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Jiang S.,New Jersey Institute of Technology | Luo L.-S.,Computational Science Research Center | Luo L.-S.,Old Dominion University
Journal of Computational Physics | Year: 2016

The integral equation for the flow velocity u(x;k) in the steady Couette flow derived from the linearized Bhatnagar-Gross-Krook-Welander kinetic equation is studied in detail both theoretically and numerically in a wide range of the Knudsen number k between 0.003 and 100.0. First, it is shown that the integral equation is a Fredholm equation of the second kind in which the norm of the compact integral operator is less than 1 on Lp for any 1≤p≤∞ and thus there exists a unique solution to the integral equation via the Neumann series. Second, it is shown that the solution is logarithmically singular at the endpoints. More precisely, if x=0 is an endpoint, then the solution can be expanded as a double power series of the form ∑n=0∞∑m=0∞cn,mxn(xln x)m about x=0 on a small interval x∈(0, a) for some a>0. And third, a high-order adaptive numerical algorithm is designed to compute the solution numerically to high precision. The solutions for the flow velocity u(x;k), the stress Pxy(k), and the half-channel mass flow rate Q(k) are obtained in a wide range of the Knudsen number 0.003≤k≤100.0; and these solutions are accurate for at least twelve significant digits or better, thus they can be used as benchmark solutions. © 2016 Elsevier Inc.


Li W.,Old Dominion University | Luo L.-S.,Computational Science Research Center
Communications in Computational Physics | Year: 2016

A genuine finite volume method based on the lattice Boltzmann equation (LBE) for nearly incompressible flows is developed. The proposed finite volume lattice Boltzmann method (FV-LBM) is grid-transparent, i.e., it requires no knowledge of cell topology, thus it can be implemented on arbitrary unstructured meshes for effective and efficient treatment of complex geometries. Due to the linear advection term in the LBE, it is easy to construct multi-dimensional schemes. In addition, inviscid and viscous fluxes are computed in one step in the LBE, as opposed to in two separate steps for the traditional finite-volume discretization of the Navier-Stokes equations. Because of its conservation constraints, the collision term of the kinetic equation can be treated implicitly without linearization or any other approximation, thus the computational efficiency is enhanced. The collision with multiple-relaxation-time (MRT) model is used in the LBE. The developed FV-LBM is of second-order convergence. The proposed FV-LBM is validated with three test cases in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the Blasius boundary layer; and (c) the steady flow past a cylinder at the Reynolds numbers Re=10, 20, and 40. The results verify the designed accuracy and efficacy of the proposed FV-LBM. Copyright © Global-Science Press 2016.


Yong W.-A.,Tsinghua University | Luo L.-S.,Old Dominion University | Luo L.-S.,Computational Science Research Center
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2012

Based on the theory of asymptotic analysis, we prove that the viscous stress tensor computed with the lattice Boltzmann equation (LBE) in a two-dimensional domain is indeed second-order accurate in space. We only consider simple bounce-back boundary conditions which can be reduced to the periodic boundary conditions by using the method of image. While the LBE with nine velocities on two-dimensional square lattice (i.e., the D2Q9 model) and with the Bhatnagar-Gross-Krook collision model is used as an example in this work, our proof can be extended to the LBE with any linear relaxation collision models in both two and three dimensions. © 2012 American Physical Society.


Luo L.-S.,Old Dominion University | Luo L.-S.,Computational Science Research Center
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2012

This Reply addresses two issues raised in the Comment by Karlin, Succi, and Chikatamarla (KSC): (1) A lattice Boltzmann (LB) model, which is claimed to have an H theorem, is not qualified to be called an entropic lattice Boltzmann equation (ELBE); and (2) the real ELBE with a variable relaxation time performs exceedingly well, as exhibited by their simulations of decaying "Kida vortex" flow in a three-dimensional periodic cube free of no-slip boundary. The first issue is a semantic one. We note that it was Karlin, Succi, and others who "prove the H theorem for lattice Bhatnagar-Gross-Krook models," which is the model we called ELBE in our original study to distinguish it from the usual lattice BGK model without the H theorem. Regardless of how this model is named, it does not affect the results and conclusions of our study in any way. Second, the focus of our original study is to quantify the errors of various LB models near no-slip boundaries. Hence, KSC's example, which is free of no-slip boundaries, is not relevant to our study. The results in our original paper are valid and its conclusions remain unchallenged. On the other hand, KSC's assertion that their real ELBE "provides a reliable subgrid simulation" of turbulence is not substantiated. © 2012 American Physical Society.


Roy Bardhan B.,Louisiana State University | Jiang K.,Louisiana State University | Dowling J.P.,Louisiana State University | Dowling J.P.,Computational Science Research Center
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2013

We study effects of phase fluctuations on phase sensitivity and visibility of a class of robust path-entangled photon Fock states (known as mm' states) as compared to the maximally path-entangled NOON states in the presence of realistic phase fluctuations such as turbulence noise. Our results demonstrate that the mm' states, which are more robust than the NOON state against photon loss, perform equally well when subject to such fluctuations. We derive the quantum Fisher information with the phase-fluctuation noise and show that the phase sensitivity with parity detection for both of the above states saturates the quantum Cramér-Rao bound in the presence of such noise, suggesting that parity detection is an optimal detection strategy. © 2013 American Physical Society.


Motes K.R.,Macquarie University | Dowling J.P.,Louisiana State University | Dowling J.P.,Computational Science Research Center | Rohde P.P.,Macquarie University
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2013

Boson sampling has emerged as a promising avenue towards postclassical optical quantum computation, and numerous elementary demonstrations have recently been performed. Spontaneous parametric down-conversion (SPDC) is the mainstay for single-photon state preparation, the technique employed in most optical quantum information processing implementations to date. Here we present a simple architecture for boson sampling based on multiplexed SPDC sources and demonstrate that the architecture is limited only by the postselection detection efficiency assuming that other errors, such as spectral impurity, dark counts, and interferometric instability, are negligible. For any given number of input photons, there exists a minimum detector efficiency that allows postselection. If this efficiency is achieved, photon-number errors in the SPDC sources are sufficiently low as to guarantee correct boson sampling most of the time. In this scheme, the required detector efficiency must increase exponentially in the photon number. Thus, we show that idealized SPDC sources will not present a bottleneck for future boson-sampling implementations. Rather, photodetection efficiency is the limiting factor, and thus, future implementations may continue to employ SPDC sources. © 2013 American Physical Society.


Roy Bardhan B.,Louisiana State University | Brown K.L.,Louisiana State University | Dowling J.P.,Louisiana State University | Dowling J.P.,Computational Science Research Center
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2013

We address the issue of dephasing effects in flying polarization qubits propagating through optical fiber by using the method of dynamical decoupling. The control pulses are implemented with half-wave plates suitably placed along the realistic lengths of the single-mode optical fiber. The effects of the finite widths of the wave plates on the polarization rotation are modeled using tailored refractive index profiles inside the wave plates. We show that dynamical decoupling is effective in preserving the input qubit state with the fidelity close to unity when the polarization qubit is subject to the random birefringent noise in the fiber, as well the rotational imperfections (flip-angle errors) due to the finite width of the wave plates. © 2013 American Physical Society.


Gard B.T.,Louisiana State University | Cross R.M.,Louisiana State University | Anisimov P.M.,Louisiana State University | Lee H.,Louisiana State University | And 2 more authors.
Journal of the Optical Society of America B: Optical Physics | Year: 2013

We show a simulation of quantum random walks (QRWs) with multiple photons using a staggered array of 50/50 beam splitters with a bank of detectors at any desired level. We discuss the multiphoton interference effects that are inherent to this setup, and introduce one, two, and threefold coincidence detection schemes. Feynman diagrams are used to intuitively explain the unique multiphoton interference effects of these QRWs. © 2013 Optical Society of America.


Seshadreesan K.P.,Louisiana State University | Olson J.P.,Louisiana State University | Motes K.R.,Macquarie University | Rohde P.P.,Macquarie University | And 3 more authors.
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2015

Boson sampling is a specific quantum computation, which is likely hard to implement efficiently on a classical computer. The task is to sample the output photon-number distribution of a linear-optical interferometric network, which is fed with single-photon Fock-state inputs. A question that has been asked is if the sampling problems associated with any other input quantum states of light (other than the Fock states) to a linear-optical network and suitable output detection strategies are also of similar computational complexity as boson sampling. We consider the states that differ from the Fock states by a displacement operation, namely the displaced Fock states and the photon-added coherent states. It is easy to show that the sampling problem associated with displaced single-photon Fock states and a displaced photon-number detection scheme is in the same complexity class as boson sampling for all values of displacement. On the other hand, we show that the sampling problem associated with single-photon-added coherent states and the same displaced photon-number detection scheme demonstrates a computational-complexity transition. It transitions from being just as hard as boson sampling when the input coherent amplitudes are sufficiently small to a classically simulatable problem in the limit of large coherent amplitudes. © 2015 American Physical Society.


Gard B.T.,Louisiana State University | Olson J.P.,Louisiana State University | Cross R.M.,University of Rochester | Kim M.B.,Louisiana State University | And 3 more authors.
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2014

Aaronson and Arkhipov recently used computational complexity theory to argue that classical computers very likely cannot efficiently simulate linear, multimode, quantum-optical interferometers with arbitrary Fock-state inputs [Aaronson and Arkhipov, Theory Comput. 9, 143 (2013)1557-286210.4086/toc.2013. v009a004]. Here we present an elementary argument that utilizes only techniques from quantum optics. We explicitly construct the Hilbert space for such an interferometer and show that its dimension scales exponentially with all the physical resources. We also show in a simple example just how the Schrödinger and Heisenberg pictures of quantum theory, while mathematically equivalent, are not in general computationally equivalent. Finally, we conclude our argument by comparing the symmetry requirements of multiparticle bosonic to fermionic interferometers and, using simple physical reasoning, connect the nonsimulatability of the bosonic device to the complexity of computing the permanent of a large matrix. © 2014 American Physical Society.

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