Displaying similar documents to “Nanoscale Systems: Mathematical Modeling, Theory and Applications. Subject Index, Volume 1, 2012”

On unitary Cauchy filters on topological monoids

Boris G. Averbukh (2013)

Topological Algebra and its Applications

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For Hausdorff topological monoids, the concept of a unitary Cauchy net is a generalization of the concept of a fundamental sequence of reals. We consider properties and applications of such nets and of corresponding filters and prove, in particular, that the underlying set of a given monoid, endowed with the family of such filters, forms a Cauchy space whose convergence structure defines a uniform topology. A commutative monoid endowed with the corresponding uniformity is uniform. A...

A numerically efficient approach to the modelling of double-Qdot channels

A. Shamloo, A.P. Sowa (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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We consider the electronic properties of a system consisting of two quantum dots in physical proximity, which we will refer to as the double-Qdot. Double-Qdots are attractive in light of their potential application to spin-based quantum computing and other electronic applications, e.g. as specialized sensors. Our main goal is to derive the essential properties of the double-Qdot from a model that is rigorous yet numerically tractable, and largely circumvents the complexities of an ab...

Quantum optimal control using the adjoint method

Alfio Borzì (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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Control of quantum systems is central in a variety of present and perspective applications ranging from quantum optics and quantum chemistry to semiconductor nanostructures, including the emerging fields of quantum computation and quantum communication. In this paper, a review of recent developments in the field of optimal control of quantum systems is given with a focus on adjoint methods and their numerical implementation. In addition, the issues of exact controllability and optimal...

Coulomb Interaction Effects on the Spin Polarization and Currents in Quantum Wires with Spin Orbit Interaction

Anton Heidar Thorolfsson, Andrei Manolescu, D.C. Marinescu, Vidar Gudmundsson (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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We analyze the charge and spin distributions induced in an interacting electron system confined inside a semiconductor quantum wire with spin orbit interaction in the presence of an external magnetic field. The wire, assumed to be infinitely long, is obtained through lateral confinement in three different materials: GaAs, InAs, and InSb. The spin-orbit coupling, linear in the electron momentum is of both Rashba and Dresselhaus type. Within the Hartree-Fock approximation the many-body...

On the derivation and mathematical analysis of some quantum–mechanical models accounting for Fokker–Planck type dissipation: Phase space, Schrödinger and hydrodynamic descriptions

José Luis López, Jesús Montejo–Gámez (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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This paper is intended to provide the reader with a review of the authors’ latest results dealing with the modeling of quantum dissipation/diffusion effects at the level of Schrödinger systems, in connection with the corresponding phase space and fluid formulations of such kind of phenomena, especially in what concerns the role of the Fokker–Planck mechanism in the description of open quantum systems and the macroscopic dynamics associated with some viscous hydrodynamic models of Euler...

Mathematical modeling of semiconductor quantum dots based on the nonparabolic effective-mass approximation

Jinn-Liang Liu (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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Within the effective mass and nonparabolic band theory, a general framework of mathematical models and numerical methods is developed for theoretical studies of semiconductor quantum dots. It includes single-electron models and many-electron models of Hartree-Fock, configuration interaction, and current-spin density functional theory approaches. These models result in nonlinear eigenvalue problems from a suitable discretization. Cubic and quintic Jacobi-Davidson methods of block or nonblock...

Theory of space-time dissipative elasticity and scale effects

S.A. Lurie, P.A. Belov (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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In this article a model of irreversible dynamic thermoelasticity of an ideal continuua is constructed from an elasticity theory of asymmetrical, transversely isotropic in time direction, dissipative defectless 4D-continuum. In the model the fourth component of the 4D-displacement vector is locally irregular time R. The kinematic model comprises 3D-tensor of distortion, 3Dvector of velocity, 3D-gradient vector of local irregular time and entropy in unified tensor object which is an asymmetrical...

Mesoscopic description of boundary effects in nanoscale heat transport

F.X. Àlvarez, V.A. Cimmelli, D. Jou, A. Sellitto (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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We review some of the most important phenomena due to the phonon-wall collisions in nonlocal heat transport in nanosystems, and show how they may be described through certain slip boundary conditions in phonon hydrodynamics. Heat conduction in nanowires of different cross sections and in thin layers is analyzed, and the dependence of the thermal conductivity on the geometry, as well as on the roughness is pointed out. We also analyze the effects of the roughness of the surface of the...

Progress in developing Poisson-Boltzmann equation solvers

Chuan Li, Lin Li, Marharyta Petukh, Emil Alexov (2013)

Molecular Based Mathematical Biology

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This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nanoobjects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task...

Non-Fourier heat removal from hot nanosystems through graphene layer

A. Sellitto, F.X. Alvarez (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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Nonlocal effects on heat transport beyond a simple Fourier description are analyzed in a thermodynamical model. In the particular case of hot nanosystems cooled through a graphene layer, it is shown that these effects may increase in a ten percent the amount of removed heat, as compared with classical predictions based on the Fourier law.

Fully implicit ADI schemes for solving the nonlinear Poisson-Boltzmann equation

Weihua Geng, Shan Zhao (2013)

Molecular Based Mathematical Biology

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The Poisson-Boltzmann (PB) model is an effective approach for the electrostatics analysis of solvated biomolecules. The nonlinearity associated with the PB equation is critical when the underlying electrostatic potential is strong, but is extremely difficult to solve numerically. In this paper, we construct two operator splitting alternating direction implicit (ADI) schemes to efficiently and stably solve the nonlinear PB equation in a pseudo-transient continuation approach. The operator...