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physics.comp-ph

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preprint2013arXiv

Fast computation of computer-generated hologram using Xeon Phi coprocessor

We report fast computation of computer-generated holograms (CGHs) using Xeon Phi coprocessors, which have massively x86-based processors on one chip, recently released by Intel. CGHs can generate arbitrary light wavefronts, and therefore, are promising technology for many applications: for example, three-dimensional displays, diffractive optical elements, and the generation of arbitrary beams. CGHs incur enormous computational cost. In this paper, we describe the implementations of several CGH generating algorithms on the Xeon Phi, and the comparisons in terms of the performance and the ease of programming between the Xeon Phi, a CPU and graphics processing unit (GPU).

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preprint2016arXiv

On the equivalence between the Scheduled Relaxation Jacobi method and Richardson's non-stationary method

The Scheduled Relaxation Jacobi (SRJ) method is an extension of the classical Jacobi iterative method to solve linear systems of equations ($Au=b$) associated with elliptic problems. It inherits its robustness and accelerates its convergence rate computing a set of $P$ relaxation factors that result from a minimization problem. In a typical SRJ scheme, the former set of factors is employed in cycles of $M$ consecutive iterations until a prescribed tolerance is reached. We present the analytic form for the optimal set of relaxation factors for the case in which all of them are different, and find that the resulting algorithm is equivalent to a non-stationary generalized Richardson's method. Our method to estimate the weights has the advantage that the explicit computation of the maximum and minimum eigenvalues of the matrix $A$ is replaced by the (much easier) calculation of the maximum and minimum frequencies derived from a von Neumann analysis. This set of weights is also optimal for the general problem, resulting in the fastest convergence of all possible SRJ schemes for a given grid structure. We also show that with the set of weights computed for the optimal SRJ scheme for

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preprint2016arXiv

Systematic parameter inference in stochastic mesoscopic modeling

We propose a method to efficiently determine the optimal coarse-grained force field in mesoscopic stochastic simulations of Newtonian fluid and polymer melt systems modeled by dissipative particle dynamics (DPD) and energy conserving dissipative particle dynamics (eDPD). The response surfaces of various target properties (viscosity, diffusivity, pressure, etc.) with respect to model parameters are constructed based on the generalized polynomial chaos (gPC) expansion using simulation results on sampling points (e.g., individual parameter sets). To alleviate the computational cost to evaluate the target properties, we employ the compressive sensing method to compute the coefficients of the dominant gPC terms given the prior knowledge that the coefficients are sparse. The proposed method shows comparable accuracy with the standard probabilistic collocation method (PCM) while it imposes a much weaker restriction on the number of the simulation samples especially for systems with high dimensional parametric space. Fully access to the response surfaces within the confidence range enables us to infer the optimal force parameters given the desirable values of target properties at the macro

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preprint2013arXiv

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm

A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen, Chacon, Barnes, J. Comput. Phys. 230 (2011) 7018). The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation of Maxwell's equations, which avoids radiative aliasing noise issues by ordering out the light wave. An implicit, orbit-averaged time-space-centered finite difference scheme is applied to both the 1D Darwin field equations (in potential form) and the 1D-3V particle orbit equations to produce a discrete system that remains exactly charge- and energy-conserving. Furthermore, enabled by the implicit Darwin equations, exact conservation of the canonical momentum per particle in any ignorable direction is enforced via a suitable scattering rule for the magnetic field. Several 1D numerical experiments demonstrate the accuracy and the conservation properties of the algorithm.

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preprint2016arXiv

SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Isolated clusters

As the first component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory (DFT) for isolated clusters. Specifically, utilizing a local reformulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local component of the force, we develop a framework using the finite-difference representation that enables the efficient evaluation of energies and atomic forces to within the desired accuracies in DFT. Through selected examples consisting of a variety of elements, we demonstrate that SPARC obtains exponential convergence in energy and forces with domain size; systematic convergence in the energy and forces with mesh-size to reference plane-wave result at comparably high rates; forces that are consistent with the energy, both free from any noticeable `egg-box' effect; and accurate ground-state properties including equilibrium geometries and vibrational spectra. In addition, for systems consisting up to thousands of electrons, SPARC displays weak and strong parallel scalin

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preprint2016arXiv

Strain effect engineered in α-Al2O3/monolayer MoS2 interface by first principle calculations

With the advances in low dimensional transition metal dichalcolgenides (TMDCs) based metal oxide semiconductor field effect transistor (MOSFET), the interface between semiconductors and dielectrics has received considerable attention due to its dramatic effects on the morphology and charge transport of semiconductors. In this study, first principle calculations were utilized to investigate the strain effect induced by the interface between Al2O3 (0001) and monolayer MoS2. The results indicate that Al2O3 in 1.3nm thickness can apply the strain of 0.3% on MoS2 monolayer. The strain effect monotonically increases with the larger thickness of the dielectric layer. Also, the study on temperature effect indicates the monotonic lattice expansion induced by the higher temperature. Our study proposes that the dielectric engineering can be an effective tool for strain effect in the nanotechnology.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

A unified operator splitting approach for multi-scale fluid-particle coupling in the lattice Boltzmann method

A unified framework to derive discrete time-marching schemes for coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order time-accurate schemes for the immersed boundary method, viscous force coupling and external boundary force are derived. Furthermore, a modified formulation of the external boundary force is introduced that leads to a more accurate no-slip boundary condition. The derivation also reveals that the coupling methods can be cast into a unified form, and that the immersed boundary method can be interpreted as the limit of force coupling for vanishing particle mass. In practice, the ratio between fluid and particle mass determines the strength of the force transfer in the coupling. The integration schemes formally improve the accuracy of first-order algorithms that are commonly employed when coupling immersed objects to a lattice Boltzmann fluid. It is anticipated that they will also lead to superior long-time stability in simulations of complex fluids with multiple scales.

0 citations0 reviewsNo code linkedOpen access
preprint2017arXiv

Mathematical and numerical validation of the simplified spherical harmonics approach for time-dependent anisotropic-scattering transport problems in homogeneous media

In this work, we extend the solid harmonics derivation, which was used by Ackroyd et al to derive the steady-state SP$_N$ equations, to transient problems. The derivation expands the angular flux in ordinary surface harmonics but uses harmonic polynomials to generate additional surface spherical harmonic terms to be used in Galerkin projection. The derivation shows the equivalence between the SP$_N$ and the P$_N$ approximation. Also, we use the line source problem and McClarren's "box" problem to demonstrate such equivalence numerically. Both problems were initially proposed for isotropic scattering, but here we add higher-order scattering moments to them. Results show that the difference between the SP$_N$ and P$_N$ scalar flux solution is at the roundoff level.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Dynamics of ferrofluidic flow in the Taylor-Couette system with a small aspect ratio

We investigate fundamental nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined between two concentric independently rotating cylinders - consider small aspect ratio by solving the ferrohydrodynamical equations, carrying out systematic bifurcation analysis. Without magnetic field, we find steady flow patterns, previously observed with a simple fluid, such as those containing normal one- or two vortex cells, as well as anomalous one-cell and twin-cell flow states. However, when a symmetry-breaking transverse magnetic field is present, all flow states exhibit stimulated, finite two-fold mode. Various bifurcations between steady and unsteady states can occur, corresponding to the transitions between the two-cell and one-cell states. While unsteady, axially oscillating flow states can arise, we also detect the emergence of new unsteady flow states. In particular, we uncover two new states: one contains only the azimuthally oscillating solution in the configuration of the twin-cell flow state, and another a rotating flow state. Topologically, these flow states are a limit cycle and a quasiperiodic solution on a two-torus, respectively. Emergence of new flow states in a

0 citations0 reviewsNo code linkedOpen access
preprint2017arXiv

Monte Carlo Study of Temperature-dependent Non-diffusive Thermal Transport in Si Nanowires

Non-diffusive thermal transport has gained extensive research interest recently due to its important implications on fundamental understanding of material phonon mean free path distributions and many nanoscale energy applications. In this work, we systematically investigate the role of boundary scattering and nanowire length on the nondiffusive thermal transport in thin silicon nanowires by rigorously solving the phonon Boltzmann transport equation using a variance reduced Monte Carlo technique across a range of temperatures. The simulations use the complete phonon dispersion and spectral lifetime data obtained from first-principle density function theory calculations as input without any adjustable parameters. Our BTE simulation results show that the nanowire length plays an important role in determining the thermal conductivity of silicon nanowires. In addition, our simulation results suggest significant phonon confinement effect for the previously measured silicon nanowires. These findings are important for a comprehensive understanding of microscopic non-diffusive thermal transport in silicon nanowires.

0 citations0 reviewsNo code linkedOpen access
preprint2017arXiv

Searching chaotic saddles in high dimensions

We propose new methods to numerically approximate non-attracting sets governing transiently-chaotic systems. Trajectories starting in a vicinity $Ω$ of these sets escape $Ω$ in a finite time $τ$ and the problem is to find initial conditions ${\bf x} \in Ω$ with increasingly large $τ= τ({\bf x})$. We search points ${\bf x}'$ with $τ({\bf x}')>τ({\bf x})$ in a {\it search domain} in $Ω$. Our first method considers a search domain with size that decreases exponentially in $τ$, with an exponent proportional to the largest Lyapunov exponent $λ_1$. Our second method considers anisotropic search domains in the {\it tangent} unstable manifold, where each direction scale as the inverse of the corresponding {\it expanding} singular value of the Jacobian matrix of the iterated map. We show that both methods outperform the state-of-the-art {\it Stagger-and-Step} method (Sweet, Nusse, and York, Phys. Rev. Lett. {\bf 86}, 2261, 2001) but that only the anisotropic method achieves an efficiency independent of $τ$ for the case of high-dimensional systems with multiple positive Lyapunov exponents. We perform simulations in a chain of coupled Hénon maps in up to 24 dimensions ($12$ positive L

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Large influence of capping layers on tunnel magnetoresistance in magnetic tunnel junctions

It has been reported in experiments that capping layers which enhance the perpendicular magnetic anisotropy (PMA) of magnetic tunnel junctions (MTJs) induce great impact on the tunnel magnetoresistance (TMR). To explore the essential influence caused by capping layers, we carry out ab initio calculations on TMR in the X(001)|CoFe(001)|MgO(001)|CoFe(001)|X(001) MTJ, where X represents the capping layer material which can be tungsten, tantalum or hafnium. We report TMR in different MTJs and demonstrate that tungsten is an ideal candidate for a giant TMR ratio. The transmission spectrum in Brillouin zone is presented. It can be seen that in the parallel condition of MTJ, sharp transmission peaks appear in the minority-spin channel. This phenomenon is attributed to the resonant tunnel transmission effect and we explained it by the layer-resolved density of states (DOS). In order to explore transport properties in MTJs, the density of scattering states (DOSS) was studied from the point of band symmetry. It has been found that CoFe|tungsten interface blocks scattering states transmission in the anti-parallel condition. This work reports TMR and transport properties in MTJs with different

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Scaling of the dynamics of flexible Lennard-Jones chains. II. Effects of harmonic bonds

The previous paper [Veldhorst et al., J. Chem. Phys. 141, 054904 (2014)] demonstrated that the isomorph theory explains the scaling properties of a liquid of flexible chains consisting of ten Lennard-Jones particles connected by rigid bonds. We here investigate the same model with harmonic bonds. The introduction of harmonic bonds almost completely destroys the correlations in the equilibrium fluctuations of the potential energy and the virial. According to the isomorph theory, if these correlations are strong a system has isomorphs, curves in the phase diagram along which structure, dynamics and the excess entropy are invariant. The Lennard-Jones chain liquid with harmonic bonds does have curves in the phase diagram along which the structure and dynamics are invariant. The excess entropy is not invariant on these curves, which we refer to as "pseudoisomorphs". In particular this means that Rosenfeld's excess-entropy scaling (the dynamics being a function of excess entropy only) does not apply for the Lennard-Jones chain with harmonic bonds.

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preprint2009arXiv

A Double Layer Electromagnetic Cloak And GL EM Modeling

In this paper, we propose a novel electromagnetic (EM) cloaking structure that consists of two annular layers between three spherical shells and model its performance numerically and theoretically by using a Global and Local EM field (GL) method. The two annular layers contain distinct cloaking materials: the outer layer provides invisibility; the inner layer is fully absorbing. The cloaking materials are weakly degenerative. The wavefield from an EM source located outside the cloak propagates as in free space outside the outer shell, never be disturbed by the cloak and does not penetrate into the inner absorbing layer and concealment. The field of a source located inside inner layer or the cloaked concealment is completely absorbed by the inner layer and never reaches the outside of the middle shell, Moreover, the EM wavefield excited in concealment is not disrupted by the cloak. There exists no Maxwell EM wavefield can be excited in a single layer cloaked concealment which is filled by normal material. Moreover, we find a negative dielectric and positive susceptibility metamaterial to fill into the concealment, such that the interior EM wave propagates from the concealment to fre

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preprint2016arXiv

A finite element approach to self-consistent field theory calculations of multiblock polymers

Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibrium polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected compl

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preprint2017arXiv

Irreversible Markov chain Monte Carlo algorithm for self-avoiding walk

We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk (SAW), which violates the detailed balance condition and satisfies the balance condition. Its performance improves significantly compared to that of the Berretti-Sokal algorithm, which is a variant of the Metropolis-Hastings method. The gained efficiency increases with the spatial dimension (D), from approximately $10$ times in 2D to approximately $40$ times in 5D. We simulate the SAW on a 5D hypercubic lattice with periodic boundary conditions, for a system with a linear size up to $L=128$, and confirm that as for the 5D Ising model, the finite-size scaling of the SAW is governed by renormalized exponents $ν^*=2/d$ and $γ/ν^*=d/2$. The critical point is determined, which is approximately $8$ times more precise than the best available estimate.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

ProMC: Input-output data format for HEP applications using varint encoding

A new data format for Monte Carlo (MC) events, or any structural data, including experimental data, is discussed. The format is designed to store data in a compact binary form using variable-size integer encoding as implemented in the Google's Protocol Buffers package. This approach is implemented in the ProMC library which produces smaller file sizes for MC records compared to the existing input-output libraries used in high-energy physics (HEP). Other important features of the proposed format are a separation of abstract data layouts from concrete programming implementations, self-description and random access. Data stored in ProMC files can be written, read and manipulated in a number of programming languages, such C++, JAVA, FORTRAN and PYTHON.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.

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preprint2014arXiv

A rigorous sequential update strategy for parallel kinetic Monte Carlo simulation

The kinetic Monte Carlo (kMC) method is used in many scientific fields in applications involving rare-event transitions. Due to its discrete stochastic nature, efforts to parallelize kMC approaches often produce unbalanced time evolutions requiring complex implementations to ensure correct statistics. In the context of parallel kMC, the sequential update technique has shown promise by generating high quality distributions with high relative efficiencies for short-range systems. In this work, we provide an extension of the sequential update method in a parallel context that rigorously obeys detailed balance, which guarantees exact equilibrium statistics for all parallelization settings. Our approach also preserves nonequilibrium dynamics with minimal error for many parallelization settings, and can be used to achieve highly precise sampling.

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preprint2016arXiv

A first principles TDDFT framework for spin and time-resolved ARPES in periodic systems

We present a novel theoretical approach to simulate spin, time and angular-resolved photoelectron spectroscopy (ARPES) from first principles that is applicable to surfaces, thin films, few layer systems, and low-dimensional nanostructures. The method is based on a general formulation in the framework of time-dependent density functional theory (TDDFT) to describe the real time-evolution of electrons escaping from a surface under the effect of any external (arbitrary) laser field. By extending the so called t-SURFF method to periodic systems one can calculate the final photoelectron spectrum by collecting the flux of the ionization current trough an analysing surface. The resulting approach, that we named t-SURFFP, allows to describe a wide range of irradiation conditions without any assumption on the dynamics of the ionization process allowing for pump-probe simulations on an equal footing. To illustrate the wide scope of applicability of the method we present applications to graphene, mono- and bi-layer WSe$_2$, and hexagonal BN under different laser configurations.

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preprint2016arXiv

Hard rectangles near curved hard walls: tuning the sign of the Tolman length

Combining analytic calculations, computer simulations, and classical density functional theory we determine the interfacial tension of orientable two-dimensional hard rectangles near a curved hard wall. Both a circular cavity holding the particles and a hard circular obstacle surrounded by particles are considered. We focus on moderate bulk densities (corresponding to area fractions up to 50 percent) where the bulk phase is isotropic and vary the aspect ratio of the rectangles and the curvature of the wall. The Tolman length, which gives the leading curvature correction of the interfacial tension, is found to change sign at a finite density, which can be tuned via the aspect ratio of the rectangles.

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preprint2016arXiv

Hybrid Adaptive Ray-Moment Method (HARM$^2$): A Highly Parallel Method for Radiation Hydrodynamics on Adaptive Grids

We present a highly-parallel multi-frequency hybrid radiation hydrodynamics algorithm that combines a spatially-adaptive long characteristics method for the radiation field from point sources with a moment method that handles the diffuse radiation field produced by a volume-filling fluid. Our Hybrid Adaptive Ray-Moment Method (HARM$^2$) operates on patch-based adaptive grids, is compatible with asynchronous time stepping, and works with any moment method. In comparison to previous long characteristics methods, we have greatly improved the parallel performance of the adaptive long-characteristics method by developing a new completely asynchronous and non-blocking communication algorithm. As a result of this improvement, our implementation achieves near-perfect scaling up to $\mathcal{O}(10^3)$ processors on distributed memory machines. We present a series of tests to demonstrate the accuracy and performance of the method.

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preprint2016arXiv

A partially mesh-free scheme for representing anisotropic spatial variations along field lines

A common numerical task is to represent functions which are highly spatially anisotropic, and to solve differential equations related to these functions. One way such anisotropy arises is that information transfer along one spatial direction is much faster than in others. In this situation, the derivative of the function is small in the local direction of a vector field $\mathbf{b}$. In order to define a discrete representation, a set of surfaces $M_i$ indexed by an integer $i$ are chosen such that mapping along the field $\mathbf{b}$ induces a one-to-one relation between the points on surface $M_i$ to those on $M_{i+1}$. For simple cases $M_i$ may be surfaces of constant coordinate value. On each surface $M_i$, a function description is constructed using basis functions defined on a regular structured mesh. The definition of each basis function is extended from the surface $M$ along the lines of the field $\mathbf{b}$ by multiplying it by a smooth compact support function whose argument increases with distance along $\mathbf{b}$. Function values are evaluated by summing contributions associated with each surface $M_i$. This does not require any special connectivity of the meshes u

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preprint2016arXiv

Coupling sample paths to the partial thermodynamic limit in stochastic chemical reaction networks

Many biochemical systems appearing in applications have a multiscale structure so that they converge to piecewise deterministic Markov processes in a thermodynamic limit. The statistics of the piecewise deterministic process can be obtained much more efficiently than those of the exact process. We explore the possibility of coupling sample paths of the exact model to the piecewise deterministic process in order to reduce the variance of their difference. We then apply this coupling to reduce the computational complexity of a Monte Carlo estimator. In addition to rigorous results concerning the asymptotic computational complexity of the Monte Carlo estimator, numerical simulations are performed on some simple biological models confirming that computational gains are made.

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