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

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...

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...

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...

Signals generated in memristive circuits

Artur Sowa (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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Signals generated in circuits that include nano-structured elements typically have strongly distinct characteristics, particularly the hysteretic distortion. This is due to memristance, which is one of the key electronic properties of nanostructured materials. In this article, we consider signals generated from a memrsitive circuit model. We demonstrate numerically that such signals can be efficiently represented in certain custom-designed nonorthogonal bases. The proposed method ensures...

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...

Quantum graph spectra of a graphyne structure

Ngoc T. Do, Peter Kuchment (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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We study the dispersion relations and spectra of invariant Schrödinger operators on a graphyne structure (lithographite). In particular, description of different parts of the spectrum, band-gap structure, and Dirac points are provided.

An inverse problem for adhesive contact and non-direct evaluation of material properties for nanomechanics applications

F.M. Borodich, B.A. Galanov, S.N. Gorb, M.Y. Prostov, Y.I. Prostov, M.M. Suarez-Alvarez (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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We show how the values of the effective elastic modulus of contacting solids and the work of adhesion, that are the crucial material parameters for application of theories of adhesive contact to nanomechanics, may be quantified from a single test using a non-direct approach (the Borodich-Galanov (BG) method). Usually these characteristics are not determined from the same test, e.g. often sharp pyramidal indenters are used to determine the elastic modulus from a nanoindentation test,...

Bounds on Capital Requirements For Bivariate Risk with Given Marginals and Partial Information on the Dependence

Carole Bernard, Yuntao Liu, Niall MacGillivray, Jinyuan Zhang (2013)

Dependence Modeling

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Nelsen et al. [20] find bounds for bivariate distribution functions when there are constraints on the values of its quartiles. Tankov [25] generalizes this work by giving explicit expressions for the best upper and lower bounds for a bivariate copula when its values on a compact subset of [0; 1]2 are known. He shows that they are quasi-copulas and not necessarily copulas. Tankov [25] and Bernard et al. [3] both give sufficient conditions for these bounds to be copulas. In this note we...

Genetic Exponentially Fitted Method for Solving Multi-dimensional Drift-diffusion Equations

M. R. Swager, Y. C. Zhou (2013)

Molecular Based Mathematical Biology

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A general approach was proposed in this article to develop high-order exponentially fitted basis functions for finite element approximations of multi-dimensional drift-diffusion equations for modeling biomolecular electrodiffusion processes. Such methods are highly desirable for achieving numerical stability and efficiency. We found that by utilizing the one-to-one correspondence between the continuous piecewise polynomial space of degree k + 1 and the divergencefree vector space of...

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...

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...