109 research outputs found
Homogeneous Open Quantum Random Walks on a lattice
We study Open Quantum Random Walks for which the underlying graph is a
lattice, and the generators of the walk are translation-invariant. We consider
the quantum trajectory associated with the OQRW, which is described by a
position process and a state process. We obtain a central limit theorem and a
large deviation principle for the position process, and an ergodic result for
the state process. We study in detail the case of homogeneous OQRWs on a
lattice, with internal space
A global method for coupling transport with chemistry in heterogeneous porous media
Modeling reactive transport in porous media, using a local chemical
equilibrium assumption, leads to a system of advection-diffusion PDE's coupled
with algebraic equations. When solving this coupled system, the algebraic
equations have to be solved at each grid point for each chemical species and at
each time step. This leads to a coupled non-linear system. In this paper a
global solution approach that enables to keep the software codes for transport
and chemistry distinct is proposed. The method applies the Newton-Krylov
framework to the formulation for reactive transport used in operator splitting.
The method is formulated in terms of total mobile and total fixed
concentrations and uses the chemical solver as a black box, as it only requires
that on be able to solve chemical equilibrium problems (and compute
derivatives), without having to know the solution method. An additional
advantage of the Newton-Krylov method is that the Jacobian is only needed as an
operator in a Jacobian matrix times vector product. The proposed method is
tested on the MoMaS reactive transport benchmark.Comment: Computational Geosciences (2009)
http://www.springerlink.com/content/933p55085742m203/?p=db14bb8c399b49979ba8389a3cae1b0f&pi=1
Treatment of rising damp in historical buildings: wall base ventilation
Intervention in older buildings increasingly requires extensive and objective knowledge of what one will be working with. The multifaceted aspect of work carried out on buildings tends to encompass a growing number of specialities, with marked emphasis on learning the causes of many of the problems that affect these buildings and the possible treatments that can solve them. Moisture transfer in walls of old buildings, which are in direct contact with the ground, leads to a migration of soluble salts responsible for many building pathologies.http://www.sciencedirect.com/science/article/B6V23-4H7T0H7-1/1/f5e8a4ec173c5dadf120770678facf4
Conjugate Direction Methods and Polarity for Quadratic Hypersurfaces
We use some results from polarity theory to recast several geometric properties of Conjugate Gradient-based methods, for the solution of nonsingular symmetric linear systems. This approach allows us to pursue three main theoretical objectives. First, we can provide a novel geometric perspective on the generation of conjugate directions, in the context of positive definite systems. Second, we can extend the above geometric perspective to treat the generation of conjugate directions for handling indefinite linear systems. Third, by exploiting the geometric insight suggested by polarity theory, we can easily study the possible degeneracy (pivot breakdown) of Conjugate Gradient- based methods on indefinite linear systems. In particular, we prove that the degeneracy of the standard Conjugate Gradient on nonsingular indefinite linear systems can occur only once in the execution of the Conjugate Gradient
Phonon distributions of a single bath mode coupled to a quantum dot
The properties of an unconventional, single mode phonon bath coupled to a
quantum dot, are investigated within the rotating wave approximation. The
electron current through the dot induces an out of equilibrium bath, with a
phonon distribution qualitatively different from the thermal one. In selected
transport regimes, such a distribution is characterized by a peculiar selective
population of few phonon modes and can exhibit a sub-Poissonian behavior. It is
shown that such a sub-Poissonian behavior is favored by a double occupancy of
the dot. The crossover from a unequilibrated to a conventional thermal bath is
explored, and the limitations of the rotating wave approximation are discussed.Comment: 21 Pages, 7 figures, to appear in New Journal of Physics - Focus on
Quantum Dissipation in Unconventional Environment
Disguised and new quasi-Newton methods for nonlinear eigenvalue problems
In this paper we take a quasi-Newton approach to nonlinear eigenvalue
problems (NEPs) of the type , where
is a holomorphic function. We
investigate which types of approximations of the Jacobian matrix lead to
competitive algorithms, and provide convergence theory. The convergence
analysis is based on theory for quasi-Newton methods and Keldysh's theorem for
NEPs. We derive new algorithms and also show that several well-established
methods for NEPs can be interpreted as quasi-Newton methods, and thereby
provide insight to their convergence behavior. In particular, we establish
quasi-Newton interpretations of Neumaier's residual inverse iteration and
Ruhe's method of successive linear problems
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