Search results for " equations"
showing 10 items of 783 documents
The interaction of amino acids with the major constituents of natural waters at different ionic strengths
2000
Abstract The interaction of amino acids with the major constituents of natural waters has been studied potentiometrically by determining protonation constants at different ionic strengths (e.g., I ≤5.6 mol (kg H 2 O) −1 (NaCl)) and in artificial seawater (containing Na + , K + , Ca 2+ , Mg 2+ , Cl − and SO 4 2− ) at different salinities. For glycine determinations in mixed NaCl–MgCl 2 , electrolyte solutions were also performed. The data included in this work, together with some already published, make it possible to calculate parameters for dependence on ionic strength using different models, i.e. an extended Debye–Huckel type equation and Pitzer equations. The results can be interpreted b…
Protonation of Carbonate in Aqueous Tetraalkylammonium Salts at 25°C.
2006
Protonation constants of carbonate were determined in tetramethylammonium chloride (Me4NClaq 0.1≤I/mol kg−1 ≤4) and tetraethylammonium iodide (Et4NIaq 0.1≤I/mol kg−1 ≤1) by potentiometric ([H+]-glass electrode) measurements. Dependence of protonation constants on ionic strength was taken into account by modified specific ion interaction theory (SIT) and by Pitzer models. Literature data on the protonation of carbonate in NaClaq (0.1≤I/mol kg−1 ≤6) were also critically analysed. Both protonation constants of carbonate follow the trend Et4NI>Me4NCl > NaCl. An ion pair formation model designed to take into account the different protonation behaviours of carbonate in different supporting electr…
Qualitative Analysis of Differential, Difference Equations, and Dynamic Equations on Time Scales
2015
and Applied Analysis 3 thank Guest Editors Josef Dibĺik, Alexander Domoshnitsky, Yuriy V. Rogovchenko, Felix Sadyrbaev, and Qi-Ru Wang for their unfailing support with editorial work that ensured timely preparation of this special edition. Tongxing Li Josef Dibĺik Alexander Domoshnitsky Yuriy V. Rogovchenko Felix Sadyrbaev Qi-Ru Wang
Minimally implicit Runge-Kutta methods for Resistive Relativistic MHD
2016
The Relativistic Resistive Magnetohydrodynamic (RRMHD) equations are a hyperbolic system of partial differential equations used to describe the dynamics of relativistic magnetized fluids with a finite conductivity. Close to the ideal magnetohydrodynamic regime, the source term proportional to the conductivity becomes potentially stiff and cannot be handled with standard explicit time integration methods. We propose a new class of methods to deal with the stiffness fo the system, which we name Minimally Implicit Runge-Kutta methods. These methods avoid the development of numerical instabilities without increasing the computational costs in comparison with explicit methods, need no iterative …
Solutions of the Einstein field equations for a bounded and finite discontinuous source, and its generalization: Metric matching conditions and jumpi…
2019
We consider the metrics of the General Relativity, whose energy-momentum tensor has a bounded support where it is continuous except for a finite step across the corresponding boundary surface. As a consequence, the first derivative of the metric across this boundary could perhaps present a finite step too. However, we can assume that the metric is ${\cal C}^1$ class everywhere. In such a case, although the partial second derivatives of the metric exhibit finite (no Dirac $\delta$ functions) discontinuities, the Dirac $\delta$ functions will still appear in the conservation equation of the energy-momentum tensor. As a consequence, strictly speaking, the corresponding metric solutions of the …
Filter approach to the stochastic analysis of MDOF wind-excited structures
1999
Abstract In this paper, an approach useful for stochastic analysis of the Gaussian and non-Gaussian behavior of the response of multi-degree-of-freedom (MDOF) wind-excited structures is presented. This approach is based on a particular model of the multivariate stochastic wind field based upon a particular diagonalization of the power spectral density (PSD) matrix of the fluctuating part of wind velocity. This diagonalization is performed in the space of eigenvectors and eigenvalues that are called here wind-eigenvalues and wind-eigenvectors, respectively. From the examination of these quantities it can be recognized that the wind-eigenvectors change slowly with frequency while the first wi…
ASYMPTOTIC ANALYSIS OF THE LINEARIZED NAVIER–STOKES EQUATION ON AN EXTERIOR CIRCULAR DOMAIN: EXPLICIT SOLUTION AND THE ZERO VISCOSITY LIMIT
2001
In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity. Copyright © 2001 by Marcel Dekker, Inc.
A reexamination of the equilibrium conditions in the theory of water drop nucleation
1975
The thermodynamic equations necessary to describe the conditions for equilibrium between a highly curved surface of a liquid and its vapour are re-examined. The complete equilibrium behaviour is reduced to one single differential equation for each component in an arbitrary c -component system. It is shown that this general formulation can be specialized to describe the conditions for equilibrium between water vapour and a pure water drop, the drop carrying an electric charge, containing a water soluble substance and/or containing a water insoluble nucleus. In the light of the present formulation, some incorrect physical statements of treatments by various authors reported in literature are …
A numerical study of atmospheric signals in the Earth-ionosphere electromagnetic cavity with the Transmission Line Matrix method
2006
[1] The effect of the Earth-ionosphere electromagnetic cavity on the spectrum of an atmospheric signal generated by a broadband electrical current source is analyzed numerically by means of the Transmission Line Matrix (TLM) method. Two new TLM meshes are developed, one with transmission lines connected in parallel and the other with connections in series. The equations describing propagation through these parallel or series meshes are equivalent to the Maxwell equations for TEr or TMr modes in the spherical Earth-ionosphere cavity, respectively. The numerical algorithm obtains Schumann resonance frequencies very close to the experimental ones, confirming that this methodology is a valid nu…
Quadratic backward stochastic differential equations
2017
Tässä tutkielmassa analysoimme takaperoisia stokastisia differentiaaliyhtälöitä. Aloitamme esittelemällä stokastiset prosessit, Brownin liikkeen, stokastiset integraalit ja Itôn kaavan. Tämän jälkeen siirrymme tarkastelemaan stokastisia differentiaaliyhtälöitä ja lopulta takaperoisia stokastisia differentiaaliyhtälöitä. Tämän tutkielman pääaiheena on takaperoiset stokastiset differentiaaliyhtälöt kvadraattisilla oletuksilla. Näillä oletuksilla todistamme olemassaoloteoreeman ja tietyt säännöllisyysehdot takaperoisen stokastisen differentiaaliyhtälön ratkaisulle. In this thesis, we analyze backward stochastic differential equations. We begin by introducing stochastic processes, Brownian moti…