Search results for "Equations"
showing 10 items of 955 documents
Challenges in truncating the hierarchy of time-dependent reduced density matrices equations
2012
In this work, we analyze the Born, Bogoliubov, Green, Kirkwood, and Yvon (BBGKY) hierarchy of equations for describing the full time evolution of a many-body fermionic system in terms of its reduced density matrices (at all orders). We provide an exhaustive study of the challenges and open problems linked to the truncation of such a hierarchy of equations to make them practically applicable. We restrict our analysis to the coupled evolution of the one- and two-body reduced density matrices, where higher-order correlation effects are embodied into the approximation used to close the equations. We prove that within this approach, the number of electrons and total energy are conserved, regardl…
Effects of soil gas permeability and recirculation flux on soil CO2 flux measurements performed using a closed dynamic accumulation chamber
2009
Abstract Dynamic accumulation chamber methods have been extensively used to estimate the total output of CO2 released from active volcanic area. In order to asses the performance and reliability of a closed dynamic system several tests were carried out with different soil permeabilities and soil CO2 fluxes. A special device was used to create a constant one-dimensional CO2 flux through a soil column with a known permeability. Three permeabilities were investigated, ranging between 3.6 × 10− 2 and 3.5 × 10 μm2, as were several CO2 fluxes (ranging between 1.1 × 10− 6 and 6.3 × 10− 5 kg m− 2 s− 1). The results highlight that the accuracy of soil CO2 flux measurements strictly depends on the so…
LONG TIME BEHAVIOR OF A SHALLOW WATER MODEL FOR A BASIN WITH VARYING BOTTOM TOPOGRAPHY
2002
We study the long time behavior of a shallow water model introduced by Levermore and Sammartino to describe the motion of a viscous incompressible fluid confined in a basin with topography. Here we prove the existence of a global attractor and give an estimate on its Hausdorff and fractal dimension.
Finite-Element Modeling of Floodplain Flow
2000
A new methodology for a robust solution of the diffusive shallow water equations is proposed. The methodology splits the unknowns of the momentum and continuity equations into one kinematic and one parabolic component. The kinematic component is solved using the slope of the water level surface computed in the previous time-step and a zero-order approximation of the water head inside the mass-balance area around each node of the mesh. The parabolic component is found by applying a standard finite-element Galerkin procedure, where the source terms can be computed from the solution of the previous kinematic problem. A simple 1D case, with a known analytical solution, is used to test the accur…
Improved Hölder regularity for strongly elliptic PDEs
2019
We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new relations between these two equations. In particular, we show that solutions to an autonomous Beltrami equation enjoy a quantitative improved degree of H\"older regularity, higher than what is given by the classical exponent $1/K$.
Numerical methods to compute sentinels for parabolic systems with an application to source terms identification
1994
We apply the method of sentinels to the identification of source terms in parabolic systems. We present two numerical approaches; the first one is based on the solution of an optimal control problem, and the second one is based on the solution of a linear system of equations. In numerical experiments, we compare these approaches in terms of accuracy and computational cost.
Long time behavior for a dissipative shallow water model
2013
We consider the two-dimensional shallow water model derived by Levermore and Sammartino (Nonlinearity 14,2001), describing the motion of an incompressible fluid, confined in a shallow basin, with varying bottom topography. We construct the approximate inertial manifolds for the associated dynamical system and estimate its order. Finally, considering the whole domain R^2 and under suitable conditions on the time dependent forcing term, we prove the L^2 asymptotic decay of the weak solutions.
Hydrolysis and chemical speciation of (C2H5)2Sn2+, (C2H5)3Sn+ and (C3H7)3Sn+ in aqueous media simulating the major composition of natural waters
2001
The hydrolysis of (C 2 H 5 ) 2 Sn 2+ , (C 2 H 5 ) 3 Sn + and (n-C 3 H 7 ) 3 Sn + has been studied, by potentiometric measurements ([H + ]-glass electrode), in NaNO 3 , NaCl, NaCl/Na 2 SO 4 mixtures and in a synthetic seawater (SSWE), as an ionic medium simulating the major composition of natural seawater, at different ionic strengths (0 ≤ I ≤ 5 mol dm -3 ) and salinities (15 ≤ S ≤ 45), and at t = 25 °C. Five hydrolytic species for (C 2 H 5 ) 2 Sn 2+ , three for (C 2 H 5 ) 3 Sn + and two for (C 3 H 7 ) 3 Sn + are found. Interactions with the anion components of SSWE, considered as single-salt seawater, are determined by means of a complex formation model. A predictive equation for the calcul…
A new result on impulsive differential equations involving non-absolutely convergent integrals
2009
AbstractIn this paper we obtain, as an application of a Darbo-type theorem, global solutions for differential equations with impulse effects, under the assumption that the function on the right-hand side is integrable in the Henstock sense. We thus generalize several previously given results in literature, for ordinary or impulsive equations.
Partial data inverse problems for Maxwell equations via Carleman estimates
2015
In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured on a possibly very small set. This is an extension of earlier scalar results of Bukhgeim-Uhlmann and Kenig-Sj\"ostrand-Uhlmann to the Maxwell system. The main contribution is to show that the Carleman estimate approach to scalar partial data inverse problems introduced in those works can be carried over to the Maxwell system.