Search results for "equation"
showing 10 items of 4219 documents
Infinite lie groups of point transformations leaving invariant the linear equation which describes in the hodograph plane the isentropic one-dimensio…
1991
Abstract The group analysis of the hodograph equation which is equivalent to the non-linear system of one-dimensional isentropic gas dynamics reveals the existence of infinite groups of symmetry in correspondence with particular pressure laws. These turn out to be polytropes with selected indices, as is expected, as well as a new type of pressure. In all these cases the hodograph equation can be transformed, by a suitable change of variables, into the wave equationψ ζ = 0.
Path integral solution for non-linear system enforced by Poisson White Noise
2008
Abstract In this paper the response in terms of probability density function of non-linear systems under Poisson White Noise is considered. The problem is handled via path integral (PI) solution that may be considered as a step-by-step solution technique in terms of probability density function. First the extension of the PI to the case of Poisson White Noise is derived, then it is shown that at the limit when the time step becomes an infinitesimal quantity the Kolmogorov–Feller (K–F) equation is fully restored enforcing the validity of the approximations made in obtaining the conditional probability appearing in the Chapman Kolmogorov equation (starting point of the PI). Spectral counterpa…
Approximate Osher–Solomon schemes for hyperbolic systems
2016
This paper is concerned with a new kind of Riemann solvers for hyperbolic systems, which can be applied both in the conservative and nonconservative cases. In particular, the proposed schemes constitute a simple version of the classical Osher-Solomon Riemann solver, and extend in some sense the schemes proposed in Dumbser and Toro (2011) 19,20. The viscosity matrix of the numerical flux is constructed as a linear combination of functional evaluations of the Jacobian of the flux at several quadrature points. Some families of functions have been proposed to this end: Chebyshev polynomials and rational-type functions. Our schemes have been tested with different initial value Riemann problems f…
Sequestration of organomettalic compounds by synthetic and naturally occuring polycarboxylate ligands. Binding of monomethylmercury(II) by polyacryli…
2007
The sequestering capacity of synthetic and naturally occurring polycarboxylate ligands towards mono- methylmercury(II) was evaluated by stability quantitative data on the interaction of CH3Hgþ with different molecular weight synthetic polyacrylates (2 and 20 kDa average M.wt) and alginate (70– 100 kDa) extracted from brown algae Macrocystis pyrifera. The influence of ionic medium was evaluated by measurements on the CH3Hgþ-polyacrylate systems in NaNO3 medium at different ionic strengths (0.10, 0.25, 0.50 and 0.75mol Lÿ1), and a Debye–Hu¨ ckel type equation was used for the dependence of complex formation constants on ionic strength. Measurements on the CH3Hgþ - alginate system were carried…
Pressure-induced phase transitions in AgClO4
2011
11 pags, 9 figs, 4 tabs. -- PACS number(s): 62.50.−p, 64.70.K−, 61 .50.Ks, 64.30.−t
Levy flights in confining environments: Random paths and their statistics
2013
We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise. In view of the L\'{e}vy noise sensitivity to the confining "potential landscape" where jumps take place (in other words, to environmental inhomogeneities), the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) $\rho_*(x) \sim \exp [-\Phi (x)]$. Since there is no Langevin representation of the dynamics in question, our main goal here is to establish the appropriate path-wise description of the underlying jump-type process and next infer the $\rho (x,t)$ dynamics directly from the random paths statistics. A pr…
Electric field enhanced water dissociation at the bipolar membrane junction from ac impedance spectra measurements
1998
Abstract Preliminary experimental results of the ac impedance spectra of a bipolar ion-exchange membrane are reported and interpreted on the basis of a previous theoretical model based on the Nernst–Planck/Poisson equations. It is shown that the experiments can provide valuable electrochemical information about the bipolar junction structure and the electric-field enhanced water dissociation phenomenon that occurs at this junction, although the high number of unknown parameters involved makes it difficult to obtain accurate values for the parameters characteristic of this phenomenon.
Kinetische untersuchungen zur strahleninduzierten festkörperpolymerisation von trioxan und tetroxan IV. Mitt. der Reihe “kinetische und morphologisch…
1971
Die strahlungsinduzierte Polymerisation von kristallinem Tetroxan und Trioxan wurde untersucht und der Einflus von Strahlendosis, Reaktionszeit und -temperatur auf den Umsatz und das Molekulargewicht der entstehenden POM, insbesondere bei der Nachpolymerisation, studiert. Die Zeit-Umsatz-Kurven fur die Nachpolymerisation laufen bei beiden Monomeren asymptotisch gegen einem Grenzwert des Umsatzes, der mit steigender Reaktionstemperatur ansteigt. Die Aktivierungsenergie der Nachpolymerisation wurde zu 24 ± 2 kcal/Mol fur Tetroxan und zu 36–38 kcal/Mol fur Trioxan bestimmt. Die Zeit(t)-Umsatz(x)-Kurven fur Tetroxan lassen sich durch die empirische Gleichung: beschreiben, wobei k1 und k2 Konsta…
Data Treatment in Kinetics
2000
Chemical kinetics is an important part of chemistry devoted to study how reactions proceed and quantify the rate of the process. The reaction mechanism is the chemical model that describes how the chemical change occurs. From the proposed mechanism, a mathematical model can be obtained to explain the evolution of the chemical species with time. In many cases, the mechanism can be simplified to a single rate law that relates the reaction rate with concentrations. In the last decades, the study of kinetic systems has benefited from the development of instrumentation, the increasing availability of specialized computer software, and the advances in data treatment techniques. A comprehensive re…
Molecular association and dynamics in n-pentanol and 2-methyl-2-butanol
1985
Static dielectric constant, viscosity, density, ultrasonic and dielectric relaxation measurements are reported for two pentanol isomers (n-pentanol and 2-methyl-2-butanol) in a wide range of temperatures. The results show a different extent of H-bonds self-association in relation to the molecular geometry of the alcohol. The activation energies obtained from dielectric and ultrasonic studies are compared with those obtained from viscous flow. Such a comparison, together with the analysis of all the dielectric and ultrasonic relaxation data, show that in n-pentanol a correlation between viscosity and ultrasonic relaxation exists, while dielectric relaxation is not correlated with the other t…