–12.50) at different temperatures. The kinetic data obtained have been correlated with those previously collected for the rearrangement of ortho -, meta - and para -substituted Z -arylhydrazones ( 19a – 38a ) by means of an extension of the linear free-energy relationship (LFER) proposed by Fujita and Nishioka, thus considering steric ( E s ) and field ( F o ) proximity effects in additi…
Modelling Bacterial Dynamics in Food Products: Role of Environmental Noise and Interspecific Competition
2013
In this paper we review some results obtained within the context of the predictive microbiology, which is a specific field of the population dynamics. In particular we discuss three models, which exploit tools of statistical mechanics, for bacterial dynamics in food of animal origin. In the first model, the random fluctuating behaviour, experimentally measured, of the temperature is considered. In the second model stochastic differential equations are introduced to take into account the influence of physical and chemical variables, such as temperature, pH and activity water, subject to deterministic and random variations. The third model, which is an extended version of the second one, negl…
A stochastic interspecific competition model to predict the behaviour of Listeria monocytogenes in the fermentation process of a traditional Sicilian…
2008
The present paper discusses the use of modified Lotka-Volterra equations in order to stochastically simulate the behaviour of Listeria monocytogenes and Lactic Acid Bacteria (LAB) during the fermentation period (168 h) of a typical Sicilian salami. For this purpose, the differential equation system is set considering T, pH and aw as stochastic variables. Each of them is governed by dynamics that involve a deterministic linear decrease as a function of the time t and an "additive noise" term which instantaneously mimics the fluctuations of T, pH and aw. The choice of a suitable parameter accounting for the interaction of LAB on L. monocytogenes as well as the introduction of appropriate nois…
Stochastic acceleration in generalized squared Bessel processes
2015
We analyze the time behavior of generalized squared Bessel processes, which are useful for modeling the relevant scales of stochastic acceleration problems. These nonstationary stochastic processes obey a Langevin equation with a non-Gaussian multiplicative noise. We obtain the long-time asymptotic behavior of the probability density function for non-Gaussian white and colored noise sources. We find that the functional form of the probability density functions is independent of the statistics of the noise source considered. Theoretical results are in good agreement with those obtained by numerical simulations of the Langevin equation with pulse noise sources.
A Fokker–Planck control framework for multidimensional stochastic processes
2013
AbstractAn efficient framework for the optimal control of probability density functions (PDFs) of multidimensional stochastic processes is presented. This framework is based on the Fokker–Planck equation that governs the time evolution of the PDF of stochastic processes and on tracking objectives of terminal configuration of the desired PDF. The corresponding optimization problems are formulated as a sequence of open-loop optimality systems in a receding-horizon control strategy. Many theoretical results concerning the forward and the optimal control problem are provided. In particular, it is shown that under appropriate assumptions the open-loop bilinear control function is unique. The res…
A class of stochastic differential equations with non-Lipschitzian coefficients: pathwise uniqueness and no explosion
2003
Abstract A new result for the pathwise uniqueness of solutions of stochastic differential equations with non-Lipschitzian coefficients is established. Furthermore, we prove that the solution has no explosion under the growth ξlogξ. To cite this article: S. Fang, T. Zhang, C. R. Acad. Sci. Paris, Ser. I 337 (2003).
What is Differential Stochastic Calculus?
1999
Some well known concepts of stochastic differential calculus of non linear systems corrupted by parametric normal white noise are here outlined. Ito and Stratonovich integrals concepts as well as Ito differential rule are discussed. Applications to the statistics of the response of some linear and non linear systems is also presented.