Displaying similar documents to “Nanonetworks: The graph theory framework for modeling nanoscale systems”

Vibrational properties of nanographene

Sandeep Kumar Singh, F.M. Peeters (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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The eigenmodes and the vibrational density of states of the ground state configuration of graphene clusters are calculated using atomistic simulations. The modified Brenner potential is used to describe the carbon-carbon interaction and carbon-hydrogen interaction in case of H-passivated edges. For a given configuration of the C-atoms the eigenvectors and eigenfrequencies of the normal modes are obtained after diagonalisation of the dynamical matrix whose elements are the second derivative...

Analysis of fast boundary-integral approximations for modeling electrostatic contributions of molecular binding

Amelia B. Kreienkamp, Lucy Y. Liu, Mona S. Minkara, Matthew G. Knepley, Jaydeep P. Bardhan, Mala L. Radhakrishnan (2013)

Molecular Based Mathematical Biology

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We analyze and suggest improvements to a recently developed approximate continuum-electrostatic model for proteins. The model, called BIBEE/I (boundary-integral based electrostatics estimation with interpolation), was able to estimate electrostatic solvation free energies to within a mean unsigned error of 4% on a test set of more than 600 proteins¶a significant improvement over previous BIBEE models. In this work, we tested the BIBEE/I model for its capability to predict residue-by-residue...

High-order fractional partial differential equation transform for molecular surface construction

Langhua Hu, Duan Chen, Guo-Wei Wei (2013)

Molecular Based Mathematical Biology

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Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions....

Graphical Processing Unit accelerated Poisson equation solver and its application for calculation of single ion potential in ion-channels

Nikolay A. Simakov, Maria G. Kurnikova (2013)

Molecular Based Mathematical Biology

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Poisson and Poisson-Boltzmann equations (PE and PBE) are widely used in molecular modeling to estimate the electrostatic contribution to the free energy of a system. In such applications, PE often needs to be solved multiple times for a large number of system configurations. This can rapidly become a highly demanding computational task. To accelerate such calculations we implemented a graphical processing unit (GPU) PE solver described in this work. The GPU solver performance is compared...

Multi-core CPU or GPU-accelerated Multiscale Modeling for Biomolecular Complexes

Tao Liao, Yongjie Zhang, Peter M. Kekenes-Huskey, Yuhui Cheng, Anushka Michailova, Andrew D. McCulloch, Michael Holst, J. Andrew McCammon (2013)

Molecular Based Mathematical Biology

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Multi-scale modeling plays an important role in understanding the structure and biological functionalities of large biomolecular complexes. In this paper, we present an efficient computational framework to construct multi-scale models from atomic resolution data in the Protein Data Bank (PDB), which is accelerated by multi-core CPU and programmable Graphics Processing Units (GPU). A multi-level summation of Gaussian kernel functions is employed to generate implicit models for biomolecules....

A Stochastic Solver of the Generalized Born Model

Robert C. Harris, Travis Mackoy, Marcia O. Fenley (2013)

Molecular Based Mathematical Biology

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A stochastic generalized Born (GB) solver is presented which can give predictions of energies arbitrarily close to those that would be given by exact effective GB radii, and, unlike analytical GB solvers, these errors are Gaussian with estimates that can be easily obtained from the algorithm. This method was tested by computing the electrostatic solvation energies (ΔGsolv) and the electrostatic binding energies (ΔGbind) of a set of DNA-drug complexes, a set of protein-drug complexes,...

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...

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...

Efficient simulation of unidirectional pulse propagation in high-contrast nonlinear nanowaveguides

Jonathan Andreasen, Miroslav Kolesik (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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This work demonstrates an improved method to simulate long-distance femtosecond pulse propagation in highcontrast nanowaveguides. Different from typical beam propagation methods, the foundational tool here is capable of simulating strong spatiotemporal waveform reshaping and extreme spectral dynamics. Meanwhile, the ability to fully capture effects due to index contrast in the transverse direction is retained, without requiring a decomposition of the electric field in terms of waveguide...

Theory, Experiment and Computation of Half Metals for Spintronics: Recent Progress in Si-based Materials

C. Y. Fong, M. Shaughnessy, L. Damewood, L. H. Yang (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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Since the term “spintronics” was conceived in 1996, there have been several directions taken to develop new semiconductor-based magnetic materials for device applications using spin, or spin and charge, as the operational paradigm. Anticipating their integration into mature semiconductor technologies, one direction is to make use of materials involving Si. In this review, we focus on the progress made, since 2005, in Si-based half metallic spintronic materials. In addition to commenting...

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...