Erscheinungsdatum: 07/2012, Medium: Taschenbuch, Einband: Kartoniert / Broschiert, Titel: Application of Sobolev gradient to Poisson Boltzmann system, Titelzusatz: Sobolev inner products as preconditiong operators in the steepest descent minimization process, Autor: Majid, Abdul // Sial, Sultan, Verlag: LAP Lambert Academic Publishing, Sprache: Englisch, Rubrik: Mathematik // Sonstiges, Seiten: 144, Informationen: Paperback, Gewicht: 231 gr, Verkäufer: averdo
EXTENDED SYMMETRIC POISSON-BOLTZMANN THEORY ab 49 € als Taschenbuch: EXTENSION OF THE SYMMETRIC POISSON-BOLTZMANN EQUATION UPTO A SIX-COMPONENT MIXTURE OF ELECTROLYTES AND NEUTRAL PARTICLES. Aus dem Bereich: Bücher, Wissenschaft, Chemie,
Application of Sobolev gradient to Poisson Boltzmann system ab 59 € als Taschenbuch: Sobolev inner products as preconditiong operators in the steepest descent minimization process. Aus dem Bereich: Bücher, Wissenschaft, Mathematik,
Application of Sobolev gradient to Poisson Boltzmann system ab 59 EURO Sobolev inner products as preconditiong operators in the steepest descent minimization process
To study the structural and thermodynamic properties of electrolyte solutions the Symmetric Poisson-Boltzmann theory has been extended up to six components and the resulting coupled equations for the mean electrostatic potentials have been solved numerically using a quasi-linearization iterative procedure. The exclusion volume term approximated by PY hard sphere RDF has been calculated using Perram's method along with Verlet and Weis corrections. The RDFs have been computed for four-component systems comprising a single electrolyte with two other neutral components for various cases. Excellent agreement has been found for each case when compared with MC data. The theory predicts the experimental trends when applied to measure the second virial coefficient in a colloidal system of silicotungstate, in a solution of HCl, LiCl or NaCl. The extended theory and the numerical solution techniques can be utilized to study the structural and thermodynamic properties of multicomponent electrolytes which are of great interest because of their frequent presence in industrial processes and in branches of sciences like colloid and surface science, polymer science, biophysics and chemistry.
We discuss the historical development of classical fluid dynamics consisting with four parts. Part 1 : Exact differential as the criteria of equilibrium/motion and irrotational motion/rotary motion, Part 2 : The two-constant theory and tensor function underlying the Navier-Stokes equations, Part 3 : The Microscopically-descriptive hydrodynamical equations in the gas theory, Part 4 : The early studies of solutions of Navier-Stokes equations. Owing to the arrival of continuum theory, many mathematical developments are brought in today s fluid mechanics, such as the Euler equations, the Navier-Stokes equations, the Stokes equations, the Helmholtz vorticity equations, Boltzmann s transport equations. We introduce the thinking methods and modeling of these equations, including capillarity theories of fluid particles in continuum by Laplace, Gauss and Poisson, with the classical notation and styles, the disputing contents of their themes discussed among progenitors. Microscopically-descriptive expressions are succeeded into Boltzmann s equations, and contribute to the quantum mechanics such as Schrödinger equations. Now, this is hitting by peerers on Tokyo Metro. Univ. Repository.
The important lapse in the failure of Debye-Huckel theory was established during the last century by detailed theoretical and experimental work of Glueckauff, Pitzer, Buchner, Barthel and the Nobel Prize winners Eigen and Tamm. The omission of incorporation of dielectric permittivity variation with concentration is attributed to be sole cause for several interesting mechanisms observed in electrolytic solutions. This book developed a model to fill the void. A nonlinear equation for Dielectric constant as a function of three different powers of concentration was proposed. Gauss-Newton method was used in curve fitting the Dielectric data. The Poisson-Boltzmann equation provided access to apply the proposed correction to the Debye-Huckel theory. The governing equations for an EOF of an aqueous electrolyte solution were developed by fully coupled Navier - Stokes, Maxwell - Stefan, Poisson - Boltzmann equations. The Finite difference method and Finite element method were used to solve the governing equations.
This book offers an application of Sobolev gradient approach to Poisson Boltzmann system. A detailed description of Sobolev gradient method is given and its application is demonstrated on the Poisson Boltzmann system when there are large non-linearities and discontinuities in the coefficient functions. Poisson Boltzmann is a physical model that governs the electrostatic potential of macromolecules when immersed in solvent. It is shown that in some cases Sobolev gradient performs better in terms of efficiency than other existing fast methods such as multigrid and Newton's methods. The experiments' results are given in both finite element and finite difference settings. This book presents a fine blend of Functional Analysis, Numerical Analysis and Biophysics. It is the Ph.D. work that Dr. Abdul Majid completed under the supervision of Dr. Sultan Sial.