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Searcóid, Mícheál Ó

doi:10.1007/978-1-4471-0179-6_12

Cited by 3 publications

(3 citation statements)

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“…Indeed, for a hypercubic lattice of arbitrary dimension d, the following relation holds (see e.g. [43]): where k − j denotes the Euclidean distance between the lattice points k and j chosen arbitrarily. By averaging each term of the previous equation with respect to the transfer probability π k,j (t) (we can again exploit the translational invariance of the substrate and fix j = 0), we find that the average Euclidean distance also scales linearly with time with a multiplicative factor bounded between 4d/( √ 3π) ≈ 2.31d/π and 4d/π.…”

Section: Discussionmentioning

confidence: 99%

Dynamics of continuous-time quantum walks in restricted geometries

Agliari¹,

Blumen²,

Muelken³

2008

J. Phys. A: Math. Theor.

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Abstract. We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average displacement of the walker as a function of time. Indeed, a fast growth of the average displacement can be advantageously exploited to build up efficient search algorithms. By means of analytical and numerical investigations, we show that the finiteness and the inhomogeneity of the substrate jointly weaken the quantum walk performance. We further highlight the interplay between the quantum-walk dynamics and the underlying topology by studying the temporal evolution of the transfer probability distribution and the lower bound of long time averages.

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Section: Discussionmentioning

confidence: 99%

Dynamics of continuous-time quantum walks in restricted geometries

Agliari¹,

Blumen²,

Muelken³

2008

J. Phys. A: Math. Theor.

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“…q is a metric on the product space X N Y . 58 Using Euclidean product metric we can define distances in complex spaces with different kinds of coordinates, and in particular it is convenient to breakdown large multivariable spaces like those of biomolecules in subspaces with obvious correlations among variables, for example, for rotations, translations, position-orientations and rotations about contiguous torsional angles. In these subspaces we can make use of the Euclidean product metric, and treat correlations among different variables or group of variables with specific tools (vide infra).…”

Section: Distances In External Coordinates and Bat Spacementioning

confidence: 99%

The kth nearest neighbor method for estimation of entropy changes from molecular ensembles

Fogolari,

Borelli,

Dovier

et al. 2023

WIREs Comput Mol Sci

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All processes involving molecular systems entail a balance between associated enthalpic and entropic changes. Molecular dynamics simulations of the end‐points of a process provide in a straightforward way the enthalpy as an ensemble average. Obtaining absolute entropies is still an open problem and most commonly pathway methods are used to obtain free energy changes and thereafter entropy changes. The kth nearest neighbor (kNN) method has been first proposed as a general method for entropy estimation in the mathematical community 20 years ago. Later, it has been applied to compute conformational, positional–orientational, and hydration entropies of molecules. Programs to compute entropies from molecular ensembles, for example, from molecular dynamics (MD) trajectories, based on the kNN method, are currently available. The kNN method has distinct advantages over traditional methods, namely that it is possible to address high‐dimensional spaces, impossible to treat without loss of resolution or drastic approximations with, for example, histogram‐based methods. Application of the method requires understanding the features of: the kth nearest neighbor method for entropy estimation; the variables relevant to biomolecular and in general molecular processes; the metrics associated with such variables; the practical implementation of the method, including requirements and limitations intrinsic to the method; and the applications for conformational, position/orientation and solvation entropy. Coupling the method with general approximations for the multivariable entropy based on mutual information, it is possible to address high dimensional problems like those involving the conformation of proteins, nucleic acids, binding of molecules and hydration.This article is categorized under: Molecular and Statistical Mechanics > Free Energy Methods Theoretical and Physical Chemistry > Statistical Mechanics Structure and Mechanism > Computational Biochemistry and Biophysics

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“…The finite volume Method.-Formulation of the finite volume method.-The basic idea for the finite volume method is to solve for the integral form of the original PDE. We assume the diffusion coefficient function D(c) is globally Lipschitz, 23 then integrate both sides of Eq. 1 over the interval [r i , r i+1 ], to get,…”

Section: The Finite Volume and Control Volume Formulationsmentioning

confidence: 99%

Efficient Conservative Numerical Schemes for 1D Nonlinear Spherical Diffusion Equations with Applications in Battery Modeling

Zeng

Albertus

Klein

et al. 2013

J. Electrochem. Soc.

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Mathematical models of batteries which make use of the intercalation of a species into a solid phase need to solve the corresponding mass transfer problem. Because solving this equation can significantly add to the computational cost of a model, various methods have been devised to reduce the computational time. In this paper we focus on a comparison of the formulation, accuracy, and order of the accuracy for two numerical methods of solving the spherical diffusion problem with a constant or non-constant diffusion coefficient: the finite volume method and the control volume method. Both methods provide perfect mass conservation and second order accuracy in mesh spacing, but the control volume method provides the surface concentration directly, has a higher accuracy for a given numbers of mesh points and can also be easily extended to variable mesh spacing. Variable mesh spacing can significantly reduce the number of points that are required to achieve a given degree of accuracy in the surface concentration (which is typically coupled to the other battery equations) by locating more points where the concentration gradients are highest.

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Cited by 3 publications

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Dynamics of continuous-time quantum walks in restricted geometries

Dynamics of continuous-time quantum walks in restricted geometries

The kth nearest neighbor method for estimation of entropy changes from molecular ensembles

Efficient Conservative Numerical Schemes for 1D Nonlinear Spherical Diffusion Equations with Applications in Battery Modeling

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