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In this talk, we discuss the approximation and computation for the linear and nonlinear eigenvalue problems in photonic crystals. We discretize the shifted Maxwell operator with edge finite elements a...
Phononic crystals are composite materials with periodic distribution of two or more media. The difficulty of computing the band structure of the phononic crystals lies in capturing the complex geometr...
We propose a scheme to realize scalable quantum computation in a planar ion crystal confined by a Paul trap. We show that the inevitable in-plane micromotion affects the gate design via three separate...
A new recursive procedure to compute the Zassenhaus formula up to high order is presented, providing each exponent in the factorization directly as a linear combination of independent commutators and ...
Sensitivity analysis can be a powerful tool for multi-disciplinary design optimization of nonlinear flow structure interaction. For computing sensitivity of time averaged quantities in chaotic oscilla...
This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivativ...
Abstract: The performance potential for simulating quantum electron transport on graphical processing units (GPUs) is studied. Using graphene ribbons of realistic sizes as an example it is shown that ...
Abstract: We devise a hierarchy of computational algorithms to enumerate the microstates of a system comprising N independent, distinguishable particles. An important challenge is to cope with integer...
Abstract: The aim of this paper is to develop a multiscale hierarchical hybrid model based on finite element analysis and neural network computation to link mesoscopic scale (trabecular network level)...
Abstract: Inspired by the work of Feynman, Deutsch, We formally propose the theory of physical computability and accordingly, the physical complexity theory. To achieve this, a framework that can eval...
Abstract: We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of t...
Abstract: We present a simple and fast algorithm for the computation of the coefficients of the expansion of a function f(cos u) in ultraspherical (Gegenbauer) polynomials. We prove that these coeffic...
Background: Many recent statistical applications involve inference under complex models, where it is computationally prohibitive to calculate likelihoods but possible to simulate data. Approximate Bay...
Let 􀀀a be Dirac matrices in d-dimensional Minkowski spacetime, and let i = Bab i 􀀀ab, where 􀀀ab = 􀀀[a􀀀b] and Bab i are arbitrary antisymmetric tensors. Th...
An efficient algorithm for the computation of the trace of the symmetrized product of an arbitrary number of Dirac matrices with two indices.

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