Compatible discrete operator schemes on polyhedral meshes for elliptic and Stokes equations

International Nuclear Information System (INIS)

Bonelle, Jerome

2014-01-01

This thesis presents a new class of spatial discretization schemes on polyhedral meshes, called Compatible Discrete Operator (CDO) schemes and their application to elliptic and Stokes equations In CDO schemes, preserving the structural properties of the continuous equations is the leading principle to design the discrete operators. De Rham maps define the degrees of freedom according to the physical nature of fields to discretize. CDO schemes operate a clear separation between topological relations (balance equations) and constitutive relations (closure laws). Topological relations are related to discrete differential operators, and constitutive relations to discrete Hodge operators. A feature of CDO schemes is the explicit use of a second mesh, called dual mesh, to build the discrete Hodge operator. Two families of CDO schemes are considered: vertex-based schemes where the potential is located at (primal) mesh vertices, and cell-based schemes where the potential is located at dual mesh vertices (dual vertices being in one-to-one correspondence with primal cells). The CDO schemes related to these two families are presented and their convergence is analyzed. A first analysis hinges on an algebraic definition of the discrete Hodge operator and allows one to identify three key properties: symmetry, stability, and P0-consistency. A second analysis hinges on a definition of the discrete Hodge operator using reconstruction operators, and the requirements on these reconstruction operators are identified. In addition, CDO schemes provide a unified vision on a broad class of schemes proposed in the literature (finite element, finite element, mimetic schemes... ). Finally, the reliability and the efficiency of CDO schemes are assessed on various test cases and several polyhedral meshes. (author)

Slab geometry spatial discretization schemes with infinite-order convergence

International Nuclear Information System (INIS)

Adams, M.L.; Martin, W.R.

1985-01-01

Spatial discretization schemes for the slab geometry discrete ordinates transport equation have received considerable attention in the past several years, with particular interest shown in developing methods that are more computationally efficient that standard schemes. Here the authors apply to the discrete ordinates equations a spectral method that is significantly more efficient than previously proposed schemes for high-accuracy calculations of homogeneous problems. This is a direct consequence of the exponential (infinite-order) convergence of spectral methods for problems with every smooth solutions. For heterogeneous problems where smooth solutions do not exist and exponential convergence is not observed with spectral methods, a spectral element method is proposed which does exhibit exponential convergence

Space-Time Transformation in Flux-form Semi-Lagrangian Schemes

Directory of Open Access Journals (Sweden)

Peter C. Chu Chenwu Fan

2010-01-01

Full Text Available With a finite volume approach, a flux-form semi-Lagrangian (TFSL scheme with space-time transformation was developed to provide stable and accurate algorithm in solving the advection-diffusion equation. Different from the existing flux-form semi-Lagrangian schemes, the temporal integration of the flux from the present to the next time step is transformed into a spatial integration of the flux at the side of a grid cell (space for the present time step using the characteristic-line concept. The TFSL scheme not only keeps the good features of the semi-Lagrangian schemes (no Courant number limitation, but also has higher accuracy (of a second order in both time and space. The capability of the TFSL scheme is demonstrated by the simulation of the equatorial Rossby-soliton propagation. Computational stability and high accuracy makes this scheme useful in ocean modeling, computational fluid dynamics, and numerical weather prediction.

Discretization of convection-diffusion equations with finite-difference scheme derived from simplified analytical solutions

International Nuclear Information System (INIS)

Kriventsev, Vladimir

2000-09-01

Most of thermal hydraulic processes in nuclear engineering can be described by general convection-diffusion equations that are often can be simulated numerically with finite-difference method (FDM). An effective scheme for finite-difference discretization of such equations is presented in this report. The derivation of this scheme is based on analytical solutions of a simplified one-dimensional equation written for every control volume of the finite-difference mesh. These analytical solutions are constructed using linearized representations of both diffusion coefficient and source term. As a result, the Efficient Finite-Differencing (EFD) scheme makes it possible to significantly improve the accuracy of numerical method even using mesh systems with fewer grid nodes that, in turn, allows to speed-up numerical simulation. EFD has been carefully verified on the series of sample problems for which either analytical or very precise numerical solutions can be found. EFD has been compared with other popular FDM schemes including novel, accurate (as well as sophisticated) methods. Among the methods compared were well-known central difference scheme, upwind scheme, exponential differencing and hybrid schemes of Spalding. Also, newly developed finite-difference schemes, such as the the quadratic upstream (QUICK) scheme of Leonard, the locally analytic differencing (LOAD) scheme of Wong and Raithby, the flux-spline scheme proposed by Varejago and Patankar as well as the latest LENS discretization of Sakai have been compared. Detailed results of this comparison are given in this report. These tests have shown a high efficiency of the EFD scheme. For most of sample problems considered EFD has demonstrated the numerical error that appeared to be in orders of magnitude lower than that of other discretization methods. Or, in other words, EFD has predicted numerical solution with the same given numerical error but using much fewer grid nodes. In this report, the detailed

Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2012-01-01

We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms of the τ function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation. (paper)

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

Science.gov (United States)

Mabuza, Sibusiso; Shadid, John N.; Kuzmin, Dmitri

2018-05-01

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. For time discretization, Crank-Nicolson scheme and backward Euler scheme are utilized.

Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements

Science.gov (United States)

Crean, Jared; Hicken, Jason E.; Del Rey Fernández, David C.; Zingg, David W.; Carpenter, Mark H.

2018-03-01

We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we consider general multidimensional SBP elements, building on and generalizing previous work with tensor-product discretizations. In the absence of dissipation, we prove that the semi-discrete scheme conserves entropy; significantly, this proof of nonlinear L2 stability does not rely on integral exactness. Furthermore, interior penalties can be incorporated into the discretization to ensure that the total (mathematical) entropy decreases monotonically, producing an entropy-stable scheme. SBP discretizations with curved elements remain accurate, conservative, and entropy stable provided the mapping Jacobian satisfies the discrete metric invariants; polynomial mappings at most one degree higher than the SBP operators automatically satisfy the metric invariants in two dimensions. In three-dimensions, we describe an elementwise optimization that leads to suitable Jacobians in the case of polynomial mappings. The properties of the semi-discrete scheme are verified and investigated using numerical experiments.

A discrete-time adaptive control scheme for robot manipulators

Science.gov (United States)

Tarokh, M.

1990-01-01

A discrete-time model reference adaptive control scheme is developed for trajectory tracking of robot manipulators. The scheme utilizes feedback, feedforward, and auxiliary signals, obtained from joint angle measurement through simple expressions. Hyperstability theory is utilized to derive the adaptation laws for the controller gain matrices. It is shown that trajectory tracking is achieved despite gross robot parameter variation and uncertainties. The method offers considerable design flexibility and enables the designer to improve the performance of the control system by adjusting free design parameters. The discrete-time adaptation algorithm is extremely simple and is therefore suitable for real-time implementation. Simulations and experimental results are given to demonstrate the performance of the scheme.

Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids

KAUST Repository

Chen, Huangxin

2017-09-01

In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i.e., the linear implicit scheme for time discretization with the finite difference method (FDM) on staggered grids for spatial discretization, pressure-correction schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations, and pressure-stabilization schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations. The energy stability estimates are obtained for the above each fully discrete scheme. The upwind scheme is used in the discretization of the convection term which plays an important role in the design of unconditionally stable discrete schemes. Numerical results are given to verify the theoretical analysis.

A discrete variational identity on semi-direct sums of Lie algebras

Energy Technology Data Exchange (ETDEWEB)

M, Wenxiu [Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700 (United States)

2007-12-14

The discrete variational identity under general bilinear forms on semi-direct sums of Lie algebras is established. The constant {gamma} involved in the variational identity is determined through the corresponding solution to the stationary discrete zero-curvature equation. An application of the resulting variational identity to a class of semi-direct sums of Lie algebras in the Volterra lattice case furnishes Hamiltonian structures for the associated integrable couplings of the Volterra lattice hierarchy.

A discrete variational identity on semi-direct sums of Lie algebras

International Nuclear Information System (INIS)

M, Wenxiu

2007-01-01

The discrete variational identity under general bilinear forms on semi-direct sums of Lie algebras is established. The constant γ involved in the variational identity is determined through the corresponding solution to the stationary discrete zero-curvature equation. An application of the resulting variational identity to a class of semi-direct sums of Lie algebras in the Volterra lattice case furnishes Hamiltonian structures for the associated integrable couplings of the Volterra lattice hierarchy

A semi-discrete integrable multi-component coherently coupled nonlinear Schrödinger system

International Nuclear Information System (INIS)

Zhao, Hai-qiong; Yuan, Jinyun

2016-01-01

A new integrable semi-discrete version is proposed for the multi-component coherently coupled nonlinear Schrödinger equation. The integrability of the semi-discrete system is confirmed by existence of Lax pair and infinite number of conservation laws. With the aid of gauge transformations, explicit formulas for N -fold Darboux transformations are derived whereby some physically important solutions of the system are presented. Furthermore, the theory of the semi-discrete system including Lax pair, Darboux transformations, exact solutions and infinite number of conservation laws are shown for their continuous counterparts in the continuous limit. (paper)

Asynchronous discrete event schemes for PDEs

Science.gov (United States)

Stone, D.; Geiger, S.; Lord, G. J.

2017-08-01

A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations is introduced, based on the principle of allowing quanta of mass to pass through faces of a (regular, structured) Cartesian finite volume grid. The timescales of these events are linked to the flux on the face. The resulting schemes are self-adaptive, and local in both time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate reference solutions where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased, and we outline a framework for analysis.

Third Order Reconstruction of the KP Scheme for Model of River Tinnelva

Directory of Open Access Journals (Sweden)

Susantha Dissanayake

2017-01-01

Full Text Available The Saint-Venant equation/Shallow Water Equation is used to simulate flow of river, flow of liquid in an open channel, tsunami etc. The Kurganov-Petrova (KP scheme which was developed based on the local speed of discontinuity propagation, can be used to solve hyperbolic type partial differential equations (PDEs, hence can be used to solve the Saint-Venant equation. The KP scheme is semi discrete: PDEs are discretized in the spatial domain, resulting in a set of Ordinary Differential Equations (ODEs. In this study, the common 2nd order KP scheme is extended into 3rd order scheme while following the Weighted Essentially Non-Oscillatory (WENO and Central WENO (CWENO reconstruction steps. Both the 2nd order and 3rd order schemes have been used in simulation in order to check the suitability of the KP schemes to solve hyperbolic type PDEs. The simulation results indicated that the 3rd order KP scheme shows some better stability compared to the 2nd order scheme. Computational time for the 3rd order KP scheme for variable step-length ode solvers in MATLAB is less compared to the computational time of the 2nd order KP scheme. In addition, it was confirmed that the order of the time integrators essentially should be lower compared to the order of the spatial discretization. However, for computation of abrupt step changes, the 2nd order KP scheme shows a more accurate solution.

A Spatial Discretization Scheme for Solving the Transport Equation on Unstructured Grids of Polyhedra

International Nuclear Information System (INIS)

Thompson, K.G.

2000-01-01

In this work, we develop a new spatial discretization scheme that may be used to numerically solve the neutron transport equation. This new discretization extends the family of corner balance spatial discretizations to include spatial grids of arbitrary polyhedra. This scheme enforces balance on subcell volumes called corners. It produces a lower triangular matrix for sweeping, is algebraically linear, is non-negative in a source-free absorber, and produces a robust and accurate solution in thick diffusive regions. Using an asymptotic analysis, we design the scheme so that in thick diffusive regions it will attain the same solution as an accurate polyhedral diffusion discretization. We then refine the approximations in the scheme to reduce numerical diffusion in vacuums, and we attempt to capture a second order truncation error. After we develop this Upstream Corner Balance Linear (UCBL) discretization we analyze its characteristics in several limits. We complete a full diffusion limit analysis showing that we capture the desired diffusion discretization in optically thick and highly scattering media. We review the upstream and linear properties of our discretization and then demonstrate that our scheme captures strictly non-negative solutions in source-free purely absorbing media. We then demonstrate the minimization of numerical diffusion of a beam and then demonstrate that the scheme is, in general, first order accurate. We also note that for slab-like problems our method actually behaves like a second-order method over a range of cell thicknesses that are of practical interest. We also discuss why our scheme is first order accurate for truly 3D problems and suggest changes in the algorithm that should make it a second-order accurate scheme. Finally, we demonstrate 3D UCBL's performance on several very different test problems. We show good performance in diffusive and streaming problems. We analyze truncation error in a 3D problem and demonstrate robustness in a

Commutativity of the source generation procedure and integrable semi-discretizations: the two-dimensional Leznov lattice

International Nuclear Information System (INIS)

Hu Juan; Yu Guofu; Tam, Hon-Wah

2012-01-01

The source generation procedure (SGP) is applied to a y-directional discrete version and an x-directional discrete version of the Leznov lattice. Consequently, a y-discrete Leznov lattice equation with self-consistent sources (y-discrete Leznov ESCS) and an x-discrete Leznov ESCS are presented. Also utilizing the SGP, a new type of Leznov lattice equation with self-consistent sources (new Leznov ESCS) is derived. It is interesting that the two semi-discrete Leznov ESCS produced constitute a y-discretization for the Leznov ESCS given by Wang et al (2007 J. Phys. A: Math. Theor. 40 12691) and an x-discretization for the new Leznov ESCS, respectively. This means that the commutativity of SGP and integrable semi-discretizations is valid for the two-dimensional Leznov lattice equation. (paper)

Finite-element semi-discretization of linearized compressible and resistive MHD

International Nuclear Information System (INIS)

Kerner, W.; Jakoby, A.; Lerbinger, K.

1985-08-01

The full resistive MHD equations are linearized around an equilibrium with cylindrical symmetry and solved numerically as an initial-value problem. The semi-discretization using cubic and quadratic finite elements for the spatial discretization and a fully implicit time advance yields very accurate results even for small values of the resistivity. In the application different phenomena such as waves, resistive instabilities and overstable modes are addressed. (orig.)

Integrable lattices and their sublattices: From the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme

International Nuclear Information System (INIS)

Doliwa, A.; Grinevich, P.; Nieszporski, M.; Santini, P. M.

2007-01-01

We present the sublattice approach, a procedure to generate, from a given integrable lattice, a sublattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point equation and its sublattice, the self-adjoint 5-point scheme on the star of the square lattice, which are relevant in the theory of the integrable discrete geometries and in the theory of discrete holomorphic and harmonic functions (in this last context, the discrete Moutard equation is called discrete Cauchy-Riemann equation). Therefore an integrable, at one energy, discretization of elliptic two-dimensional operators is considered. We use the sublattice point of view to derive, from the Darboux transformations and superposition formulas of the discrete Moutard equation, the Darboux transformations and superposition formulas of the self-adjoint 5-point scheme. We also construct, from algebro-geometric solutions of the discrete Moutard equation, algebro-geometric solutions of the self-adjoint 5-point scheme. In particular, we show that the corresponding restrictions on the finite-gap data are of the same type as those for the fixed energy problem for the two-dimensional Schroedinger operator. We finally use these solutions to construct explicit examples of discrete holomorphic and harmonic functions, as well as examples of quadrilateral surfaces in R 3

The approximate inverse in action: IV. Semi-discrete equations in a Banach space setting

International Nuclear Information System (INIS)

Schuster, T; Schöpfer, F; Rieder, A

2012-01-01

This article concerns the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search for a solution in an infinite-dimensional Banach space having only a finite number of data available. In this sense the situation is applicable to a large variety of applications where a measurement process delivers a discretization of an infinite-dimensional data space. The method of approximate inverse computes scalar products of the data with pre-computed reconstruction kernels which are associated with mollifiers and the dual of the model operator. The convergence, approximation power and regularization property of this method when applied to semi-discrete operator equations in Hilbert spaces has been investigated in three prequels to this paper. Here we extend these results to a Banach space setting. We prove convergence and stability for general Banach spaces and reproduce the results specifically for the integration operator acting on the space of continuous functions. (paper)

Semi-quantum Secure Direct Communication Scheme Based on Bell States

Science.gov (United States)

Xie, Chen; Li, Lvzhou; Situ, Haozhen; He, Jianhao

2018-06-01

Recently, the idea of semi-quantumness has been often used in designing quantum cryptographic schemes, which allows some of the participants of a quantum cryptographic scheme to remain classical. One of the reasons why this idea is popular is that it allows a quantum information processing task to be accomplished by using quantum resources as few as possible. In this paper, we extend the idea to quantum secure direct communication(QSDC) by proposing a semi-quantum secure direct communication scheme. In the scheme, the message sender, Alice, encodes each bit into a Bell state |φ+> = 1/{√2}(|00> +|11> ) or |{Ψ }+> = 1/{√ 2}(|01> +|10> ), and the message receiver, Bob, who is classical in the sense that he can either let the qubit he received reflect undisturbed, or measure the qubit in the computational basis |0>, |1> and then resend it in the state he found. Moreover, the security analysis of our scheme is also given.

Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids

KAUST Repository

Chen, Huangxin; Sun, Shuyu; Zhang, Tao

2017-01-01

In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i

Lie Symmetry Analysis of the Inhomogeneous Toda Lattice Equation via Semi-Discrete Exterior Calculus

International Nuclear Information System (INIS)

Liu Jiang; Wang Deng-Shan; Yin Yan-Bin

2017-01-01

In this work, the Lie point symmetries of the inhomogeneous Toda lattice equation are obtained by semi-discrete exterior calculus, which is a semi-discrete version of Harrison and Estabrook’s geometric approach. A four-dimensional Lie algebra and its one-, two- and three-dimensional subalgebras are given. Two similarity reductions of the inhomogeneous Toda lattice equation are obtained by using the symmetry vectors. (paper)

High Order Semi-Lagrangian Advection Scheme

Science.gov (United States)

Malaga, Carlos; Mandujano, Francisco; Becerra, Julian

2014-11-01

In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).

Arbitrary Dimension Convection-Diffusion Schemes for Space-Time Discretizations

Energy Technology Data Exchange (ETDEWEB)

Bank, Randolph E. [Univ. of California, San Diego, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Zikatanov, Ludmil T. [Bulgarian Academy of Sciences, Sofia (Bulgaria)

2016-01-20

This note proposes embedding a time dependent PDE into a convection-diffusion type PDE (in one space dimension higher) with singularity, for which two discretization schemes, the classical streamline-diffusion and the EAFE (edge average finite element) one, are investigated in terms of stability and error analysis. The EAFE scheme, in particular, is extended to be arbitrary order which is of interest on its own. Numerical results, in combined space-time domain demonstrate the feasibility of the proposed approach.

An Efficient, Semi-implicit Pressure-based Scheme Employing a High-resolution Finitie Element Method for Simulating Transient and Steady, Inviscid and Viscous, Compressible Flows on Unstructured Grids

Energy Technology Data Exchange (ETDEWEB)

Richard C. Martineau; Ray A. Berry

2003-04-01

A new semi-implicit pressure-based Computational Fluid Dynamics (CFD) scheme for simulating a wide range of transient and steady, inviscid and viscous compressible flow on unstructured finite elements is presented here. This new CFD scheme, termed the PCICEFEM (Pressure-Corrected ICE-Finite Element Method) scheme, is composed of three computational phases, an explicit predictor, an elliptic pressure Poisson solution, and a semiimplicit pressure-correction of the flow variables. The PCICE-FEM scheme is capable of second-order temporal accuracy by incorporating a combination of a time-weighted form of the two-step Taylor-Galerkin Finite Element Method scheme as an explicit predictor for the balance of momentum equations and the finite element form of a time-weighted trapezoid rule method for the semi-implicit form of the governing hydrodynamic equations. Second-order spatial accuracy is accomplished by linear unstructured finite element discretization. The PCICE-FEM scheme employs Flux-Corrected Transport as a high-resolution filter for shock capturing. The scheme is capable of simulating flows from the nearly incompressible to the high supersonic flow regimes. The PCICE-FEM scheme represents an advancement in mass-momentum coupled, pressurebased schemes. The governing hydrodynamic equations for this scheme are the conservative form of the balance of momentum equations (Navier-Stokes), mass conservation equation, and total energy equation. An operator splitting process is performed along explicit and implicit operators of the semi-implicit governing equations to render the PCICE-FEM scheme in the class of predictor-corrector schemes. The complete set of semi-implicit governing equations in the PCICE-FEM scheme are cast in this form, an explicit predictor phase and a semi-implicit pressure-correction phase with the elliptic pressure Poisson solution coupling the predictor-corrector phases. The result of this predictor-corrector formulation is that the pressure Poisson

Forcing scheme analysis for the axisymmetric lattice Boltzmann method under incompressible limit.

Science.gov (United States)

Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Chen, Jie; Yin, Linmao; Chew, Jia Wei

2017-04-01

Because the standard lattice Boltzmann (LB) method is proposed for Cartesian Navier-Stokes (NS) equations, additional source terms are necessary in the axisymmetric LB method for representing the axisymmetric effects. Therefore, the accuracy and applicability of the axisymmetric LB models depend on the forcing schemes adopted for discretization of the source terms. In this study, three forcing schemes, namely, the trapezium rule based scheme, the direct forcing scheme, and the semi-implicit centered scheme, are analyzed theoretically by investigating their derived macroscopic equations in the diffusive scale. Particularly, the finite difference interpretation of the standard LB method is extended to the LB equations with source terms, and then the accuracy of different forcing schemes is evaluated for the axisymmetric LB method. Theoretical analysis indicates that the discrete lattice effects arising from the direct forcing scheme are part of the truncation error terms and thus would not affect the overall accuracy of the standard LB method with general force term (i.e., only the source terms in the momentum equation are considered), but lead to incorrect macroscopic equations for the axisymmetric LB models. On the other hand, the trapezium rule based scheme and the semi-implicit centered scheme both have the advantage of avoiding the discrete lattice effects and recovering the correct macroscopic equations. Numerical tests applied for validating the theoretical analysis show that both the numerical stability and the accuracy of the axisymmetric LB simulations are affected by the direct forcing scheme, which indicate that forcing schemes free of the discrete lattice effects are necessary for the axisymmetric LB method.

Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site.

Science.gov (United States)

Jason, Peter; Johansson, Magnus

2016-01-01

We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.

A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue

International Nuclear Information System (INIS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2017-01-01

In the present paper, we propose a two-component generalization of the reduced Ostrovsky (Vakhnenko) equation, whose differential form can be viewed as the short-wave limit of a two-component Degasperis–Procesi (DP) equation. They are integrable due to the existence of Lax pairs. Moreover, we have shown that the two-component reduced Ostrovsky equation can be reduced from an extended BKP hierarchy with negative flow through a pseudo 3-reduction and a hodograph (reciprocal) transform. As a by-product, its bilinear form and N -soliton solution in terms of pfaffians are presented. One- and two-soliton solutions are provided and analyzed. In the second part of the paper, we start with a modified BKP hierarchy, which is a Bäcklund transformation of the above extended BKP hierarchy, an integrable semi-discrete analogue of the two-component reduced Ostrovsky equation is constructed by defining an appropriate discrete hodograph transform and dependent variable transformations. In particular, the backward difference form of above semi-discrete two-component reduced Ostrovsky equation gives rise to the integrable semi-discretization of the short wave limit of a two-component DP equation. Their N -soliton solutions in terms of pffafians are also provided. (paper)

Normal scheme for solving the transport equation independently of spatial discretization

International Nuclear Information System (INIS)

Zamonsky, O.M.

1993-01-01

To solve the discrete ordinates neutron transport equation, a general order nodal scheme is used, where nodes are allowed to have different orders of approximation and the whole system reaches a final order distribution. Independence in the election of system discretization and order of approximation is obtained without loss of accuracy. The final equations and the iterative method to reach a converged order solution were implemented in a two-dimensional computer code to solve monoenergetic, isotropic scattering, external source problems. Two benchmark problems were solved using different automatic selection order methods. Results show accurate solutions without spatial discretization, regardless of the initial selection of distribution order. (author)

Implicit and semi-implicit schemes in the Versatile Advection Code : numerical tests

NARCIS (Netherlands)

Tóth, G.; Keppens, R.; Bochev, Mikhail A.

1998-01-01

We describe and evaluate various implicit and semi-implicit time integration schemes applied to the numerical simulation of hydrodynamical and magnetohydrodynamical problems. The schemes were implemented recently in the software package Versatile Advection Code, which uses modern shock capturing

Nonparametric Estimation of Interval Reliability for Discrete-Time Semi-Markov Systems

DEFF Research Database (Denmark)

Georgiadis, Stylianos; Limnios, Nikolaos

2016-01-01

In this article, we consider a repairable discrete-time semi-Markov system with finite state space. The measure of the interval reliability is given as the probability of the system being operational over a given finite-length time interval. A nonparametric estimator is proposed for the interval...

Distortional solutions for loaded semi-discretized thin-walled beams

DEFF Research Database (Denmark)

Andreassen, Michael Joachim; Jönsson, Jeppe

2012-01-01

distortional displacement fields which decouple the reduced order differential equations. In this process the cross section is discretized into finite cross-section elements, and the natural distortional modes as well as the related axial variations are found as solutions to the established coupled fourth...... order homogeneous differential equations of GBT.In this paper the non-homogeneous distortional differential equations of GBT are formulated using this novel semi-discretization process. Transforming these non-homogeneous distortional differential equations into the natural eigenmode space by using...... the distortional modal matrix found for the homogeneous system, we get the uncoupled set of differential equations including the distributed loads. This uncoupling is very important in GBT, since the shear stiffness contribution from St. Venant torsional shear stress as well as “Bredt's shear flow” cannot...

Lie Symmetry Analysis of the Inhomogeneous Toda Lattice Equation via Semi-Discrete Exterior Calculus

Science.gov (United States)

Liu, Jiang; Wang, Deng-Shan; Yin, Yan-Bin

2017-06-01

In this work, the Lie point symmetries of the inhomogeneous Toda lattice equation are obtained by semi-discrete exterior calculus, which is a semi-discrete version of Harrison and Estabrook’s geometric approach. A four-dimensional Lie algebra and its one-, two- and three-dimensional subalgebras are given. Two similarity reductions of the inhomogeneous Toda lattice equation are obtained by using the symmetry vectors. Supported by National Natural Science Foundation of China under Grant Nos. 11375030, 11472315, and Department of Science and Technology of Henan Province under Grant No. 162300410223 and Beijing Finance Funds of Natural Science Program for Excellent Talents under Grant No. 2014000026833ZK19

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

OpenAIRE

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres

2007-01-01

Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller–Pearce–White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which res...

A Price-Based Demand Response Scheme for Discrete Manufacturing in Smart Grids

Directory of Open Access Journals (Sweden)

Zhe Luo

2016-08-01

Full Text Available Demand response (DR is a key technique in smart grid (SG technologies for reducing energy costs and maintaining the stability of electrical grids. Since manufacturing is one of the major consumers of electrical energy, implementing DR in factory energy management systems (FEMSs provides an effective way to manage energy in manufacturing processes. Although previous studies have investigated DR applications in process manufacturing, they were not conducted for discrete manufacturing. In this study, the state-task network (STN model is implemented to represent a discrete manufacturing system. On this basis, a DR scheme with a specific DR algorithm is applied to a typical discrete manufacturing—automobile manufacturing—and operational scenarios are established for the stamping process of the automobile production line. The DR scheme determines the optimal operating points for the stamping process using mixed integer linear programming (MILP. The results show that parts of the electricity demand can be shifted from peak to off-peak periods, reducing a significant overall energy costs without degrading production processes.

Pressure correction schemes for compressible flows

International Nuclear Information System (INIS)

Kheriji, W.

2011-01-01

This thesis is concerned with the development of semi-implicit fractional step schemes, for the compressible Navier-Stokes equations; these schemes are part of the class of the pressure correction methods. The chosen spatial discretization is staggered: non conforming mixed finite elements (Crouzeix-Raviart or Rannacher-Turek) or the classic MA C scheme. An upwind finite volume discretization of the mass balance guarantees the positivity of the density. The positivity of the internal energy is obtained by discretizing the internal energy balance by an upwind finite volume scheme and b y coupling the discrete internal energy balance with the pressure correction step. A special finite volume discretization on dual cells is performed for the convection term in the momentum balance equation, and a renormalisation step for the pressure is added to the algorithm; this ensures the control in time of the integral of the total energy over the domain. All these a priori estimates imply the existence of a discrete solution by a topological degree argument. The application of this scheme to Euler equations raises an additional difficulty. Indeed, obtaining correct shocks requires the scheme to be consistent with the total energy balance, property which we obtain as follows. First of all, a local discrete kinetic energy balance is established; it contains source terms winch we somehow compensate in the internal energy balance. The kinetic and internal energy equations are associated with the dual and primal meshes respectively, and thus cannot be added to obtain a total energy balance; its continuous counterpart is however recovered at the limit: if we suppose that a sequence of discrete solutions converges when the space and time steps tend to 0, we indeed show, in 1D at least, that the limit satisfies a weak form of the equation. These theoretical results are comforted by numerical tests. Similar results are obtained for the baro-tropic Navier-Stokes equations. (author)

Cryptanalysis of a semi-quantum secret sharing scheme based on Bell states

Science.gov (United States)

Gao, Gan; Wang, Yue; Wang, Dong

2018-03-01

In the paper [Mod. Phys. Lett. B 31 (2017) 1750150], Yin et al. proposed a semi-quantum secret sharing scheme by using Bell states. We find that the proposed scheme cannot finish the quantum secret sharing task. In addition, we also find that the proposed scheme has a security loophole, that is, it will not be detected that the dishonest participant, Charlie attacks on the quantum channel.

Spectral collocation method with a flexible angular discretization scheme for radiative transfer in multi-layer graded index medium

Science.gov (United States)

Wei, Linyang; Qi, Hong; Sun, Jianping; Ren, Yatao; Ruan, Liming

2017-05-01

The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional SN discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.

An extended discrete gradient formula for oscillatory Hamiltonian systems

International Nuclear Information System (INIS)

Liu Kai; Shi Wei; Wu Xinyuan

2013-01-01

In this paper, incorporating the idea of the discrete gradient method into the extended Runge–Kutta–Nyström integrator, we derive and analyze an extended discrete gradient formula for the oscillatory Hamiltonian system with the Hamiltonian H(p,q)= 1/2 p T p+ 1/2 q T Mq+U(q), where q:R→R d represents generalized positions, p:R→R d represents generalized momenta and M is an element of R dxd is a symmetric and positive semi-definite matrix. The solution of this system is a nonlinear oscillator. Basically, many nonlinear oscillatory mechanical systems with a partitioned Hamiltonian function lend themselves to this approach. The extended discrete gradient formula presented in this paper exactly preserves the energy H(p, q). We derive some properties of the new formula. The convergence is analyzed for the implicit schemes based on the discrete gradient formula, and it turns out that the convergence of the implicit schemes based on the extended discrete gradient formula is independent of ‖M‖, which is a significant property for the oscillatory Hamiltonian system. Thus, it transpires that a larger step size can be chosen for the new energy-preserving schemes than that for the traditional discrete gradient methods when applied to the oscillatory Hamiltonian system. Illustrative examples show the competence and efficiency of the new schemes in comparison with the traditional discrete gradient methods in the scientific literature. (paper)

Variable discrete ordinates method for radiation transfer in plane-parallel semi-transparent media with variable refractive index

Science.gov (United States)

Sarvari, S. M. Hosseini

2017-09-01

The traditional form of discrete ordinates method is applied to solve the radiative transfer equation in plane-parallel semi-transparent media with variable refractive index through using the variable discrete ordinate directions and the concept of refracted radiative intensity. The refractive index are taken as constant in each control volume, such that the direction cosines of radiative rays remain non-variant through each control volume, and then, the directions of discrete ordinates are changed locally by passing each control volume, according to the Snell's law of refraction. The results are compared by the previous studies in this field. Despite simplicity, the results show that the variable discrete ordinate method has a good accuracy in solving the radiative transfer equation in the semi-transparent media with arbitrary distribution of refractive index.

A Semi-implicit Numerical Scheme for a Two-dimensional, Three-field Thermo-Hydraulic Modeling

International Nuclear Information System (INIS)

Hwang, Moonkyu; Jeong, Jaejoon

2007-07-01

The behavior of two-phase flow is modeled, depending on the purpose, by either homogeneous model, drift flux model, or separated flow model, Among these model, in the separated flow model, the behavior of each flow phase is modeled by its own governing equation, together with the interphase models which describe the thermal and mechanical interactions between the phases involved. In this study, a semi-implicit numerical scheme for two-dimensional, transient, two-fluid, three-field is derived. The work is an extension to the previous study for the staggered, semi-implicit numerical scheme in one-dimensional geometry (KAERI/TR-3239/2006). The two-dimensional extension is performed by specifying a relevant governing equation set and applying the related finite differencing method. The procedure for employing the semi-implicit scheme is also described in detail. Verifications are performed for a 2-dimensional vertical plate for a single-phase and two-phase flows. The calculations verify the mass and energy conservations. The symmetric flow behavior, for the verification problem, also confirms the momentum conservation of the numerical scheme

Accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations on rectangular domains

Science.gov (United States)

Ji, Songsong; Yang, Yibo; Pang, Gang; Antoine, Xavier

2018-01-01

The aim of this paper is to design some accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations in rectangular domains. The Laplace transform in time and discrete Fourier transform in space are applied to get Green's functions of the semi-discretized equations in unbounded domains with single-source. An algorithm is given to compute these Green's functions accurately through some recurrence relations. Furthermore, the finite-difference method is used to discretize the reduced problem with accurate boundary conditions. Numerical simulations are presented to illustrate the accuracy of our method in the case of the linear Schrödinger and heat equations. It is shown that the reflection at the corners is correctly eliminated.

Discrete maximal regularity of time-stepping schemes for fractional evolution equations.

Science.gov (United States)

Jin, Bangti; Li, Buyang; Zhou, Zhi

2018-01-01

In this work, we establish the maximal [Formula: see text]-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text], [Formula: see text], in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank-Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis (Math Ann 319:735-758, 2001. doi:10.1007/PL00004457) and its discrete analogue due to Blunck (Stud Math 146:157-176, 2001. doi:10.4064/sm146-2-3). These results generalize the corresponding results for parabolic problems.

Development of a discrete gas-kinetic scheme for simulation of two-dimensional viscous incompressible and compressible flows.

Science.gov (United States)

Yang, L M; Shu, C; Wang, Y

2016-03-01

In this work, a discrete gas-kinetic scheme (DGKS) is presented for simulation of two-dimensional viscous incompressible and compressible flows. This scheme is developed from the circular function-based GKS, which was recently proposed by Shu and his co-workers [L. M. Yang, C. Shu, and J. Wu, J. Comput. Phys. 274, 611 (2014)]. For the circular function-based GKS, the integrals for conservation forms of moments in the infinity domain for the Maxwellian function-based GKS are simplified to those integrals along the circle. As a result, the explicit formulations of conservative variables and fluxes are derived. However, these explicit formulations of circular function-based GKS for viscous flows are still complicated, which may not be easy for the application by new users. By using certain discrete points to represent the circle in the phase velocity space, the complicated formulations can be replaced by a simple solution process. The basic requirement is that the conservation forms of moments for the circular function-based GKS can be accurately satisfied by weighted summation of distribution functions at discrete points. In this work, it is shown that integral quadrature by four discrete points on the circle, which forms the D2Q4 discrete velocity model, can exactly match the integrals. Numerical results showed that the present scheme can provide accurate numerical results for incompressible and compressible viscous flows with roughly the same computational cost as that needed by the Roe scheme.

Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation

Directory of Open Access Journals (Sweden)

Walter H. Aschbacher

2009-01-01

Full Text Available We study the time dependent Hartree equation in the continuum, the semidiscrete, and the fully discrete setting. We prove existence-uniqueness, regularity, and approximation properties for the respective schemes, and set the stage for a controlled numerical computation of delicate nonlinear and nonlocal features of the Hartree dynamics in various physical applications.

Development of discrete gas kinetic scheme for simulation of 3D viscous incompressible and compressible flows

Science.gov (United States)

Yang, L. M.; Shu, C.; Wang, Y.; Sun, Y.

2016-08-01

The sphere function-based gas kinetic scheme (GKS), which was presented by Shu and his coworkers [23] for simulation of inviscid compressible flows, is extended to simulate 3D viscous incompressible and compressible flows in this work. Firstly, we use certain discrete points to represent the spherical surface in the phase velocity space. Then, integrals along the spherical surface for conservation forms of moments, which are needed to recover 3D Navier-Stokes equations, are approximated by integral quadrature. The basic requirement is that these conservation forms of moments can be exactly satisfied by weighted summation of distribution functions at discrete points. It was found that the integral quadrature by eight discrete points on the spherical surface, which forms the D3Q8 discrete velocity model, can exactly match the integral. In this way, the conservative variables and numerical fluxes can be computed by weighted summation of distribution functions at eight discrete points. That is, the application of complicated formulations resultant from integrals can be replaced by a simple solution process. Several numerical examples including laminar flat plate boundary layer, 3D lid-driven cavity flow, steady flow through a 90° bending square duct, transonic flow around DPW-W1 wing and supersonic flow around NACA0012 airfoil are chosen to validate the proposed scheme. Numerical results demonstrate that the present scheme can provide reasonable numerical results for 3D viscous flows.

Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems

International Nuclear Information System (INIS)

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2015-01-01

Highlights: • Using high-resolution spatial scheme in solving two-phase flow problems. • Fully implicit time integrations scheme. • Jacobian-free Newton–Krylov method. • Analytical solution for two-phase water faucet problem. - Abstract: The majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many nuclear thermal–hydraulics applications, it is desirable to use higher-order numerical schemes to reduce numerical errors. High-resolution spatial discretization schemes provide high order spatial accuracy in smooth regions and capture sharp spatial discontinuity without nonphysical spatial oscillations. In this work, we adapted an existing high-resolution spatial discretization scheme on staggered grids in two-phase flow applications. Fully implicit time integration schemes were also implemented to reduce numerical errors from operator-splitting types of time integration schemes. The resulting nonlinear system has been successfully solved using the Jacobian-free Newton–Krylov (JFNK) method. The high-resolution spatial discretization and high-order fully implicit time integration numerical schemes were tested and numerically verified for several two-phase test problems, including a two-phase advection problem, a two-phase advection with phase appearance/disappearance problem, and the water faucet problem. Numerical results clearly demonstrated the advantages of using such high-resolution spatial and high-order temporal numerical schemes to significantly reduce numerical diffusion and therefore improve accuracy. Our study also demonstrated that the JFNK method is stable and robust in solving two-phase flow problems, even when phase appearance/disappearance exists

Finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws

International Nuclear Information System (INIS)

Botchorishvili, Ramaz; Pironneau, Olivier

2003-01-01

We develop here a new class of finite volume schemes on unstructured meshes for scalar conservation laws with stiff source terms. The schemes are of equilibrium type, hence with uniform bounds on approximate solutions, valid in cell entropy inequalities and exact for some equilibrium states. Convergence is investigated in the framework of kinetic schemes. Numerical tests show high computational efficiency and a significant advantage over standard cell centered discretization of source terms. Equilibrium type schemes produce accurate results even on test problems for which the standard approach fails. For some numerical tests they exhibit exponential type convergence rate. In two of our numerical tests an equilibrium type scheme with 441 nodes on a triangular mesh is more accurate than a standard scheme with 5000 2 grid points

Different-Level Simultaneous Minimization Scheme for Fault Tolerance of Redundant Manipulator Aided with Discrete-Time Recurrent Neural Network.

Science.gov (United States)

Jin, Long; Liao, Bolin; Liu, Mei; Xiao, Lin; Guo, Dongsheng; Yan, Xiaogang

2017-01-01

By incorporating the physical constraints in joint space, a different-level simultaneous minimization scheme, which takes both the robot kinematics and robot dynamics into account, is presented and investigated for fault-tolerant motion planning of redundant manipulator in this paper. The scheme is reformulated as a quadratic program (QP) with equality and bound constraints, which is then solved by a discrete-time recurrent neural network. Simulative verifications based on a six-link planar redundant robot manipulator substantiate the efficacy and accuracy of the presented acceleration fault-tolerant scheme, the resultant QP and the corresponding discrete-time recurrent neural network.

Improvements on nonlinear gyrokinetic particle simulations based on δf-discretization scheme

International Nuclear Information System (INIS)

Zorat, R.; Tessarotto, M.

1998-01-01

In this work various issues regarding the definition of improved theoretical models appropriate to describe the dynamics of confined magnetoplasmas by particle simulation methods are proposed. These concern in particular an improved non linear δf discretization scheme and the treatment of binary, i.e. Coulomb, and collective interactions. (orig.)

Road maintenance optimization through a discrete-time semi-Markov decision process

International Nuclear Information System (INIS)

Zhang Xueqing; Gao Hui

2012-01-01

Optimization models are necessary for efficient and cost-effective maintenance of a road network. In this regard, road deterioration is commonly modeled as a discrete-time Markov process such that an optimal maintenance policy can be obtained based on the Markov decision process, or as a renewal process such that an optimal maintenance policy can be obtained based on the renewal theory. However, the discrete-time Markov process cannot capture the real time at which the state transits while the renewal process considers only one state and one maintenance action. In this paper, road deterioration is modeled as a semi-Markov process in which the state transition has the Markov property and the holding time in each state is assumed to follow a discrete Weibull distribution. Based on this semi-Markov process, linear programming models are formulated for both infinite and finite planning horizons in order to derive optimal maintenance policies to minimize the life-cycle cost of a road network. A hypothetical road network is used to illustrate the application of the proposed optimization models. The results indicate that these linear programming models are practical for the maintenance of a road network having a large number of road segments and that they are convenient to incorporate various constraints on the decision process, for example, performance requirements and available budgets. Although the optimal maintenance policies obtained for the road network are randomized stationary policies, the extent of this randomness in decision making is limited. The maintenance actions are deterministic for most states and the randomness in selecting actions occurs only for a few states.

Three semi-direct sum Lie algebras and three discrete integrable couplings associated with the modified K dV lattice equation

International Nuclear Information System (INIS)

Yu Zhang; Zhang Yufeng

2009-01-01

Three semi-direct sum Lie algebras are constructed, which is an efficient and new way to obtain discrete integrable couplings. As its applications, three discrete integrable couplings associated with the modified K dV lattice equation are worked out. The approach can be used to produce other discrete integrable couplings of the discrete hierarchies of soliton equations.

Multiscale analysis for ill-posed problems with semi-discrete Tikhonov regularization

International Nuclear Information System (INIS)

Zhong, Min; Lu, Shuai; Cheng, Jin

2012-01-01

Using compactly supported radial basis functions of varying radii, Wendland has shown how a multiscale analysis can be applied to the approximation of Sobolev functions on a bounded domain, when the available data are discrete and noisy. Here, we examine the application of this analysis to the solution of linear moderately ill-posed problems using semi-discrete Tikhonov–Phillips regularization. As in Wendland’s work, the actual multiscale approximation is constructed by a sequence of residual corrections, where different support radii are employed to accommodate different scales. The convergence of the algorithm for noise-free data is given. Based on the Morozov discrepancy principle, a posteriori parameter choice rule and error estimates for the noisy data are derived. Two numerical examples are presented to illustrate the appropriateness of the proposed method. (paper)

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

International Nuclear Information System (INIS)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-01-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

Energy Technology Data Exchange (ETDEWEB)

Densmore, Jeffery D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Lowrie, Robert B [Los Alamos National Laboratory; Morel, Jim E [TEXAS A& M UNIV

2008-01-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

Science.gov (United States)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-09-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

New PDE-based methods for image enhancement using SOM and Bayesian inference in various discretization schemes

International Nuclear Information System (INIS)

Karras, D A; Mertzios, G B

2009-01-01

A novel approach is presented in this paper for improving anisotropic diffusion PDE models, based on the Perona–Malik equation. A solution is proposed from an engineering perspective to adaptively estimate the parameters of the regularizing function in this equation. The goal of such a new adaptive diffusion scheme is to better preserve edges when the anisotropic diffusion PDE models are applied to image enhancement tasks. The proposed adaptive parameter estimation in the anisotropic diffusion PDE model involves self-organizing maps and Bayesian inference to define edge probabilities accurately. The proposed modifications attempt to capture not only simple edges but also difficult textural edges and incorporate their probability in the anisotropic diffusion model. In the context of the application of PDE models to image processing such adaptive schemes are closely related to the discrete image representation problem and the investigation of more suitable discretization algorithms using constraints derived from image processing theory. The proposed adaptive anisotropic diffusion model illustrates these concepts when it is numerically approximated by various discretization schemes in a database of magnetic resonance images (MRI), where it is shown to be efficient in image filtering and restoration applications

A fully discrete energy stable scheme for a phase filed moving contact line model with variable densities and viscosities

KAUST Repository

Zhu, Guangpu; Chen, Huangxin; Sun, Shuyu; Yao, Jun

2018-01-01

In this paper, a fully discrete scheme which considers temporal and spatial discretizations is presented for the coupled Cahn-Hilliard equation in conserved form with the dynamic contact line condition and the Navier-Stokes equation

Central upwind scheme for a compressible two-phase flow model.

Science.gov (United States)

Ahmed, Munshoor; Saleem, M Rehan; Zia, Saqib; Qamar, Shamsul

2015-01-01

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

Central upwind scheme for a compressible two-phase flow model.

Directory of Open Access Journals (Sweden)

Munshoor Ahmed

Full Text Available In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

Central-Upwind Schemes for Two-Layer Shallow Water Equations

KAUST Repository

Kurganov, Alexander; Petrova, Guergana

2009-01-01

We derive a second-order semidiscrete central-upwind scheme for one- and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is well-balanced in the sense that stationary steady-state solutions

Shift-invariant discrete wavelet transform analysis for retinal image classification.

Science.gov (United States)

Khademi, April; Krishnan, Sridhar

2007-12-01

This work involves retinal image classification and a novel analysis system was developed. From the compressed domain, the proposed scheme extracts textural features from wavelet coefficients, which describe the relative homogeneity of localized areas of the retinal images. Since the discrete wavelet transform (DWT) is shift-variant, a shift-invariant DWT was explored to ensure that a robust feature set was extracted. To combat the small database size, linear discriminant analysis classification was used with the leave one out method. 38 normal and 48 abnormal (exudates, large drusens, fine drusens, choroidal neovascularization, central vein and artery occlusion, histoplasmosis, arteriosclerotic retinopathy, hemi-central retinal vein occlusion and more) were used and a specificity of 79% and sensitivity of 85.4% were achieved (the average classification rate is 82.2%). The success of the system can be accounted to the highly robust feature set which included translation, scale and semi-rotational, features. Additionally, this technique is database independent since the features were specifically tuned to the pathologies of the human eye.

A Semi-Discrete Landweber-Kaczmarz Method for Cone Beam Tomography and Laminography Exploiting Geometric Prior Information

Science.gov (United States)

Vogelgesang, Jonas; Schorr, Christian

2016-12-01

We present a semi-discrete Landweber-Kaczmarz method for solving linear ill-posed problems and its application to Cone Beam tomography and laminography. Using a basis function-type discretization in the image domain, we derive a semi-discrete model of the underlying scanning system. Based on this model, the proposed method provides an approximate solution of the reconstruction problem, i.e. reconstructing the density function of a given object from its projections, in suitable subspaces equipped with basis function-dependent weights. This approach intuitively allows the incorporation of additional information about the inspected object leading to a more accurate model of the X-rays through the object. Also, physical conditions of the scanning geometry, like flat detectors in computerized tomography as used in non-destructive testing applications as well as non-regular scanning curves e.g. appearing in computed laminography (CL) applications, are directly taken into account during the modeling process. Finally, numerical experiments of a typical CL application in three dimensions are provided to verify the proposed method. The introduction of geometric prior information leads to a significantly increased image quality and superior reconstructions compared to standard iterative methods.

Improvement of spatial discretization error on the semi-analytic nodal method using the scattered source subtraction method

International Nuclear Information System (INIS)

Yamamoto, Akio; Tatsumi, Masahiro

2006-01-01

In this paper, the scattered source subtraction (SSS) method is newly proposed to improve the spatial discretization error of the semi-analytic nodal method with the flat-source approximation. In the SSS method, the scattered source is subtracted from both side of the diffusion or the transport equation to make spatial variation of the source term to be small. The same neutron balance equation is still used in the SSS method. Since the SSS method just modifies coefficients of node coupling equations (those used in evaluation for the response of partial currents), its implementation is easy. Validity of the present method is verified through test calculations that are carried out in PWR multi-assemblies configurations. The calculation results show that the SSS method can significantly improve the spatial discretization error. Since the SSS method does not have any negative impact on execution time, convergence behavior and memory requirement, it will be useful to reduce the spatial discretization error of the semi-analytic nodal method with the flat-source approximation. (author)

An induced charge readout scheme incorporating image charge splitting on discrete pixels

International Nuclear Information System (INIS)

Kataria, D.O.; Lapington, J.S.

2003-01-01

Top hat electrostatic analysers used in space plasma instruments typically use microchannel plates (MCPs) followed by discrete pixel anode readout for the angular definition of the incoming particles. Better angular definition requires more pixels/readout electronics channels but with stringent mass and power budgets common in space applications, the number of channels is restricted. We describe here a technique that improves the angular definition using induced charge and an interleaved anode pattern. The technique adopts the readout philosophy used on the CRRES and CLUSTER I instruments but has the advantages of the induced charge scheme and significantly reduced capacitance. Charge from the MCP collected by an anode pixel is inductively split onto discrete pixels whose geometry can be tailored to suit the scientific requirements of the instrument. For our application, the charge is induced over two pixels. One of them is used for a coarse angular definition but is read out by a single channel of electronics, allowing a higher rate handling. The other provides a finer angular definition but is interleaved and hence carries the expense of lower rate handling. Using the technique and adding four channels of electronics, a four-fold increase in the angular resolution is obtained. Details of the scheme and performance results are presented

A Discrete Numerical Scheme of Modified Leslie-Gower With Harvesting Model

Directory of Open Access Journals (Sweden)

Riski Nur Istiqomah Dinnullah

2018-05-01

Full Text Available Recently, exploitation of biological resources and the harvesting of two populations or more are widely practiced, such as fishery or foresty. The simplest way to describe the interaction of two species is by using predator prey model, that is one species feeds on another. The Leslie-Gower predator prey model has been studied in many works. In this paper, we use Euler method to discretisize the modified Leslie-Gower with harvesting model. The model consists of two simultanious predator prey equations. We show numerically that this discrete numerical scheme model is dynamically consistent with its continuous model only for relatively small step-size. By using computer simulation software, we show that equlibrium points can be stable, saddles, and unstable. It is shown that the numerical simulations not only illustrate the results, but also show the rich dynamics behaviors of the discrete system.

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.

2017-05-23

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.

Three-dimensional coupled Monte Carlo-discrete ordinates computational scheme for shielding calculations of large and complex nuclear facilities

International Nuclear Information System (INIS)

Chen, Y.; Fischer, U.

2005-01-01

Shielding calculations of advanced nuclear facilities such as accelerator based neutron sources or fusion devices of the tokamak type are complicated due to their complex geometries and their large dimensions, including bulk shields of several meters thickness. While the complexity of the geometry in the shielding calculation can be hardly handled by the discrete ordinates method, the deep penetration of radiation through bulk shields is a severe challenge for the Monte Carlo particle transport technique. This work proposes a dedicated computational scheme for coupled Monte Carlo-Discrete Ordinates transport calculations to handle this kind of shielding problems. The Monte Carlo technique is used to simulate the particle generation and transport in the target region with both complex geometry and reaction physics, and the discrete ordinates method is used to treat the deep penetration problem in the bulk shield. The coupling scheme has been implemented in a program system by loosely integrating the Monte Carlo transport code MCNP, the three-dimensional discrete ordinates code TORT and a newly developed coupling interface program for mapping process. Test calculations were performed with comparison to MCNP solutions. Satisfactory agreements were obtained between these two approaches. The program system has been chosen to treat the complicated shielding problem of the accelerator-based IFMIF neutron source. The successful application demonstrates that coupling scheme with the program system is a useful computational tool for the shielding analysis of complex and large nuclear facilities. (authors)

Laguerre-Freud Equations for the Recurrence Coefficients of Some Discrete Semi-Classical Orthogonal Polynomials of Class Two

Science.gov (United States)

Hounga, C.; Hounkonnou, M. N.; Ronveaux, A.

2006-10-01

In this paper, we give Laguerre-Freud equations for the recurrence coefficients of discrete semi-classical orthogonal polynomials of class two, when the polynomials in the Pearson equation are of the same degree. The case of generalized Charlier polynomials is also presented.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

Science.gov (United States)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

An Efficient Semi-fragile Watermarking Scheme for Tamper Localization and Recovery

Science.gov (United States)

Hou, Xiang; Yang, Hui; Min, Lianquan

2018-03-01

To solve the problem that remote sensing images are vulnerable to be tampered, a semi-fragile watermarking scheme was proposed. Binary random matrix was used as the authentication watermark, which was embedded by quantizing the maximum absolute value of directional sub-bands coefficients. The average gray level of every non-overlapping 4×4 block was adopted as the recovery watermark, which was embedded in the least significant bit. Watermarking detection could be done directly without resorting to the original images. Experimental results showed our method was robust against rational distortions to a certain extent. At the same time, it was fragile to malicious manipulation, and realized accurate localization and approximate recovery of the tampered regions. Therefore, this scheme can protect the security of remote sensing image effectively.

Emulation-based comparative study of centralized and distributed control schemes for optical networks

Science.gov (United States)

Xin, Chunsheng; Ye, Yinghua; Dixit, Sudhir; Qiao, Chunming

2001-07-01

Recently there are considerable amount of research about the automatic control and provisioning in all optical networks. One of the critical issues is how to provide effective lightpath provisioning to improve network performance, such as blocking probability and decision time. Depending on the network topology, configuration, and administration policy, a distributed or centralized control scheme can be employed to manage the routing and signaling. In a distributed control scheme, each node exchanges information with other nodes, but performs routing and signaling independently from other nodes. On the other hand, in a centralized scheme, each node communicates with a central controller and the controller performs routing and signaling on behalf of all other nodes. Intuitively, the centralized scheme can obtain a lower blocking probability since the controller has the complete resource availability information. We have studied the two schemes through emulations, determined the signaling and processing overheads and quantified the conditions that favor one approach over the other.

An assessment of unstructured grid finite volume schemes for cold gas hypersonic flow calculations

Directory of Open Access Journals (Sweden)

João Luiz F. Azevedo

2009-06-01

Full Text Available A comparison of five different spatial discretization schemes is performed considering a typical high speed flow application. Flowfields are simulated using the 2-D Euler equations, discretized in a cell-centered finite volume procedure on unstructured triangular meshes. The algorithms studied include a central difference-type scheme, and 1st- and 2nd-order van Leer and Liou flux-vector splitting schemes. These methods are implemented in an efficient, edge-based, unstructured grid procedure which allows for adaptive mesh refinement based on flow property gradients. Details of the unstructured grid implementation of the methods are presented together with a discussion of the data structure and of the adaptive refinement strategy. The application of interest is the cold gas flow through a typical hypersonic inlet. Results for different entrance Mach numbers and mesh topologies are discussed in order to assess the comparative performance of the various spatial discretization schemes.

Numerical solution of special ultra-relativistic Euler equations using central upwind scheme

Science.gov (United States)

Ghaffar, Tayabia; Yousaf, Muhammad; Qamar, Shamsul

2018-06-01

This article is concerned with the numerical approximation of one and two-dimensional special ultra-relativistic Euler equations. The governing equations are coupled first-order nonlinear hyperbolic partial differential equations. These equations describe perfect fluid flow in terms of the particle density, the four-velocity and the pressure. A high-resolution shock-capturing central upwind scheme is employed to solve the model equations. To avoid excessive numerical diffusion, the considered scheme avails the specific information of local propagation speeds. By using Runge-Kutta time stepping method and MUSCL-type initial reconstruction, we have obtained 2nd order accuracy of the proposed scheme. After discussing the model equations and the numerical technique, several 1D and 2D test problems are investigated. For all the numerical test cases, our proposed scheme demonstrates very good agreement with the results obtained by well-established algorithms, even in the case of highly relativistic 2D test problems. For validation and comparison, the staggered central scheme and the kinetic flux-vector splitting (KFVS) method are also implemented to the same model. The robustness and efficiency of central upwind scheme is demonstrated by the numerical results.

ON THE CONSTRUCTION OF PARTIAL DIFFERENCE SCHEMES II: DISCRETE VARIABLES AND SCHWARZIAN LATTICES

Directory of Open Access Journals (Sweden)

Decio Levi

2016-06-01

Full Text Available In the process of constructing invariant difference schemes which approximate partial differential equations we write down a procedure for discretizing a partial differential equation on an arbitrary lattice. An open problem is the meaning of a lattice which does not satisfy the Clairaut–Schwarz–Young theorem. To analyze it we apply the procedure on a simple example, the potential Burgers equation with two different lattices, an orthogonal lattice which is invariant under the symmetries of the equation and satisfies the commutativity of the partial difference operators and an exponential lattice which is not invariant and does not satisfy the Clairaut–Schwarz–Young theorem. A discussion on the numerical results is presented showing the different behavior of both schemes for two different exact solutions and their numerical approximations.

Analysis of a discrete element method and coupling with a compressible fluid flow method

International Nuclear Information System (INIS)

Monasse, L.

2011-01-01

This work aims at the numerical simulation of compressible fluid/deformable structure interactions. In particular, we have developed a partitioned coupling algorithm between a Finite Volume method for the compressible fluid and a Discrete Element method capable of taking into account fractures in the solid. A survey of existing fictitious domain methods and partitioned algorithms has led to choose an Embedded Boundary method and an explicit coupling scheme. We first showed that the Discrete Element method used for the solid yielded the correct macroscopic behaviour and that the symplectic time-integration scheme ensured the preservation of energy. We then developed an explicit coupling algorithm between a compressible inviscid fluid and an un-deformable solid. Mass, momentum and energy conservation and consistency properties were proved for the coupling scheme. The algorithm was then extended to the coupling with a deformable solid, in the form of a semi implicit scheme. Finally, we applied this method to unsteady inviscid flows around moving structures: comparisons with existing numerical and experimental results demonstrate the excellent accuracy of our method. (author) [fr

OLT-centralized sampling frequency offset compensation scheme for OFDM-PON.

Science.gov (United States)

Chen, Ming; Zhou, Hui; Zheng, Zhiwei; Deng, Rui; Chen, Qinghui; Peng, Miao; Liu, Cuiwei; He, Jing; Chen, Lin; Tang, Xionggui

2017-08-07

We propose an optical line terminal (OLT)-centralized sampling frequency offset (SFO) compensation scheme for adaptively-modulated OFDM-PON systems. By using the proposed SFO scheme, the phase rotation and inter-symbol interference (ISI) caused by SFOs between OLT and multiple optical network units (ONUs) can be centrally compensated in the OLT, which reduces the complexity of ONUs. Firstly, the optimal fast Fourier transform (FFT) size is identified in the intensity-modulated and direct-detection (IMDD) OFDM system in the presence of SFO. Then, the proposed SFO compensation scheme including phase rotation modulation (PRM) and length-adaptive OFDM frame has been experimentally demonstrated in the downlink transmission of an adaptively modulated optical OFDM with the optimal FFT size. The experimental results show that up to ± 300 ppm SFO can be successfully compensated without introducing any receiver performance penalties.

Six-component semi-discrete integrable nonlinear Schrödinger system

Science.gov (United States)

Vakhnenko, Oleksiy O.

2018-01-01

We suggest the six-component integrable nonlinear system on a quasi-one-dimensional lattice. Due to its symmetrical form, the general system permits a number of reductions; one of which treated as the semi-discrete integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell is considered in considerable details. Besides six truly independent basic field variables, the system is characterized by four concomitant fields whose background values produce three additional types of inter-site resonant interactions between the basic fields. As a result, the system dynamics becomes associated with the highly nonstandard form of Poisson structure. The elementary Poisson brackets between all field variables are calculated and presented explicitly. The richness of system dynamics is demonstrated on the multi-component soliton solution written in terms of properly parameterized soliton characteristics.

Semi-Discrete Ingham-Type Inequalities

International Nuclear Information System (INIS)

Komornik, Vilmos; Loreti, Paola

2007-01-01

One of the general methods in linear control theory is based on harmonic and non-harmonic Fourier series. The key of this approach is the establishment of various suitable adaptations and generalizations of the classical Parseval equality. A new and systematic approach was begun in our papers in collaboration with Baiocchi. Many recent results of this kind, obtained through various Ingham-type theorems, were exposed recently. Although this work concentrated on continuous models, in connection with numerical simulations a natural question is whether these results also admit useful discrete versions. The purpose of this paper is to establish discrete versions of various Ingham-type theorems by using our approach. They imply the earlier continuous results by a simple limit process

Semi-passive, Chemical Oxidation Schemes for the Long-term Treatment of Contaminants

Energy Technology Data Exchange (ETDEWEB)

Frank W. Schwartz

2005-12-13

This research involves a combined experimental and modeling study that builds on our previous DOE-sponsored work in investigating how KMnO{sub 4} can be better used with in situ remediation of groundwater contaminated by chlorinated ethylenes (e.g., PCE, TCE, DCE). This study aims to provide scientific basis for developing a new long-term, semi-passive ISCO scheme that uses controlled release KMnO{sub 4} as a reactive barrier component. Specific objectives of the study are (1) to construct controlled release KMnO{sub 4} as a new reactive barrier component that could deliver permanganate at a controlled rate over long time periods of years, (2) to quantitatively describe release mechanisms associated with the controlled release KMnO{sub 4}, (3) to demonstrate efficacy of the new remediation scheme using proof-of-concept experiments, and (4) to design advanced forms of controlled release systems through numerical optimization. The new scheme operates in a long-term, semi-passive manner to control spreading of a dissolved contaminant plume with periodic replacement of the controlled release KMnO{sub 4} installed in the subsurface. As a first step in developing this remedial concept, we manufactured various prototype controlled release KMnO{sub 4} forms. Then we demonstrated using column experiments that the controlled release KMnO{sub 4} could deliver small amount of permanganate into flowing water at controlled rates over long time periods of years. An analytical model was also used to estimate the diffusivities and durations of the controlled release KMnO{sub 4}. Finally, proof-of-concept flow-tank experiments were performed to demonstrate the efficacy of the controlled release KMnO{sub 4} scheme in controlling dissolved TCE plume in a long-term, semi-passive manner. Another important thrust of our research effort involved numerical optimization of controlled release systems. This study used a numerical model that is capable of describing release patterns of active

A new scheme for biomonitoring heavy metal concentrations in semi-natural wetlands.

Science.gov (United States)

Batzias, A F; Siontorou, C G

2008-10-30

This work introduces a semi-natural wetland biomonitoring framework for heavy metal concentrations based on a robust dynamic integration between biological assemblages and relevant biosensors. The cooperative/synergistic scheme developed minimizes uncertainty and monitoring costs and increases reliability of pollution control and abatement. Attention is given to establishing a fully functioning and reliable network approach for monitoring inflows and achieving dose-response relations and calibration of biomonitoring species. The biomonitoring network initially consists of both, biosensors and species, as a validation phase in each wetland of the surveillance area; once the species monitoring efficiency is verified by the biosensors, the biosensor network moves to the next wetland and so on, following a circular pattern until all area wetlands have a fully functional natural monitoring scheme. By means of species recalibration with periodic revisiting of the biosensors, the scheme progressively reaches a quasi steady-state (including seasonality), thus ensuring reliability and robustness. This framework, currently pilot-tested in Voiotia, Greece, for assessing chromium levels, has been built to cover short-, medium- and long-term monitoring requirements. The results gathered so far, support the employment of the proposed scheme in heavy metal monitoring, and, further, arise the need for volunteer involvement to achieve long-term viability.

Numerical schemes for explosion hazards

International Nuclear Information System (INIS)

Therme, Nicolas

2015-01-01

In nuclear facilities, internal or external explosions can cause confinement breaches and radioactive materials release in the environment. Hence, modeling such phenomena is crucial for safety matters. Blast waves resulting from explosions are modeled by the system of Euler equations for compressible flows, whereas Navier-Stokes equations with reactive source terms and level set techniques are used to simulate the propagation of flame front during the deflagration phase. The purpose of this thesis is to contribute to the creation of efficient numerical schemes to solve these complex models. The work presented here focuses on two major aspects: first, the development of consistent schemes for the Euler equations, then the buildup of reliable schemes for the front propagation. In both cases, explicit in time schemes are used, but we also introduce a pressure correction scheme for the Euler equations. Staggered discretization is used in space. It is based on the internal energy formulation of the Euler system, which insures its positivity and avoids tedious discretization of the total energy over staggered grids. A discrete kinetic energy balance is derived from the scheme and a source term is added in the discrete internal energy balance equation to preserve the exact total energy balance at the limit. High order methods of MUSCL type are used in the discrete convective operators, based solely on material velocity. They lead to positivity of density and internal energy under CFL conditions. This ensures that the total energy cannot grow and we can furthermore derive a discrete entropy inequality. Under stability assumptions of the discrete L8 and BV norms of the scheme's solutions one can prove that a sequence of converging discrete solutions necessarily converges towards the weak solution of the Euler system. Besides it satisfies a weak entropy inequality at the limit. Concerning the front propagation, we transform the flame front evolution equation (the so called

Discrete control systems

CERN Document Server

Okuyama, Yoshifumi

2014-01-01

Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...

Development of Non-staggered, semi-implicit ICE numerical scheme for a two-fluid, three-field model

Energy Technology Data Exchange (ETDEWEB)

Jeong, Jae Jun; Yoon, H. Y.; Bae, S. W

2007-11-15

A pilot code for one-dimensional, transient, two-fluid, three-field model has been developed. In this code, the semi-implicit ICE numerical scheme has been adapted to a 'non-staggered' grid. Using several conceptual problems, the numerical scheme has been verified. The results of the verifications are summarized below: - It was confirmed that the basic pilot code can simulate various flow conditions (such as single-phase liquid flow, two-phase mixture flow, and single-phase vapor flow) and transitions of the flow conditions. A mist flow was not simulated, but it seems that the basic pilot code can simulate mist flow conditions. - The mass and energy conservation was confirmed for single-phase liquid and single-phase vapor flows. - It was confirmed that the inlet pressure and velocity boundary conditions work properly. - It was confirmed that, for single- and two-phase flows, the velocity and temperature of non-existing phase are calculated as intended. The non-staggered, semi-implicit ICE numerical scheme, which has been developed in this study, will be a starting point of a new code development that adopts an unstructured finite volume method.

Time-Discrete Higher-Order ALE Formulations: Stability

KAUST Repository

Bonito, Andrea; Kyza, Irene; Nochetto, Ricardo H.

2013-01-01

on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time

Ambiguity attacks on robust blind image watermarking scheme based on redundant discrete wavelet transform and singular value decomposition

Directory of Open Access Journals (Sweden)

Khaled Loukhaoukha

2017-12-01

Full Text Available Among emergent applications of digital watermarking are copyright protection and proof of ownership. Recently, Makbol and Khoo (2013 have proposed for these applications a new robust blind image watermarking scheme based on the redundant discrete wavelet transform (RDWT and the singular value decomposition (SVD. In this paper, we present two ambiguity attacks on this algorithm that have shown that this algorithm fails when used to provide robustness applications like owner identification, proof of ownership, and transaction tracking. Keywords: Ambiguity attack, Image watermarking, Singular value decomposition, Redundant discrete wavelet transform

Central-Upwind Schemes for Two-Layer Shallow Water Equations

KAUST Repository

Kurganov, Alexander

2009-01-01

We derive a second-order semidiscrete central-upwind scheme for one- and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is well-balanced in the sense that stationary steady-state solutions are exactly preserved by the scheme and positivity preserving; that is, the depth of each fluid layer is guaranteed to be nonnegative. We also propose a new technique for the treatment of the nonconservative products describing the momentum exchange between the layers. The performance of the proposed method is illustrated on a number of numerical examples, in which we successfully capture (quasi) steady-state solutions and propagating interfaces. © 2009 Society for Industrial and Applied Mathematics.

Semi-active control of helicopter vibration using controllable stiffness and damping devices

Science.gov (United States)

Anusonti-Inthra, Phuriwat

Semi-active concepts for helicopter vibration reduction are developed and evaluated in this dissertation. Semi-active devices, controllable stiffness devices or controllable orifice dampers, are introduced; (i) in the blade root region (rotor-based concept) and (ii) between the rotor and the fuselage as semi-active isolators (in the non-rotating frame). Corresponding semi-active controllers for helicopter vibration reduction are also developed. The effectiveness of the rotor-based semi-active vibration reduction concept (using stiffness and damping variation) is demonstrated for a 4-bladed hingeless rotor helicopter in moderate- to high-speed forward flight. A sensitivity study shows that the stiffness variation of root element can reduce hub vibrations when proper amplitude and phase are used. Furthermore, the optimal semi-active control scheme can determine the combination of stiffness variations that produce significant vibration reduction in all components of vibratory hub loads simultaneously. It is demonstrated that desired cyclic variations in properties of the blade root region can be practically achieved using discrete controllable stiffness devices and controllable dampers, especially in the flap and lag directions. These discrete controllable devices can produce 35--50% reduction in a composite vibration index representing all components of vibratory hub loads. No detrimental increases are observed in the lower harmonics of blade loads and blade response (which contribute to the dynamic stresses) and controllable device internal loads, when the optimal stiffness and damping variations are introduced. The effectiveness of optimal stiffness and damping variations in reducing hub vibration is retained over a range of cruise speeds and for variations in fundamental rotor properties. The effectiveness of the semi-active isolator is demonstrated for a simplified single degree of freedom system representing the semi-active isolation system. The rotor

Assessing the groundwater recharge under various irrigation schemes in Central Taiwan

Science.gov (United States)

Chen, Shih-Kai; Jang, Cheng-Shin; Lin, Zih-Ciao; Tsai, Cheng-Bin

2014-05-01

The flooded paddy fields can be considered as a major source of groundwater recharge in Central Taiwan. The risk of rice production has increased notably due to climate change in this area. To respond to agricultural water shortage caused by climate change without affecting rice yield in the future, the application of water-saving irrigation is the substantial resolution. The System of Rice Intensification (SRI) was developed as a set of insights and practices used in growing irrigated rice. Based on the water-saving irrigation practice of SRI, impacts of the new methodology on the reducing of groundwater recharge were assessed in central Taiwan. The three-dimensional finite element groundwater model (FEMWATER) with the variable boundary condition analog functions, was applied in simulating groundwater recharge under different irrigation schemes. According to local climatic and environmental characteristics associated with SRI methodology, the change of infiltration rate was evaluated and compared with the traditional irrigation schemes, including continuous irrigation and rotational irrigation scheme. The simulation results showed that the average infiltration rate in the rice growing season decreased when applying the SRI methodology, and the total groundwater recharge amount of SRI with a 5-day irrigation interval reduced 12% and 9% compared with continuous irrigation (6cm constant ponding water depth) and rotational scheme (5-day irrigation interval with 6 cm initial ponding water depth), respectively. The results could be used as basis for planning long-term adaptive water resource management strategies to climate change in Central Taiwan. Keywords: SRI, Irrigation schemes, Groundwater recharge, Infiltration

Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations

Science.gov (United States)

Yousaf, Muhammad; Ghaffar, Tayabia; Qamar, Shamsul

2015-01-01

The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD). Such models are more complicated than the non-relativistic ones due to the nonlinear relations between the conserved and state variables. A high-resolution shock-capturing central upwind scheme is implemented to solve the given set of equations. The proposed technique uses the precise information of local propagation speeds to avoid the excessive numerical diffusion. The second order accuracy of the scheme is obtained with the use of MUSCL-type initial reconstruction and Runge-Kutta time stepping method. After a discussion of the equations solved and of the techniques employed, a series of one and two-dimensional test problems are carried out. To validate the method and assess its accuracy, the staggered central and the kinetic flux-vector splitting schemes are also applied to the same model. The scheme is robust and efficient. Its results are comparable to those obtained from the sophisticated algorithms, even in the case of highly relativistic two-dimensional test problems. PMID:26070067

Analysis of a fourth-order compact scheme for convection-diffusion

International Nuclear Information System (INIS)

Yavneh, I.

1997-01-01

In, 1984 Gupta et al. introduced a compact fourth-order finite-difference convection-diffusion operator with some very favorable properties. In particular, this scheme does not seem to suffer excessively from spurious oscillatory behavior, and it converges with standard methods such as Gauss Seidel or SOR (hence, multigrid) regardless of the diffusion. This scheme has been rederived, developed (including some variations), and applied in both convection-diffusion and Navier-Stokes equations by several authors. Accurate solutions to high Reynolds-number flow problems at relatively coarse resolutions have been reported. These solutions were often compared to those obtained by lower order discretizations, such as second-order central differences and first-order upstream discretizations. The latter, it was stated, achieved far less accurate results due to the artificial viscosity, which the compact scheme did not include. We show here that, while the compact scheme indeed does not suffer from a cross-stream artificial viscosity (as does the first-order upstream scheme when the characteristic direction is not aligned with the grid), it does include a streamwise artificial viscosity that is inversely proportional to the natural viscosity. This term is not always benign. 7 refs., 1 fig., 1 tab

A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION.

Science.gov (United States)

Mang, Andreas; Biros, George

2017-01-01

We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20 × speedup for a two dimensional, real world multi-subject medical image registration problem.

Discrete integrable couplings associated with Toda-type lattice and two hierarchies of discrete soliton equations

International Nuclear Information System (INIS)

Zhang Yufeng; Fan Engui; Zhang Yongqing

2006-01-01

With the help of two semi-direct sum Lie algebras, an efficient way to construct discrete integrable couplings is proposed. As its applications, the discrete integrable couplings of the Toda-type lattice equations are obtained. The approach can be devoted to establishing other discrete integrable couplings of the discrete lattice integrable hierarchies of evolution equations

A mass and momentum conserving unsplit semi-Lagrangian framework for simulating multiphase flows

Energy Technology Data Exchange (ETDEWEB)

Owkes, Mark, E-mail: mark.owkes@montana.edu [Mechanical and Industrial Engineering, Montana State University, Bozeman, MT 59717 (United States); Desjardins, Olivier [Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853 (United States)

2017-03-01

In this work, we present a computational methodology for convection and advection that handles discontinuities with second order accuracy and maintains conservation to machine precision. This method can transport a variety of discontinuous quantities and is used in the context of an incompressible gas–liquid flow to transport the phase interface, momentum, and scalars. The proposed method provides a modification to the three-dimensional, unsplit, second-order semi-Lagrangian flux method of Owkes & Desjardins (JCP, 2014). The modification adds a refined grid that provides consistent fluxes of mass and momentum defined on a staggered grid and discrete conservation of mass and momentum, even for flows with large density ratios. Additionally, the refined grid doubles the resolution of the interface without significantly increasing the computational cost over previous non-conservative schemes. This is possible due to a novel partitioning of the semi-Lagrangian fluxes into a small number of simplices. The proposed scheme is tested using canonical verification tests, rising bubbles, and an atomizing liquid jet.

Relaxation approximations to second-order traffic flow models by high-resolution schemes

International Nuclear Information System (INIS)

Nikolos, I.K.; Delis, A.I.; Papageorgiou, M.

2015-01-01

A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reported demonstrate the simplicity and versatility of relaxation schemes as numerical solvers

Semi-continuous and multigroup models in extended kinetic theory

International Nuclear Information System (INIS)

Koller, W.

2000-01-01

The aim of this thesis is to study energy discretization of the Boltzmann equation in the framework of extended kinetic theory. In case that external fields can be neglected, the semi- continuous Boltzmann equation yields a sound basis for various generalizations. Semi-continuous kinetic equations describing a three component gas mixture interacting with monochromatic photons as well as a four component gas mixture undergoing chemical reactions are established and investigated. These equations reflect all major aspects (conservation laws, equilibria, H-theorem) of the full continuous kinetic description. For the treatment of the spatial dependence, an expansion of the distribution function in terms of Legendre polynomials is carried out. An implicit finite differencing scheme is combined with the operator splitting method. The obtained numerical schemes are applied to the space homogeneous study of binary chemical reactions and to spatially one-dimensional laser-induced acoustic waves. In the presence of external fields, the developed overlapping multigroup approach (with the spline-interpolation as its extension) is well suited for numerical studies. Furthermore, two formulations of consistent multigroup approaches to the non-linear Boltzmann equation are presented. (author)

A splitting scheme based on the space-time CE/SE method for solving multi-dimensional hydrodynamical models of semiconductor devices

Science.gov (United States)

Nisar, Ubaid Ahmed; Ashraf, Waqas; Qamar, Shamsul

2016-08-01

Numerical solutions of the hydrodynamical model of semiconductor devices are presented in one and two-space dimension. The model describes the charge transport in semiconductor devices. Mathematically, the models can be written as a convection-diffusion type system with a right hand side describing the relaxation effects and interaction with a self consistent electric field. The proposed numerical scheme is a splitting scheme based on the conservation element and solution element (CE/SE) method for hyperbolic step, and a semi-implicit scheme for the relaxation step. The numerical results of the suggested scheme are compared with the splitting scheme based on Nessyahu-Tadmor (NT) central scheme for convection step and the same semi-implicit scheme for the relaxation step. The effects of various parameters such as low field mobility, device length, lattice temperature and voltages for one-space dimensional hydrodynamic model are explored to further validate the generic applicability of the CE/SE method for the current model equations. A two dimensional simulation is also performed by CE/SE method for a MESFET device, producing results in good agreement with those obtained by NT-central scheme.

Integrable discretizations of the (2+1)-dimensional sinh-Gordon equation

International Nuclear Information System (INIS)

Hu, Xing-Biao; Yu, Guo-Fu

2007-01-01

In this paper, we propose two semi-discrete equations and one fully discrete equation and study them by Hirota's bilinear method. These equations have continuum limits into a system which admits the (2+1)-dimensional generalization of the sinh-Gordon equation. As a result, two integrable semi-discrete versions and one fully discrete version for the sinh-Gordon equation are found. Baecklund transformations, nonlinear superposition formulae, determinant solution and Lax pairs for these discrete versions are presented

Averaged multivalued solutions and time discretization for conservation laws

International Nuclear Information System (INIS)

Brenier, Y.

1985-01-01

It is noted that the correct shock solutions can be approximated by averaging in some sense the multivalued solution given by the method of characteristics for the nonlinear scalar conservation law (NSCL). A time discretization for the NSCL equation based on this principle is considered. An equivalent analytical formulation is shown to lead quite easily to a convergence result, and a third formulation is introduced which can be generalized for the systems of conservation laws. Various numerical schemes are constructed from the proposed time discretization. The first family of schemes is obtained by using a spatial grid and projecting the results of the time discretization. Many known schemes are then recognized (mainly schemes by Osher, Roe, and LeVeque). A second way to discretize leads to a particle scheme without space grid, which is very efficient (at least in the scalar case). Finally, a close relationship between the proposed method and the Boltzmann type schemes is established. 14 references

A coarse-mesh diffusion synthetic acceleration of the scattering source iteration scheme for one-speed slab-geometry discrete ordinates problems

International Nuclear Information System (INIS)

Santos, Frederico P.; Alves Filho, Hermes; Barros, Ricardo C.; Xavier, Vinicius S.

2011-01-01

The scattering source iterative (SI) scheme is traditionally applied to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S N ) neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as initial guess for the fine-mesh scattering source, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the classical S N prescribed boundary conditions, including vacuum boundary conditions. Therefore, we first implement a spectral nodal method that generates coarse-mesh diffusion solution that is completely free from spatial truncation errors, then we reconstruct this coarse-mesh solution within each spatial cell of the discretization grid, to further yield the initial guess for the fine-mesh scattering source in the first S N transport sweep (μm > 0 and μm < 0, m = 1:N) across the spatial grid. We consider a number of numerical experiments to illustrate the efficiency of the offered diffusion synthetic acceleration (DSA) technique. (author)

India : Note on Public Financial Management and Accountability in Centrally Sponsored Schemes

OpenAIRE

World Bank

2006-01-01

The budget outlay for Centrally Sponsored Schemes (CSS) for India in 2005-06 is significantly higher as compared to the previous year's level of Rs.395,000 million. This includes increased allocations for rural roads, rural employment, and education and nutritional support for pre-school children. At present there are over 200 such schemes in operation, of which a dozen accounts for more t...

Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation

International Nuclear Information System (INIS)

Feng, Bao-Feng; Chen, Junchao; Chen, Yong; Maruno, Ken-ichi; Ohta, Yasuhiro

2015-01-01

In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a self-adaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well. (paper)

A parallel 3-D discrete wavelet transform architecture using pipelined lifting scheme approach for video coding

Science.gov (United States)

Hegde, Ganapathi; Vaya, Pukhraj

2013-10-01

This article presents a parallel architecture for 3-D discrete wavelet transform (3-DDWT). The proposed design is based on the 1-D pipelined lifting scheme. The architecture is fully scalable beyond the present coherent Daubechies filter bank (9, 7). This 3-DDWT architecture has advantages such as no group of pictures restriction and reduced memory referencing. It offers low power consumption, low latency and high throughput. The computing technique is based on the concept that lifting scheme minimises the storage requirement. The application specific integrated circuit implementation of the proposed architecture is done by synthesising it using 65 nm Taiwan Semiconductor Manufacturing Company standard cell library. It offers a speed of 486 MHz with a power consumption of 2.56 mW. This architecture is suitable for real-time video compression even with large frame dimensions.

Tightly Secure Signatures From Lossy Identification Schemes

OpenAIRE

Abdalla , Michel; Fouque , Pierre-Alain; Lyubashevsky , Vadim; Tibouchi , Mehdi

2015-01-01

International audience; In this paper, we present three digital signature schemes with tight security reductions in the random oracle model. Our first signature scheme is a particularly efficient version of the short exponent discrete log-based scheme of Girault et al. (J Cryptol 19(4):463–487, 2006). Our scheme has a tight reduction to the decisional short discrete logarithm problem, while still maintaining the non-tight reduction to the computational version of the problem upon which the or...

A dynamic discretization method for reliability inference in Dynamic Bayesian Networks

International Nuclear Information System (INIS)

Zhu, Jiandao; Collette, Matthew

2015-01-01

The material and modeling parameters that drive structural reliability analysis for marine structures are subject to a significant uncertainty. This is especially true when time-dependent degradation mechanisms such as structural fatigue cracking are considered. Through inspection and monitoring, information such as crack location and size can be obtained to improve these parameters and the corresponding reliability estimates. Dynamic Bayesian Networks (DBNs) are a powerful and flexible tool to model dynamic system behavior and update reliability and uncertainty analysis with life cycle data for problems such as fatigue cracking. However, a central challenge in using DBNs is the need to discretize certain types of continuous random variables to perform network inference while still accurately tracking low-probability failure events. Most existing discretization methods focus on getting the overall shape of the distribution correct, with less emphasis on the tail region. Therefore, a novel scheme is presented specifically to estimate the likelihood of low-probability failure events. The scheme is an iterative algorithm which dynamically partitions the discretization intervals at each iteration. Through applications to two stochastic crack-growth example problems, the algorithm is shown to be robust and accurate. Comparisons are presented between the proposed approach and existing methods for the discretization problem. - Highlights: • A dynamic discretization method is developed for low-probability events in DBNs. • The method is compared to existing approaches on two crack growth problems. • The method is shown to improve on existing methods for low-probability events

Semi-Markov processes

CERN Document Server

Grabski

2014-01-01

Semi-Markov Processes: Applications in System Reliability and Maintenance is a modern view of discrete state space and continuous time semi-Markov processes and their applications in reliability and maintenance. The book explains how to construct semi-Markov models and discusses the different reliability parameters and characteristics that can be obtained from those models. The book is a useful resource for mathematicians, engineering practitioners, and PhD and MSc students who want to understand the basic concepts and results of semi-Markov process theory. Clearly defines the properties and

A coarse-mesh diffusion synthetic acceleration of the source iteration scheme for one-speed discrete ordinates transport calculations in Slab geometry

International Nuclear Information System (INIS)

Santos, Frederico P.; Xavier, Vinicius S.; Alves Filho, Hermes; Barros, Ricardo C.

2011-01-01

The scattering source iterative (SI) scheme is traditionally applied to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S N ) neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as initial guess for the fine-mesh scattering source, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the classical S N prescribed boundary conditions, including vacuum boundary conditions. Therefore, we first implement a spectral nodal method that generates coarse-mesh diffusion solution that is completely free from spatial truncation errors, then we reconstruct this coarse-mesh solution within each spatial cell of the discretization grid, to further yield the initial guess for the fine-mesh scattering source in the first S N transport sweep (μm > 0 and μm < 0, m = 1:N) across the spatial grid. We consider a number of numerical experiments to illustrate the efficiency of the offered diffusion synthetic acceleration (DSA) technique. (author)

Maximum principle and convergence of central schemes based on slope limiters

KAUST Repository

Mehmetoglu, Orhan; Popov, Bojan

2012-01-01

A maximum principle and convergence of second order central schemes is proven for scalar conservation laws in dimension one. It is well known that to establish a maximum principle a nonlinear piecewise linear reconstruction is needed and a typical choice is the minmod limiter. Unfortunately, this implies that the scheme uses a first order reconstruction at local extrema. The novelty here is that we allow local nonlinear reconstructions which do not reduce to first order at local extrema and still prove maximum principle and convergence. © 2011 American Mathematical Society.

Direct and semi-direct approaches to lepton mixing with a massless neutrino

International Nuclear Information System (INIS)

King, Stephen F.; Ludl, Patrick Otto

2016-01-01

We discuss the possibility of enforcing a massless Majorana neutrino in the direct and semi-direct approaches to lepton mixing, in which the PMNS matrix is partly predicted by subgroups of a discrete family symmetry, extending previous group searches up to order 1535. We find a phenomenologically viable scheme for the semi-direct approach based on Q(648) which contains Δ(27) and the quaternion group as subgroups. This leads to novel predictions for the first column of the PMNS matrix corresponding to a normal neutrino mass hierarchy with m_1=0, and sum rules for the mixing angles and phase which are characterised by the solar angle being on the low side θ_1_2∼31"∘ and the Dirac (oscillation) CP phase δ being either about ±45"∘ or ±π.

Efficiency and Flexibility of Fingerprint Scheme Using Partial Encryption and Discrete Wavelet Transform to Verify User in Cloud Computing.

Science.gov (United States)

Yassin, Ali A

2014-01-01

Now, the security of digital images is considered more and more essential and fingerprint plays the main role in the world of image. Furthermore, fingerprint recognition is a scheme of biometric verification that applies pattern recognition techniques depending on image of fingerprint individually. In the cloud environment, an adversary has the ability to intercept information and must be secured from eavesdroppers. Unluckily, encryption and decryption functions are slow and they are often hard. Fingerprint techniques required extra hardware and software; it is masqueraded by artificial gummy fingers (spoof attacks). Additionally, when a large number of users are being verified at the same time, the mechanism will become slow. In this paper, we employed each of the partial encryptions of user's fingerprint and discrete wavelet transform to obtain a new scheme of fingerprint verification. Moreover, our proposed scheme can overcome those problems; it does not require cost, reduces the computational supplies for huge volumes of fingerprint images, and resists well-known attacks. In addition, experimental results illustrate that our proposed scheme has a good performance of user's fingerprint verification.

A modified symplectic PRK scheme for seismic wave modeling

Science.gov (United States)

Liu, Shaolin; Yang, Dinghui; Ma, Jian

2017-02-01

A new scheme for the temporal discretization of the seismic wave equation is constructed based on symplectic geometric theory and a modified strategy. The ordinary differential equation in terms of time, which is obtained after spatial discretization via the spectral-element method, is transformed into a Hamiltonian system. A symplectic partitioned Runge-Kutta (PRK) scheme is used to solve the Hamiltonian system. A term related to the multiplication of the spatial discretization operator with the seismic wave velocity vector is added into the symplectic PRK scheme to create a modified symplectic PRK scheme. The symplectic coefficients of the new scheme are determined via Taylor series expansion. The positive coefficients of the scheme indicate that its long-term computational capability is more powerful than that of conventional symplectic schemes. An exhaustive theoretical analysis reveals that the new scheme is highly stable and has low numerical dispersion. The results of three numerical experiments demonstrate the high efficiency of this method for seismic wave modeling.

A semi-symmetric image encryption scheme based on the function projective synchronization of two hyperchaotic systems.

Directory of Open Access Journals (Sweden)

Xiaoqiang Di

Full Text Available Both symmetric and asymmetric color image encryption have advantages and disadvantages. In order to combine their advantages and try to overcome their disadvantages, chaos synchronization is used to avoid the key transmission for the proposed semi-symmetric image encryption scheme. Our scheme is a hybrid chaotic encryption algorithm, and it consists of a scrambling stage and a diffusion stage. The control law and the update rule of function projective synchronization between the 3-cell quantum cellular neural networks (QCNN response system and the 6th-order cellular neural network (CNN drive system are formulated. Since the function projective synchronization is used to synchronize the response system and drive system, Alice and Bob got the key by two different chaotic systems independently and avoid the key transmission by some extra security links, which prevents security key leakage during the transmission. Both numerical simulations and security analyses such as information entropy analysis, differential attack are conducted to verify the feasibility, security, and efficiency of the proposed scheme.

Conservative numerical schemes for Euler-Lagrange equations

Energy Technology Data Exchange (ETDEWEB)

Vazquez, L. [Universidad Complutense, Madrid (Spain). Dept. de Matematica Aplicada; Jimenez, S. [Universidad Alfonso X El Sabio, Madrid (Spain). Dept. de Matematica Aplicada

1999-05-01

As a preliminary step to study magnetic field lines, the authors seek numerical schemes that reproduce at discrete level the significant feature of the continuous model, based on an underling Lagrangian structure. The resulting scheme give discrete counterparts of the variation law for the energy as well of as the Euler-Lagrange equations and their symmetries.

Flux form Semi-Lagrangian methods for parabolic problems

Directory of Open Access Journals (Sweden)

Bonaventura Luca

2016-09-01

Full Text Available A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and stability analysis is proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection diffusion and nonlinear parabolic problems.

Euler-Poincare reduction for discrete field theories

International Nuclear Information System (INIS)

Vankerschaver, Joris

2007-01-01

In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed

Multiscale solutions of radiative heat transfer by the discrete unified gas kinetic scheme

Science.gov (United States)

Luo, Xiao-Ping; Wang, Cun-Hai; Zhang, Yong; Yi, Hong-Liang; Tan, He-Ping

2018-06-01

The radiative transfer equation (RTE) has two asymptotic regimes characterized by the optical thickness, namely, optically thin and optically thick regimes. In the optically thin regime, a ballistic or kinetic transport is dominant. In the optically thick regime, energy transport is totally dominated by multiple collisions between photons; that is, the photons propagate by means of diffusion. To obtain convergent solutions to the RTE, conventional numerical schemes have a strong dependence on the number of spatial grids, which leads to a serious computational inefficiency in the regime where the diffusion is predominant. In this work, a discrete unified gas kinetic scheme (DUGKS) is developed to predict radiative heat transfer in participating media. Numerical performances of the DUGKS are compared in detail with conventional methods through three cases including one-dimensional transient radiative heat transfer, two-dimensional steady radiative heat transfer, and three-dimensional multiscale radiative heat transfer. Due to the asymptotic preserving property, the present method with relatively coarse grids gives accurate and reliable numerical solutions for large, small, and in-between values of optical thickness, and, especially in the optically thick regime, the DUGKS demonstrates a pronounced computational efficiency advantage over the conventional numerical models. In addition, the DUGKS has a promising potential in the study of multiscale radiative heat transfer inside the participating medium with a transition from optically thin to optically thick regimes.

Integrable discretizations for the short-wave model of the Camassa-Holm equation

International Nuclear Information System (INIS)

Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro

2010-01-01

The link between the short-wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice equation is clarified. The parametric form of the N-cuspon solution of the SCHE in Casorati determinant is then given. Based on the above finding, integrable semi-discrete and full-discrete analogues of the SCHE are constructed. The determinant solutions of both semi-discrete and fully discrete analogues of the SCHE are also presented.

Comparative ecobalancing accounting of semi-central house heat supply from wood residues

International Nuclear Information System (INIS)

Biemann, Kirsten

2015-01-01

In 2008 almost 40 percent of the German final energy demand was used for room heating and hot water supply. To decrease environmental burdens and to save fossil resources a restructuring of the heating sector is needed. Therefore legislation enforces higher insulation standards of buildings and a more frequent use of renewable energies as well as heating networks. Wood as a renewable and storable energy source is an attractive fuel. However, it must be used as efficiently as possible because of limited wood supplies. Connecting buildings via a heating network is a good option since bigger heating plants can operate at higher efficiencies than small heaters. However, the higher insulation standards of the buildings often oppose the construction of a heating network, because heating networks work best with high energy demands and low network lengths. Therefore the environmental and economic feasibility of new heating networks needs to be checked beforehand. This thesis explores the environmental burdens of different semi- centralized heating networks using wood residues as fuel. A semi- centralized heating network is a network with no more than 500 customers and a heating plant with less than 5 MWth. While wood residues are used in the base load plant, peak load is covered by a gas heating plant. As a method to analyze the potential environmental burdens of the heat supply a life cycle assessment according to ISO 14040/44 is used. Opposed to former life cycle assessment studies, construction and operation of the network is included in the assessment. Even though the environmental impacts of the semi- centralized heating from wood residues are dominated by the heat supply, an observation of the impacts solely at the heating plant is not sufficient. By varying the boundary conditions of the heating network two main contributors to the environmental impacts are found. In addition to the heat production at the plant the type of the buildings in the settlement has a huge

String constraints on discrete symmetries in MSSM type II quivers

Energy Technology Data Exchange (ETDEWEB)

Anastasopoulos, Pascal [Technische Univ. Wien (Austria). Inst. fur Theor. Phys.; Cvetic, Mirjam [Univ. of Pennsylvania, Philadelphia PA (United States). Dept. of Physics and Astronomy; Univ. of Maribor (Slovenia). Center for Applied Mathematics and Theoretical Physics; Richter, Robert [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2012-11-15

We study the presence of discrete gauge symmetries in D-brane semirealistic compactifications. After establishing the constraints on the transformation behaviour of the chiral matter for the presence of a discrete gauge symmetry we perform a systematic search for discrete gauge symmetries within semi-realistic D-brane realizations, based on four D-brane stacks, of the MSSM and the MSSM with three right-handed neutrinos. The systematic search reveals that Proton hexality, a discrete symmetry which ensures the absence of R-parity violating terms as well as the absence of dangerous dimension 5 proton decay operators, is only rarely realized. Moreover, none of the semi-realistic local D-brane configurations exhibit any family dependent discrete gauge symmetry.

Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method

Energy Technology Data Exchange (ETDEWEB)

Le Hardy, D. [Université de Nantes, LTN UMR CNRS 6607 (France); Favennec, Y., E-mail: yann.favennec@univ-nantes.fr [Université de Nantes, LTN UMR CNRS 6607 (France); Rousseau, B. [Université de Nantes, LTN UMR CNRS 6607 (France); Hecht, F. [Sorbonne Universités, UPMC Université Paris 06, UMR 7598, inria de Paris, Laboratoire Jacques-Louis Lions, F-75005, Paris (France)

2017-04-01

The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken into account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.

Comparative ecobalancing accounting of semi-central house heat supply from wood residues; Vergleichende Oekobilanzierung der semi-zentralen Hauswaermebereitstellung aus Holzreststoffen

Energy Technology Data Exchange (ETDEWEB)

Biemann, Kirsten

2015-07-01

In 2008 almost 40 percent of the German final energy demand was used for room heating and hot water supply. To decrease environmental burdens and to save fossil resources a restructuring of the heating sector is needed. Therefore legislation enforces higher insulation standards of buildings and a more frequent use of renewable energies as well as heating networks. Wood as a renewable and storable energy source is an attractive fuel. However, it must be used as efficiently as possible because of limited wood supplies. Connecting buildings via a heating network is a good option since bigger heating plants can operate at higher efficiencies than small heaters. However, the higher insulation standards of the buildings often oppose the construction of a heating network, because heating networks work best with high energy demands and low network lengths. Therefore the environmental and economic feasibility of new heating networks needs to be checked beforehand. This thesis explores the environmental burdens of different semi- centralized heating networks using wood residues as fuel. A semi- centralized heating network is a network with no more than 500 customers and a heating plant with less than 5 MWth. While wood residues are used in the base load plant, peak load is covered by a gas heating plant. As a method to analyze the potential environmental burdens of the heat supply a life cycle assessment according to ISO 14040/44 is used. Opposed to former life cycle assessment studies, construction and operation of the network is included in the assessment. Even though the environmental impacts of the semi- centralized heating from wood residues are dominated by the heat supply, an observation of the impacts solely at the heating plant is not sufficient. By varying the boundary conditions of the heating network two main contributors to the environmental impacts are found. In addition to the heat production at the plant the type of the buildings in the settlement has a huge

Semi-Markov Chains and Hidden Semi-Markov Models toward Applications Their Use in Reliability and DNA Analysis

CERN Document Server

Barbu, Vlad

2008-01-01

Semi-Markov processes are much more general and better adapted to applications than the Markov ones because sojourn times in any state can be arbitrarily distributed, as opposed to the geometrically distributed sojourn time in the Markov case. This book concerns with the estimation of discrete-time semi-Markov and hidden semi-Markov processes

Lyapunov-Based Control Scheme for Single-Phase Grid-Connected PV Central Inverters

NARCIS (Netherlands)

Meza, C.; Biel, D.; Jeltsema, D.; Scherpen, J. M. A.

A Lyapunov-based control scheme for single-phase single-stage grid-connected photovoltaic central inverters is presented. Besides rendering the closed-loop system globally stable, the designed controller is able to deal with the system uncertainty that depends on the solar irradiance. A laboratory

Frames and semi-frames

International Nuclear Information System (INIS)

Antoine, Jean-Pierre; Balazs, Peter

2011-01-01

Loosely speaking, a semi-frame is a generalized frame for which one of the frame bounds is absent. More precisely, given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded inverse, whereas a lower semi-frame has an unbounded frame operator, with a bounded inverse. We study mostly upper semi-frames, both in the continuous and discrete case, and give some remarks for the dual situation. In particular, we show that reconstruction is still possible in certain cases.

A semi-physical simulation platform of attitude determination and control system for satellite

Directory of Open Access Journals (Sweden)

Yuanjin Yu

2016-05-01

Full Text Available A semi-physical simulation platform for attitude determination and control system is proposed to verify the attitude estimator and controller on ground. A simulation target, a host PC, many attitude sensors, and actuators compose the simulation platform. The simulation target is composed of a central processing unit board with VxWorks operating system and many input/output boards connected via Compact Peripheral Component Interconnect bus. The executable programs in target are automatically generated from the simulation models in Simulink based on Real-Time Workshop of MATLAB. A three-axes gyroscope, a three-axes magnetometer, a sun sensor, a star tracer, three flywheels, and a Global Positioning System receiver are connected to the simulation target, which formulates the attitude control cycle of a satellite. The simulation models of the attitude determination and control system are described in detail. Finally, the semi-physical simulation platform is used to demonstrate the availability and rationality of the control scheme of a micro-satellite. Comparing the results between the numerical simulation in Simulink and the semi-physical simulation, the semi-physical simulation platform is available and the control scheme successfully achieves three-axes stabilization.

Semi-Lagrangian methods in air pollution models

Directory of Open Access Journals (Sweden)

A. B. Hansen

2011-06-01

Full Text Available Various semi-Lagrangian methods are tested with respect to advection in air pollution modeling. The aim is to find a method fulfilling as many of the desirable properties by Rasch andWilliamson (1990 and Machenhauer et al. (2008 as possible. The focus in this study is on accuracy and local mass conservation.

The methods tested are, first, classical semi-Lagrangian cubic interpolation, see e.g. Durran (1999, second, semi-Lagrangian cubic cascade interpolation, by Nair et al. (2002, third, semi-Lagrangian cubic interpolation with the modified interpolation weights, Locally Mass Conserving Semi-Lagrangian (LMCSL, by Kaas (2008, and last, semi-Lagrangian cubic interpolation with a locally mass conserving monotonic filter by Kaas and Nielsen (2010.

Semi-Lagrangian (SL interpolation is a classical method for atmospheric modeling, cascade interpolation is more efficient computationally, modified interpolation weights assure mass conservation and the locally mass conserving monotonic filter imposes monotonicity.

All schemes are tested with advection alone or with advection and chemistry together under both typical rural and urban conditions using different temporal and spatial resolution. The methods are compared with a current state-of-the-art scheme, Accurate Space Derivatives (ASD, see Frohn et al. (2002, presently used at the National Environmental Research Institute (NERI in Denmark. To enable a consistent comparison only non-divergent flow configurations are tested.

The test cases are based either on the traditional slotted cylinder or the rotating cone, where the schemes' ability to model both steep gradients and slopes are challenged.

The tests showed that the locally mass conserving monotonic filter improved the results significantly for some of the test cases, however, not for all. It was found that the semi-Lagrangian schemes, in almost every case, were not able to outperform the current ASD scheme

A more accurate scheme for calculating Earth's skin temperature

Science.gov (United States)

Tsuang, Ben-Jei; Tu, Chia-Ying; Tsai, Jeng-Lin; Dracup, John A.; Arpe, Klaus; Meyers, Tilden

2009-02-01

The theoretical framework of the vertical discretization of a ground column for calculating Earth’s skin temperature is presented. The suggested discretization is derived from the evenly heat-content discretization with the optimal effective thickness for layer-temperature simulation. For the same level number, the suggested discretization is more accurate in skin temperature as well as surface ground heat flux simulations than those used in some state-of-the-art models. A proposed scheme (“op(3,2,0)”) can reduce the normalized root-mean-square error (or RMSE/STD ratio) of the calculated surface ground heat flux of a cropland site significantly to 2% (or 0.9 W m-2), from 11% (or 5 W m-2) by a 5-layer scheme used in ECMWF, from 19% (or 8 W m-2) by a 5-layer scheme used in ECHAM, and from 74% (or 32 W m-2) by a single-layer scheme used in the UCLA GCM. Better accuracy can be achieved by including more layers to the vertical discretization. Similar improvements are expected for other locations with different land types since the numerical error is inherited into the models for all the land types. The proposed scheme can be easily implemented into state-of-the-art climate models for the temperature simulation of snow, ice and soil.

Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system

KAUST Repository

Bryson, Steve

2010-10-11

We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves "lake at rest" steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples. © EDP Sciences, SMAI, 2010.

Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system

KAUST Repository

Bryson, Steve; Epshteyn, Yekaterina; Kurganov, Alexander; Petrova, Guergana

2010-01-01

We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves "lake at rest" steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples. © EDP Sciences, SMAI, 2010.

Discrete integrable systems and deformations of associative algebras

International Nuclear Information System (INIS)

Konopelchenko, B G

2009-01-01

Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. Theory of deformations for associative algebras is presented. Closed left ideal generated by the elements representing the multiplication table plays a central role in this theory. Deformations of the structure constants are generated by the deformation driving algebra and governed by the central system of equations. It is demonstrated that many discrete equations such as discrete Boussinesq equation, discrete WDVV equation, discrete Schwarzian KP and BKP equations, discrete Hirota-Miwa equations for KP and BKP hierarchies are particular realizations of the central system. An interaction between the theories of discrete integrable systems and discrete deformations of associative algebras is reciprocal and fruitful. An interpretation of the Menelaus relation (discrete Schwarzian KP equation), discrete Hirota-Miwa equation for KP hierarchy, consistency around the cube as the associativity conditions and the concept of gauge equivalence, for instance, between the Menelaus and KP configurations are particular examples.

How update schemes influence crowd simulations

International Nuclear Information System (INIS)

Seitz, Michael J; Köster, Gerta

2014-01-01

Time discretization is a key modeling aspect of dynamic computer simulations. In current pedestrian motion models based on discrete events, e.g. cellular automata and the Optimal Steps Model, fixed-order sequential updates and shuffle updates are prevalent. We propose to use event-driven updates that process events in the order they occur, and thus better match natural movement. In addition, we present a parallel update with collision detection and resolution for situations where computational speed is crucial. Two simulation studies serve to demonstrate the practical impact of the choice of update scheme. Not only do density-speed relations differ, but there is a statistically significant effect on evacuation times. Fixed-order sequential and random shuffle updates with a short update period come close to event-driven updates. The parallel update scheme overestimates evacuation times. All schemes can be employed for arbitrary simulation models with discrete events, such as car traffic or animal behavior. (paper)

Lax Pairs for Discrete Integrable Equations via Darboux Transformations

International Nuclear Information System (INIS)

Cao Ce-Wen; Zhang Guang-Yao

2012-01-01

A method is developed to construct discrete Lax pairs using Darboux transformations. More kinds of Lax pairs are found for some newly appeared discrete integrable equations, including the H1, the special H3 and the Q1 models in the Adler—Bobenko—Suris list and the closely related discrete and semi-discrete pKdV, pMKdV, SG and Liouville equations. (general)

Spectrum Control through Discrete Frequency Diffraction in the Presence of Photonic Gauge Potentials

Science.gov (United States)

Qin, Chengzhi; Zhou, Feng; Peng, Yugui; Sounas, Dimitrios; Zhu, Xuefeng; Wang, Bing; Dong, Jianji; Zhang, Xinliang; Alù; , Andrea; Lu, Peixiang

2018-03-01

By using optical phase modulators in a fiber-optical circuit, we theoretically and experimentally demonstrate large control over the spectrum of an impinging signal, which may evolve analogously to discrete diffraction in spatial waveguide arrays. The modulation phase acts as a photonic gauge potential in the frequency dimension, realizing efficient control of the central frequency and bandwidth of frequency combs. We experimentally achieve a 50 GHz frequency shift and threefold bandwidth expansion of an impinging comb, as well as the frequency analogue of various refraction phenomena, including negative refraction and perfect focusing in the frequency domain, both for discrete and continuous incident spectra. Our study paves a promising way towards versatile frequency management for optical communications and signal processing using time modulation schemes.

Optimized waveform relaxation domain decomposition method for discrete finite volume non stationary convection diffusion equation

International Nuclear Information System (INIS)

Berthe, P.M.

2013-01-01

In the context of nuclear waste repositories, we consider the numerical discretization of the non stationary convection diffusion equation. Discontinuous physical parameters and heterogeneous space and time scales lead us to use different space and time discretizations in different parts of the domain. In this work, we choose the discrete duality finite volume (DDFV) scheme and the discontinuous Galerkin scheme in time, coupled by an optimized Schwarz waveform relaxation (OSWR) domain decomposition method, because this allows the use of non-conforming space-time meshes. The main difficulty lies in finding an upwind discretization of the convective flux which remains local to a sub-domain and such that the multi domain scheme is equivalent to the mono domain one. These difficulties are first dealt with in the one-dimensional context, where different discretizations are studied. The chosen scheme introduces a hybrid unknown on the cell interfaces. The idea of up winding with respect to this hybrid unknown is extended to the DDFV scheme in the two-dimensional setting. The well-posedness of the scheme and of an equivalent multi domain scheme is shown. The latter is solved by an OSWR algorithm, the convergence of which is proved. The optimized parameters in the Robin transmission conditions are obtained by studying the continuous or discrete convergence rates. Several test-cases, one of which inspired by nuclear waste repositories, illustrate these results. (author) [fr

Adaptive Control and Function Projective Synchronization in 2D Discrete-Time Chaotic Systems

International Nuclear Information System (INIS)

Li Yin; Chen Yong; Li Biao

2009-01-01

This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discrete-time chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.

Variational discretization of the nonequilibrium thermodynamics of simple systems

Science.gov (United States)

Gay-Balmaz, François; Yoshimura, Hiroaki

2018-04-01

In this paper, we develop variational integrators for the nonequilibrium thermodynamics of simple closed systems. These integrators are obtained by a discretization of the Lagrangian variational formulation of nonequilibrium thermodynamics developed in (Gay-Balmaz and Yoshimura 2017a J. Geom. Phys. part I 111 169–93 Gay-Balmaz and Yoshimura 2017b J. Geom. Phys. part II 111 194–212) and thus extend the variational integrators of Lagrangian mechanics, to include irreversible processes. In the continuous setting, we derive the structure preserving property of the flow of such systems. This property is an extension of the symplectic property of the flow of the Euler–Lagrange equations. In the discrete setting, we show that the discrete flow solution of our numerical scheme verifies a discrete version of this property. We also present the regularity conditions which ensure the existence of the discrete flow. We finally illustrate our discrete variational schemes with the implementation of an example of a simple and closed system.

Four-level conservative finite-difference schemes for Boussinesq paradigm equation

Science.gov (United States)

Kolkovska, N.

2013-10-01

In this paper a two-parametric family of four level conservative finite difference schemes is constructed for the multidimensional Boussinesq paradigm equation. The schemes are explicit in the sense that no inner iterations are needed for evaluation of the numerical solution. The preservation of the discrete energy with this method is proved. The schemes have been numerically tested on one soliton propagation model and two solitons interaction model. The numerical experiments demonstrate that the proposed family of schemes has second order of convergence in space and time steps in the discrete maximal norm.

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

Mohamed, Mamdouh S.

2016-02-11

A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

Science.gov (United States)

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-05-01

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

On the mixed discretization of the time domain magnetic field integral equation

KAUST Repository

Ulku, Huseyin Arda

2012-09-01

Time domain magnetic field integral equation (MFIE) is discretized using divergence-conforming Rao-Wilton-Glisson (RWG) and curl-conforming Buffa-Christiansen (BC) functions as spatial basis and testing functions, respectively. The resulting mixed discretization scheme, unlike the classical scheme which uses RWG functions as both basis and testing functions, is proper: Testing functions belong to dual space of the basis functions. Numerical results demonstrate that the marching on-in-time (MOT) solution of the mixed discretized MFIE yields more accurate results than that of classically discretized MFIE. © 2012 IEEE.

Function Projective Synchronization in Discrete-Time Chaotic System with Uncertain Parameters

International Nuclear Information System (INIS)

Chen Yong; Li Xin

2009-01-01

The function projective synchronization of discrete-time chaotic systems is presented. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate function projective synchronization (FPS) of discrete-time chaotic systems with uncertain parameters. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate FPS between two identical 3D Henon-like maps with uncertain parameters. Numeric simulations are used to verify the effectiveness of our scheme. (general)

Semi-quantum communication: protocols for key agreement, controlled secure direct communication and dialogue

Science.gov (United States)

Shukla, Chitra; Thapliyal, Kishore; Pathak, Anirban

2017-12-01

Semi-quantum protocols that allow some of the users to remain classical are proposed for a large class of problems associated with secure communication and secure multiparty computation. Specifically, first-time semi-quantum protocols are proposed for key agreement, controlled deterministic secure communication and dialogue, and it is shown that the semi-quantum protocols for controlled deterministic secure communication and dialogue can be reduced to semi-quantum protocols for e-commerce and private comparison (socialist millionaire problem), respectively. Complementing with the earlier proposed semi-quantum schemes for key distribution, secret sharing and deterministic secure communication, set of schemes proposed here and subsequent discussions have established that almost every secure communication and computation tasks that can be performed using fully quantum protocols can also be performed in semi-quantum manner. Some of the proposed schemes are completely orthogonal-state-based, and thus, fundamentally different from the existing semi-quantum schemes that are conjugate coding-based. Security, efficiency and applicability of the proposed schemes have been discussed with appropriate importance.

Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

Directory of Open Access Journals (Sweden)

Baogui Xin

2015-04-01

Full Text Available A projective synchronization scheme for a kind of n-dimensional discrete dynamical system is proposed by means of a linear feedback control technique. The scheme consists of master and slave discrete dynamical systems coupled by linear state error variables. A kind of novel 3-D chaotic discrete system is constructed, to which the test for chaos is applied. By using the stability principles of an upper or lower triangular matrix, two controllers for achieving projective synchronization are designed and illustrated with the novel systems. Lastly some numerical simulations are employed to validate the effectiveness of the proposed projective synchronization scheme.

Charge-conserving FEM-PIC schemes on general grids

International Nuclear Information System (INIS)

Campos Pinto, M.; Jund, S.; Salmon, S.; Sonnendruecker, E.

2014-01-01

Particle-In-Cell (PIC) solvers are a major tool for the understanding of the complex behavior of a plasma or a particle beam in many situations. An important issue for electromagnetic PIC solvers, where the fields are computed using Maxwell's equations, is the problem of discrete charge conservation. In this article, we aim at proposing a general mathematical formulation for charge-conserving finite-element Maxwell solvers coupled with particle schemes. In particular, we identify the finite-element continuity equations that must be satisfied by the discrete current sources for several classes of time-domain Vlasov-Maxwell simulations to preserve the Gauss law at each time step, and propose a generic algorithm for computing such consistent sources. Since our results cover a wide range of schemes (namely curl-conforming finite element methods of arbitrary degree, general meshes in two or three dimensions, several classes of time discretization schemes, particles with arbitrary shape factors and piecewise polynomial trajectories of arbitrary degree), we believe that they provide a useful roadmap in the design of high-order charge-conserving FEM-PIC numerical schemes. (authors)

Random discrete Morse theory and a new library of triangulations

DEFF Research Database (Denmark)

Benedetti, Bruno; Lutz, Frank Hagen

2014-01-01

We introduce random discrete Morse theory as a computational scheme to measure the complexity of a triangulation. The idea is to try to quantify the frequency of discrete Morse matchings with few critical cells. Our measure will depend on the topology of the space, but also on how nicely the space...... is triangulated. The scheme we propose looks for optimal discrete Morse functions with an elementary random heuristic. Despite its naiveté, this approach turns out to be very successful even in the case of huge inputs. In our view, the existing libraries of examples in computational topology are “too easy......” for testing algorithms based on discrete Morse theory. We propose a new library containing more complicated (and thus more meaningful) test examples....

Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method

Energy Technology Data Exchange (ETDEWEB)

Yang, Xiaofeng, E-mail: xfyang@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Zhao, Jia, E-mail: zhao62@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 (United States); Wang, Qi, E-mail: qwang@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Beijing Computational Science Research Center, Beijing (China); School of Materials Science and Engineering, Nankai University, Tianjin (China)

2017-03-15

The Molecular Beam Epitaxial model is derived from the variation of a free energy, that consists of either a fourth order Ginzburg–Landau double well potential or a nonlinear logarithmic potential in terms of the gradient of a height function. One challenge in solving the MBE model numerically is how to develop proper temporal discretization for the nonlinear terms in order to preserve energy stability at the time-discrete level. In this paper, we resolve this issue by developing a first and second order time-stepping scheme based on the “Invariant Energy Quadratization” (IEQ) method. The novelty is that all nonlinear terms are treated semi-explicitly, and the resulted semi-discrete equations form a linear system at each time step. Moreover, the linear operator is symmetric positive definite and thus can be solved efficiently. We then prove that all proposed schemes are unconditionally energy stable. The semi-discrete schemes are further discretized in space using finite difference methods and implemented on GPUs for high-performance computing. Various 2D and 3D numerical examples are presented to demonstrate stability and accuracy of the proposed schemes.

Optimized low-order explicit Runge-Kutta schemes for high- order spectral difference method

KAUST Repository

Parsani, Matteo

2012-01-01

Optimal explicit Runge-Kutta (ERK) schemes with large stable step sizes are developed for method-of-lines discretizations based on the spectral difference (SD) spatial discretization on quadrilateral grids. These methods involve many stages and provide the optimal linearly stable time step for a prescribed SD spectrum and the minimum leading truncation error coefficient, while admitting a low-storage implementation. Using a large number of stages, the new ERK schemes lead to efficiency improvements larger than 60% over standard ERK schemes for 4th- and 5th-order spatial discretization.

Semi-classical signal analysis

KAUST Repository

Laleg-Kirati, Taous-Meriem; Cré peau, Emmanuelle; Sorine, Michel

2012-01-01

This study introduces a new signal analysis method, based on a semi-classical approach. The main idea in this method is to interpret a pulse-shaped signal as a potential of a Schrödinger operator and then to use the discrete spectrum

Application of a discrete-energy, discrete-ordinates technique to the study of neutron transport in iron

International Nuclear Information System (INIS)

Ching, J.T.

1975-01-01

An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated which allows the development of a discrete-energy, discrete-ordinates method for the solution of radiation transport problems. The method utilizes a modified version of a cross section processing scheme devised for the moments method code BMT and the transport equation solution algorithm from the one-dimensional discrete-ordinates transport code ANISN. The combined system, identified as MOMANS, computes fluxes directly from point cross sections in a single operation. In the cross-section processing, the group averaging required for multigroup calculations is replaced by a fast numerical scheme capable of generating a set of transfer cross sections containing all the physical features of interest, thereby increasing the detail in the calculated results. Test calculations in which the discrete-energy method was compared with the multigroup method have shown that for the same energy grid (number of points = number of groups), the discrete-energy method is faster but somewhat less accurate than the multigroup method. However, the accuracy of the discrete-energy method increases rapidly as the spacing between energy points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum the discrete-energy method has therefore proven to be as accurate as, and more economical than, the multigroup technique. This was demonstrated by the application of the method to the study of the transport of neutrons in an iron sphere. Using the capability of the discrete-energy method for rapidly treating changes in cross-section sets, the propagation of neutrons from a 14 MeV source in a 22 cm radius sphere of iron was analyzed for sensitivity to changes in the microscopic scattering mechanisms

A novel system architecture for the national integration of electronic health records: a semi-centralized approach.

Science.gov (United States)

AlJarullah, Asma; El-Masri, Samir

2013-08-01

The goal of a national electronic health records integration system is to aggregate electronic health records concerning a particular patient at different healthcare providers' systems to provide a complete medical history of the patient. It holds the promise to address the two most crucial challenges to the healthcare systems: improving healthcare quality and controlling costs. Typical approaches for the national integration of electronic health records are a centralized architecture and a distributed architecture. This paper proposes a new approach for the national integration of electronic health records, the semi-centralized approach, an intermediate solution between the centralized architecture and the distributed architecture that has the benefits of both approaches. The semi-centralized approach is provided with a clearly defined architecture. The main data elements needed by the system are defined and the main system modules that are necessary to achieve an effective and efficient functionality of the system are designed. Best practices and essential requirements are central to the evolution of the proposed architecture. The proposed architecture will provide the basis for designing the simplest and the most effective systems to integrate electronic health records on a nation-wide basis that maintain integrity and consistency across locations, time and systems, and that meet the challenges of interoperability, security, privacy, maintainability, mobility, availability, scalability, and load balancing.

The Performance-based Funding Scheme of Universities

Directory of Open Access Journals (Sweden)

Juha KETTUNEN

2016-05-01

Full Text Available The purpose of this study is to analyse the effectiveness of the performance-based funding scheme of the Finnish universities that was adopted at the beginning of 2013. The political decision-makers expect that the funding scheme will create incentives for the universities to improve performance, but these funding schemes have largely failed in many other countries, primarily because public funding is only a small share of the total funding of universities. This study is interesting because Finnish universities have no tuition fees, unlike in many other countries, and the state allocates funding based on the objectives achieved. The empirical evidence of the graduation rates indicates that graduation rates increased when a new scheme was adopted, especially among male students, who have more room for improvement than female students. The new performance-based funding scheme allocates the funding according to the output-based indicators and limits the scope of strategic planning and the autonomy of the university. The performance-based funding scheme is transformed to the strategy map of the balanced scorecard. The new funding scheme steers universities in many respects but leaves the research and teaching skills to the discretion of the universities. The new scheme has also diminished the importance of the performance agreements between the university and the Ministry. The scheme increases the incentives for universities to improve the processes and structures in order to attain as much public funding as possible. It is optimal for the central administration of the university to allocate resources to faculties and other organisational units following the criteria of the performance-based funding scheme. The new funding scheme has made the universities compete with each other, because the total funding to the universities is allocated to each university according to the funding scheme. There is a tendency that the funding schemes are occasionally

Determination of central q and effective mass on textor based on discrete Alfven wave (DAW) spectrum measurements

International Nuclear Information System (INIS)

Descamps, P.; Wassenhove, G. van; Koch, R.; Messiaen, A.M.; Vandenplas, P.E.; Lister, J.B.; Marmillod, P.

1990-01-01

The use of the discrete Alfven wave spectrum to determine the current density profile and the effective mass density of the plasma in the TEXTOR tokamak is studied; the measurement, the validity of which is discussed, confirms independently the central q(r=0)<1 already obtained by polarimetry. (orig.)

Towards the ultimate variance-conserving convection scheme

International Nuclear Information System (INIS)

Os, J.J.A.M. van; Uittenbogaard, R.E.

2004-01-01

In the past various arguments have been used for applying kinetic energy-conserving advection schemes in numerical simulations of incompressible fluid flows. One argument is obeying the programmed dissipation by viscous stresses or by sub-grid stresses in Direct Numerical Simulation and Large Eddy Simulation, see e.g. [Phys. Fluids A 3 (7) (1991) 1766]. Another argument is that, according to e.g. [J. Comput. Phys. 6 (1970) 392; 1 (1966) 119], energy-conserving convection schemes are more stable i.e. by prohibiting a spurious blow-up of volume-integrated energy in a closed volume without external energy sources. In the above-mentioned references it is stated that nonlinear instability is due to spatial truncation rather than to time truncation and therefore these papers are mainly concerned with the spatial integration. In this paper we demonstrate that discretized temporal integration of a spatially variance-conserving convection scheme can induce non-energy conserving solutions. In this paper the conservation of the variance of a scalar property is taken as a simple model for the conservation of kinetic energy. In addition, the derivation and testing of a variance-conserving scheme allows for a clear definition of kinetic energy-conserving advection schemes for solving the Navier-Stokes equations. Consequently, we first derive and test a strictly variance-conserving space-time discretization for the convection term in the convection-diffusion equation. Our starting point is the variance-conserving spatial discretization of the convection operator presented by Piacsek and Williams [J. Comput. Phys. 6 (1970) 392]. In terms of its conservation properties, our variance-conserving scheme is compared to other spatially variance-conserving schemes as well as with the non-variance-conserving schemes applied in our shallow-water solver, see e.g. [Direct and Large-eddy Simulation Workshop IV, ERCOFTAC Series, Kluwer Academic Publishers, 2001, pp. 409-287

An unstaggered central scheme on nonuniform grids for the simulation of a compressible two-phase flow model

Energy Technology Data Exchange (ETDEWEB)

Touma, Rony [Department of Computer Science & Mathematics, Lebanese American University, Beirut (Lebanon); Zeidan, Dia [School of Basic Sciences and Humanities, German Jordanian University, Amman (Jordan)

2016-06-08

In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potential of the proposed scheme.

Long-time behaviour of discretizations of the simple pendulum equation

Energy Technology Data Exchange (ETDEWEB)

Cieslinski, Jan L [Uniwersytet w Bialymstoku, Wydzial Fizyki, ul. Lipowa 41, 15-424 Bialystok (Poland); Ratkiewicz, Boguslaw [Doctoral Studies, Wydzial Fizyki, Uniwersytet Adama Mickiewicza, Poznan (Poland)], E-mail: janek@alpha.uwb.edu.pl, E-mail: bograt@poczta.onet.pl

2009-03-13

We compare several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. The chosen numerical schemes are either symplectic maps or integrable (energy-preserving) maps, or both. Therefore, they preserve qualitative features of solutions (such as periodicity). We describe characteristic periodic time dependences of numerical estimates of the period and the amplitude, and explain them as systematic numerical by-effects produced by any method. Finally, we propose a new numerical scheme which is a modification of the discrete gradient method. This modified discrete gradient method preserves (almost exactly) the period of small oscillations for any time step.

Long-time behaviour of discretizations of the simple pendulum equation

International Nuclear Information System (INIS)

Cieslinski, Jan L; Ratkiewicz, Boguslaw

2009-01-01

We compare several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. The chosen numerical schemes are either symplectic maps or integrable (energy-preserving) maps, or both. Therefore, they preserve qualitative features of solutions (such as periodicity). We describe characteristic periodic time dependences of numerical estimates of the period and the amplitude, and explain them as systematic numerical by-effects produced by any method. Finally, we propose a new numerical scheme which is a modification of the discrete gradient method. This modified discrete gradient method preserves (almost exactly) the period of small oscillations for any time step

An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids

Science.gov (United States)

English, R. Elliot; Qiu, Linhai; Yu, Yue; Fedkiw, Ronald

2013-12-01

We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we address separately through the development of a method for solving the heat diffusion equations. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. Internal curved boundaries such as at solid interfaces are handled using a simple immersed boundary approach which is directly applied to the Voronoi mesh in both the viscosity and pressure solves. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with stationary and moving solid bodies.

On Darboux-integrable semi-discrete chains

International Nuclear Information System (INIS)

Habibullin, Ismagil; Sakieva, Alfia; Zheltukhina, Natalya

2010-01-01

A differential-difference equation d/dx t (n+1,x) = f(x,t(n,x),t(n+1,x),d/dx t (n,x)) with unknown t(n, x) depending on the continuous and discrete variables x and n is studied. We call an equation of such kind Darboux integrable if there exist two functions (called integrals) F and I of a finite number of dynamical variables such that D x F = 0 and DI = I, where D x is the operator of total differentiation with respect to x and D is the shift operator: Dp(n) = p(n + 1). It is proved that the integrals can be brought to some canonical form. A method of construction of an explicit formula for a general solution to Darboux-integrable chains is discussed and such solutions are found for a class of chains.

Study of the seismic activity in central Ionian Islands via semi-Markov modelling

Science.gov (United States)

Pertsinidou, Christina Elisavet; Tsaklidis, George; Papadimitriou, Eleftheria

2017-06-01

The seismicity of the central Ionian Islands ( M ≥ 5.2, 1911-2014) is studied via a semi-Markov chain which is investigated in terms of the destination probabilities (occurrence probabilities). The interevent times are considered to follow geometric (in which case the semi-Markov model reduces to a Markov model) or Pareto distributions. The study of the destination probabilities is useful for forecasting purposes because they can provide the more probable earthquake magnitude and occurrence time. Using the first half of the data sample for the estimation procedure and the other half for forecasting purposes it is found that the time windows obtained by the destination probabilities include 72.9% of the observed earthquake occurrence times (for all magnitudes) and 71.4% for the larger ( M ≥ 6.0) ones.

A Fourth Order Formulation of DDM for Crack Analysis in Brittle Solids

Directory of Open Access Journals (Sweden)

Abolfazl Abdollahipour

2017-01-01

Full Text Available A fourth order formulation of the displacement discontinuity method (DDM is proposed for the crack analysis of brittle solids such as rocks, glasses, concretes and ceramics. A fourth order boundary collocation scheme is used for the discretization of each boundary element (the source element. In this approach, the source boundary element is divided into five sub-elements each recognized by a central node where the displacement discontinuity components are to be numerically evaluated. Three different formulating procedures are presented and their corresponding discretization schemes are discussed. A new discretization scheme is also proposed to use the fourth order formulation for the special crack tip elements which may be used to increase the accuracy of the stress and displacement fields near the crack ends. Therefore, these new crack tips discretizing schemes are also improved by using the proposed fourth order displacement discontinuity formulation and the corresponding shape functions for a bunch of five special crack tip elements. Some example problems in brittle fracture mechanics are solved for estimating the Mode I and Mode II stress intensity factors near the crack ends. These semi-analytical results are compared to those cited in the fracture mechanics literature whereby the high accuracy of the fourth order DDM formulation is demonstrated.

One-way functions based on the discrete logarithm problem in the groups meeting conditions C(3-T (6

Directory of Open Access Journals (Sweden)

N. V. Bezverkhniy

2014-01-01

Full Text Available In this work we are consider a possibility to create schemes of open key distribution in the groups meeting conditions C(3-T(6. Our constructions use the following algorithms.1. The algorithm that solves the membership problem for cyclic subgroups, also known as the discrete logarithm problem.2. The algorithm that solves the word problem in this class of groups.Our approach is based on the geometric methods of combinatorial group theory (the method of diagrams in groups.In a cryptographic scheme based on the open key distribution one-way functions are used, i.e. functions direct calculation of which must be much easier than that of the inverse one. Our task was to construct a one-way function using groups with small cancelation conditions C(3-T(6 and to compare the calculation complexity of this function with the calculation complexity of its inverse.P.W. Shor has shown in the paper that there exists a polynomial algorithm that can be implemented in a quantum computer to solve the discrete logarithm problem in the groups of units of finite fields and the rings of congruences mod n. This stimulated a series of investigations trying to find alternative complicated mathematical problems that can be used for construction of new asymmetric cryptosystems. For example, open key distribution systems based on the conjugacy problem in matrix groups and the braid groups were proposed.In the other papers the constructions used the discrete logarithm problem in the groups of inner automorphisms of semi-direct products of SL(2,Z and Zp and GL(2,Zp and Zp. groups. The paper of E. Sakalauskas, P. Tvarijonas, A. Raulinaitis proposed a scheme that uses a composition of two problems of group theory, namely the conjugacy problem and the discrete logarithm problem.Our results show that the scheme that we propose is of polynomial complexity. Therefore its security is not sufficient for further applications in communications. However the security can be improved

Geometric Structure-Preserving Discretization Schemes for Nonlinear Elasticity

Science.gov (United States)

2015-08-13

sufficient conditions for the compatibility of displacement gradient and the existence of stress functions on non-contractible bodies. The main...conditions. 15.  SUBJECT TERMS geometric theory for nonlinear elasticity, discrete exterior calculus 16.  SECURITY CLASSIFICATION OF: 17.  LIMITATION...complex allows one to readily derive the necessary and sufficient conditions for the compatibility of displacement gradient and the existence of stress

A Semi-Analytical Methodology for Multiwell Productivity Index of Well-Industry-Production-Scheme in Tight Oil Reservoirs

Directory of Open Access Journals (Sweden)

Guangfeng Liu

2018-04-01

Full Text Available Recently, the well-industry-production-scheme (WIPS has attracted more and more attention to improve tight oil recovery. However, multi-well pressure interference (MWPI induced by well-industry-production-scheme (WIPS strongly challenges the traditional transient pressure analysis methods, which focus on single multi-fractured horizontal wells (SMFHWs without MWPI. Therefore, a semi-analytical methodology for multiwell productivity index (MPI was proposed to study well performance of WIPS scheme in tight reservoir. To facilitate methodology development, the conceptual models of tight formation and WIPS scheme were firstly described. Secondly, seepage models of tight reservoir and hydraulic fractures (HFs were sequentially established and then dynamically coupled. Numerical simulation was utilized to validate our model. Finally, identification of flow regimes and sensitivity analysis were conducted. Our results showed that there was good agreement between our proposed model and numerical simulation; moreover, our approach also gave promising calculation speed over numerical simulation. Some expected flow regimes were significantly distorted due to WIPS. The slope of type curves which characterize the linear or bi-linear flow regime is bigger than 0.5 or 0.25. The horizontal line which characterize radial flow regime is also bigger 0.5. The smaller the oil rate, the more severely flow regimes were distorted. Well rate mainly determines the distortion of MPI curves, while fracture length, well spacing, fracture spacing mainly determine when the distortion of the MPI curves occurs. The bigger the well rate, the more severely the MPI curves are distorted. While as the well spacing decreases, fracture length increases, fracture spacing increases, occurrence of MWPI become earlier. Stress sensitivity coefficient mainly affects the MPI at the formation pseudo-radial flow stage, almost has no influence on the occurrence of MWPI. This work gains some

Globally asymptotically stable analysis in a discrete time eco-epidemiological system

International Nuclear Information System (INIS)

Hu, Zengyun; Teng, Zhidong; Zhang, Tailei; Zhou, Qiming; Chen, Xi

2017-01-01

Highlights: • Dynamical behaviors of a discrete time eco-epidemiological system are discussed. • Global asymptotical stability of this system is obtained by an iteration scheme which can be expended to general dimensional discrete system. • More complex dynamical behaviors are obtained by numerical simulations. - Abstract: In this study, the dynamical behaviors of a discrete time eco-epidemiological system are discussed. The local stability, bifurcation and chaos are obtained. Moreover, the global asymptotical stability of this system is explored by an iteration scheme. The numerical simulations illustrate the theoretical results and exhibit the complex dynamical behaviors such as flip bifurcation, Hopf bifurcation and chaotic dynamical behaviors. Our main results provide an efficient method to analyze the global asymptotical stability for general three dimensional discrete systems.

About several classes of bi-orthogonal polynomials and discrete integrable systems

International Nuclear Information System (INIS)

Chang, Xiang-Ke; Chen, Xiao-Min; Hu, Xing-Biao; Tam, Hon-Wah

2015-01-01

By introducing some special bi-orthogonal polynomials, we derive the so-called discrete hungry quotient-difference (dhQD) algorithm and a system related to the QD-type discrete hungry Lotka–Volterra (QD-type dhLV) system, together with their Lax pairs. These two known equations can be regarded as extensions of the QD algorithm. When this idea is applied to a higher analogue of the discrete-time Toda (HADT) equation and the quotient–quotient-difference (QQD) scheme proposed by Spicer, Nijhoff and van der Kamp, two extended systems are constructed. We call these systems the hungry forms of the higher analogue discrete-time Toda (hHADT) equation and the quotient-quotient-difference (hQQD) scheme, respectively. In addition, the corresponding Lax pairs are provided. (paper)

Discrete energy formulation of neutron transport theory applied to solving the discrete ordinates equations

International Nuclear Information System (INIS)

Ching, J.; Oblow, E.M.; Goldstein, H.

1976-01-01

An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated that allows the development of a discrete energy, discrete ordinates method for the solution of radiation transport problems. In the discrete energy method, the group averaging required in the cross-section processing for multigroup calculations is replaced by a faster numerical quadrature scheme capable of generating transfer cross sections describing all the physical processes of interest on a fine point-energy grid. Test calculations in which the discrete energy method is compared with the multigroup method show that, for the same energy grid, the discrete energy method is much faster, although somewhat less accurate, than the multigroup method. However, the accuracy of the discrete energy method increases rapidly as the spacing between energy grid points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum, the discrete energy method is therefore expected to be far more economical than the multigroup technique for equivalent accuracy solutions. This advantage of the point method is demonstrated by application to the study of neutron transport in a thick iron slab

Discrete unified gas kinetic scheme for all Knudsen number flows. III. Binary gas mixtures of Maxwell molecules

Science.gov (United States)

Zhang, Yue; Zhu, Lianhua; Wang, Ruijie; Guo, Zhaoli

2018-05-01

Recently a discrete unified gas kinetic scheme (DUGKS) in a finite-volume formulation based on the Boltzmann model equation has been developed for gas flows in all flow regimes. The original DUGKS is designed for flows of single-species gases. In this work, we extend the DUGKS to flows of binary gas mixtures of Maxwell molecules based on the Andries-Aoki-Perthame kinetic model [P. Andries et al., J. Stat. Phys. 106, 993 (2002), 10.1023/A:1014033703134. A particular feature of the method is that the flux at each cell interface is evaluated based on the characteristic solution of the kinetic equation itself; thus the numerical dissipation is low in comparison with that using direct reconstruction. Furthermore, the implicit treatment of the collision term enables the time step to be free from the restriction of the relaxation time. Unlike the DUGKS for single-species flows, a nonlinear system must be solved to determine the interaction parameters appearing in the equilibrium distribution function, which can be obtained analytically for Maxwell molecules. Several tests are performed to validate the scheme, including the shock structure problem under different Mach numbers and molar concentrations, the channel flow driven by a small gradient of pressure, temperature, or concentration, the plane Couette flow, and the shear driven cavity flow under different mass ratios and molar concentrations. The results are compared with those from other reliable numerical methods. The results show that the proposed scheme is an effective and reliable method for binary gas mixtures in all flow regimes.

Free vibration of thin axisymmetric structures by a semi-analytical finite element scheme and isoparametric solid elements

International Nuclear Information System (INIS)

Akeju, T.A.I.; Kelly, D.W.; Zienkiewicz, O.C.; Kanaka Raju, K.

1981-01-01

The eigenvalue equations governing the free vibration of axisymmetric solids are derived by means of a semi-analytical finite element scheme. In particular we investigated the use of an 8-node solid element in structures which exhibit a 'shell-like' behaviour. Bathe-Wilson subspace iteration algorithm is employed for the solution of the equations. The element is shown to give good results for beam and shell vibration problems. It is also utilised to solve a complex solid in the form of an internal component of a modern jet engine. This particular application is of considerable practical importance as the dynamics of such components form a dominant design constraint. (orig./HP)

有理Runge-Kutta法を用いたSemi-Lagrangian海洋モデルの開発

OpenAIRE

上原, 克人; Uehara, Katsuto

1997-01-01

A new Semi-Lagrangian scheme using Rational Runge-Kutta method (RKSL scheme)is developed for reduced-gravity ocean model. It is superior to Semi-Implicit/Semi-Lagrangian (SISL) scheme in handling lateral boundaries, whereas it can take longer time-step than usual external Eulerian schemes. To evaluate this new scheme, experiments simulating the mid-depth circulation of the Mediterranean outflow region in the eastern North Atlantic were made by using the RKSL scheme, the SISL scheme, and cente...

Multi-party semi-quantum key distribution-convertible multi-party semi-quantum secret sharing

Science.gov (United States)

Yu, Kun-Fei; Gu, Jun; Hwang, Tzonelih; Gope, Prosanta

2017-08-01

This paper proposes a multi-party semi-quantum secret sharing (MSQSS) protocol which allows a quantum party (manager) to share a secret among several classical parties (agents) based on GHZ-like states. By utilizing the special properties of GHZ-like states, the proposed scheme can easily detect outside eavesdropping attacks and has the highest qubit efficiency among the existing MSQSS protocols. Then, we illustrate an efficient way to convert the proposed MSQSS protocol into a multi-party semi-quantum key distribution (MSQKD) protocol. The proposed approach is even useful to convert all the existing measure-resend type of semi-quantum secret sharing protocols into semi-quantum key distribution protocols.

Central extensions and semi-infinite wedge representations of Krichever-Novikov algebras for more than two points

International Nuclear Information System (INIS)

Schlichenmaier, M.

1990-01-01

For the generalized Krichever-Novikov algebras of meromorphic vector fields and their induced modules of weight λ a different basis is given. With respect to this basis the module structure is generalized graded. 'Local' central extensions of these algebras and their representations on the space of semi-infinite wedge product of forms of weight λ are studied. In this generalization, one again obtains c = -2(6λ 2 -6λ+1) as the value for the central charge. (orig.)

Discrete-time semi-Markov modeling of human papillomavirus persistence

Science.gov (United States)

Mitchell, C. E.; Hudgens, M. G.; King, C. C.; Cu-Uvin, S.; Lo, Y.; Rompalo, A.; Sobel, J.; Smith, J. S.

2011-01-01

Multi-state modeling is often employed to describe the progression of a disease process. In epidemiological studies of certain diseases, the disease state is typically only observed at periodic clinical visits, producing incomplete longitudinal data. In this paper we consider fitting semi-Markov models to estimate the persistence of human papillomavirus (HPV) type-specific infection in studies where the status of HPV type(s) is assessed periodically. Simulation study results are presented indicating the semi-Markov estimator is more accurate than an estimator currently used in the HPV literature. The methods are illustrated using data from the HIV Epidemiology Research Study (HERS). PMID:21538985

Comparative study of numerical schemes of TVD3, UNO3-ACM and optimized compact scheme

Science.gov (United States)

Lee, Duck-Joo; Hwang, Chang-Jeon; Ko, Duck-Kon; Kim, Jae-Wook

1995-01-01

Three different schemes are employed to solve the benchmark problem. The first one is a conventional TVD-MUSCL (Monotone Upwind Schemes for Conservation Laws) scheme. The second scheme is a UNO3-ACM (Uniformly Non-Oscillatory Artificial Compression Method) scheme. The third scheme is an optimized compact finite difference scheme modified by us: the 4th order Runge Kutta time stepping, the 4th order pentadiagonal compact spatial discretization with the maximum resolution characteristics. The problems of category 1 are solved by using the second (UNO3-ACM) and third (Optimized Compact) schemes. The problems of category 2 are solved by using the first (TVD3) and second (UNO3-ACM) schemes. The problem of category 5 is solved by using the first (TVD3) scheme. It can be concluded from the present calculations that the Optimized Compact scheme and the UN03-ACM show good resolutions for category 1 and category 2 respectively.

Sensitivity experiments of a regional climate model to the different convective schemes over Central Africa

Science.gov (United States)

Armand J, K. M.

2017-12-01

In this study, version 4 of the regional climate model (RegCM4) is used to perform 6 years simulation including one year for spin-up (from January 2001 to December 2006) over Central Africa using four convective schemes: The Emmanuel scheme (MIT), the Grell scheme with Arakawa-Schulbert closure assumption (GAS), the Grell scheme with Fritsch-Chappell closure assumption (GFC) and the Anthes-Kuo scheme (Kuo). We have investigated the ability of the model to simulate precipitation, surface temperature, wind and aerosols optical depth. Emphasis in the model results were made in December-January-February (DJF) and July-August-September (JAS) periods. Two subregions have been identified for more specific analysis namely: zone 1 which corresponds to the sahel region mainly classified as desert and steppe and zone 2 which is a region spanning the tropical rain forest and is characterised by a bimodal rain regime. We found that regardless of periods or simulated parameters, MIT scheme generally has a tendency to overestimate. The GAS scheme is more suitable in simulating the aforementioned parameters, as well as the diurnal cycle of precipitations everywhere over the study domain irrespective of the season. In JAS, model results are similar in the representation of regional wind circulation. Apart from the MIT scheme, all the convective schemes give the same trends in aerosols optical depth simulations. Additional experiment reveals that the use of BATS instead of Zeng scheme to calculate ocean flux appears to improve the quality of the model simulations.

An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations

Science.gov (United States)

Xia, Xilin; Liang, Qiuhua; Ming, Xiaodong; Hou, Jingming

2017-05-01

Numerical models solving the full 2-D shallow water equations (SWEs) have been increasingly used to simulate overland flows and better understand the transient flow dynamics of flash floods in a catchment. However, there still exist key challenges that have not yet been resolved for the development of fully dynamic overland flow models, related to (1) the difficulty of maintaining numerical stability and accuracy in the limit of disappearing water depth and (2) inaccurate estimation of velocities and discharges on slopes as a result of strong nonlinearity of friction terms. This paper aims to tackle these key research challenges and present a new numerical scheme for accurately and efficiently modeling large-scale transient overland flows over complex terrains. The proposed scheme features a novel surface reconstruction method (SRM) to correctly compute slope source terms and maintain numerical stability at small water depth, and a new implicit discretization method to handle the highly nonlinear friction terms. The resulting shallow water overland flow model is first validated against analytical and experimental test cases and then applied to simulate a hypothetic rainfall event in the 42 km2 Haltwhistle Burn, UK.

Time-Discrete Higher-Order ALE Formulations: Stability

KAUST Repository

Bonito, Andrea

2013-01-01

Arbitrary Lagrangian Eulerian (ALE) formulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. This arbitrary extension has no effect on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time-dependent advection-diffusion-model problem in moving domains, and study their stability properties. The analysis hinges on the validity of the Reynold\\'s identity for dG. Exploiting the variational structure and assuming exact integration, we prove that our conservative and nonconservative dG schemes are equivalent and unconditionally stable. The same results remain true for piecewise polynomial ALE maps of any degree and suitable quadrature that guarantees the validity of the Reynold\\'s identity. This approach generalizes the so-called geometric conservation law to higher-order methods. We also prove that simpler Runge-Kutta-Radau methods of any order are conditionally stable, that is, subject to a mild ALE constraint on the time steps. Numerical experiments corroborate and complement our theoretical results. © 2013 Society for Industrial and Applied Mathematics.

Discrete Painlevé equations: an integrability paradigm

International Nuclear Information System (INIS)

Grammaticos, B; Ramani, A

2014-01-01

In this paper we present a review of results on discrete Painlevé equations. We begin with an introduction which serves as a refresher on the continuous Painlevé equations. Next, in the first, main part of the paper, we introduce the discrete Painlevé equations, the various methods for their derivation, and their properties as well as their classification scheme. Along the way we present a brief summary of the two major discrete integrability detectors and of Quispel–Roberts–Thompson mapping, which plays a primordial role in the derivation of discrete Painlevé equations. The second part of the paper is more technical and focuses on the presentation of new results on what are called asymmetric discrete Painlevé equations. (comment)

A Non-blind Color Image Watermarking Scheme Resistent Against Geometric Attacks

Directory of Open Access Journals (Sweden)

A. Ghafoor

2012-12-01

Full Text Available A non-blind color image watermarking scheme using principle component analysis, discrete wavelet transform and singular value decomposition is proposed. The color components are uncorrelated using principle component analysis. The watermark is embedded into the singular values of discrete wavelet transformed sub-band associated with principle component containing most of the color information. The scheme was tested against various attacks (including histogram equalization, rotation, Gaussian noise, scaling, cropping, Y-shearing, X-shearing, median filtering, affine transformation, translation, salt & pepper, sharpening, to check robustness. The results of proposed scheme are compared with state-of-the-art existing color watermarking schemes using normalized correlation coefficient and peak signal to noise ratio. The simulation results show that proposed scheme is robust and imperceptible.

Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

Science.gov (United States)

Bridges, Thomas J.; Reich, Sebastian

2001-06-01

The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

Discrete ellipsoidal statistical BGK model and Burnett equations

Science.gov (United States)

Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua; Wang, Pei

2018-06-01

A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.

Discrete Green’s functions for propagators between complex objects in discrete space-time nonlinear electromagnetics

NARCIS (Netherlands)

Arnold, J.M.; Hon, de B.P.; Graglia, R.D.

2007-01-01

We propose a potential-based form of the FDTD scheme, with potentials driven by sources that are themselves simple dynamical systems. This formulation admits a radiative boundary condition for the discrete-mesh Maxwell's equations in a multiply connected exterior domain, which facilitates

Application of kinetic flux vector splitting scheme for solving multi-dimensional hydrodynamical models of semiconductor devices

Science.gov (United States)

Nisar, Ubaid Ahmed; Ashraf, Waqas; Qamar, Shamsul

In this article, one and two-dimensional hydrodynamical models of semiconductor devices are numerically investigated. The models treat the propagation of electrons in a semiconductor device as the flow of a charged compressible fluid. It plays an important role in predicting the behavior of electron flow in semiconductor devices. Mathematically, the governing equations form a convection-diffusion type system with a right hand side describing the relaxation effects and interaction with a self consistent electric field. The proposed numerical scheme is a splitting scheme based on the kinetic flux-vector splitting (KFVS) method for the hyperbolic step, and a semi-implicit Runge-Kutta method for the relaxation step. The KFVS method is based on the direct splitting of macroscopic flux functions of the system on the cell interfaces. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Several case studies are considered. For validation, the results of current scheme are compared with those obtained from the splitting scheme based on the NT central scheme. The effects of various parameters such as low field mobility, device length, lattice temperature and voltage are analyzed. The accuracy, efficiency and simplicity of the proposed KFVS scheme validates its generic applicability to the given model equations. A two dimensional simulation is also performed by KFVS method for a MESFET device, producing results in good agreement with those obtained by NT-central scheme.

Boudot's Range-Bounded Commitment Scheme Revisited

Science.gov (United States)

Cao, Zhengjun; Liu, Lihua

Checking whether a committed integer lies in a specific interval has many cryptographic applications. In Eurocrypt'98, Chan et al. proposed an instantiation (CFT Proof). Based on CFT, Boudot presented a popular range-bounded commitment scheme in Eurocrypt'2000. Both CFT Proof and Boudot Proof are based on the encryption E(x, r)=g^xh^r mod n, where n is an RSA modulus whose factorization is unknown by the prover. They did not use a single base as usual. Thus an increase in cost occurs. In this paper, we show that it suffices to adopt a single base. The cost of the modified Boudot Proof is about half of that of the original scheme. Moreover, the key restriction in the original scheme, i.e., both the discrete logarithm of g in base h and the discrete logarithm of h in base g are unknown by the prover, which is a potential menace to the Boudot Proof, is definitely removed.

Ulam's scheme revisited digital modeling of chaotic attractors via micro-perturbations

CERN Document Server

Domokos, Gabor K

2002-01-01

We consider discretizations $f_N$ of expanding maps $f:I \\to I$ in the strict sense: i.e. we assume that the only information available on the map is a finite set of integers. Using this definition for computability, we show that by adding a random perturbation of order $1/N$, the invariant measure corresponding to $f$ can be approximated and we can also give estimates of the error term. We prove that the randomized discrete scheme is equivalent to Ulam's scheme applied to the polygonal approximation of $f$, thus providing a new interpretation of Ulam's scheme. We also compare the efficiency of the randomized iterative scheme to the direct solution of the $N \\times N$ linear system.

On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations

International Nuclear Information System (INIS)

Zhang Yu-Feng; Tam, Honwah

2016-01-01

In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A_1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz–Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A_1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. (paper)

Discrete Calculus by Analogy

CERN Document Server

Izadi, F A; Bagirov, G

2009-01-01

With its origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology, especially in discrete mathematics, numerical analysis, statistics and probability theory as well as in electrical engineering, but our viewpoint here is that these topics belong to a much more general realm of mathematics; namely calculus and differential equations because of the remarkable analogy of the subject to this branch of mathemati

A robust and efficient finite volume scheme for the discretization of diffusive flux on extremely skewed meshes in complex geometries

Science.gov (United States)

Traoré, Philippe; Ahipo, Yves Marcel; Louste, Christophe

2009-08-01

In this paper an improved finite volume scheme to discretize diffusive flux on a non-orthogonal mesh is proposed. This approach, based on an iterative technique initially suggested by Khosla [P.K. Khosla, S.G. Rubin, A diagonally dominant second-order accurate implicit scheme, Computers and Fluids 2 (1974) 207-209] and known as deferred correction, has been intensively utilized by Muzaferija [S. Muzaferija, Adaptative finite volume method for flow prediction using unstructured meshes and multigrid approach, Ph.D. Thesis, Imperial College, 1994] and later Fergizer and Peric [J.H. Fergizer, M. Peric, Computational Methods for Fluid Dynamics, Springer, 2002] to deal with the non-orthogonality of the control volumes. Using a more suitable decomposition of the normal gradient, our scheme gives accurate solutions in geometries where the basic idea of Muzaferija fails. First the performances of both schemes are compared for a Poisson problem solved in quadrangular domains where control volumes are increasingly skewed in order to test their robustness and efficiency. It is shown that convergence properties and the accuracy order of the solution are not degraded even on extremely skewed mesh. Next, the very stable behavior of the method is successfully demonstrated on a randomly distorted grid as well as on an anisotropically distorted one. Finally we compare the solution obtained for quadrilateral control volumes to the ones obtained with a finite element code and with an unstructured version of our finite volume code for triangular control volumes. No differences can be observed between the different solutions, which demonstrates the effectiveness of our approach.

Stabilizing the discrete vortex of topological charge S=2

International Nuclear Information System (INIS)

Kevrekidis, P.G.; Frantzeskakis, D.J.

2005-01-01

We study the instability of the discrete vortex with topological charge S=2 in a prototypical lattice model and observe its mediation through the central lattice site. Motivated by this finding, we analyze the model with the central site being inert. We identify analytically and observe numerically the existence of a range of linearly stable discrete vortices with S=2 in the latter model. The range of stability is comparable to that of the recently observed experimentally S=1 discrete vortex, suggesting the potential for observation of such higher charge discrete vortices

Discrete-time inverse optimal control for nonlinear systems

CERN Document Server

Sanchez, Edgar N

2013-01-01

Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th

The large discretization step method for time-dependent partial differential equations

Science.gov (United States)

Haras, Zigo; Taasan, Shlomo

1995-01-01

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

A pressure-based semi-implicit space-time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier-Stokes equations at all Mach numbers

Science.gov (United States)

Tavelli, Maurizio; Dumbser, Michael

2017-07-01

We propose a new arbitrary high order accurate semi-implicit space-time discontinuous Galerkin (DG) method for the solution of the two and three dimensional compressible Euler and Navier-Stokes equations on staggered unstructured curved meshes. The method is pressure-based and semi-implicit and is able to deal with all Mach number flows. The new DG scheme extends the seminal ideas outlined in [1], where a second order semi-implicit finite volume method for the solution of the compressible Navier-Stokes equations with a general equation of state was introduced on staggered Cartesian grids. Regarding the high order extension we follow [2], where a staggered space-time DG scheme for the incompressible Navier-Stokes equations was presented. In our scheme, the discrete pressure is defined on the primal grid, while the discrete velocity field and the density are defined on a face-based staggered dual grid. Then, the mass conservation equation, as well as the nonlinear convective terms in the momentum equation and the transport of kinetic energy in the energy equation are discretized explicitly, while the pressure terms appearing in the momentum and energy equation are discretized implicitly. Formal substitution of the discrete momentum equation into the total energy conservation equation yields a linear system for only one unknown, namely the scalar pressure. Here the equation of state is assumed linear with respect to the pressure. The enthalpy and the kinetic energy are taken explicitly and are then updated using a simple Picard procedure. Thanks to the use of a staggered grid, the final pressure system is a very sparse block five-point system for three dimensional problems and it is a block four-point system in the two dimensional case. Furthermore, for high order in space and piecewise constant polynomials in time, the system is observed to be symmetric and positive definite. This allows to use fast linear solvers such as the conjugate gradient (CG) method. In

Computation of 2-D pinhole image-formation process of large-scale furnaces using the discrete ordinates method

CERN Document Server

Li Hong; Lu Ji Dong; Zheng Chu Guan

2003-01-01

In most of the discrete ordinate schemes (DOS) reported in the literature, the discrete directions are fixed, and unable to be arbitrarily adjusted; therefore, it is difficult to employ these schemes to calculate the radiative energy image-formation of pulverized-coal furnaces. On the basis of a new DOS, named the discrete ordinate scheme with (an) infinitely small weight(s), which was recently proposed by the authors, a novel algorithm for computing the pinhole image-formation process is developed in this work. The performance of this algorithm is tested, and is found to be also suitable for parallel computation.

Computation of 2-D pinhole image-formation process of large-scale furnaces using the discrete ordinates method

International Nuclear Information System (INIS)

Li Hongshun; Zhou Huaichun; Lu Jidong; Zheng Chuguang

2003-01-01

In most of the discrete ordinate schemes (DOS) reported in the literature, the discrete directions are fixed, and unable to be arbitrarily adjusted; therefore, it is difficult to employ these schemes to calculate the radiative energy image-formation of pulverized-coal furnaces. On the basis of a new DOS, named the discrete ordinate scheme with (an) infinitely small weight(s), which was recently proposed by the authors, a novel algorithm for computing the pinhole image-formation process is developed in this work. The performance of this algorithm is tested, and is found to be also suitable for parallel computation

Load Distribution of Semi-Central Evaporative Cooling Air-Conditioning System Based on the TRNSYS Platform

Directory of Open Access Journals (Sweden)

Ji Li

2018-05-01

Full Text Available Evaporative cooling is a green, energy-efficient cooling technology adopted in hot and dry regions, which has wider application in the field of air-conditioning systems. Outdoor meteorological parameters have a great influence on the operation mode and control strategy of evaporative cooling air-conditioning systems, and the system load distribution and system configuration will be affected. This paper aims at investigating the load distribution of semi-central evaporative cooling air-conditioning systems under the condition of hourly outdoor meteorological parameters. Firstly, this paper introduced the design partition, operation mode, controlling strategy and load distribution method on semi-central evaporative cooling air-conditioning system. Then, taking an office building in Lanzhou (China as an example, the evaporative cooling air-conditioning system was divided into five regions and the load distribution was simulated by TRNSYS (The Transient Energy System Simulation Tool under the condition of hourly outdoor meteorological parameters. Finally, the results have shown that the evaporative cooling air-conditioning system can provide 25.46% of the building loads, which was of great significance to reduce the energy consumption of air-conditioning system.

Galerkin v. discrete-optimal projection in nonlinear model reduction

Energy Technology Data Exchange (ETDEWEB)

Carlberg, Kevin Thomas [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Barone, Matthew Franklin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Antil, Harbir [George Mason Univ., Fairfax, VA (United States)

2015-04-01

Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes. We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.

Optimization strategies for discrete multi-material stiffness optimization

DEFF Research Database (Denmark)

Hvejsel, Christian Frier; Lund, Erik; Stolpe, Mathias

2011-01-01

Design of composite laminated lay-ups are formulated as discrete multi-material selection problems. The design problem can be modeled as a non-convex mixed-integer optimization problem. Such problems are in general only solvable to global optimality for small to moderate sized problems. To attack...... which numerically confirm the sought properties of the new scheme in terms of convergence to a discrete solution....

A gas dynamics scheme for a two moments model of radiative transfer

International Nuclear Information System (INIS)

Buet, Ch.; Despres, B.

2007-01-01

We address the discretization of the Levermore's two moments and entropy model of the radiative transfer equation. We present a new approach for the discretization of this model: first we rewrite the moment equations as a Compressible Gas Dynamics equation by introducing an additional quantity that plays the role of a density. After that we discretize using a Lagrange-projection scheme. The Lagrange-projection scheme permits us to incorporate the source terms in the fluxes of an acoustic solver in the Lagrange step, using the well-known piecewise steady approximation and thus to capture correctly the diffusion regime. Moreover we show that the discretization is entropic and preserve the flux-limited property of the moment model. Numerical examples illustrate the feasibility of our approach. (authors)

Discrete level schemes sublibrary. Progress report by Budapest group

International Nuclear Information System (INIS)

Oestor, J.; Belgya, T.; Molnar, G.L.

1997-01-01

An entirely new discrete levels file has been created by the Budapest group according to the recommended principles, using the Evaluated Nuclear Structure Data File, ENSDF as a source. The resulting library contains 96,834 levels and 105,423 gamma rays for 2,585 nuclei, with their characteristics such as energy, spin, parity, half-life as well gamma-ray energy and branching percentage

A fast iterative model for discrete velocity calculations on triangular grids

International Nuclear Information System (INIS)

Szalmas, Lajos; Valougeorgis, Dimitris

2010-01-01

A fast synthetic type iterative model is proposed to speed up the slow convergence of discrete velocity algorithms for solving linear kinetic equations on triangular lattices. The efficiency of the scheme is verified both theoretically by a discrete Fourier stability analysis and computationally by solving a rarefied gas flow problem. The stability analysis of the discrete kinetic equations yields the spectral radius of the typical and the proposed iterative algorithms and reveal the drastically improved performance of the latter one for any grid resolution. This is the first time that stability analysis of the full discrete kinetic equations related to rarefied gas theory is formulated, providing the detailed dependency of the iteration scheme on the discretization parameters in the phase space. The corresponding characteristics of the model deduced by solving numerically the rarefied gas flow through a duct with triangular cross section are in complete agreement with the theoretical findings. The proposed approach may open a way for fast computation of rarefied gas flows on complex geometries in the whole range of gas rarefaction including the hydrodynamic regime.

Kernel Optimum Nearly-analytical Discretization (KOND) algorithm

International Nuclear Information System (INIS)

Kondoh, Yoshiomi; Hosaka, Yasuo; Ishii, Kenji

1992-10-01

Two applications of the Kernel Optimum Nearly-analytical Discretization (KOND) algorithm to the parabolic- and the hyperbolic type equations a presented in detail to lead to novel numerical schemes with very high numerical accuracy. It is demonstrated numerically that the two dimensional KOND-P scheme for the parabolic type yields quite less numerical error by over 2-3 orders and reduces the CPU time to about 1/5 for a common numerical accuracy, compared with the conventional explicit scheme of reference. It is also demonstrated numerically that the KOND-H scheme for the hyperbolic type yields fairly less diffusive error and has fairly high stability for both of the linear- and the nonlinear wave propagations compared with other conventional schemes. (author)

Displacement in the parameter space versus spurious solution of discretization with large time step

International Nuclear Information System (INIS)

Mendes, Eduardo; Letellier, Christophe

2004-01-01

In order to investigate a possible correspondence between differential and difference equations, it is important to possess discretization of ordinary differential equations. It is well known that when differential equations are discretized, the solution thus obtained depends on the time step used. In the majority of cases, such a solution is considered spurious when it does not resemble the expected solution of the differential equation. This often happens when the time step taken into consideration is too large. In this work, we show that, even for quite large time steps, some solutions which do not correspond to the expected ones are still topologically equivalent to solutions of the original continuous system if a displacement in the parameter space is considered. To reduce such a displacement, a judicious choice of the discretization scheme should be made. To this end, a recent discretization scheme, based on the Lie expansion of the original differential equations, proposed by Monaco and Normand-Cyrot will be analysed. Such a scheme will be shown to be sufficient for providing an adequate discretization for quite large time steps compared to the pseudo-period of the underlying dynamics

Comparison of reactivity estimation performance between two extended Kalman filtering schemes

International Nuclear Information System (INIS)

Peng, Xingjie; Cai, Yun; Li, Qing; Wang, Kan

2016-01-01

Highlights: • The performances of two EKF schemes using different Jacobian matrices are compared. • Numerical simulations are used for the validation and comparison of these two EKF schemes. • The simulation results show that the EKF scheme adopted by this paper performs better than the one adopted by previous literatures. - Abstract: The extended Kalman filtering (EKF) technique has been utilized in the estimation of reactivity which is a significantly important parameter to indicate the status of the nuclear reactor. In this paper, the performances of two EKF schemes using different Jacobian matrices are compared. Numerical simulations are used for the validation and comparison of these two EKF schemes, and the results show that the Jacobian matrix obtained directly from the discrete-time state model performs better than the one which is the discretization form of the Jacobian matrix obtained from the continuous-time state model.

Discretization of 3d gravity in different polarizations

Science.gov (United States)

Dupuis, Maïté; Freidel, Laurent; Girelli, Florian

2017-10-01

We study the discretization of three-dimensional gravity with Λ =0 following the loop quantum gravity framework. In the process, we realize that different choices of polarization are possible. This allows us to introduce a new discretization based on the triad as opposed to the connection as in the standard loop quantum gravity framework. We also identify the classical nontrivial symmetries of discrete gravity, namely the Drinfeld double, given in terms of momentum maps. Another choice of polarization is given by the Chern-Simons formulation of gravity. Our framework also provides a new discretization scheme of Chern-Simons, which keeps track of the link between the continuum variables and the discrete ones. We show how the Poisson bracket we recover between the Chern-Simons holonomies allows us to recover the Goldman bracket. There is also a transparent link between the discrete Chern-Simons formulation and the discretization of gravity based on the connection (loop gravity) or triad variables (dual loop gravity).

The analytical evolution of NLS solitons due to the numerical discretization error

Science.gov (United States)

Hoseini, S. M.; Marchant, T. R.

2011-12-01

Soliton perturbation theory is used to obtain analytical solutions describing solitary wave tails or shelves, due to numerical discretization error, for soliton solutions of the nonlinear Schrödinger equation. Two important implicit numerical schemes for the nonlinear Schrödinger equation, with second-order temporal and spatial discretization errors, are considered. These are the Crank-Nicolson scheme and a scheme, due to Taha [1], based on the inverse scattering transform. The first-order correction for the solitary wave tail, or shelf, is in integral form and an explicit expression is found for large time. The shelf decays slowly, at a rate of t^{-{1\\over 2}}, which is characteristic of the nonlinear Schrödinger equation. Singularity theory, usually used for combustion problems, is applied to the explicit large-time expression for the solitary wave tail. Analytical results are then obtained, such as the parameter regions in which qualitatively different types of solitary wave tails occur, the location of zeros and the location and amplitude of peaks. It is found that three different types of tail occur for the Crank-Nicolson and Taha schemes and that the Taha scheme exhibits some unusual symmetry properties, as the tails for left and right moving solitary waves are different. Optimal choices of the discretization parameters for the numerical schemes are also found, which minimize the amplitude of the solitary wave tail. The analytical solutions are compared with numerical simulations, and an excellent comparison is found.

The analytical evolution of NLS solitons due to the numerical discretization error

International Nuclear Information System (INIS)

Hoseini, S M; Marchant, T R

2011-01-01

Soliton perturbation theory is used to obtain analytical solutions describing solitary wave tails or shelves, due to numerical discretization error, for soliton solutions of the nonlinear Schrödinger equation. Two important implicit numerical schemes for the nonlinear Schrödinger equation, with second-order temporal and spatial discretization errors, are considered. These are the Crank–Nicolson scheme and a scheme, due to Taha, based on the inverse scattering transform. The first-order correction for the solitary wave tail, or shelf, is in integral form and an explicit expression is found for large time. The shelf decays slowly, at a rate of t -1/2 , which is characteristic of the nonlinear Schrödinger equation. Singularity theory, usually used for combustion problems, is applied to the explicit large-time expression for the solitary wave tail. Analytical results are then obtained, such as the parameter regions in which qualitatively different types of solitary wave tails occur, the location of zeros and the location and amplitude of peaks. It is found that three different types of tail occur for the Crank–Nicolson and Taha schemes and that the Taha scheme exhibits some unusual symmetry properties, as the tails for left and right moving solitary waves are different. Optimal choices of the discretization parameters for the numerical schemes are also found, which minimize the amplitude of the solitary wave tail. The analytical solutions are compared with numerical simulations, and an excellent comparison is found. (paper)

A Framework of Secured Embedding Scheme Using Vector Discrete Wavelet Transformation and Lagrange Interpolation

Directory of Open Access Journals (Sweden)

Maheswari Subramanian

2018-01-01

Full Text Available Information hiding techniques have a significant role in recent application areas. Steganography is the embedding of information within an innocent cover work in a way which cannot be detected by any person without accessing the steganographic key. The proposed work uses a steganographic scheme for useful information with the help of human skin tone regions as cover image. The proposed algorithm has undergone Lagrange interpolation encryption for enhancement of the security of the hidden information. First, the skin tone regions are identified by using YCbCr color space which can be used as a cover image. Image pixels which belong to the skin regions are used to carry more secret bits, and the secret information is hidden in both horizontal and vertical sequences of the skin areas of the cover image. The secret information will hide behind the human skin regions rather than other objects in the same image because the skin pixels have high intensity value. The performance of embedding is done and is quite invisible by the vector discrete wavelet transformation (VDWT technique. A new Lagrange interpolation-based encryption method is introduced to achieve high security of the hidden information with higher payload and better visual quality.

The theta/gamma discrete phase code occuring during the hippocampal phase precession may be a more general brain coding scheme.

Science.gov (United States)

Lisman, John

2005-01-01

In the hippocampus, oscillations in the theta and gamma frequency range occur together and interact in several ways, indicating that they are part of a common functional system. It is argued that these oscillations form a coding scheme that is used in the hippocampus to organize the readout from long-term memory of the discrete sequence of upcoming places, as cued by current position. This readout of place cells has been analyzed in several ways. First, plots of the theta phase of spikes vs. position on a track show a systematic progression of phase as rats run through a place field. This is termed the phase precession. Second, two cells with nearby place fields have a systematic difference in phase, as indicated by a cross-correlation having a peak with a temporal offset that is a significant fraction of a theta cycle. Third, several different decoding algorithms demonstrate the information content of theta phase in predicting the animal's position. It appears that small phase differences corresponding to jitter within a gamma cycle do not carry information. This evidence, together with the finding that principle cells fire preferentially at a given gamma phase, supports the concept of theta/gamma coding: a given place is encoded by the spatial pattern of neurons that fire in a given gamma cycle (the exact timing within a gamma cycle being unimportant); sequential places are encoded in sequential gamma subcycles of the theta cycle (i.e., with different discrete theta phase). It appears that this general form of coding is not restricted to readout of information from long-term memory in the hippocampus because similar patterns of theta/gamma oscillations have been observed in multiple brain regions, including regions involved in working memory and sensory integration. It is suggested that dual oscillations serve a general function: the encoding of multiple units of information (items) in a way that preserves their serial order. The relationship of such coding to

Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation

Science.gov (United States)

Litaker, Eric T.

1994-12-01

The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.

An efficient permeability scaling-up technique applied to the discretized flow equations

Energy Technology Data Exchange (ETDEWEB)

Urgelli, D.; Ding, Yu [Institut Francais du Petrole, Rueil Malmaison (France)

1997-08-01

Grid-block permeability scaling-up for numerical reservoir simulations has been discussed for a long time in the literature. It is now recognized that a full permeability tensor is needed to get an accurate reservoir description at large scale. However, two major difficulties are encountered: (1) grid-block permeability cannot be properly defined because it depends on boundary conditions; (2) discretization of flow equations with a full permeability tensor is not straightforward and little work has been done on this subject. In this paper, we propose a new method, which allows us to get around both difficulties. As the two major problems are closely related, a global approach will preserve the accuracy. So, in the proposed method, the permeability up-scaling technique is integrated in the discretized numerical scheme for flow simulation. The permeability is scaled-up via the transmissibility term, in accordance with the fluid flow calculation in the numerical scheme. A finite-volume scheme is particularly studied, and the transmissibility scaling-up technique for this scheme is presented. Some numerical examples are tested for flow simulation. This new method is compared with some published numerical schemes for full permeability tensor discretization where the full permeability tensor is scaled-up through various techniques. Comparing the results with fine grid simulations shows that the new method is more accurate and more efficient.

Semi-intelligent trigger-generation scheme for Cherenkov light imaging cameras

International Nuclear Information System (INIS)

Bhat, C.L.; Tickoo, A.K.; Koul, R.; Kaul, I.K.

1994-01-01

We propose here an improved trigger-generation scheme for TeV gamma-ray imaging telescopes. Based on a memory-based Majority Coincidence Circuit, this scheme involves deriving two-or three-pixel nearest-neighbour coincidences as against the conventional approach of generating prompt coincidences using any two photomultiplier detector pixels of an imaging-camera. As such, the new method can discriminate better against shot-noise-generated triggers and, to a significant extent, also against cosmic-ray and local-muon-generated background events, without compromising on the telescope response to events of γ-ray origin. An optional feature of the proposed scheme is that a suitably scaled-up value of the chance-trigger rate can be independently derived, thereby making it possible to use this parameter reliably for keeping a log of the ''health'' of the experimental system. (orig.)

Semi-intelligent trigger-generation scheme for Cherenkov light imaging cameras

Science.gov (United States)

Bhat, C. L.; Tickoo, A. K.; Koul, R.; Kaul, I. K.

1994-02-01

We propose here an improved trigger-generation scheme for TeV gamma-ray imaging telescopes. Based on a memory-based Majority Coincidence Circuit, this scheme involves deriving two- or three-pixel nearest-neighbour coincidences as against the conventional approach of generating prompt coincidences using any two photomultiplier detector pixels of an imaging-camera. As such, the new method can discriminate better against shot-noise-generated triggers and, to a significant extent, also against cosmic-ray and local-muon-generated background events, without compromising on the telescope response to events of γ-ray origin. An optional feature of the proposed scheme is that a suitably scaled-up value of the chance-trigger rate can be independently derived, thereby making it possible to use this parameter reliably for keeping a log of the ``health'' of the experimental system.

A three–step discretization scheme for direct numerical solution of ...

African Journals Online (AJOL)

In this paper, a three-step discretization (numerical) formula is developed for direct integration of second-order initial value problems in ordinary differential equations. The development of the method and analysis of its basic properties adopt Taylor series expansion and Dahlquist stability test methods. The results show that ...

A spatio-temporal evaluation of the WRF physical parameterisations for numerical rainfall simulation in semi-humid and semi-arid catchments of Northern China

Science.gov (United States)

Tian, Jiyang; Liu, Jia; Wang, Jianhua; Li, Chuanzhe; Yu, Fuliang; Chu, Zhigang

2017-07-01

Mesoscale Numerical Weather Prediction systems can provide rainfall products at high resolutions in space and time, playing an increasingly more important role in water management and flood forecasting. The Weather Research and Forecasting (WRF) model is one of the most popular mesoscale systems and has been extensively used in research and practice. However, for hydrologists, an unsolved question must be addressed before each model application in a different target area. That is, how are the most appropriate combinations of physical parameterisations from the vast WRF library selected to provide the best downscaled rainfall? In this study, the WRF model was applied with 12 designed parameterisation schemes with different combinations of physical parameterisations, including microphysics, radiation, planetary boundary layer (PBL), land-surface model (LSM) and cumulus parameterisations. The selected study areas are two semi-humid and semi-arid catchments located in the Daqinghe River basin, Northern China. The performance of WRF with different parameterisation schemes is tested for simulating eight typical 24-h storm events with different evenness in space and time. In addition to the cumulative rainfall amount, the spatial and temporal patterns of the simulated rainfall are evaluated based on a two-dimensional composed verification statistic. Among the 12 parameterisation schemes, Scheme 4 outperforms the other schemes with the best average performance in simulating rainfall totals and temporal patterns; in contrast, Scheme 6 is generally a good choice for simulations of spatial rainfall distributions. Regarding the individual parameterisations, Single-Moment 6 (WSM6), Yonsei University (YSU), Kain-Fritsch (KF) and Grell-Devenyi (GD) are better choices for microphysics, planetary boundary layers (PBL) and cumulus parameterisations, respectively, in the study area. These findings provide helpful information for WRF rainfall downscaling in semi-humid and semi

Collective effects in Au(100-800 AMeV) + Au semi-central collisions; Effets collectifs dans les collisions semi-centrales Au(100-800 AMeV) + Au

Energy Technology Data Exchange (ETDEWEB)

Crochet, P.

1996-04-04

The present work has been carried out in the framework of the experimental program of the FOPI collaboration. It is devoted to a systematic study of the different forms of collective expansion of nuclear matter in semi-central Au+Au collisions at incident energies ranging from 100 AMeV to 800 AMeV. The aim is to investigate the influence of compressional effects, momentum dependence of the nuclear interaction and nucleon-nucleon cross section on the observed phenomena. Important changes in the reaction mechanisms are evidenced, in particular at low incident energies where one observes, on the one hand, a transition from an enhanced in-plane emission to a preferential out-of-plane emission pattern and, on the other hand, a strong reduction of the directed in-plane component. Experimental results are compared to the predictions of the Quantum Molecular Dynamics (QMD) model for different parametrizations of the nuclear interaction. (author).

A discrete control model of PLANT

Science.gov (United States)

Mitchell, C. M.

1985-01-01

A model of the PLANT system using the discrete control modeling techniques developed by Miller is described. Discrete control models attempt to represent in a mathematical form how a human operator might decompose a complex system into simpler parts and how the control actions and system configuration are coordinated so that acceptable overall system performance is achieved. Basic questions include knowledge representation, information flow, and decision making in complex systems. The structure of the model is a general hierarchical/heterarchical scheme which structurally accounts for coordination and dynamic focus of attention. Mathematically, the discrete control model is defined in terms of a network of finite state systems. Specifically, the discrete control model accounts for how specific control actions are selected from information about the controlled system, the environment, and the context of the situation. The objective is to provide a plausible and empirically testable accounting and, if possible, explanation of control behavior.

A Hybrid DGTD-MNA Scheme for Analyzing Complex Electromagnetic Systems

KAUST Repository

Li, Peng

2015-01-07

A hybrid electromagnetics (EM)-circuit simulator for analyzing complex systems consisting of EM devices loaded with nonlinear multi-port lumped circuits is described. The proposed scheme splits the computational domain into two subsystems: EM and circuit subsystems, where field interactions are modeled using Maxwell and Kirchhoff equations, respectively. Maxwell equations are discretized using a discontinuous Galerkin time domain (DGTD) scheme while Kirchhoff equations are discretized using a modified nodal analysis (MNA)-based scheme. The coupling between the EM and circuit subsystems is realized at the lumped ports, where related EM fields and circuit voltages and currents are allowed to “interact’’ via numerical flux. To account for nonlinear lumped circuit elements, the standard Newton-Raphson method is applied at every time step. Additionally, a local time-stepping scheme is developed to improve the efficiency of the hybrid solver. Numerical examples consisting of EM systems loaded with single and multiport linear/nonlinear circuit networks are presented to demonstrate the accuracy, efficiency, and applicability of the proposed solver.

Manifestly gauge invariant discretizations of the Schrödinger equation

International Nuclear Information System (INIS)

Halvorsen, Tore Gunnar; Kvaal, Simen

2012-01-01

Grid-based discretizations of the time dependent Schrödinger equation coupled to an external magnetic field are converted to manifest gauge invariant discretizations. This is done using generalizations of ideas used in classical lattice gauge theory, and the process defined is applicable to a large class of discretized differential operators. In particular, popular discretizations such as pseudospectral discretizations using the fast Fourier transform can be transformed to gauge invariant schemes. Also generic gauge invariant versions of generic time integration methods are considered, enabling completely gauge invariant calculations of the time dependent Schrödinger equation. Numerical examples illuminating the differences between a gauge invariant discretization and conventional discretization procedures are also presented. -- Highlights: ► We investigate the Schrödinger equation coupled to an external magnetic field. ► Any grid-based discretization is made trivially gauge invariant. ► An extension of classical lattice gauge theory.

Histogram plots and cutoff energies for nuclear discrete levels

International Nuclear Information System (INIS)

Belgya, T.; Molnar, G.; Fazekas, B.; Oestoer, J.

1997-05-01

Discrete level schemes for 1277 nuclei, from 6 Li through 251 Es, extracted from the Evaluated Nuclear Structure Data File were analyzed. Cutoff energies (U max ), indicating the upper limit of level scheme completeness, were deduced from the inspection of histograms of the cumulative number of levels. Parameters of the constant-temperature level density formula (nuclear temperature T and energy shift U 0 ) were obtained by means of the least square fit of the formula to the known levels below cutoff energy. The results are tabulated for all 1277 nuclei allowing for an easy and reliable application of the constant-temperature level density approach. A complete set of cumulative plots of discrete levels is also provided. (author). 5 figs, 2 tabs

Exactly and quasi-exactly solvable 'discrete' quantum mechanics.

Science.gov (United States)

Sasaki, Ryu

2011-03-28

A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.

Nuclear Reactor Component Code CUPID-I: Numerical Scheme and Preliminary Assessment Results

International Nuclear Information System (INIS)

Cho, Hyoung Kyu; Jeong, Jae Jun; Park, Ik Kyu; Kim, Jong Tae; Yoon, Han Young

2007-12-01

A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components of a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAC, semi-implicit ICE, SIMPLE, Row Scheme and so on. Among them, the ICE scheme for the three-field model was presented in the present report. The CUPID code is utilizing unstructured mesh for the simulation of complicated geometries of the nuclear reactor components. The conventional ICE scheme that was applied to RELAP5 and COBRA-TF, therefore, were modified for the application to the unstructured mesh. Preliminary calculations for the unstructured semi-implicit ICE scheme have been conducted for a verification of the numerical method from a qualitative point of view. The preliminary calculation results showed that the present numerical scheme is robust and efficient for the prediction of phase changes and flow transitions due to a boiling and a flashing. These calculation results also showed the strong coupling between the pressure and void fraction changes. Thus, it is believed that the semi-implicit ICE scheme can be utilized for transient two-phase flows in a component of a nuclear reactor

Nuclear Reactor Component Code CUPID-I: Numerical Scheme and Preliminary Assessment Results

Energy Technology Data Exchange (ETDEWEB)

Cho, Hyoung Kyu; Jeong, Jae Jun; Park, Ik Kyu; Kim, Jong Tae; Yoon, Han Young

2007-12-15

A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components of a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAC, semi-implicit ICE, SIMPLE, Row Scheme and so on. Among them, the ICE scheme for the three-field model was presented in the present report. The CUPID code is utilizing unstructured mesh for the simulation of complicated geometries of the nuclear reactor components. The conventional ICE scheme that was applied to RELAP5 and COBRA-TF, therefore, were modified for the application to the unstructured mesh. Preliminary calculations for the unstructured semi-implicit ICE scheme have been conducted for a verification of the numerical method from a qualitative point of view. The preliminary calculation results showed that the present numerical scheme is robust and efficient for the prediction of phase changes and flow transitions due to a boiling and a flashing. These calculation results also showed the strong coupling between the pressure and void fraction changes. Thus, it is believed that the semi-implicit ICE scheme can be utilized for transient two-phase flows in a component of a nuclear reactor.

Integer valued autoregressive processes with generalized discrete Mittag-Leffler marginals

Directory of Open Access Journals (Sweden)

Kanichukattu K. Jose

2013-05-01

Full Text Available In this paper we consider a generalization of discrete Mittag-Leffler distributions. We introduce and study the properties of a new distribution called geometric generalized discrete Mittag-Leffler distribution. Autoregressive processes with geometric generalized discrete Mittag-Leffler distributions are developed and studied. The distributions are further extended to develop a more general class of geometric generalized discrete semi-Mittag-Leffler distributions. The processes are extended to higher orders also. An application with respect to an empirical data on customer arrivals in a bank counter is also given. Various areas of potential applications like human resource development, insect growth, epidemic modeling, industrial risk modeling, insurance and actuaries, town planning etc are also discussed.

Simulating continuous-time Hamiltonian dynamics by way of a discrete-time quantum walk

International Nuclear Information System (INIS)

Schmitz, A.T.; Schwalm, W.A.

2016-01-01

Much effort has been made to connect the continuous-time and discrete-time quantum walks. We present a method for making that connection for a general graph Hamiltonian on a bigraph. Furthermore, such a scheme may be adapted for simulating discretized quantum models on a quantum computer. A coin operator is found for the discrete-time quantum walk which exhibits the same dynamics as the continuous-time evolution. Given the spectral decomposition of the graph Hamiltonian and certain restrictions, the discrete-time evolution is solved for explicitly and understood at or near important values of the parameters. Finally, this scheme is connected to past results for the 1D chain. - Highlights: • A discrete-time quantum walk is purposed which approximates a continuous-time quantum walk. • The purposed quantum walk could be used to simulate Hamiltonian dynamics on a quantum computer. • Given the spectra decomposition of the Hamiltonian, the quantum walk is solved explicitly. • The method is demonstrated and connected to previous work done on the 1D chain.

Validation of a semi-automatic protocol for the assessment of the tear meniscus central area based on open-source software

Science.gov (United States)

Pena-Verdeal, Hugo; Garcia-Resua, Carlos; Yebra-Pimentel, Eva; Giraldez, Maria J.

2017-08-01

Purpose: Different lower tear meniscus parameters can be clinical assessed on dry eye diagnosis. The aim of this study was to propose and analyse the variability of a semi-automatic method for measuring lower tear meniscus central area (TMCA) by using open source software. Material and methods: On a group of 105 subjects, one video of the lower tear meniscus after fluorescein instillation was generated by a digital camera attached to a slit-lamp. A short light beam (3x5 mm) with moderate illumination in the central portion of the meniscus (6 o'clock) was used. Images were extracted from each video by a masked observer. By using an open source software based on Java (NIH ImageJ), a further observer measured in a masked and randomized order the TMCA in the short light beam illuminated area by two methods: (1) manual method, where TMCA images was "manually" measured; (2) semi-automatic method, where TMCA images were transformed in an 8-bit-binary image, then holes inside this shape were filled and on the isolated shape, the area size was obtained. Finally, both measurements, manual and semi-automatic, were compared. Results: Paired t-test showed no statistical difference between both techniques results (p = 0.102). Pearson correlation between techniques show a significant positive near to perfect correlation (r = 0.99; p Conclusions: This study showed a useful tool to objectively measure the frontal central area of the meniscus in photography by free open source software.

A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation

Directory of Open Access Journals (Sweden)

Yunying Zheng

2011-01-01

Full Text Available The spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis.

A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers

KAUST Repository

Bagci, Hakan

2015-01-07

Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability

A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers

KAUST Repository

Bagci, Hakan

2015-01-01

Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability

Hexaquark states as possible candidates for di-baryonic molecular states with Yukawa potential in a semi-relativistic scheme

Energy Technology Data Exchange (ETDEWEB)

Patel, Smruti J., E-mail: fizix.smriti@gmail.com; Vinodkumar, P. C. [P. G. Department of Physics, Sardar Patel University, VallabhVidyanagar - 388120, Gujarat (India)

2016-05-06

We study the mass spectra of hexaquark states as di-hadronic molecules with Yukawa potential in a semi-relativistic scheme. We have solved numerically the relevant equation using mathematica notebook of Range-Kutta method including effective Yukawa like potential between two baryons to model the two-body interaction and have calculated their masses and binding energy. We have been able to assign the J{sup P} values for many of the exotic states according to their compositions. We have predicted some of the di-baryonic exotic states for which experimental as well as theoretical data are not available and we look forward to see the experimental support in favour of our predictions. So in the absence of such results our predictions can be used as guidelines for future experimental and theoretical analysis of exotic states.

Hexaquark states as possible candidates for di-baryonic molecular states with Yukawa potential in a semi-relativistic scheme

International Nuclear Information System (INIS)

Patel, Smruti J.; Vinodkumar, P. C.

2016-01-01

We study the mass spectra of hexaquark states as di-hadronic molecules with Yukawa potential in a semi-relativistic scheme. We have solved numerically the relevant equation using mathematica notebook of Range-Kutta method including effective Yukawa like potential between two baryons to model the two-body interaction and have calculated their masses and binding energy. We have been able to assign the J"P values for many of the exotic states according to their compositions. We have predicted some of the di-baryonic exotic states for which experimental as well as theoretical data are not available and we look forward to see the experimental support in favour of our predictions. So in the absence of such results our predictions can be used as guidelines for future experimental and theoretical analysis of exotic states.

Generalized semi-Markovian dividend discount model: risk and return

OpenAIRE

D'Amico, Guglielmo

2016-01-01

The article presents a general discrete time dividend valuation model when the dividend growth rate is a general continuous variable. The main assumption is that the dividend growth rate follows a discrete time semi-Markov chain with measurable space. The paper furnishes sufficient conditions that assure finiteness of fundamental prices and risks and new equations that describe the first and second order price-dividend ratios. Approximation methods to solve equations are provided and some new...

Newton-type methods for the mixed finite element discretization of some degenerate parabolic equations

NARCIS (Netherlands)

Radu, F.A.; Pop, I.S.; Knabner, P.; Bermúdez de Castro, A.; Gómez, D.; Quintela, P.; Salgado, P.

2006-01-01

In this paper we discuss some iterative approaches for solving the nonlinear algebraic systems encountered as fully discrete counterparts of some degenerate (fast diffusion) parabolic problems. After regularization, we combine a mixed finite element discretization with the Euler implicit scheme. For

Discrete dark matter

CERN Document Server

Hirsch, M; Peinado, E; Valle, J W F

2010-01-01

We propose a new motivation for the stability of dark matter (DM). We suggest that the same non-abelian discrete flavor symmetry which accounts for the observed pattern of neutrino oscillations, spontaneously breaks to a Z2 subgroup which renders DM stable. The simplest scheme leads to a scalar doublet DM potentially detectable in nuclear recoil experiments, inverse neutrino mass hierarchy, hence a neutrinoless double beta decay rate accessible to upcoming searches, while reactor angle equal to zero gives no CP violation in neutrino oscillations.

Quantum election scheme based on anonymous quantum key distribution

International Nuclear Information System (INIS)

Zhou Rui-Rui; Yang Li

2012-01-01

An unconditionally secure authority-certified anonymous quantum key distribution scheme using conjugate coding is presented, based on which we construct a quantum election scheme without the help of an entanglement state. We show that this election scheme ensures the completeness, soundness, privacy, eligibility, unreusability, fairness, and verifiability of a large-scale election in which the administrator and counter are semi-honest. This election scheme can work even if there exist loss and errors in quantum channels. In addition, any irregularity in this scheme is sensible. (general)

An efficient entire chaos-based scheme for deniable authentication

International Nuclear Information System (INIS)

Xiao Di; Liao Xiaofeng; Wong, K.W.

2005-01-01

By using a chaotic encryption-hash parallel algorithm and the semi-group property of Chebyshev chaotic map, we propose a secure and efficient scheme for the deniable authentication. The scheme is efficient, practicable and reliable, with high potential to be adopted for e-commerce

An efficient entire chaos-based scheme for deniable authentication

Energy Technology Data Exchange (ETDEWEB)

Xiao Di [College of Computer Science and Engineering, Chongqing University, Chongqing, 400044 (China) and College of Mechanical Engineering, Chongqing University, Chongqing, 400044 (China)]. E-mail: xiaodi_cqu@hotmail.com; Liao Xiaofeng [College of Computer Science and Engineering, Chongqing University, Chongqing, 400044 (China); Wong, K.W. [Department of Computer Engineering and Information Technology, City University of Hong Kong, Hong Kong (China)

2005-02-01

By using a chaotic encryption-hash parallel algorithm and the semi-group property of Chebyshev chaotic map, we propose a secure and efficient scheme for the deniable authentication. The scheme is efficient, practicable and reliable, with high potential to be adopted for e-commerce.

Birkhoffian Symplectic Scheme for a Quantum System

International Nuclear Information System (INIS)

Su Hongling

2010-01-01

In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure-preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f. Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system. (general)

Mechanical model for steel frames with discretely connected precast concrete infill panels with window openings

NARCIS (Netherlands)

Teeuwen, P.A.; Kleinman, C.S.; Snijder, H.H.

2012-01-01

This paper presents a mechanical model for a structure comprising of steel frames with discretely connected precast concrete infill panels having window openings, termed semi-integral infilled frames. The discrete panel-to-frame connections are realized by structural bolts acting under compression.

Strong Stability Preserving Property of the Deferred Correction Time Discretization

National Research Council Canada - National Science Library

Liu, Yuan; Shu, Chi-Wang; Zhang, Mengping

2007-01-01

In this paper, we study the strong stability preserving "SSP" property of a class of deferred correction time discretization methods, for solving the method-of-lines schemes approximating hyperbolic...

About the unitary discretizations of Heisenberg equations of motion

International Nuclear Information System (INIS)

Vazquez, L.

1986-01-01

In a recent paper Bender et al. (1985) have used a unitary discretization of Heisenberg equations for a one-dimensional quantum system in order to obtain information about the spectrum of the underlying continuum theory. The method consists in comparing the matrix elements between adjacent Fock states of the operators and at two steps. At the same time a very simple variational approach must be made. The purpose of this paper is to show that with unitary schemes, accurate either to order τ or τ 2 , we obtain the same spectrum results in the framework of the above method. On the other hand the same eigenvalues are obtained with a non-unitary scheme (Section II). In Section III we discuss the construction of the Hamiltonian associated to the unitary discretizations. (orig.)

A qualitative semi-classical treatment of an isolated semi-polar quantum dot

International Nuclear Information System (INIS)

Young, Toby D

2011-01-01

To qualitatively determine the behaviour of micro-macro properties of a quantum dot grown in a non-polar direction, we propose a simple semi-classical model based on well established ideas. We take into account the following empirical phenomena: (i) The displacement and induced strain at heterojunctions; (ii) The electrostatic potential arising from piezoelectric and spontaneous polarisation; and (iii) The localisation of excitons (particle-hole pairs) arising from quantum confinement. After some algebraic manipulation used to cast the formalism into an arbitrarily rotated frame, a numerical model is developed for the case of a semi-polar wurtzite GaN quantum dot buried in a wurtzite AlN matrix. This scheme is found to provide a satisfying qualitative description of an isolated semi-polar quantum dot in a way that is accessible to further physical interpretation and quantification.

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

Directory of Open Access Journals (Sweden)

Vladimir P. Gerdt

2006-05-01

Full Text Available In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

A semi-spring and semi-edge combined contact model in CDEM and its application to analysis of Jiweishan landslide

Directory of Open Access Journals (Sweden)

Chun Feng

2014-02-01

Full Text Available Continuum-based discrete element method (CDEM is an explicit numerical method used for simulation of progressive failure of geological body. To improve the efficiency of contact detection and simplify the calculation steps for contact forces, semi-spring and semi-edge are introduced in calculation. Semi-spring is derived from block vertex, and formed by indenting the block vertex into each face (24 semi-springs for a hexahedral element. The formation process of semi-edge is the same as that of semi-spring (24 semi-edges for a hexahedral element. Based on the semi-springs and semi-edges, a new type of combined contact model is presented. According to this model, six contact types could be reduced to two, i.e. the semi-spring target face contact and semi-edge target edge contact. By the combined model, the contact force could be calculated directly (the information of contact type is not necessary, and the failure judgment could be executed in a straightforward way (each semi-spring and semi-edge own their characteristic areas. The algorithm has been successfully programmed in C++ program. Some simple numerical cases are presented to show the validity and accuracy of this model. Finally, the failure mode, sliding distance and critical friction angle of Jiweishan landslide are studied with the combined model.

A Mathematical Model of Profit-Loss Sharing Scheme of Small Investment for Traditional Market Traders using The Semi-Fuzzy Logic Approach

Directory of Open Access Journals (Sweden)

Novriana Sumarti

2017-02-01

Full Text Available A mathematical model of micro-finance investment using profit-loss sharing scheme are made and implemented to simulated data. Here profits from the venture will be shared in a portion between the investor and the entity running the business. The scheme can be classified as Musharaka type of investment in Sharia economy. The proposed model is theoretically implemented with data from small-scale traders at a local traditional market who have small turnover. They are common target of usurers who lend money with high interest rate and penalties. If the traders are in unfortunate conditions, they are potentially in poorer condition than before committing themselves to the usurer. In the conventional practices of the profit sharing scheme, the investor will get a fixed portion of the trader’s income, which is applied for all kind of small-scale traders. If the traders are diligent and hard worker and have very high turnover, then the investor will gain much more profit whether the contributed capital is small or large. In this paper, the scheme is implemented using Semi-Fuzzy Logic Approach so that the profit-loss sharing scheme can achieve its intended goal, which is to make a profitable investment not only for the investor but also for traders. The approach is not fully using Fuzzy Logic because some variables are still in crisp numbers and the optimization problem is regular in the form of crisp numbers. Based on the existing data, the results show that the optimal profit share is depended on the income of the traders. The higher the income coming from the venture, the lesser the profit share for the investor which is reasonable with the fixed initial contributed capital.

A Classification Scheme for Production System Processes

DEFF Research Database (Denmark)

Sørensen, Daniel Grud Hellerup; Brunø, Thomas Ditlev; Nielsen, Kjeld

2018-01-01

Manufacturing companies often have difficulties developing production platforms, partly due to the complexity of many production systems and difficulty determining which processes constitute a platform. Understanding production processes is an important step to identifying candidate processes...... for a production platform based on existing production systems. Reviewing a number of existing classifications and taxonomies, a consolidated classification scheme for processes in production of discrete products has been outlined. The classification scheme helps ensure consistency during mapping of existing...

Numerical solution of neutron transport equations in discrete ordinates and slab geometry

International Nuclear Information System (INIS)

Serrano Pedraza, F.

1985-01-01

An unified formalism to solve numerically, between other equation, the neutron transport in discrete ordinates, slab geometry, several energy groups and independents of time, has been developed recently. Such a formalism cover some of the conventional schemes as diamond difference, (WDD) characteristic step (SC) lineal characteristic (LC), quadratic characteristic (QC) and lineal discontinuous. Unified formation gives before hand the convergence order of the previously selected scheme. In fact it allows besides to generate a big amount of numerical schemes, with which is also possible to solve numerical equations as soon as neutron transport. The essential purpose of this work was to solve the neutron transport equations in slab geometry and discrete ordinates considering several energy groups without to take under advisement time dependence based in the above mentioned unified formalism. To reach this purpose it was necesary to design a computer code with the name TNOD1 (Neutron transport in discrete ordinates and 1 dimension) which includes each one of the schemes already pointed out. there exist two numerical schemes, also recently developed, quadratic continuous (QC) and cubic continuous (CN), although covered by unified formalism, it has been possible to include them inside this computer code without make substantial changes in its structure. In chapter I, derivative of neutron transport equation independent of time is taken, for angular flux, including boundary conditions and discontinuity. In chapter II the neutron transport equations are obtained in multigroups, independents of time, for approximation of discrete ordinates. Description of theory related with unified formalism and its relationship with mentioned discretization schemes is presented in chapter III. Chapter IV describes the computer code developed and finally, in chapter V different numerical results obtained with TNOD1 program are shown. In Appendix A theorems and mathematical arguments used

Identification of discrete chaotic maps with singular points

Directory of Open Access Journals (Sweden)

P. G. Akishin

2001-01-01

Full Text Available We investigate the ability of artificial neural networks to reconstruct discrete chaotic maps with singular points. We use as a simple test model the Cusp map. We compare the traditional Multilayer Perceptron, the Chebyshev Neural Network and the Wavelet Neural Network. The numerical scheme for the accurate determination of a singular point is also developed. We show that combining a neural network with the numerical algorithm for the determination of the singular point we are able to accurately approximate discrete chaotic maps with singularities.

Shape indexes for semi-automated detection of windbreaks in thematic tree cover maps from the central United States

Science.gov (United States)

Greg C. Liknes; Dacia M. Meneguzzo; Todd A. Kellerman

2017-01-01

Windbreaks are an important ecological resource across the large expanse of agricultural land in the central United States and are often planted in straight-line or L-shaped configurations to serve specific functions. As high-resolution (i.e., <5 m) land cover datasets become more available for these areas, semi-or fully-automated methods for distinguishing...

Discrete quantum Fourier transform in coupled semiconductor double quantum dot molecules

International Nuclear Information System (INIS)

Dong Ping; Yang Ming; Cao Zhuoliang

2008-01-01

In this Letter, we present a physical scheme for implementing the discrete quantum Fourier transform in a coupled semiconductor double quantum dot system. The main controlled-R gate operation can be decomposed into many simple and feasible unitary transformations. The current scheme would be a useful step towards the realization of complex quantum algorithms in the quantum dot system

Semi-implicit surface tension formulation with a Lagrangian surface mesh on an Eulerian simulation grid

KAUST Repository

Schroeder, Craig

2012-02-01

We present a method for applying semi-implicit forces on a Lagrangian mesh to an Eulerian discretization of the Navier Stokes equations in a way that produces a sparse symmetric positive definite system. The resulting method has semi-implicit and fully-coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of a surface tension force, which when treated explicitly leads to a tight time step restriction. By applying surface tension as a semi-implicit Lagrangian force, the resulting method benefits from improved stability and the ability to take larger time steps. The resulting discretization is also able to maintain parasitic currents at low levels. © 2011.

Recharge estimation in semi-arid karst catchments: Central West Bank, Palestine

Science.gov (United States)

Jebreen, Hassan; Wohnlich, Stefan; Wisotzky, Frank; Banning, Andre; Niedermayr, Andrea; Ghanem, Marwan

2018-03-01

Knowledge of groundwater recharge constitutes a valuable tool for sustainable management in karst systems. In this respect, a quantitative evaluation of groundwater recharge can be considered a pre-requisite for the optimal operation of groundwater resources systems, particular for semi-arid areas. This paper demonstrates the processes affecting recharge in Palestine aquifers. The Central Western Catchment is one of the main water supply sources in the West Bank. Quantification of potential recharge rates are estimated using chloride mass balance (CMB) and empirical recharge equations over the catchment. The results showing the spatialized recharge rate, which ranges from 111-216 mm/year, representing 19-37% of the long-term mean annual rainfall. Using Water Balance models and climatological data (e. g. solar radiation, monthly temperature, average monthly relative humidity and precipitation), actual evapotranspiration (AET) is estimated. The mean annual actual evapotranspiration was about 66-70% of precipitation.

On an integrable discretization of the modified Korteweg-de Vries equation

Science.gov (United States)

Suris, Yuri B.

1997-02-01

We find time discretizations for the two “second flows” of the Ablowitz-Ladik hierachy. These discretizations are described by local equations of motion, as opposed to the previously known ones, due to Taha and Ablowitz. Certain superpositions of our maps allow a one-field reduction and serve therefore as valid space-time discretizations of the modified Korteweg-de Vries equation. We expect the performance of these discretizations to be much better then that of the Taha-Ablowitz scheme. The way of finding interpolating Hamiltonians for our maps is also indicated, as well as the solution of an initial value problem in terms of matrix factorizations.

Introduction of hypermatrix and operator notation into a discrete mathematics simulation model of malignant tumour response to therapeutic schemes in vivo. Some operator properties.

Science.gov (United States)

Stamatakos, Georgios S; Dionysiou, Dimitra D

2009-10-21

The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code). However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the operators' commutativity and outline the "summarize and jump" strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83-02, thus strengthening the reliability of the model developed.

Semi-classical signal analysis

KAUST Repository

Laleg-Kirati, Taous-Meriem

2012-09-30

This study introduces a new signal analysis method, based on a semi-classical approach. The main idea in this method is to interpret a pulse-shaped signal as a potential of a Schrödinger operator and then to use the discrete spectrum of this operator for the analysis of the signal. We present some numerical examples and the first results obtained with this method on the analysis of arterial blood pressure waveforms. © 2012 Springer-Verlag London Limited.

Theoretical Basics of Teaching Discrete Mathematics

Directory of Open Access Journals (Sweden)

Y. A. Perminov

2012-01-01

Full Text Available  The paper deals with the research findings concerning the process of mastering the theoretical basics of discrete mathematics by the students of vocational pedagogic profile. The methodological analysis is based on the subject and functions of the modern discrete mathematics and its role in mathematical modeling and computing. The modern discrete mathematics (i.e. mathematics of the finite type structures plays the important role in modernization of vocational training. It is especially rele- vant to training students for vocational pedagogic qualifications, as in the future they will be responsible for training the middle and the senior level specialists in engineer- ing and technical spheres. Nowadays in different industries, there arise the problems which require for their solving both continual – based on the classical mathematical methods – and discrete modeling. The teaching course of discrete mathematics for the future vocational teachers should be relevant to the target qualification and aimed at mastering the mathematical modeling, systems of computer mathematics and computer technologies. The author emphasizes the fundamental role of mastering the language of algebraic and serial structures, as well as the logical, algorithmic, combinatory schemes dominating in dis- crete mathematics. The guidelines for selecting the content of the course in discrete mathematics are specified. The theoretical findings of the research can be put into practice whilst developing curricula and working programs for bachelors and masters’ training. 

Analytical reconstruction schemes for coarse-mesh spectral nodal solution of slab-geometry SN transport problems

International Nuclear Information System (INIS)

Barros, R. C.; Filho, H. A.; Platt, G. M.; Oliveira, F. B. S.; Militao, D. S.

2009-01-01

Coarse-mesh numerical methods are very efficient in the sense that they generate accurate results in short computational time, as the number of floating point operations generally decrease, as a result of the reduced number of mesh points. On the other hand, they generate numerical solutions that do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. In this paper we describe two analytical reconstruction schemes for the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates (S N ) transport model in slab geometry. The first scheme we describe is based on the analytical reconstruction of the coarse-mesh solution within each discretization cell of the spatial grid set up on the slab. The second scheme is based on the angular reconstruction of the discrete ordinates solution between two contiguous ordinates of the angular quadrature set used in the S N model. Numerical results are given so we can illustrate the accuracy of the two reconstruction schemes, as described in this paper. (authors)

Discrete level schemes and their gamma radiation branching ratios (CENPL-DLS). Pt. 1

International Nuclear Information System (INIS)

Su Zongdi; Zhang Limin; Zhou Chunmei; Sun Zhengjun

1994-01-01

The DLS data file, which is a sub-library (version 1) of Chinese Evaluated Nuclear Parameter Library (CENPL), consists of data and information of discrete levels and gamma radiations. The data and information of this data file are translated from the Evaluated Nuclear Structure Data File (ENSDF). The transforming code from ENSDF to DLS was written. In the DLS data file, there are the data on discrete levels with determinate energy and their gamma radiations. At present, this file contains the data of 79456 levels and 100411 gammas for 1908 nuclides

New advection schemes for free surface flows

International Nuclear Information System (INIS)

Pavan, Sara

2016-01-01

The purpose of this thesis is to build higher order and less diffusive schemes for pollutant transport in shallow water flows or 3D free surface flows. We want robust schemes which respect the main mathematical properties of the advection equation with relatively low numerical diffusion and apply them to environmental industrial applications. Two techniques are tested in this work: a classical finite volume method and a residual distribution technique combined with a finite element method. For both methods we propose a decoupled approach since it is the most advantageous in terms of accuracy and CPU time. Concerning the first technique, a vertex-centred finite volume method is used to solve the augmented shallow water system where the numerical flux is computed through an Harten-Lax-Van Leer-Contact Riemann solver. Starting from this solution, a decoupled approach is formulated and is preferred since it allows to compute with a larger time step the advection of a tracer. This idea was inspired by Audusse, E. and Bristeau, M.O. [13]. The Monotonic Upwind Scheme for Conservation Law, combined with the decoupled approach, is then used for the second order extension in space. The wetting and drying problem is also analysed and a possible solution is presented. In the second case, the shallow water system is entirely solved using the finite element technique and the residual distribution method is applied to the solution of the tracer equation, focusing on the case of time-dependent problems. However, for consistency reasons the resolution of the continuity equation must be considered in the numerical discretization of the tracer. In order to get second order schemes for unsteady cases a predictor-corrector scheme is used in this work. A first order but less diffusive version of the predictor-corrector scheme is also introduced. Moreover, we also present a new locally semi-implicit version of the residual distribution method which, in addition to good properties in

An error estimate for Tremolieres method for the discretization of parabolic variational inequalities

International Nuclear Information System (INIS)

Uko, L.U.

1990-02-01

We study a scheme for the time-discretization of parabolic variational inequalities that is often easier to use than the classical method of Rothe. We show that if the data are compatible in a certain sense, then this scheme is of order ≥1/2. (author). 10 refs

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Angstmann, C.N.; Donnelly, I.C. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Henry, B.I., E-mail: B.Henry@unsw.edu.au [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Jacobs, B.A. [School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050 (South Africa); DST–NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (South Africa); Langlands, T.A.M. [Department of Mathematics and Computing, University of Southern Queensland, Toowoomba QLD 4350 (Australia); Nichols, J.A. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia)

2016-02-15

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.

Semi-analytic solution to planar Helmholtz equation

Directory of Open Access Journals (Sweden)

Tukač M.

2013-06-01

Full Text Available Acoustic solution of interior domains is of great interest. Solving acoustic pressure fields faster with lower computational requirements is demanded. A novel solution technique based on the analytic solution to the Helmholtz equation in rectangular domain is presented. This semi-analytic solution is compared with the finite element method, which is taken as the reference. Results show that presented method is as precise as the finite element method. As the semi-analytic method doesn’t require spatial discretization, it can be used for small and very large acoustic problems with the same computational costs.

An unconditionally stable fully conservative semi-Lagrangian method

KAUST Repository

Lentine, Michael

2011-04-01

Semi-Lagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFL-based time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semi-Lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressible-style pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had. © 2011 Elsevier Inc.

A linear multiple balance method for discrete ordinates neutron transport equations

International Nuclear Information System (INIS)

Park, Chang Je; Cho, Nam Zin

2000-01-01

A linear multiple balance method (LMB) is developed to provide more accurate and positive solutions for the discrete ordinates neutron transport equations. In this multiple balance approach, one mesh cell is divided into two subcells with quadratic approximation of angular flux distribution. Four multiple balance equations are used to relate center angular flux with average angular flux by Simpson's rule. From the analysis of spatial truncation error, the accuracy of the linear multiple balance scheme is ο(Δ 4 ) whereas that of diamond differencing is ο(Δ 2 ). To accelerate the linear multiple balance method, we also describe a simplified additive angular dependent rebalance factor scheme which combines a modified boundary projection acceleration scheme and the angular dependent rebalance factor acceleration schme. It is demonstrated, via fourier analysis of a simple model problem as well as numerical calculations, that the additive angular dependent rebalance factor acceleration scheme is unconditionally stable with spectral radius < 0.2069c (c being the scattering ration). The numerical results tested so far on slab-geometry discrete ordinates transport problems show that the solution method of linear multiple balance is effective and sufficiently efficient

Particle Swarm Based Approach of a Real-Time Discrete Neural Identifier for Linear Induction Motors

Directory of Open Access Journals (Sweden)

Alma Y. Alanis

2013-01-01

Full Text Available This paper focusses on a discrete-time neural identifier applied to a linear induction motor (LIM model, whose model is assumed to be unknown. This neural identifier is robust in presence of external and internal uncertainties. The proposed scheme is based on a discrete-time recurrent high-order neural network (RHONN trained with a novel algorithm based on extended Kalman filter (EKF and particle swarm optimization (PSO, using an online series-parallel con…figuration. Real-time results are included in order to illustrate the applicability of the proposed scheme.

Certificateless Key-Insulated Generalized Signcryption Scheme without Bilinear Pairings

Directory of Open Access Journals (Sweden)

Caixue Zhou

2017-01-01

Full Text Available Generalized signcryption (GSC can be applied as an encryption scheme, a signature scheme, or a signcryption scheme with only one algorithm and one key pair. A key-insulated mechanism can resolve the private key exposure problem. To ensure the security of cloud storage, we introduce the key-insulated mechanism into GSC and propose a concrete scheme without bilinear pairings in the certificateless cryptosystem setting. We provide a formal definition and a security model of certificateless key-insulated GSC. Then, we prove that our scheme is confidential under the computational Diffie-Hellman (CDH assumption and unforgeable under the elliptic curve discrete logarithm (EC-DL assumption. Our scheme also supports both random-access key update and secure key update. Finally, we evaluate the efficiency of our scheme and demonstrate that it is highly efficient. Thus, our scheme is more suitable for users who communicate with the cloud using mobile devices.

High-order discrete ordinate transport in non-conforming 2D Cartesian meshes

International Nuclear Information System (INIS)

Gastaldo, L.; Le Tellier, R.; Suteau, C.; Fournier, D.; Ruggieri, J. M.

2009-01-01

We present in this paper a numerical scheme for solving the time-independent first-order form of the Boltzmann equation in non-conforming 2D Cartesian meshes. The flux solution technique used here is the discrete ordinate method and the spatial discretization is based on discontinuous finite elements. In order to have p-refinement capability, we have chosen a hierarchical polynomial basis based on Legendre polynomials. The h-refinement capability is also available and the element interface treatment has been simplified by the use of special functions decomposed over the mesh entities of an element. The comparison to a classical S N method using the Diamond Differencing scheme as spatial approximation confirms the good behaviour of the method. (authors)

Final Report for DOE grant DE-FG02-07ER64432 "New Grid and Discretization Technologies for Ocean and Ice Simulations"

Energy Technology Data Exchange (ETDEWEB)

Gunzburger, Max

2013-03-12

The work reported is in pursuit of these goals: high-quality unstructured, non-uniform Voronoi and Delaunay grids; improved finite element and finite volume discretization schemes; and improved finite element and finite volume discretization schemes. These are sought for application to spherical and three-dimensional applications suitable for ocean, atmosphere, ice-sheet, and other climate modeling applications.

Synchronization of discrete-time hyperchaotic systems: An application in communications

International Nuclear Information System (INIS)

Aguilar-Bustos, A.Y.; Cruz-Hernandez, C.

2009-01-01

In this paper, the synchronization problem of discrete-time complex dynamics is presented. In particular, we use the model-matching approach from nonlinear control theory to synchronize two unidirectionally coupled discrete-time hyperchaotic systems. A potential application to secure/private communication of confidential information is also given. By using different (hyperchaotic) encryption schemes with a single and two transmission channels, we show that output synchronization of hyperchaotic maps is indeed suitable for encryption, transmission, and decryption of information.

Contenido de carbono en un ecosistema semiárido del centro de México / Carbon content in a semi-arid ecosystem in central Mexico

Directory of Open Access Journals (Sweden)

Rocio Becerril-Piña

2014-01-01

Full Text Available En las últimas décadas se han propuesto diversas ecuaciones alométricas (EA para especies tropicales y subtropicales a fin de estimar el contenido de carbono (CC en la biomasa aérea, sin embargo, los ecosistemas semiáridos han sido poco estudiados a pesar de constituir cerca del 40 % de la superficie de México. El objetivo de este estudio fue desarrollar EA para determinar el CC en la biomasa aérea en mezquite (Prosopis laevigata, huizache (Acacia farnesiana y herbáceas representativas de una región semiárida del centro del país. Se seleccionaron y muestrearon por método destructivo cinco individuos de cada especie para estimar biomasa seca total y por componente (hojas, ramas y fuste, los cuales se correlacionaron con parámetros de fácil medición en campo: cobertura de la copa, radio de la copa, altura total y volumen, encontrándose valores de R2 entre 0.96 y 0.80 dependiendo de la especie. Mediante información satelital se estimó la distribución espacial del CC en la Cuenca Dolores Hidalgo (Guanajuato, localizada en la región semiárida del centro de México. La cobertura vegetal del área de estudio se reclasificó en tres tipos: abierta, semiabierta y cerrada. El contenido de carbono en la cobertura abierta fue de 2.4 Mg C ha-1, semiabierta 10.26 Mg C ha-1 y cerrada de 21.20 Mg C ha-1. Los resultados sugieren que los ecosistemas semiáridos de la zona central de México representan un potencial considerable como sumideros de carbono con un promedio de 11 Mg C ha-1.

Introduction of Hypermatrix and Operator Notation into a Discrete Mathematics Simulation Model of Malignant Tumour Response to Therapeutic Schemes In Vivo. Some Operator Properties

Directory of Open Access Journals (Sweden)

Georgios S. Stamatakos

2009-10-01

Full Text Available The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code. However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the operators’ commutativity and outline the “summarize and jump” strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83–02, thus strengthening the reliability of the model developed.

Semi-infinite fractional programming

CERN Document Server

Verma, Ram U

2017-01-01

This book presents a smooth and unified transitional framework from generalised fractional programming, with a finite number of variables and a finite number of constraints, to semi-infinite fractional programming, where a number of variables are finite but with infinite constraints. It focuses on empowering graduate students, faculty and other research enthusiasts to pursue more accelerated research advances with significant interdisciplinary applications without borders. In terms of developing general frameworks for theoretical foundations and real-world applications, it discusses a number of new classes of generalised second-order invex functions and second-order univex functions, new sets of second-order necessary optimality conditions, second-order sufficient optimality conditions, and second-order duality models for establishing numerous duality theorems for discrete minmax (or maxmin) semi-infinite fractional programming problems.   In the current interdisciplinary supercomputer-oriented research envi...

Classification of actions of discrete Kac algebras on injective factors

CERN Document Server

Masuda, Toshihiko

2017-01-01

The authors study two kinds of actions of a discrete amenable Kac algebra. The first one is an action whose modular part is normal. They construct a new invariant which generalizes a characteristic invariant for a discrete group action, and we will present a complete classification. The second is a centrally free action. By constructing a Rohlin tower in an asymptotic centralizer, the authors show that the Connes-Takesaki module is a complete invariant.

An Iteration Scheme for Contraction Mappings with an Application to Synchronization of Discrete Logistic Maps

Directory of Open Access Journals (Sweden)

Ke Ding

2017-01-01

Full Text Available This paper deals with designing a new iteration scheme associated with a given scheme for contraction mappings. This new scheme has a similar structure to that of the given scheme, in which those two iterative schemes converge to the same fixed point of the given contraction mapping. The positive influence of feedback parameters on the convergence rate of this new scheme is investigated. Moreover, the derived convergence and comparison results can be extended to nonexpansive mappings. As an application, the derived results are utilized to study the synchronization of logistic maps. Two illustrated examples are used to reveal the effectiveness of our results.

An adjoint-based scheme for eigenvalue error improvement

International Nuclear Information System (INIS)

Merton, S.R.; Smedley-Stevenson, R.P.; Pain, C.C.; El-Sheikh, A.H.; Buchan, A.G.

2011-01-01

A scheme for improving the accuracy and reducing the error in eigenvalue calculations is presented. Using a rst order Taylor series expansion of both the eigenvalue solution and the residual of the governing equation, an approximation to the error in the eigenvalue is derived. This is done using a convolution of the equation residual and adjoint solution, which is calculated in-line with the primal solution. A defect correction on the solution is then performed in which the approximation to the error is used to apply a correction to the eigenvalue. The method is shown to dramatically improve convergence of the eigenvalue. The equation for the eigenvalue is shown to simplify when certain normalizations are applied to the eigenvector. Two such normalizations are considered; the rst of these is a fission-source type of normalisation and the second is an eigenvector normalisation. Results are demonstrated on a number of demanding elliptic problems using continuous Galerkin weighted nite elements. Moreover, the correction scheme may also be applied to hyperbolic problems and arbitrary discretization. This is not limited to spatial corrections and may be used throughout the phase space of the discrete equation. The applied correction not only improves fidelity of the calculation, it allows assessment of the reliability of numerical schemes to be made and could be used to guide mesh adaption algorithms or to automate mesh generation schemes. (author)

Geometric Integration Of The Valsov-Maxwell System With A Variational Particle-in-cell Scheme

International Nuclear Information System (INIS)

Squire, J.; Qin, H.; Tang, W.M.

2012-01-01

A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus [1], the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.

Discretization of Stationary Solutions of Stochastic Systems Driven by Fractional Brownian Motion

International Nuclear Information System (INIS)

Garrido-Atienza, Maria J.; Kloeden, Peter E.; Neuenkirch, Andreas

2009-01-01

In this article we study the behavior of dissipative systems with additive fractional noise of any Hurst parameter. Under a one-sided dissipative Lipschitz condition on the drift the continuous stochastic system is shown to have a unique stationary solution, which pathwise attracts all other solutions. The same holds for the discretized stochastic system, if the drift-implicit Euler method is used for the discretization. Moreover, the unique stationary solution of the drift-implicit Euler scheme converges to the unique stationary solution of the original system as the stepsize of the discretization decreases

Time-discrete higher order ALE formulations: a priori error analysis

KAUST Repository

Bonito, Andrea; Kyza, Irene; Nochetto, Ricardo H.

2013-01-01

We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete schemes of any order applied to an advection-diffusion model defined on moving domains and written in the Arbitrary Lagrangian Eulerian (ALE) framework. Our

Preferences of the central bank of Brazil under the inflation targeting regime: commitment vs. discretion

Directory of Open Access Journals (Sweden)

Andreza Aparecida Palma

2011-12-01

Full Text Available This work aims to estimate the preferences of the Central Bank of Brazil during the inflation targeting regime, using a standard new keynesian model with forward-looking expectations, as proposed by Givens (2010. The presence of rational expectations in the model makes a distinction between two modes of optimization, commitment and discretion, and thus allows us to evaluate which of these specifications is favored by the data. Using quarterly data for the period from 2000-1 to 2010-4, the obtained results allow us to affirm that the data favor a discretionary policy. Estimates of the loss function show that the monetary authority gives great weight to inflation stabilization, followed by interest rate smoothing and stabilization of the output gap.

Low-frequency logarithmic discretization of the reservoir spectrum for improving the efficiency of hierarchical equations of motion approach.

Science.gov (United States)

Ye, LvZhou; Zhang, Hou-Dao; Wang, Yao; Zheng, Xiao; Yan, YiJing

2017-08-21

An efficient low-frequency logarithmic discretization (LFLD) scheme for the decomposition of fermionic reservoir spectrum is proposed for the investigation of quantum impurity systems. The scheme combines the Padé spectrum decomposition (PSD) and a logarithmic discretization of the residual part in which the parameters are determined based on an extension of the recently developed minimum-dissipaton ansatz [J. J. Ding et al., J. Chem. Phys. 145, 204110 (2016)]. A hierarchical equations of motion (HEOM) approach is then employed to validate the proposed scheme by examining the static and dynamic system properties in both the Kondo and noninteracting regimes. The LFLD scheme requires a much smaller number of exponential functions than the conventional PSD scheme to reproduce the reservoir correlation function and thus facilitates the efficient implementation of the HEOM approach in extremely low temperature regimes.

Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media

International Nuclear Information System (INIS)

Coelho, Pedro J.

2014-01-01

Many methods are available for the solution of radiative heat transfer problems in participating media. Among these, the discrete ordinates method (DOM) and the finite volume method (FVM) are among the most widely used ones. They provide a good compromise between accuracy and computational requirements, and they are relatively easy to integrate in CFD codes. This paper surveys recent advances on these numerical methods. Developments concerning the grid structure (e.g., new formulations for axisymmetrical geometries, body-fitted structured and unstructured meshes, embedded boundaries, multi-block grids, local grid refinement), the spatial discretization scheme, and the angular discretization scheme are described. Progress related to the solution accuracy, solution algorithm, alternative formulations, such as the modified DOM and FVM, even-parity formulation, discrete-ordinates interpolation method and method of lines, and parallelization strategies is addressed. The application to non-gray media, variable refractive index media, and transient problems is also reviewed. - Highlights: • We survey recent advances in the discrete ordinates and finite volume methods. • Developments in spatial and angular discretization schemes are described. • Progress in solution algorithms and parallelization methods is reviewed. • Advances in the transient solution of the radiative transfer equation are appraised. • Non-gray media and variable refractive index media are briefly addressed

Théorie de Perron-Frobenius non linéaire et méthodes numériques max-plus pour la résolution d'équations d'Hamilton-Jacobi

OpenAIRE

Qu , Zheng

2013-01-01

Dynamic programming is one of the main approaches to solve optimal control problems. It reduces the latter problems to Hamilton-Jacobi partial differential equations (PDE). Several techniques have been proposed in the literature to solve these PDE. We mention, for example, finite difference schemes, the so-called discrete dynamic programming method or semi-Lagrangian method, or the antidiffusive schemes. All these methods are grid-based, i.e., they require a discretization of the state space,...

Higher-order schemes for the Laplace transformation method for parabolic problems

KAUST Repository

Douglas, C.

2011-01-01

In this paper we solve linear parabolic problems using the three stage noble algorithms. First, the time discretization is approximated using the Laplace transformation method, which is both parallel in time (and can be in space, too) and extremely high order convergent. Second, higher-order compact schemes of order four and six are used for the the spatial discretization. Finally, the discretized linear algebraic systems are solved using multigrid to show the actual convergence rate for numerical examples, which are compared to other numerical solution methods. © 2011 Springer-Verlag.

The Function of Credit Scheme to Improve Family Income among Beef Cattle Farmers in Central Java Province

Science.gov (United States)

Prasetyo, E.; Ekowati, T.; Roessali, W.; Gayatri, S.

2018-02-01

The aims of study were: (i) identify of beef cattle fattening credit scheme, (ii) calculating and analyze of beef cattle farmers’ income, (iii) analyze of factors influencing beef cattle credit scheme towards farmer’s income. The research was held in five regencies in Central Java Province. Beef cattle fattening farm was standardized as an elementary unit. Survey method was used, while Two Stage Cluster Purposive Sampling was used for determining of sample. Data were analyzed using statistical method of quantitative descriptive and inferential statistics in term of income analysis and multiple linear regression models. The result showed that farmers used their own capital to run the farm. The average amount was IDR 10,769,871. Kredit Ketahanan Pangan dan Energi was credit scheme which was dominantly access by farmers. The average credit was IDR 23,312,200/farmer with rate of credit equal to 6.46%, the time of credit returning equal to 24.60 monthand the prediction of average collateral equal to IDR 35,800,00. The average of farmers’ income was IDR 4,361,611.60/2.96 head of beef cattle/fattening period. If the labour cost did not calculate as a cost production, hence the farmer’ income was IDR 7,608,630.41 or in other word the farmer’ income increase 74.44%. Factors of credit scheme which partially significant influence to the farmers’ income were number of own capital usage and value of credit collateral. Meanwhile, name of credit scheme, financing institution as a creditor, amount of credit, rate of credit scheme and time of returning credit were not significantly influence towards farmers’ income.

Discrete quintic spline for boundary value problem in plate deflation theory

Science.gov (United States)

Wong, Patricia J. Y.

2017-07-01

We propose a numerical scheme for a fourth-order boundary value problem arising from plate deflation theory. The scheme involves a discrete quintic spline, and it is of order 4 if a parameter takes a specific value, else it is of order 2. We also present a well known numerical example to illustrate the efficiency of our method as well as to compare with other numerical methods proposed in the literature.

Efficient light scattering through thin semi-transparent objects

DEFF Research Database (Denmark)

Frisvad, Jeppe Revall; Christensen, Niels Jørgen; Falster, Peter

2005-01-01

This paper concerns real-time rendering of thin semi-transparent objects. An object in this category could be a piece of cloth, eg. a curtain. Semi-transparent objects are visualized most correctly using volume rendering techniques. In general such techniques are, however, intractable for real-ti...... in this new area gives far better results than what is obtainable with a traditional real-time rendering scheme using a constant factor for alpha blending....

A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models

Directory of Open Access Journals (Sweden)

Shengwu Zhou

2012-01-01

Full Text Available A positivity-preserving numerical method for nonlinear Black-Scholes models is developed in this paper. The numerical method is based on a nonstandard approximation of the second partial derivative. The scheme is not only unconditionally stable and positive, but also allows us to solve the discrete equation explicitly. Monotone properties are studied in order to avoid unwanted oscillations of the numerical solution. The numerical results for European put option and European butterfly spread are compared to the standard finite difference scheme. It turns out that the proposed scheme is efficient and reliable.

Designing carbon taxation schemes for automobiles: A simulation exercise for Germany

OpenAIRE

Adamou, Adamos; Clerides, Sofronis; Zachariadis, Theodoros

2011-01-01

Vehicle taxation based on CO2 emissions is increasingly being adopted worldwide in order to shift consumer purchases to low-carbon cars, yet little is known about the effectiveness and overall economic impact of these schemes. We focus on feebate schemes, which impose a fee on high-carbon vehicles and give a rebate to purchasers of low-carbon automobiles. We estimate a discrete choice model of demand for automobiles in Germany and simulate the impact of alternative feebate schemes on emission...

Discrete diffusion Lyman α radiative transfer

Science.gov (United States)

Smith, Aaron; Tsang, Benny T.-H.; Bromm, Volker; Milosavljević, Miloš

2018-06-01

Due to its accuracy and generality, Monte Carlo radiative transfer (MCRT) has emerged as the prevalent method for Lyα radiative transfer in arbitrary geometries. The standard MCRT encounters a significant efficiency barrier in the high optical depth, diffusion regime. Multiple acceleration schemes have been developed to improve the efficiency of MCRT but the noise from photon packet discretization remains a challenge. The discrete diffusion Monte Carlo (DDMC) scheme has been successfully applied in state-of-the-art radiation hydrodynamics (RHD) simulations. Still, the established framework is not optimal for resonant line transfer. Inspired by the DDMC paradigm, we present a novel extension to resonant DDMC (rDDMC) in which diffusion in space and frequency are treated on equal footing. We explore the robustness of our new method and demonstrate a level of performance that justifies incorporating the method into existing Lyα codes. We present computational speedups of ˜102-106 relative to contemporary MCRT implementations with schemes that skip scattering in the core of the line profile. This is because the rDDMC runtime scales with the spatial and frequency resolution rather than the number of scatterings—the latter is typically ∝τ0 for static media, or ∝(aτ0)2/3 with core-skipping. We anticipate new frontiers in which on-the-fly Lyα radiative transfer calculations are feasible in 3D RHD. More generally, rDDMC is transferable to any computationally demanding problem amenable to a Fokker-Planck approximation of frequency redistribution.

Mathematical properties of a semi-classical signal analysis method: Noisy signal case

KAUST Repository

Liu, Dayan

2012-08-01

Recently, a new signal analysis method based on a semi-classical approach has been proposed [1]. The main idea in this method is to interpret a signal as a potential of a Schrodinger operator and then to use the discrete spectrum of this operator to analyze the signal. In this paper, we are interested in a mathematical analysis of this method in discrete case considering noisy signals. © 2012 IEEE.

Mathematical properties of a semi-classical signal analysis method: Noisy signal case

KAUST Repository

Liu, Dayan; Laleg-Kirati, Taous-Meriem

2012-01-01

Recently, a new signal analysis method based on a semi-classical approach has been proposed [1]. The main idea in this method is to interpret a signal as a potential of a Schrodinger operator and then to use the discrete spectrum of this operator to analyze the signal. In this paper, we are interested in a mathematical analysis of this method in discrete case considering noisy signals. © 2012 IEEE.

Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks.

Science.gov (United States)

Chen, Wu-Hua; Lu, Xiaomei; Zheng, Wei Xing

2015-04-01

This paper investigates the problems of impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks (DDNNs). Two types of DDNNs with stabilizing impulses are studied. By introducing the time-varying Lyapunov functional to capture the dynamical characteristics of discrete-time impulsive delayed neural networks (DIDNNs) and by using a convex combination technique, new exponential stability criteria are derived in terms of linear matrix inequalities. The stability criteria for DIDNNs are independent of the size of time delay but rely on the lengths of impulsive intervals. With the newly obtained stability results, sufficient conditions on the existence of linear-state feedback impulsive controllers are derived. Moreover, a novel impulsive synchronization scheme for two identical DDNNs is proposed. The novel impulsive synchronization scheme allows synchronizing two identical DDNNs with unknown delays. Simulation results are given to validate the effectiveness of the proposed criteria of impulsive stabilization and impulsive synchronization of DDNNs. Finally, an application of the obtained impulsive synchronization result for two identical chaotic DDNNs to a secure communication scheme is presented.

Convergence of discrete Aubry–Mather model in the continuous limit

Science.gov (United States)

Su, Xifeng; Thieullen, Philippe

2018-05-01

We develop two approximation schemes for solving the cell equation and the discounted cell equation using Aubry–Mather–Fathi theory. The Hamiltonian is supposed to be Tonelli, time-independent and periodic in space. By Legendre transform it is equivalent to find a fixed point of some nonlinear operator, called Lax-Oleinik operator, which may be discounted or not. By discretizing in time, we are led to solve an additive eigenvalue problem involving a discrete Lax–Oleinik operator. We show how to approximate the effective Hamiltonian and some weak KAM solutions by letting the time step in the discrete model tend to zero. We also obtain a selected discrete weak KAM solution as in Davini et al (2016 Invent. Math. 206 29–55), and show that it converges to a particular solution of the cell equation. In order to unify the two settings, continuous and discrete, we develop a more general formalism of the short-range interactions.

Physics-preserving averaging scheme based on Grunwald-Letnikov formula for gas flow in fractured media

KAUST Repository

Amir, Sahar Z.

2018-01-02

The heterogeneous natures of rock fabrics, due to the existence of multi-scale fractures and geological formations, led to the deviations from unity in the flux-equations fractional-exponent magnitudes. In this paper, the resulting non-Newtonian non-Darcy fractional-derivatives flux equations are solved using physics-preserving averaging schemes that incorporates both, original and shifted, Grunwald-Letnikov (GL) approximation formulas preserving the physics, by reducing the shifting effects, while maintaining the stability of the system, by keeping one shifted expansion. The proposed way of using the GL expansions also generate symmetrical coefficient matrices that significantly reduces the discretization complexities appearing with all shifted cases from literature, and help considerably in 2D and 3D systems. Systems equations derivations and discretization details are discussed. Then, the physics-preserving averaging scheme is explained and illustrated. Finally, results are presented and reviewed. Edge-based original GL expansions are unstable as also illustrated in literatures. Shifted GL expansions are stable but add a lot of additional weights to both discretization sides affecting the physical accuracy. In comparison, the physics-preserving averaging scheme balances the physical accuracy and stability requirements leading to a more physically conservative scheme that is more stable than the original GL approximation but might be slightly less stable than the shifted GL approximations. It is a locally conservative Single-Continuum averaging scheme that applies a finite-volume viewpoint.

Physics-preserving averaging scheme based on Grunwald-Letnikov formula for gas flow in fractured media

KAUST Repository

Amir, Sahar Z.; Sun, Shuyu

2018-01-01

The heterogeneous natures of rock fabrics, due to the existence of multi-scale fractures and geological formations, led to the deviations from unity in the flux-equations fractional-exponent magnitudes. In this paper, the resulting non-Newtonian non-Darcy fractional-derivatives flux equations are solved using physics-preserving averaging schemes that incorporates both, original and shifted, Grunwald-Letnikov (GL) approximation formulas preserving the physics, by reducing the shifting effects, while maintaining the stability of the system, by keeping one shifted expansion. The proposed way of using the GL expansions also generate symmetrical coefficient matrices that significantly reduces the discretization complexities appearing with all shifted cases from literature, and help considerably in 2D and 3D systems. Systems equations derivations and discretization details are discussed. Then, the physics-preserving averaging scheme is explained and illustrated. Finally, results are presented and reviewed. Edge-based original GL expansions are unstable as also illustrated in literatures. Shifted GL expansions are stable but add a lot of additional weights to both discretization sides affecting the physical accuracy. In comparison, the physics-preserving averaging scheme balances the physical accuracy and stability requirements leading to a more physically conservative scheme that is more stable than the original GL approximation but might be slightly less stable than the shifted GL approximations. It is a locally conservative Single-Continuum averaging scheme that applies a finite-volume viewpoint.

A numerical method for the quasi-incompressible Cahn–Hilliard–Navier–Stokes equations for variable density flows with a discrete energy law

International Nuclear Information System (INIS)

Guo, Z.; Lin, P.; Lowengrub, J.S.

2014-01-01

In this paper, we investigate numerically a diffuse interface model for the Navier–Stokes equation with fluid–fluid interface when the fluids have different densities [48]. Under minor reformulation of the system, we show that there is a continuous energy law underlying the system, assuming that all variables have reasonable regularities. It is shown in the literature that an energy law preserving method will perform better for multiphase problems. Thus for the reformulated system, we design a C 0 finite element method and a special temporal scheme where the energy law is preserved at the discrete level. Such a discrete energy law (almost the same as the continuous energy law) for this variable density two-phase flow model has never been established before with C 0 finite element. A Newton method is introduced to linearise the highly non-linear system of our discretization scheme. Some numerical experiments are carried out using the adaptive mesh to investigate the scenario of coalescing and rising drops with differing density ratio. The snapshots for the evolution of the interface together with the adaptive mesh at different times are presented to show that the evolution, including the break-up/pinch-off of the drop, can be handled smoothly by our numerical scheme. The discrete energy functional for the system is examined to show that the energy law at the discrete level is preserved by our scheme

Progress with multigrid schemes for hypersonic flow problems

International Nuclear Information System (INIS)

Radespiel, R.; Swanson, R.C.

1995-01-01

Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm employs upwind spatial discretization with explicit multistage time stepping. Two-level versions of the various multigrid algorithms are applied to the two-dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving three different hypersonic flow problems. Some new multigrid schemes based on semicoarsening strategies are shown to be quite effective in relieving the stiffness caused by the high-aspect-ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 X 10 6 and Mach numbers up to 25. 32 refs., 31 figs., 1 tab

Non Standard Finite Difference Scheme for Mutualistic Interaction Description

OpenAIRE

Gabbriellini, Gianluca

2012-01-01

One of the more interesting themes of the mathematical ecology is the description of the mutualistic interaction between two interacting species. Based on continuous-time model developed by Holland and DeAngelis 2009 for consumer-resource mutualism description, this work deals with the application of the Mickens Non Standard Finite Difference method to transform the continuous-time scheme into a discrete-time one. It has been proved that the Mickens scheme is dynamically consistent with the o...

Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials

International Nuclear Information System (INIS)

Aquilanti, V; Marinelli, D; Marzuoli, A

2014-01-01

Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schrödinger–like equation which provides a semiclassical Hamiltonian picture of the evolution of a 'quantum of space', as shown by the authors in [1]. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed

On the integration scheme along a trajectory for the characteristics method

International Nuclear Information System (INIS)

Le Tellier, Romain; Hebert, Alain

2006-01-01

The issue of the integration scheme along a trajectory which appears for all tracking-based transport methods is discussed from the point of view of the method of characteristics. The analogy with the discrete ordinates method in slab geometry is highlighted along with the practical limitation in transposing high-order S N schemes to a trajectory-based method. We derived an example of such a transposition starting from the linear characteristic scheme. This new scheme is compared with the standard flat-source approximation of the step characteristic scheme and with the diamond differencing scheme. The numerical study covers a 1D analytical case, 2D one-group critical and fixed-source benchmarks and finally a realistic multigroup calculation on a BWR-MOX assembly

Discrete-time control system design with applications

CERN Document Server

Rabbath, C A

2014-01-01

This book presents practical techniques of discrete-time control system design. In general, the design techniques lead to low-order dynamic compensators that ensure satisfactory closed-loop performance for a wide range of sampling rates. The theory is given in the form of theorems, lemmas, and propositions. The design of the control systems is presented as step-by-step procedures and algorithms. The proposed feedback control schemes are applied to well-known dynamic system models. This book also discusses: Closed-loop performance of generic models of mobile robot and airborne pursuer dynamic systems under discrete-time feedback control with limited computing capabilities Concepts of discrete-time models and sampled-data models of continuous-time systems, for both single- and dual-rate operation Local versus global digital redesign Optimal, closed-loop digital redesign methods Plant input mapping design Generalized holds and samplers for use in feedback control loops, Numerical simulation of fixed-point arithm...

The Full—Discrete Mixed Finite Element Methods for Nonlinear Hyperbolic Equations

Institute of Scientific and Technical Information of China (English)

YanpingCHEN; YunqingHUANG

1998-01-01

This article treats mixed finite element methods for second order nonlinear hyperbolic equations.A fully discrete scheme is presented and improved L2-error estimates are established.The convergence of both the function value andthe flux is demonstrated.

Lean planning in the semi-process industry, a case study

NARCIS (Netherlands)

Pool, Arnout; Wijngaard, Jacob; van der Zee, D.J.

The lean approach is an idealizing improvement approach that has an enormous impact in the field of operations management. It started in the automotive industry and has since been widely applied in discrete manufacturing. However, extensions to the (semi-) process industry have been much slower.

Convergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Media

KAUST Repository

Saad, Bilal Mohammed; Saad, Mazen

2014-01-01

We study the convergence of a combined finite volume nonconforming finite element scheme on general meshes for a partially miscible two-phase flow model in anisotropic porous media. This model includes capillary effects and exchange between the phase. The diffusion term,which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. The convergence of the scheme is proved thanks to an estimate on the two pressures which allows to show estimates on the discrete time and compactness results in the case of degenerate relative permeabilities. A key point in the scheme is to use particular averaging formula for the dissolution function arising in the diffusion term. We show also a simulation of CO2 injection in a water saturated reservoir and nuclear waste management. Numerical results are obtained by in-house numerical code. © Springer International Publishing Switzerland 2014.

Using the electron localization function to correct for confinement physics in semi-local density functional theory

International Nuclear Information System (INIS)

Hao, Feng; Mattsson, Ann E.; Armiento, Rickard

2014-01-01

We have previously proposed that further improved functionals for density functional theory can be constructed based on the Armiento-Mattsson subsystem functional scheme if, in addition to the uniform electron gas and surface models used in the Armiento-Mattsson 2005 functional, a model for the strongly confined electron gas is also added. However, of central importance for this scheme is an index that identifies regions in space where the correction provided by the confined electron gas should be applied. The electron localization function (ELF) is a well-known indicator of strongly localized electrons. We use a model of a confined electron gas based on the harmonic oscillator to show that regions with high ELF directly coincide with regions where common exchange energy functionals have large errors. This suggests that the harmonic oscillator model together with an index based on the ELF provides the crucial ingredients for future improved semi-local functionals. For a practical illustration of how the proposed scheme is intended to work for a physical system we discuss monoclinic cupric oxide, CuO. A thorough discussion of this system leads us to promote the cell geometry of CuO as a useful benchmark for future semi-local functionals. Very high ELF values are found in a shell around the O ions, and take its maximum value along the Cu–O directions. An estimate of the exchange functional error from the effect of electron confinement in these regions suggests a magnitude and sign that could account for the error in cell geometry

Network Regulation and Support Schemes

DEFF Research Database (Denmark)

Ropenus, Stephanie; Schröder, Sascha Thorsten; Jacobsen, Henrik

2009-01-01

-in tariffs to market-based quota systems, and network regulation approaches, comprising rate-of-return and incentive regulation. National regulation and the vertical structure of the electricity sector shape the incentives of market agents, notably of distributed generators and network operators......At present, there exists no explicit European policy framework on distributed generation. Various Directives encompass distributed generation; inherently, their implementation is to the discretion of the Member States. The latter have adopted different kinds of support schemes, ranging from feed....... This article seeks to investigate the interactions between the policy dimensions of support schemes and network regulation and how they affect the deployment of distributed generation. Firstly, a conceptual analysis examines how the incentives of the different market agents are affected. In particular...

A space-time mixed galerkin marching-on-in-time scheme for the time-domain combined field integral equation

KAUST Repository

Beghein, Yves

2013-03-01

The time domain combined field integral equation (TD-CFIE), which is constructed from a weighted sum of the time domain electric and magnetic field integral equations (TD-EFIE and TD-MFIE) for analyzing transient scattering from closed perfect electrically conducting bodies, is free from spurious resonances. The standard marching-on-in-time technique for discretizing the TD-CFIE uses Galerkin and collocation schemes in space and time, respectively. Unfortunately, the standard scheme is theoretically not well understood: stability and convergence have been proven for only one class of space-time Galerkin discretizations. Moreover, existing discretization schemes are nonconforming, i.e., the TD-MFIE contribution is tested with divergence conforming functions instead of curl conforming functions. We therefore introduce a novel space-time mixed Galerkin discretization for the TD-CFIE. A family of temporal basis and testing functions with arbitrary order is introduced. It is explained how the corresponding interactions can be computed efficiently by existing collocation-in-time codes. The spatial mixed discretization is made fully conforming and consistent by leveraging both Rao-Wilton-Glisson and Buffa-Christiansen basis functions and by applying the appropriate bi-orthogonalization procedures. The combination of both techniques is essential when high accuracy over a broad frequency band is required. © 2012 IEEE.

Analysis and control of Boolean networks a semi-tensor product approach

CERN Document Server

Cheng, Daizhan; Li, Zhiqiang

2010-01-01

This book presents a new approach to the investigation of Boolean control networks, using the semi-tensor product (STP), which can express a logical function as a conventional discrete-time linear system. This makes it possible to analyze basic control problems.

Spatial discretizations for self-adjoint forms of the radiative transfer equations

International Nuclear Information System (INIS)

Morel, Jim E.; Adams, B. Todd; Noh, Taewan; McGhee, John M.; Evans, Thomas M.; Urbatsch, Todd J.

2006-01-01

There are three commonly recognized second-order self-adjoint forms of the neutron transport equation: the even-parity equations, the odd-parity equations, and the self-adjoint angular flux equations. Because all of these equations contain second-order spatial derivatives and are self-adjoint for the mono-energetic case, standard continuous finite-element discretization techniques have proved quite effective when applied to the spatial variables. We first derive analogs of these equations for the case of time-dependent radiative transfer. The primary unknowns for these equations are functions of the angular intensity rather than the angular flux, hence the analog of the self-adjoint angular flux equation is referred to as the self-adjoint angular intensity equation. Then we describe a general, arbitrary-order, continuous spatial finite-element approach that is applied to each of the three equations in conjunction with backward-Euler differencing in time. We refer to it as the 'standard' technique. We also introduce an alternative spatial discretization scheme for the self-adjoint angular intensity equation that requires far fewer unknowns than the standard method, but appears to give comparable accuracy. Computational results are given that demonstrate the validity of both of these discretization schemes

An unconditionally stable fully conservative semi-Lagrangian method

KAUST Repository

Lentine, Michael; Gré tarsson, Jó n Tó mas; Fedkiw, Ronald

2011-01-01

of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving

Performance Comparison of Reconstruction Algorithms in Discrete Blind Multi-Coset Sampling

DEFF Research Database (Denmark)

Grigoryan, Ruben; Arildsen, Thomas; Tandur, Deepaknath

2012-01-01

This paper investigates the performance of different reconstruction algorithms in discrete blind multi-coset sampling. Multi-coset scheme is a promising compressed sensing architecture that can replace traditional Nyquist-rate sampling in the applications with multi-band frequency sparse signals...

Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme

Energy Technology Data Exchange (ETDEWEB)

Squire, J.; Tang, W. M. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Qin, H. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)

2012-08-15

A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of discrete exterior calculus [Desbrun et al., e-print arXiv:math/0508341 (2005)], the field solver, interpolation scheme, and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.

Schemes of Superradiant Emission from Electron Beams and "Spin-Flip Emission of Radiation"

CERN Document Server

Gover, A

2005-01-01

A unified analysis for Superradiant emission from bunched electron beams in various kinds of radiation scheme is presented. Radiation schemes that can be described by the formulation include Pre-bunched FEL (PB-FEL), Coherent Synchrotron Radiation (CSR), Smith-Purcell Radiation, Cerenkov-Radiation, Transition-Radiation and more. The theory is based on mode excitation formulation - either discrete or continuous (the latter - in open structures). The discrete mode formulation permits simple evaluation of the spatially coherent power and spectral power of the source. These figures of merit of the radiation source are useful for characterizing and comparing the performance of different radiation schemes. When the bunched electron beam emits superradiantly, these parameters scale like the square of the number of electrons, orders of magnitude more than spontaneous emission. The formulation applies to emission from single electron bunches, periodically bunched beams, or emission from a finite number of bunches in a...

Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics

International Nuclear Information System (INIS)

Farrell, Patricio; Koprucki, Thomas; Fuhrmann, Jürgen

2017-01-01

We compare three thermodynamically consistent numerical fluxes known in the literature, appearing in a Voronoï finite volume discretization of the van Roosbroeck system with general charge carrier statistics. Our discussion includes an extension of the Scharfetter–Gummel scheme to non-Boltzmann (e.g. Fermi–Dirac) statistics. It is based on the analytical solution of a two-point boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the non-Boltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed p-i-n benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states.

Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics

Science.gov (United States)

Farrell, Patricio; Koprucki, Thomas; Fuhrmann, Jürgen

2017-10-01

We compare three thermodynamically consistent numerical fluxes known in the literature, appearing in a Voronoï finite volume discretization of the van Roosbroeck system with general charge carrier statistics. Our discussion includes an extension of the Scharfetter-Gummel scheme to non-Boltzmann (e.g. Fermi-Dirac) statistics. It is based on the analytical solution of a two-point boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the non-Boltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed p-i-n benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states.

A hybrid Lagrangian Voronoi-SPH scheme

Science.gov (United States)

Fernandez-Gutierrez, D.; Souto-Iglesias, A.; Zohdi, T. I.

2017-11-01

A hybrid Lagrangian Voronoi-SPH scheme, with an explicit weakly compressible formulation for both the Voronoi and SPH sub-domains, has been developed. The SPH discretization is substituted by Voronoi elements close to solid boundaries, where SPH consistency and boundary conditions implementation become problematic. A buffer zone to couple the dynamics of both sub-domains is used. This zone is formed by a set of particles where fields are interpolated taking into account SPH particles and Voronoi elements. A particle may move in or out of the buffer zone depending on its proximity to a solid boundary. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.

Discrete memory schemes for finite strain thermoplasticity and application to shape memory alloys

International Nuclear Information System (INIS)

Favier, D.; Guelin, P.; Pegon, P.; Nowacki, W.K.

1987-01-01

A theory of finite strain plasticity has been proposed: The scheme of pure hysteresis with mixed transport has been extended to the case of non-rotational kinematics. Secondly, the simple shear case has been studied, taking into account Drucker's recent analysis regarding the 'appropriate simple idealizations for finite plasticity'. Illustrations are provided for general stress/strain paths. Also a new theory of isotropic hyperelasticity has been proposed. The 'reversible' relative Cauchy stress tensor (of type (1,1) and weight one) is defined in the dragged along coordinates as a tensorial isotropic function of the Almansi tensor and of its invariants (through the partial derivatives of the actual scalar density of elastic energy per unit extent of dragged along coordinates). The correspondance between strain and stress paths is then defined in a general form which is particularly convenient for the study of first order effects, limit behaviours, coupling and second order effects. Illustrations are provided. The addition of the pure hysteresis stress contribution σ a and of the reversible contribution σ rev leads to a scheme of 'superelasticity' departure to obtain a provisional scheme of shape memory effects. Some remarks are given regarding some of the possible generalizations of the scheme. (orig./GL)

Hybrid discrete-time neural networks.

Science.gov (United States)

Cao, Hongjun; Ibarz, Borja

2010-11-13

Hybrid dynamical systems combine evolution equations with state transitions. When the evolution equations are discrete-time (also called map-based), the result is a hybrid discrete-time system. A class of biological neural network models that has recently received some attention falls within this category: map-based neuron models connected by means of fast threshold modulation (FTM). FTM is a connection scheme that aims to mimic the switching dynamics of a neuron subject to synaptic inputs. The dynamic equations of the neuron adopt different forms according to the state (either firing or not firing) and type (excitatory or inhibitory) of their presynaptic neighbours. Therefore, the mathematical model of one such network is a combination of discrete-time evolution equations with transitions between states, constituting a hybrid discrete-time (map-based) neural network. In this paper, we review previous work within the context of these models, exemplifying useful techniques to analyse them. Typical map-based neuron models are low-dimensional and amenable to phase-plane analysis. In bursting models, fast-slow decomposition can be used to reduce dimensionality further, so that the dynamics of a pair of connected neurons can be easily understood. We also discuss a model that includes electrical synapses in addition to chemical synapses with FTM. Furthermore, we describe how master stability functions can predict the stability of synchronized states in these networks. The main results are extended to larger map-based neural networks.

Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene

OpenAIRE

Oettinger, D.; Mendoza, M.; Herrmann, H. J.

2013-01-01

We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later, we use these polynomials to expand the respective distribution in a moving frame, for both cases, undoped and doped graphene. In order to discretize the Boltzmann equation and make feasible the numerical implementation, we reduce the number of discrete points in m...

Supervisory control synthesis of discrete-event systems using a coordination scheme

Czech Academy of Sciences Publication Activity Database

Komenda, Jan; Masopust, Tomáš; van Schuppen, J. H.

2012-01-01

Roč. 48, č. 2 (2012), s. 247-254 ISSN 0005-1098 R&D Projects: GA ČR(CZ) GAP103/11/0517; GA ČR GPP202/11/P028 Grant - others:European Commission(XE) EU.ICT.DISC 224498 Institutional research plan: CEZ:AV0Z10190503 Keywords : discrete-event systems * supervisory control * distributed control * closed-loop systems * controllability Subject RIV: BA - General Mathematics Impact factor: 2.919, year: 2012 http://www.sciencedirect.com/science/article/pii/S0005109811005395

Supervisory control synthesis of discrete-event systems using a coordination scheme

Czech Academy of Sciences Publication Activity Database

Komenda, Jan; Masopust, Tomáš; van Schuppen, J. H.

2012-01-01

Roč. 48, č. 2 (2012), s. 247-254 ISSN 0005-1098 R&D Projects: GA ČR(CZ) GAP103/11/0517; GA ČR GPP202/11/P028 Grant - others:European Commission(XE) EU. ICT .DISC 224498 Institutional research plan: CEZ:AV0Z10190503 Keywords : discrete-event systems * supervisory control * distributed control * closed-loop systems * controllability Subject RIV: BA - General Mathematics Impact factor: 2.919, year: 2012 http://www.sciencedirect.com/science/article/pii/S0005109811005395

Generalized Second-Order Parametric Optimality Conditions in Semiinfinite Discrete Minmax Fractional Programming and Second-Order Univexity

Directory of Open Access Journals (Sweden)

Ram Verma

2016-02-01

Full Text Available This paper deals with mainly establishing numerous sets of generalized second order paramertic sufficient optimality conditions for a semiinfinite discrete minmax fractional programming problem, while the results on semiinfinite discrete minmax fractional programming problem achieved based on some partitioning schemes under various types of generalized second order univexity assumptions. 

Discrete bacteria foraging optimization algorithm for graph based problems - a transition from continuous to discrete

Science.gov (United States)

Sur, Chiranjib; Shukla, Anupam

2018-03-01

Bacteria Foraging Optimisation Algorithm is a collective behaviour-based meta-heuristics searching depending on the social influence of the bacteria co-agents in the search space of the problem. The algorithm faces tremendous hindrance in terms of its application for discrete problems and graph-based problems due to biased mathematical modelling and dynamic structure of the algorithm. This had been the key factor to revive and introduce the discrete form called Discrete Bacteria Foraging Optimisation (DBFO) Algorithm for discrete problems which exceeds the number of continuous domain problems represented by mathematical and numerical equations in real life. In this work, we have mainly simulated a graph-based road multi-objective optimisation problem and have discussed the prospect of its utilisation in other similar optimisation problems and graph-based problems. The various solution representations that can be handled by this DBFO has also been discussed. The implications and dynamics of the various parameters used in the DBFO are illustrated from the point view of the problems and has been a combination of both exploration and exploitation. The result of DBFO has been compared with Ant Colony Optimisation and Intelligent Water Drops Algorithms. Important features of DBFO are that the bacteria agents do not depend on the local heuristic information but estimates new exploration schemes depending upon the previous experience and covered path analysis. This makes the algorithm better in combination generation for graph-based problems and combination generation for NP hard problems.

Discrete event systems diagnosis and diagnosability

CERN Document Server

Sayed-Mouchaweh, Moamar

2014-01-01

Discrete Event Systems: Diagnosis and Diagnosability addresses the problem of fault diagnosis of Discrete Event Systems (DES). This book provides the basic techniques and approaches necessary for the design of an efficient fault diagnosis system for a wide range of modern engineering applications. The different techniques and approaches are classified according to several criteria such as: modeling tools (Automata, Petri nets) that is used to construct the model; the information (qualitative based on events occurrences and/or states outputs, quantitative based on signal processing and data analysis) that is needed to analyze and achieve the diagnosis; the decision structure (centralized, decentralized) that is required to achieve the diagnosis. The goal of this classification is to select the efficient method to achieve the fault diagnosis according to the application constraints. This book focuses on the centralized and decentralized event based diagnosis approaches using formal language and automata as mode...

Pressure correction schemes for compressible flows: application to baro-tropic Navier-Stokes equations and to drift-flux model

International Nuclear Information System (INIS)

Gastaldo, L.

2007-11-01

We develop in this PhD thesis a simulation tool for bubbly flows encountered in some late phases of a core-melt accident in pressurized water reactors, when the flow of molten core and vessel structures comes to chemically interact with the concrete of the containment floor. The physical modelling is based on the so-called drift-flux model, consisting of mass balance and momentum balance equations for the mixture (Navier-Stokes equations) and a mass balance equation for the gaseous phase. First, we propose a pressure correction scheme for the compressible Navier-Stokes equations based on mixed non-conforming finite elements. An ad hoc discretization of the advection operator, by a finite volume technique based on a dual mesh, ensures the stability of the velocity prediction step. A priori estimates for the velocity and the pressure yields the existence of the solution. We prove that this scheme is stable, in the sense that the discrete entropy is decreasing. For the conservation equation of the gaseous phase, we build a finite volume discretization which satisfies a discrete maximum principle. From this last property, we deduce the existence and the uniqueness of the discrete solution. Finally, on the basis of these works, a conservative and monotone scheme which is stable in the low Mach number limit, is build for the drift-flux model. This scheme enjoys, moreover, the following property: the algorithm preserves a constant pressure and velocity through moving interfaces between phases (i.e. contact discontinuities of the underlying hyperbolic system). In order to satisfy this property at the discrete level, we build an original pressure correction step which couples the mass balance equation with the transport terms of the gas mass balance equation, the remaining terms of the gas mass balance being taken into account with a splitting method. We prove the existence of a discrete solution for the pressure correction step. Numerical results are presented; they

A nominally second-order cell-centered Lagrangian scheme for simulating elastic-plastic flows on two-dimensional unstructured grids

Science.gov (United States)

Maire, Pierre-Henri; Abgrall, Rémi; Breil, Jérôme; Loubère, Raphaël; Rebourcet, Bernard

2013-02-01

In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic-plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs the von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.

Semi-analytical Study of a One-dimensional Contaminant Flow in a ...

African Journals Online (AJOL)

ADOWIE PERE

ABSTRACT: The Bubnov-Galerkin weighted residual method was used to solve a one- dimensional contaminant flow problem in this paper. The governing equation of the contaminant flow, which is characterized by advection, dispersion and adsorption was discretized and solved to obtain the semi-analytical solution.

Functional entropy variables: A new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier–Stokes–Korteweg equations

Energy Technology Data Exchange (ETDEWEB)

Liu, Ju, E-mail: jliu@ices.utexas.edu [Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, 1 University Station C0200, Austin, TX 78712 (United States); Gomez, Hector [Department of Mathematical Methods, University of A Coruña, Campus de Elviña, s/n, 15192 A Coruña (Spain); Evans, John A.; Hughes, Thomas J.R. [Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, 1 University Station C0200, Austin, TX 78712 (United States); Landis, Chad M. [Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, 210 East 24th Street, 1 University Station C0600, Austin, TX 78712 (United States)

2013-09-01

We propose a new methodology for the numerical solution of the isothermal Navier–Stokes–Korteweg equations. Our methodology is based on a semi-discrete Galerkin method invoking functional entropy variables, a generalization of classical entropy variables, and a new time integration scheme. We show that the resulting fully discrete scheme is unconditionally stable-in-energy, second-order time-accurate, and mass-conservative. We utilize isogeometric analysis for spatial discretization and verify the aforementioned properties by adopting the method of manufactured solutions and comparing coarse mesh solutions with overkill solutions. Various problems are simulated to show the capability of the method. Our methodology provides a means of constructing unconditionally stable numerical schemes for nonlinear non-convex hyperbolic systems of conservation laws.

A space-time mixed galerkin marching-on-in-time scheme for the time-domain combined field integral equation

KAUST Repository

Beghein, Yves; Cools, Kristof; Bagci, Hakan; De Zutter, Danië l

2013-01-01

electrically conducting bodies, is free from spurious resonances. The standard marching-on-in-time technique for discretizing the TD-CFIE uses Galerkin and collocation schemes in space and time, respectively. Unfortunately, the standard scheme is theoretically

An analytical approach for a nodal scheme of two-dimensional neutron transport problems

International Nuclear Information System (INIS)

Barichello, L.B.; Cabrera, L.C.; Prolo Filho, J.F.

2011-01-01

Research highlights: → Nodal equations for a two-dimensional neutron transport problem. → Analytical Discrete Ordinates Method. → Numerical results compared with the literature. - Abstract: In this work, a solution for a two-dimensional neutron transport problem, in cartesian geometry, is proposed, on the basis of nodal schemes. In this context, one-dimensional equations are generated by an integration process of the multidimensional problem. Here, the integration is performed for the whole domain such that no iterative procedure between nodes is needed. The ADO method is used to develop analytical discrete ordinates solution for the one-dimensional integrated equations, such that final solutions are analytical in terms of the spatial variables. The ADO approach along with a level symmetric quadrature scheme, lead to a significant order reduction of the associated eigenvalues problems. Relations between the averaged fluxes and the unknown fluxes at the boundary are introduced as the usually needed, in nodal schemes, auxiliary equations. Numerical results are presented and compared with test problems.

Analysis of the F. Calogero Type Projection-Algebraic Scheme for Differential Operator Equations

International Nuclear Information System (INIS)

Lustyk, Miroslaw; Bogolubov, Nikolai N. Jr.; Blackmore, Denis; Prykarpatsky, Anatoliy K.

2010-12-01

The existence, convergence, realizability and stability of solutions of differential operator equations obtained via a novel projection-algebraic scheme are analyzed in detail. This analysis is based upon classical discrete approximation techniques coupled with a recent generalization of the Leray-Schauder fixed point theorem. An example is included to illustrate the efficacy of the projection scheme and analysis strategy. (author)

The parallel algorithm for the 2D discrete wavelet transform

Science.gov (United States)

Barina, David; Najman, Pavel; Kleparnik, Petr; Kula, Michal; Zemcik, Pavel

2018-04-01

The discrete wavelet transform can be found at the heart of many image-processing algorithms. Until now, the transform on general-purpose processors (CPUs) was mostly computed using a separable lifting scheme. As the lifting scheme consists of a small number of operations, it is preferred for processing using single-core CPUs. However, considering a parallel processing using multi-core processors, this scheme is inappropriate due to a large number of steps. On such architectures, the number of steps corresponds to the number of points that represent the exchange of data. Consequently, these points often form a performance bottleneck. Our approach appropriately rearranges calculations inside the transform, and thereby reduces the number of steps. In other words, we propose a new scheme that is friendly to parallel environments. When evaluating on multi-core CPUs, we consistently overcome the original lifting scheme. The evaluation was performed on 61-core Intel Xeon Phi and 8-core Intel Xeon processors.

Fast solution of Cahn–Hilliard variational inequalities using implicit time discretization and finite elements

KAUST Repository

Bosch, Jessica; Stoll, Martin; Benner, Peter

2014-01-01

We consider the efficient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton

Efficient and stable perfectly matched layer for CEM

KAUST Repository

Duru, Kenneth

2014-02-01

An efficient unsplit perfectly matched layer for numerical simulation of electromagnetic waves in unbounded domains is derived via a complex change of variables. In order to surround a Cartesian grid with the PML, the time-dependent PML requires only one (scalar) auxiliary variable in two space dimensions and six (scalar) auxiliary variables in three space dimensions. It is therefore cheap and straightforward to implement. We use Fourier and energy methods to prove the stability of the PML. We extend the stability result to a semi-discrete PML approximated by central finite differences of arbitrary order of accuracy and to a fully discrete problem for the \\'Leap-Frog\\' schemes. This makes precise the usefulness of the derived PML model for longtime simulations. Numerical experiments are presented, illustrating the accuracy and stability of the PML. © 2013 IMACS.

A discontinous Galerkin finite element method with an efficient time integration scheme for accurate simulations

KAUST Repository

Liu, Meilin

2011-07-01

A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results show that this new time integration scheme uses considerably larger time steps than the fourth-order Runge-Kutta method when combined with a DG-FEM using higher-order spatial discretization/basis functions for high accuracy. © 2011 IEEE.

The semi-Lagrangian method on curvilinear grids

Directory of Open Access Journals (Sweden)

Hamiaz Adnane

2016-09-01

Full Text Available We study the semi-Lagrangian method on curvilinear grids. The classical backward semi-Lagrangian method [1] preserves constant states but is not mass conservative. Natural reconstruction of the field permits nevertheless to have at least first order in time conservation of mass, even if the spatial error is large. Interpolation is performed with classical cubic splines and also cubic Hermite interpolation with arbitrary reconstruction order of the derivatives. High odd order reconstruction of the derivatives is shown to be a good ersatz of cubic splines which do not behave very well as time step tends to zero. A conservative semi-Lagrangian scheme along the lines of [2] is then described; here conservation of mass is automatically satisfied and constant states are shown to be preserved up to first order in time.

Discrete phase space based on finite fields

International Nuclear Information System (INIS)

Gibbons, Kathleen S.; Hoffman, Matthew J.; Wootters, William K.

2004-01-01

The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being defined on a 2Nx2N discrete phase space for a system with N orthogonal states. Here we investigate an alternative class of discrete Wigner functions, in which the field of real numbers that labels the axes of continuous phase space is replaced by a finite field having N elements. There exists such a field if and only if N is a power of a prime; so our formulation can be applied directly only to systems for which the state-space dimension takes such a value. Though this condition may seem limiting, we note that any quantum computer based on qubits meets the condition and can thus be accommodated within our scheme. The geometry of our NxN phase space also leads naturally to a method of constructing a complete set of N+1 mutually unbiased bases for the state space

Investigation of radiation effects in Hiroshima and Nagasaki using a general Monte Carlo-discrete ordinates coupling scheme

International Nuclear Information System (INIS)

Cramer, S.N.; Slater, C.O.

1990-01-01

A general adjoint Monte Carlo-forward discrete ordinates radiation transport calculational scheme has been created to study the effects of the radiation environment in Hiroshima and Nagasaki due to the bombing of these two cities. Various such studies for comparison with physical data have progressed since the end of World War II with advancements in computing machinery and computational methods. These efforts have intensified in the last several years with the U.S.-Japan joint reassessment of nuclear weapons dosimetry in Hiroshima and Nagasaki. Three principal areas of investigation are: (1) to determine by experiment and calculation the neutron and gamma-ray energy and angular spectra and total yield of the two weapons; (2) using these weapons descriptions as source terms, to compute radiation effects at several locations in the two cities for comparison with experimental data collected at various times after the bombings and thus validate the source terms; and (3) to compute radiation fields at the known locations of fatalities and surviving individuals at the time of the bombings and thus establish an absolute cause-and-effect relationship between the radiation received and the resulting injuries to these individuals and any of their descendants as indicated by their medical records. It is in connection with the second and third items, the determination of the radiation effects and the dose received by individuals, that the current study is concerned

Numerical viscosity of entropy stable schemes for systems of conservation laws. Final Report

International Nuclear Information System (INIS)

Tadmor, E.

1985-11-01

Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end conservative schemes which are also entropy conservative are constructed. These entropy conservative schemes enjoy second-order accuracy; moreover, they admit a particular interpretation within the finite-element frameworks, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable if and only if they contain more viscosity than the mentioned above entropy conservative ones

Zak Phase in Discrete-Time Quantum Walks

OpenAIRE

Puentes, G.; Santillán, O.

2015-01-01

We report on a simple scheme that may present a non-trivial geometric Zak phase ($\\Phi_{Zak}$) structure, which is based on a discrete-time quantum walk architecture. By detecting the Zak phase difference between two trajectories connecting adjacent Dirac points where the quasi-energy gap closes for opposite values of quasi-momentum ($k$), it is possible to identify geometric invariants. These geometric invariants correspond to $|\\Phi_{Zak}^{+(-)}-\\Phi_{Zak}^{-(+)}|=\\pi$ and $|\\Phi_{Zak}^{+(-...

The new Exponential Directional Iterative (EDI) 3-D Sn scheme for parallel adaptive differencing

International Nuclear Information System (INIS)

Sjoden, G.E.

2005-01-01

The new Exponential Directional Iterative (EDI) discrete ordinates (Sn) scheme for 3-D Cartesian Coordinates is presented. The EDI scheme is a logical extension of the positive, efficient Exponential Directional Weighted (EDW) Sn scheme currently used as the third level of the adaptive spatial differencing algorithm in the PENTRAN parallel discrete ordinates solver. Here, the derivation and advantages of the EDI scheme are presented; EDI uses EDW-rendered exponential coefficients as initial starting values to begin a fixed point iteration of the exponential coefficients. One issue that required evaluation was an iterative cutoff criterion to prevent the application of an unstable fixed point iteration; although this was needed in some cases, it was readily treated with a default to EDW. Iterative refinement of the exponential coefficients in EDI typically converged in fewer than four fixed point iterations. Moreover, EDI yielded more accurate angular fluxes compared to the other schemes tested, particularly in streaming conditions. Overall, it was found that the EDI scheme was up to an order of magnitude more accurate than the EDW scheme on a given mesh interval in streaming cases, and is potentially a good candidate as a fourth-level differencing scheme in the PENTRAN adaptive differencing sequence. The 3-D Cartesian computational cost of EDI was only about 20% more than the EDW scheme, and about 40% more than Diamond Zero (DZ). More evaluation and testing are required to determine suitable upgrade metrics for EDI to be fully integrated into the current adaptive spatial differencing sequence in PENTRAN. (author)

The discrete null space method for the energy-consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics

International Nuclear Information System (INIS)

Leyendecker, Sigrid; Betsch, Peter; Steinmann, Paul

2008-01-01

In the present work, the unified framework for the computational treatment of rigid bodies and nonlinear beams developed by Betsch and Steinmann (Multibody Syst. Dyn. 8, 367-391, 2002) is extended to the realm of nonlinear shells. In particular, a specific constrained formulation of shells is proposed which leads to the semi-discrete equations of motion characterized by a set of differential-algebraic equations (DAEs). The DAEs provide a uniform description for rigid bodies, semi-discrete beams and shells and, consequently, flexible multibody systems. The constraints may be divided into two classes: (i) internal constraints which are intimately connected with the assumption of rigidity of the bodies, and (ii) external constraints related to the presence of joints in a multibody framework. The present approach thus circumvents the use of rotational variables throughout the whole time discretization, facilitating the design of energy-momentum methods for flexible multibody dynamics. After the discretization has been completed a size-reduction of the discrete system is performed by eliminating the constraint forces. Numerical examples dealing with a spatial slider-crank mechanism and with intersecting shells illustrate the performance of the proposed method

The discrete adjoint method for parameter identification in multibody system dynamics.

Science.gov (United States)

Lauß, Thomas; Oberpeilsteiner, Stefan; Steiner, Wolfgang; Nachbagauer, Karin

2018-01-01

The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient. Hence, an alternative approach is the discrete adjoint method , where the adjoint differential equations are replaced by algebraic equations. Therefore, a finite difference scheme is constructed for the adjoint system directly from the numerical time integration method. The method provides the exact gradient of the discretized cost function subjected to the discretized equations of motion.

Numerical schemes for one-point closure turbulence models

International Nuclear Information System (INIS)

Larcher, Aurelien

2010-01-01

First-order Reynolds Averaged Navier-Stokes (RANS) turbulence models are studied in this thesis. These latter consist of the Navier-Stokes equations, supplemented with a system of balance equations describing the evolution of characteristic scalar quantities called 'turbulent scales'. In so doing, the contribution of the turbulent agitation to the momentum can be determined by adding a diffusive coefficient (called 'turbulent viscosity') in the Navier-Stokes equations, such that it is defined as a function of the turbulent scales. The numerical analysis problems, which are studied in this dissertation, are treated in the frame of a fractional step algorithm, consisting of an approximation on regular meshes of the Navier-Stokes equations by the nonconforming Crouzeix-Raviart finite elements, and a set of scalar convection-diffusion balance equations discretized by the standard finite volume method. A monotone numerical scheme based on the standard finite volume method is proposed so as to ensure that the turbulent scales, like the turbulent kinetic energy (k) and its dissipation rate (ε), remain positive in the case of the standard k - ε model, as well as the k - ε RNG and the extended k - ε - ν 2 models. The convergence of the proposed numerical scheme is then studied on a system composed of the incompressible Stokes equations and a steady convection-diffusion equation, which are both coupled by the viscosities and the turbulent production term. This reduced model allows to deal with the main difficulty encountered in the analysis of such problems: the definition of the turbulent production term leads to consider a class of convection-diffusion problems with an irregular right-hand side belonging to L 1 . Finally, to step towards the unsteady problem, the convergence of the finite volume scheme for a model convection-diffusion equation with L 1 data is proved. The a priori estimates on the solution and on its time derivative are obtained in discrete norms, for

Conservative Semidiscrete Difference Schemes for Timoshenko Systems

OpenAIRE

Júnior, D. S. Almeida

2014-01-01

We present a parameterized family of finite-difference schemes to analyze the energy properties for linearly elastic constant-coefficient Timoshenko systems considering shear deformation and rotatory inertia. We derive numerical energies showing the positivity, and the energy conservation property and we show how to avoid a numerical anomaly known as locking phenomenon on shear force. Our method of proof relies on discrete multiplier techniques.

From ordinary to discrete quantum mechanics: The Charlier oscillator and its coalgebra symmetry

Energy Technology Data Exchange (ETDEWEB)

Latini, D., E-mail: latini@fis.uniroma3.it [Department of Mathematics and Physics and INFN, Roma Tre University, Via della Vasca Navale 84, I-00146 Rome (Italy); Riglioni, D. [Department of Mathematics and Physics, Roma Tre University, Via della Vasca Navale 84, I-00146 Rome (Italy)

2016-10-14

The coalgebraic structure of the harmonic oscillator is used to underline possible connections between continuous and discrete superintegrable models which can be described in terms of SUSY discrete quantum mechanics. A set of 1-parameter algebraic transformations is introduced in order to generate a discrete representation for the coalgebraic harmonic oscillator. This set of transformations is shown to play a role in the generalization of classical orthogonal polynomials to the realm of discrete orthogonal polynomials in the Askey scheme. As an explicit example the connection between Hermite and Charlier oscillators, that share the same coalgebraic structure, is presented and a two-dimensional maximally superintegrable version of the Charlier oscillator is constructed. - Highlights: • We construct a discrete quantum version of the harmonic oscillator. • We solve the spectral problem on the lattice. • We introduce the coalgebra symmetry in real discrete Quantum Mechanics (rdQM). • The coalgebra is used to extend the system to higher dimensions preserving its superintegrability. • We explicitly write down a discrete version of both the angular momentum and the Demkov–Fradkin Tensor.

Breaking a chaos-noise-based secure communication scheme

Science.gov (United States)

Li, Shujun; Álvarez, Gonzalo; Chen, Guanrong; Mou, Xuanqin

2005-03-01

This paper studies the security of a secure communication scheme based on two discrete-time intermittently chaotic systems synchronized via a common random driving signal. Some security defects of the scheme are revealed: 1) The key space can be remarkably reduced; 2) the decryption is insensitive to the mismatch of the secret key; 3) the key-generation process is insecure against known/chosen-plaintext attacks. The first two defects mean that the scheme is not secure enough against brute-force attacks, and the third one means that an attacker can easily break the cryptosystem by approximately estimating the secret key once he has a chance to access a fragment of the generated keystream. Yet it remains to be clarified if intermittent chaos could be used for designing secure chaotic cryptosystems.

Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform

International Nuclear Information System (INIS)

Zhong, Zhi; Zhang, Yujie; Shan, Mingguang; Wang, Ying; Zhang, Yabin; Xie, Hong

2014-01-01

A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method. (paper)

Finite difference discretization of semiconductor drift-diffusion equations for nanowire solar cells

Science.gov (United States)

Deinega, Alexei; John, Sajeev

2012-10-01

We introduce a finite difference discretization of semiconductor drift-diffusion equations using cylindrical partial waves. It can be applied to describe the photo-generated current in radial pn-junction nanowire solar cells. We demonstrate that the cylindrically symmetric (l=0) partial wave accurately describes the electronic response of a square lattice of silicon nanowires at normal incidence. We investigate the accuracy of our discretization scheme by using different mesh resolution along the radial direction r and compare with 3D (x, y, z) discretization. We consider both straight nanowires and nanowires with radius modulation along the vertical axis. The charge carrier generation profile inside each nanowire is calculated using an independent finite-difference time-domain simulation.

Optimized Explicit Runge--Kutta Schemes for the Spectral Difference Method Applied to Wave Propagation Problems

KAUST Repository

Parsani, Matteo

2013-04-10

Explicit Runge--Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge--Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.

Optimized Explicit Runge--Kutta Schemes for the Spectral Difference Method Applied to Wave Propagation Problems

KAUST Repository

Parsani, Matteo; Ketcheson, David I.; Deconinck, W.

2013-01-01

Explicit Runge--Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge--Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.

Projection scheme for a reflected stochastic heat equation with additive noise

Science.gov (United States)

Higa, Arturo Kohatsu; Pettersson, Roger

2005-02-01

We consider a projection scheme as a numerical solution of a reflected stochastic heat equation driven by a space-time white noise. Convergence is obtained via a discrete contraction principle and known convergence results for numerical solutions of parabolic variational inequalities.

Navier-Stokes Dynamics by a Discrete Boltzmann Model

Science.gov (United States)

Rubinstein, Robet

2010-01-01

This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.

Semi-discrete approximations to nonlinear systems of conservation laws; consistency and L(infinity)-stability imply convergence. Final report

International Nuclear Information System (INIS)

Tadmor, E.

1988-07-01

A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed. It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence. Instead, a notion of consistency which takes into account both the conservation law and its augmenting entropy condition is introduced. In this context it is concluded that consistency and L(infinity)-stability guarantee for a relevant class of admissible entropy functions, that their entropy production rate belongs to a compact subset of H(loc)sup -1 (x,t). One can now use compensated compactness arguments in order to turn this conclusion into a convergence proof. The current state of the art for these arguments includes the scalar and a wide class of 2 x 2 systems of conservation laws. The general framework of the vanishing viscosity method is studied as an effective way to meet the consistency and L(infinity)-stability requirements. How this method is utilized to enforce consistency and stability for scalar conservation laws is shown. In this context we prove, under the appropriate assumptions, the convergence of finite difference approximations (e.g., the high resolution TVD and UNO methods), finite element approximations (e.g., the Streamline-Diffusion methods) and spectral and pseudospectral approximations (e.g., the Spectral Viscosity methods)

Applying LU Decomposition of Matrices to Design Anonymity Bilateral Remote User Authentication Scheme

Directory of Open Access Journals (Sweden)

Xiong Li

2013-01-01

Full Text Available We apply LU decomposition of matrices to present an anonymous bilateral authentication scheme. This paper aims at improving security and providing more excellent performances for remote user authentication scheme. The proposed scheme can provide bilateral authentication and session key agreement, can quickly check the validity of the input password, and can really protect the user anonymity. The security of the proposed scheme is based on the discrete logarithm problem (DLP, Diffie-Hellman problem (DHP, and the one-way hash function. It can resist various attacks such as insider attack, impersonation attack, server spoofing attack, and stolen smart card attack. Moreover, the presented scheme is computationally efficient for real-life implementation.

Efficient scheme for parametric fitting of data in arbitrary dimensions.

Science.gov (United States)

Pang, Ning-Ning; Tzeng, Wen-Jer; Kao, Hisen-Ching

2008-07-01

We propose an efficient scheme for parametric fitting expressed in terms of the Legendre polynomials. For continuous systems, our scheme is exact and the derived explicit expression is very helpful for further analytical studies. For discrete systems, our scheme is almost as accurate as the method of singular value decomposition. Through a few numerical examples, we show that our algorithm costs much less CPU time and memory space than the method of singular value decomposition. Thus, our algorithm is very suitable for a large amount of data fitting. In addition, the proposed scheme can also be used to extract the global structure of fluctuating systems. We then derive the exact relation between the correlation function and the detrended variance function of fluctuating systems in arbitrary dimensions and give a general scaling analysis.

Symmetry, winding number, and topological charge of vortex solitons in discrete-symmetry media

International Nuclear Information System (INIS)

Garcia-March, Miguel-Angel; Zacares, Mario; Ferrando, Albert; Sahu, Sarira; Ceballos-Herrera, Daniel E.

2009-01-01

We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schroedinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance.

Discrete Control Processes, Dynamic Games and Multicriterion Control Problems

Directory of Open Access Journals (Sweden)

Dumitru Lozovanu

2002-07-01

Full Text Available The discrete control processes with state evaluation in time of dynamical system is considered. A general model of control problems with integral-time cost criterion by a trajectory is studied and a general scheme for solving such classes of problems is proposed. In addition the game-theoretical and multicriterion models for control problems are formulated and studied.

Discrete gradients in discrete classical mechanics

International Nuclear Information System (INIS)

Renna, L.

1987-01-01

A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated

Numerical solution of one-dimensional transient, two-phase flows with temporal fully implicit high order schemes: Subcooled boiling in pipes

Energy Technology Data Exchange (ETDEWEB)

López, R., E-mail: ralope1@ing.uc3m.es; Lecuona, A., E-mail: lecuona@ing.uc3m.es; Nogueira, J., E-mail: goriba@ing.uc3m.es; Vereda, C., E-mail: cvereda@ing.uc3m.es

2017-03-15

Highlights: • A two-phase flows numerical algorithm with high order temporal schemes is proposed. • Transient solutions route depends on the temporal high order scheme employed. • ESDIRK scheme for two-phase flows events exhibits high computational performance. • Computational implementation of the ESDIRK scheme can be done in a very easy manner. - Abstract: An extension for 1-D transient two-phase flows of the SIMPLE-ESDIRK method, initially developed for incompressible viscous flows by Ijaz is presented. This extension is motivated by the high temporal order of accuracy demanded to cope with fast phase change events. This methodology is suitable for boiling heat exchangers, solar thermal receivers, etc. The methodology of the solution consist in a finite volume staggered grid discretization of the governing equations in which the transient terms are treated with the explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) method. It is suitable for stiff differential equations, present in instant boiling or condensation processes. It is combined with the semi-implicit pressure linked equations algorithm (SIMPLE) for the calculation of the pressure field. The case of study consists of the numerical reproduction of the Bartolomei upward boiling pipe flow experiment. The steady-state validation of the numerical algorithm is made against these experimental results and well known numerical results for that experiment. In addition, a detailed study reveals the benefits over the first order Euler Backward method when applying 3rd and 4th order schemes, making emphasis in the behaviour when the system is subjected to periodic square wave wall heat function disturbances, concluding that the use of the ESDIRK method in two-phase calculations presents remarkable accuracy and computational advantages.

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part II: numerical testing

OpenAIRE

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres; Zirk, Marko

2007-01-01

The semi-implicit semi-Lagrangian (SISL), two-time-level, non-hydrostatic numerical scheme, based on the non-hydrostatic, semi-elastic pressure-coordinate equations, is tested in model experiments with flow over given orography (elliptical hill, mountain ridge, system of successive ridges) in a rectangular domain with emphasis on the numerical accuracy and non-hydrostatic effect presentation capability. Comparison demonstrates good (in strong primary wave generation) to satisfactory (in weak ...

The discrete ordinate method in association with the finite-volume method in non-structured mesh; Methode des ordonnees discretes associee a la methode des volumes finis en maillage non structure

Energy Technology Data Exchange (ETDEWEB)

Le Dez, V; Lallemand, M [Ecole Nationale Superieure de Mecanique et d` Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M; Charette, A [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees

1997-12-31

The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.

The discrete ordinate method in association with the finite-volume method in non-structured mesh; Methode des ordonnees discretes associee a la methode des volumes finis en maillage non structure

Energy Technology Data Exchange (ETDEWEB)

Le Dez, V.; Lallemand, M. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M.; Charette, A. [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees

1996-12-31

The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.

Impact of semi-annihilations on dark matter phenomenology - an example of ZN symmetric scalar dark matter

International Nuclear Information System (INIS)

Belanger, G.; Kannike, K.; Pukhov, A.; Raidal, M.

2012-01-01

We study the impact of semi-annihilations χχ ↔ χX; where χ is dark matter and X is any standard model particle, on dark matter phenomenology. We formulate scalar dark matter models with minimal field content that predict non-trivial dark matter phenomenology for different discrete Abelian symmetries Z N , N > 2, and contain semi-annihilation processes. We implement such an example model in micrOMEGAs and show that semi-annihilations modify the phenomenology of this type of models. (authors)

A study to reduce the numerical diffusion of upwind scheme in two dimensional convection phenomena analysis

International Nuclear Information System (INIS)

Lee, Goung Jin; Kim, Soong Pyung

1990-01-01

In solving the convection-diffusion phenomena, it is common to use central difference scheme or upwind scheme. The central difference scheme has second order accuracy, while the upwind scheme is only first order accurate. However, since the variation rising in the convection-diffusion problem is exponential, central difference scheme ceased to be a good method for anything but extremely small values of Δx. At large values of Δx, which is all one can afford in most practical problems, it is the upwind scheme that gives more reasonable results than the central scheme. But in the conventional upwind scheme, since the accuracy is only first order, false diffusion is somewhat large, and when the real diffusion is smaller than the numerical diffusion, solutions may be very errorneous. So in this paper, a method to reduce the numerical diffusion of upwind scheme is studied. Developed scheme uses same number of nodes as conventional upwind scheme, but it considers the direction of flow more sophistically. As a conclusion, the developed scheme shows very good results. It can reduce false diffusion greatly with the cost of small complexity. Also, algorithm of the developed scheme is presented at appendix. (Author)

Approximation-Based Discrete-Time Adaptive Position Tracking Control for Interior Permanent Magnet Synchronous Motors.

Science.gov (United States)

Yu, Jinpeng; Shi, Peng; Yu, Haisheng; Chen, Bing; Lin, Chong

2015-07-01

This paper considers the problem of discrete-time adaptive position tracking control for a interior permanent magnet synchronous motor (IPMSM) based on fuzzy-approximation. Fuzzy logic systems are used to approximate the nonlinearities of the discrete-time IPMSM drive system which is derived by direct discretization using Euler method, and a discrete-time fuzzy position tracking controller is designed via backstepping approach. In contrast to existing results, the advantage of the scheme is that the number of the adjustable parameters is reduced to two only and the problem of coupling nonlinearity can be overcome. It is shown that the proposed discrete-time fuzzy controller can guarantee the tracking error converges to a small neighborhood of the origin and all the signals are bounded. Simulation results illustrate the effectiveness and the potentials of the theoretic results obtained.

Quantum attack-resistent certificateless multi-receiver signcryption scheme.

Directory of Open Access Journals (Sweden)

Huixian Li

Full Text Available The existing certificateless signcryption schemes were designed mainly based on the traditional public key cryptography, in which the security relies on the hard problems, such as factor decomposition and discrete logarithm. However, these problems will be easily solved by the quantum computing. So the existing certificateless signcryption schemes are vulnerable to the quantum attack. Multivariate public key cryptography (MPKC, which can resist the quantum attack, is one of the alternative solutions to guarantee the security of communications in the post-quantum age. Motivated by these concerns, we proposed a new construction of the certificateless multi-receiver signcryption scheme (CLMSC based on MPKC. The new scheme inherits the security of MPKC, which can withstand the quantum attack. Multivariate quadratic polynomial operations, which have lower computation complexity than bilinear pairing operations, are employed in signcrypting a message for a certain number of receivers in our scheme. Security analysis shows that our scheme is a secure MPKC-based scheme. We proved its security under the hardness of the Multivariate Quadratic (MQ problem and its unforgeability under the Isomorphism of Polynomials (IP assumption in the random oracle model. The analysis results show that our scheme also has the security properties of non-repudiation, perfect forward secrecy, perfect backward secrecy and public verifiability. Compared with the existing schemes in terms of computation complexity and ciphertext length, our scheme is more efficient, which makes it suitable for terminals with low computation capacity like smart cards.

Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients

DEFF Research Database (Denmark)

Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter

2011-01-01

We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal......, whereas the convergence of the coefficients happens only with respect to the "volumetric" Lebesgue measure. Additionally, depending on whether the stationarity conditions are stated for the discretized or the original continuous problem, two distinct concepts of stationarity at a discrete level arise. We...... provide characterizations of limit points, with respect to FV mesh size, of globally optimal solutions and two types of stationary points to the discretized problems. We illustrate the practical behaviour of our cell-based FV discretization algorithm on a numerical example....

Security and efficiency data sharing scheme for cloud storage

International Nuclear Information System (INIS)

Han, Ke; Li, Qingbo; Deng, Zhongliang

2016-01-01

With the adoption and diffusion of data sharing paradigm in cloud storage, there have been increasing demands and concerns for shared data security. Ciphertext Policy Attribute-Based Encryption (CP-ABE) is becoming a promising cryptographic solution to the security problem of shared data in cloud storage. However due to key escrow, backward security and inefficiency problems, existing CP-ABE schemes cannot be directly applied to cloud storage system. In this paper, an effective and secure access control scheme for shared data is proposed to solve those problems. The proposed scheme refines the security of existing CP-ABE based schemes. Specifically, key escrow and conclusion problem are addressed by dividing key generation center into several distributed semi-trusted parts. Moreover, secrecy revocation algorithm is proposed to address not only back secrecy but efficient problem in existing CP-ABE based scheme. Furthermore, security and performance analyses indicate that the proposed scheme is both secure and efficient for cloud storage.

An encryption scheme based on phase-shifting digital holography and amplitude-phase disturbance

International Nuclear Information System (INIS)

Hua Li-Li; Xu Ning; Yang Geng

2014-01-01

In this paper, we propose an encryption scheme based on phase-shifting digital interferometry. According to the original system framework, we add a random amplitude mask and replace the Fourier transform by the Fresnel transform. We develop a mathematical model and give a discrete formula based on the scheme, which makes it easy to implement the scheme in computer programming. The experimental results show that the improved system has a better performance in security than the original encryption method. Moreover, it demonstrates a good capability of anti-noise and anti-shear robustness

A well-balanced scheme for Ten-Moment Gaussian closure equations with source term

Science.gov (United States)

Meena, Asha Kumari; Kumar, Harish

2018-02-01

In this article, we consider the Ten-Moment equations with source term, which occurs in many applications related to plasma flows. We present a well-balanced second-order finite volume scheme. The scheme is well-balanced for general equation of state, provided we can write the hydrostatic solution as a function of the space variables. This is achieved by combining hydrostatic reconstruction with contact preserving, consistent numerical flux, and appropriate source discretization. Several numerical experiments are presented to demonstrate the well-balanced property and resulting accuracy of the proposed scheme.

Estimation of Interchannel Time Difference in Frequency Subbands Based on Nonuniform Discrete Fourier Transform

Directory of Open Access Journals (Sweden)

Qiu Bo

2008-01-01

Full Text Available Binaural cue coding (BCC is an efficient technique for spatial audio rendering by using the side information such as interchannel level difference (ICLD, interchannel time difference (ICTD, and interchannel correlation (ICC. Of the side information, the ICTD plays an important role to the auditory spatial image. However, inaccurate estimation of the ICTD may lead to the audio quality degradation. In this paper, we develop a novel ICTD estimation algorithm based on the nonuniform discrete Fourier transform (NDFT and integrate it with the BCC approach to improve the decoded auditory image. Furthermore, a new subjective assessment method is proposed for the evaluation of auditory image widths of decoded signals. The test results demonstrate that the NDFT-based scheme can achieve much wider and more externalized auditory image than the existing BCC scheme based on the discrete Fourier transform (DFT. It is found that the present technique, regardless of the image width, does not deteriorate the sound quality at the decoder compared to the traditional scheme without ICTD estimation.

Discrete Symmetries and Models of Flavour Mixing

International Nuclear Information System (INIS)

King, Stephen F

2015-01-01

In this talk we shall give an overview of the role of discrete symmetries, including both CP and family symmetry, in constructing unified models of quark and lepton (including especially neutrino) masses and mixing. Various different approaches to model building will be described, denoted as direct, semi-direct and indirect, and the pros and cons of each approach discussed. Particular examples based on Δ(6n 2 ) will be discussed and an A to Z of Flavour with Pati-Salam will be presented. (paper)

A new access scheme in OFDMA systems

Institute of Scientific and Technical Information of China (English)

GU Xue-lin; YAN Wei; TIAN Hui; ZHANG Ping

2006-01-01

This article presents a dynamic random access scheme for orthogonal frequency division multiple access (OFDMA) systems. The key features of the proposed scheme are:it is a combination of both the distributed and the centralized schemes, it can accommodate several delay sensitivity classes,and it can adjust the number of random access channels in a media access control (MAC) frame and the access probability according to the outcome of Mobile Terminals access attempts in previous MAC frames. For floating populated packet-based networks, the proposed scheme possibly leads to high average user satisfaction.

Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods - Part 1: Derivation and properties

Science.gov (United States)

Eldred, Christopher; Randall, David

2017-02-01

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restricted to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.

Discrete-time Calogero-Moser system and Lagrangian 1-form structure

International Nuclear Information System (INIS)

Yoo-Kong, Sikarin; Lobb, Sarah; Nijhoff, Frank

2011-01-01

We study the Lagrange formalism of the (rational) Calogero-Moser (CM) system, both in discrete time and continuous time, as a first example of a Lagrangian 1-form structure in the sense of the recent paper (Lobb and Nijhoff 2009 J. Phys. A: Math. Theor.42 454013). The discrete-time model of the CM system was established some time ago arising as a pole reduction of a semi-discrete version of the Kadomtsev-Petviashvili (KP) equation, and was shown to lead to an exactly integrable correspondence (multivalued map). In this paper, we present the full KP solution based on the commutativity of the discrete-time flows in the two discrete KP variables. The compatibility of the corresponding Lax matrices is shown to lead directly to the relevant closure relation on the level of the Lagrangians. Performing successive continuum limits on both the level of the KP equation and the level of the CM system, we establish the proper Lagrangian 1-form structure for the continuum case of the CM model. We use the example of the three-particle case to elucidate the implementation of the novel least-action principle, which was presented in Lobb and Nijhoff (2009), for the simpler case of Lagrangian 1-forms. (paper)

Discrete mKdV and discrete sine-Gordon flows on discrete space curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2014-01-01

In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym–Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces. (paper)

ZN graded discrete Lax pairs and Yang–Baxter maps

Science.gov (United States)

Fordy, Allan P.

2017-01-01

We recently introduced a class of ZN graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In this paper, we introduce the corresponding Yang–Baxter maps. Many well-known examples belong to this scheme for N=2, so, for N≥3, our systems may be regarded as generalizations of these. In particular, for each N we introduce a class of multi-component Yang–Baxter maps, which include HBIII (of Papageorgiou et al. 2010 SIGMA 6, 003 (9 p). (doi:10.3842/SIGMA.2010.033)), when N=2, and that associated with the discrete modified Boussinesq equation, for N=3. For N≥5 we introduce a new family of Yang–Baxter maps, which have no lower dimensional analogue. We also present new multi-component versions of the Yang–Baxter maps FIV and FV (given in the classification of Adler et al. 2004 Commun. Anal. Geom. 12, 967–1007. (doi:10.4310/CAG.2004.v12.n5.a1)). PMID:28588406

On the uncertainty inequality as applied to discrete signals

Directory of Open Access Journals (Sweden)

Y. V. Venkatesh

2006-01-01

Full Text Available Given a continuous-time bandlimited signal, the Shannon sampling theorem provides an interpolation scheme for exactly reconstructing it from its discrete samples. We analyze the relationship between concentration (or compactness in the temporal/spectral domains of the (i continuous-time and (ii discrete-time signals. The former is governed by the Heisenberg uncertainty inequality which prescribes a lower bound on the product of effective temporal and spectral spreads of the signal. On the other hand, the discrete-time counterpart seems to exhibit some strange properties, and this provides motivation for the present paper. We consider the following problem: for a bandlimited signal, can the uncertainty inequality be expressed in terms of the samples, using thestandard definitions of the temporal and spectral spreads of the signal? In contrast with the results of the literature, we present a new approach to solve this problem. We also present a comparison of the results obtained using the proposed definitions with those available in the literature.

Discrete gradient methods for solving variational image regularisation models

International Nuclear Information System (INIS)

Grimm, V; McLachlan, Robert I; McLaren, David I; Quispel, G R W; Schönlieb, C-B

2017-01-01

Discrete gradient methods are well-known methods of geometric numerical integration, which preserve the dissipation of gradient systems. In this paper we show that this property of discrete gradient methods can be interesting in the context of variational models for image processing, that is where the processed image is computed as a minimiser of an energy functional. Numerical schemes for computing minimisers of such energies are desired to inherit the dissipative property of the gradient system associated to the energy and consequently guarantee a monotonic decrease of the energy along iterations, avoiding situations in which more computational work might lead to less optimal solutions. Under appropriate smoothness assumptions on the energy functional we prove that discrete gradient methods guarantee a monotonic decrease of the energy towards stationary states, and we promote their use in image processing by exhibiting experiments with convex and non-convex variational models for image deblurring, denoising, and inpainting. (paper)

Development and estimation of a semi-compensatory model with a flexible error structure

DEFF Research Database (Denmark)

Kaplan, Sigal; Shiftan, Yoram; Bekhor, Shlomo

2012-01-01

In decisions involving many alternatives, such as residential choice, individuals conduct a two-stage decision process, consisting of eliminating non-viable alternatives and choice from the retained choice set. In light of the potential of semi-compensatory discrete choice models to mathematicall...

Infant differential behavioral responding to discrete emotions.

Science.gov (United States)

Walle, Eric A; Reschke, Peter J; Camras, Linda A; Campos, Joseph J

2017-10-01

Emotional communication regulates the behaviors of social partners. Research on individuals' responding to others' emotions typically compares responses to a single negative emotion compared with responses to a neutral or positive emotion. Furthermore, coding of such responses routinely measure surface level features of the behavior (e.g., approach vs. avoidance) rather than its underlying function (e.g., the goal of the approach or avoidant behavior). This investigation examined infants' responding to others' emotional displays across 5 discrete emotions: joy, sadness, fear, anger, and disgust. Specifically, 16-, 19-, and 24-month-old infants observed an adult communicate a discrete emotion toward a stimulus during a naturalistic interaction. Infants' responses were coded to capture the function of their behaviors (e.g., exploration, prosocial behavior, and security seeking). The results revealed a number of instances indicating that infants use different functional behaviors in response to discrete emotions. Differences in behaviors across emotions were clearest in the 24-month-old infants, though younger infants also demonstrated some differential use of behaviors in response to discrete emotions. This is the first comprehensive study to identify differences in how infants respond with goal-directed behaviors to discrete emotions. Additionally, the inclusion of a function-based coding scheme and interpersonal paradigms may be informative for future emotion research with children and adults. Possible developmental accounts for the observed behaviors and the benefits of coding techniques emphasizing the function of social behavior over their form are discussed. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Age-of-Air, Tape Recorder, and Vertical Transport Schemes

Science.gov (United States)

Lin, S.-J.; Einaudi, Franco (Technical Monitor)

2000-01-01

A numerical-analytic investigation of the impacts of vertical transport schemes on the model simulated age-of-air and the so-called 'tape recorder' will be presented using an idealized 1-D column transport model as well as a more realistic 3-D dynamical model. By comparing to the 'exact' solutions of 'age-of-air' and the 'tape recorder' obtainable in the 1-D setting, useful insight is gained on the impacts of numerical diffusion and dispersion of numerical schemes used in global models. Advantages and disadvantages of Eulerian, semi-Lagrangian, and Lagrangian transport schemes will be discussed. Vertical resolution requirement for numerical schemes as well as observing systems for capturing the fine details of the 'tape recorder' or any upward propagating wave-like structures can potentially be derived from the 1-D analytic model.

Semi-active control for vibration mitigation of structural systems incorporating uncertainties

International Nuclear Information System (INIS)

Miah, Mohammad S; Chatzi, Eleni N; Weber, Felix

2015-01-01

This study introduces a novel semi-active control scheme, where the linear-quadratic regulator (LQR) is combined with an unscented Kalman filter (UKF) observer, for the real-time mitigation of structural vibration. Due to a number of factors, such as environmental effects and ageing processes, the controlled system may be characterized by uncertainties. The UKF, which comprises a nonlinear observer, is employed herein for devising an adaptive semi-active control scheme capable of tackling such a challenge. This is achieved through the real-time realization of joint state and parameter estimation during the structural control process via the proposed LQR-UKF approach. The behavior of the introduced scheme is exemplified through two numerical applications. The efficacy of the devised methodology is firstly compared against the standard LQR-KF approach in a linear benchmark application where the system model is assumed known a priori, and secondly, the method is validated on a joint state and parameter estimation problem where the system model is assumed uncertain, formulated as nonlinear, and updated in real-time. (paper)

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-06-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.

Damping efficiency of the Tchamwa-Wielgosz explicit dissipative scheme under instantaneous loading conditions

Science.gov (United States)

Mahéo, Laurent; Grolleau, Vincent; Rio, Gérard

2009-11-01

To deal with dynamic and wave propagation problems, dissipative methods are often used to reduce the effects of the spurious oscillations induced by the spatial and time discretization procedures. Among the many dissipative methods available, the Tchamwa-Wielgosz (TW) explicit scheme is particularly useful because it damps out the spurious oscillations occurring in the highest frequency domain. The theoretical study performed here shows that the TW scheme is decentered to the right, and that the damping can be attributed to a nodal displacement perturbation. The FEM study carried out using instantaneous 1-D and 3-D compression loads shows that it is useful to display the damping versus the number of time steps in order to obtain a constant damping efficiency whatever the size of element used for the regular meshing. A study on the responses obtained with irregular meshes shows that the TW scheme is only slightly sensitive to the spatial discretization procedure used. To cite this article: L. Mahéo et al., C. R. Mecanique 337 (2009).

Discrete Green’s function diakoptics for stable FDTD interaction between multiply-connected domains

NARCIS (Netherlands)

Hon, de B.P.; Arnold, J.M.; Graglia, R.D.

2007-01-01

We have developed FDTD boundary conditions based on discrete Green's function diakoptics for arbitrary multiply-connected 2D domains. The associated Z-domain boundary operator is symmetric, with an imaginary part that can be proved to be positive semi-definite on the upper half of the unit circle in

Quasi-disjoint pentadiagonal matrix systems for the parallelization of compact finite-difference schemes and filters

Science.gov (United States)

Kim, Jae Wook

2013-05-01

This paper proposes a novel systematic approach for the parallelization of pentadiagonal compact finite-difference schemes and filters based on domain decomposition. The proposed approach allows a pentadiagonal banded matrix system to be split into quasi-disjoint subsystems by using a linear-algebraic transformation technique. As a result the inversion of pentadiagonal matrices can be implemented within each subdomain in an independent manner subject to a conventional halo-exchange process. The proposed matrix transformation leads to new subdomain boundary (SB) compact schemes and filters that require three halo terms to exchange with neighboring subdomains. The internode communication overhead in the present approach is equivalent to that of standard explicit schemes and filters based on seven-point discretization stencils. The new SB compact schemes and filters demand additional arithmetic operations compared to the original serial ones. However, it is shown that the additional cost becomes sufficiently low by choosing optimal sizes of their discretization stencils. Compared to earlier published results, the proposed SB compact schemes and filters successfully reduce parallelization artifacts arising from subdomain boundaries to a level sufficiently negligible for sophisticated aeroacoustic simulations without degrading parallel efficiency. The overall performance and parallel efficiency of the proposed approach are demonstrated by stringent benchmark tests.

Toward Optimal Manifold Hashing via Discrete Locally Linear Embedding.

Science.gov (United States)

Rongrong Ji; Hong Liu; Liujuan Cao; Di Liu; Yongjian Wu; Feiyue Huang

2017-11-01

Binary code learning, also known as hashing, has received increasing attention in large-scale visual search. By transforming high-dimensional features to binary codes, the original Euclidean distance is approximated via Hamming distance. More recently, it is advocated that it is the manifold distance, rather than the Euclidean distance, that should be preserved in the Hamming space. However, it retains as an open problem to directly preserve the manifold structure by hashing. In particular, it first needs to build the local linear embedding in the original feature space, and then quantize such embedding to binary codes. Such a two-step coding is problematic and less optimized. Besides, the off-line learning is extremely time and memory consuming, which needs to calculate the similarity matrix of the original data. In this paper, we propose a novel hashing algorithm, termed discrete locality linear embedding hashing (DLLH), which well addresses the above challenges. The DLLH directly reconstructs the manifold structure in the Hamming space, which learns optimal hash codes to maintain the local linear relationship of data points. To learn discrete locally linear embeddingcodes, we further propose a discrete optimization algorithm with an iterative parameters updating scheme. Moreover, an anchor-based acceleration scheme, termed Anchor-DLLH, is further introduced, which approximates the large similarity matrix by the product of two low-rank matrices. Experimental results on three widely used benchmark data sets, i.e., CIFAR10, NUS-WIDE, and YouTube Face, have shown superior performance of the proposed DLLH over the state-of-the-art approaches.

Parallel S/sub n/ iteration schemes

International Nuclear Information System (INIS)

Wienke, B.R.; Hiromoto, R.E.

1986-01-01

The iterative, multigroup, discrete ordinates (S/sub n/) technique for solving the linear transport equation enjoys widespread usage and appeal. Serial iteration schemes and numerical algorithms developed over the years provide a timely framework for parallel extension. On the Denelcor HEP, the authors investigate three parallel iteration schemes for solving the one-dimensional S/sub n/ transport equation. The multigroup representation and serial iteration methods are also reviewed. This analysis represents a first attempt to extend serial S/sub n/ algorithms to parallel environments and provides good baseline estimates on ease of parallel implementation, relative algorithm efficiency, comparative speedup, and some future directions. The authors examine ordered and chaotic versions of these strategies, with and without concurrent rebalance and diffusion acceleration. Two strategies efficiently support high degrees of parallelization and appear to be robust parallel iteration techniques. The third strategy is a weaker parallel algorithm. Chaotic iteration, difficult to simulate on serial machines, holds promise and converges faster than ordered versions of the schemes. Actual parallel speedup and efficiency are high and payoff appears substantial

Discrete conservation laws and the convergence of long time simulations of the mkdv equation

Science.gov (United States)

Gorria, C.; Alejo, M. A.; Vega, L.

2013-02-01

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

Research on a New Signature Scheme on Blockchain

Directory of Open Access Journals (Sweden)

Chao Yuan

2017-01-01

Full Text Available With the rise of Bitcoin, blockchain which is the core technology of Bitcoin has received increasing attention. Privacy preserving and performance on blockchain are two research points in academia and business, but there are still some unresolved issues in both respects. An aggregate signature scheme is a digital signature that supports making signatures on many different messages generated by many different users. Using aggregate signature, the size of the signature could be shortened by compressing multiple signatures into a single signature. In this paper, a new signature scheme for transactions on blockchain based on the aggregate signature was proposed. It was worth noting that elliptic curve discrete logarithm problem and bilinear maps played major roles in our signature scheme. And the security properties of our signature scheme were proved. In our signature scheme, the amount will be hidden especially in the transactions which contain multiple inputs and outputs. Additionally, the size of the signature on transaction is constant regardless of the number of inputs and outputs that the transaction contains, which can improve the performance of signature. Finally, we gave an application scenario for our signature scheme which aims to achieve the transactions of big data on blockchain.

Seakeeping with the semi-Lagrangian particle finite element method

Science.gov (United States)

Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio

2017-07-01

The application of the semi-Lagrangian particle finite element method (SL-PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.

Bayesian inference for hybrid discrete-continuous stochastic kinetic models

International Nuclear Information System (INIS)

Sherlock, Chris; Golightly, Andrew; Gillespie, Colin S

2014-01-01

We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process (MJP), computational cost can be prohibitive for networks of realistic size and complexity. In this paper, we consider an inference scheme based on a novel hybrid simulator that classifies reactions as either ‘fast’ or ‘slow’ with fast reactions evolving as a continuous Markov process whilst the remaining slow reaction occurrences are modelled through a MJP with time-dependent hazards. A linear noise approximation (LNA) of fast reaction dynamics is employed and slow reaction events are captured by exploiting the ability to solve the stochastic differential equation driving the LNA. This simulation procedure is used as a proposal mechanism inside a particle MCMC scheme, thus allowing Bayesian inference for the model parameters. We apply the scheme to a simple application and compare the output with an existing hybrid approach and also a scheme for performing inference for the underlying discrete stochastic model. (paper)

Solution of the Neutron transport equation in hexagonal geometry using strongly discontinuous nodal schemes

International Nuclear Information System (INIS)

Mugica R, C.A.; Valle G, E. del

2005-01-01

In 2002, E. del Valle and Ernest H. Mund developed a technique to solve numerically the Neutron transport equations in discrete ordinates and hexagonal geometry using two nodal schemes type finite element weakly discontinuous denominated WD 5,3 and WD 12,8 (of their initials in english Weakly Discontinuous). The technique consists on representing each hexagon in the union of three rhombuses each one of which it is transformed in a square in the one that the methods WD 5,3 and WD 12,8 were applied. In this work they are solved the mentioned equations of transport using the same discretization technique by hexagon but using two nodal schemes type finite element strongly discontinuous denominated SD 3 and SD 8 (of their initials in english Strongly Discontinuous). The application in each case as well as a reference problem for those that results are provided for the effective multiplication factor is described. It is carried out a comparison with the obtained results by del Valle and Mund for different discretization meshes so much angular as spatial. (Author)

Explicit solution of the time domain volume integral equation using a stable predictor-corrector scheme

KAUST Repository

Al Jarro, Ahmed

2012-11-01

An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.

Explicit solution of the time domain volume integral equation using a stable predictor-corrector scheme

KAUST Repository

Al Jarro, Ahmed; Salem, Mohamed; Bagci, Hakan; Benson, Trevor; Sewell, Phillip D.; Vuković, Ana

2012-01-01

An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.

Calculation Scheme Based on a Weighted Primitive: Application to Image Processing Transforms

Directory of Open Access Journals (Sweden)

Gregorio de Miguel Casado

2007-01-01

Full Text Available This paper presents a method to improve the calculation of functions which specially demand a great amount of computing resources. The method is based on the choice of a weighted primitive which enables the calculation of function values under the scope of a recursive operation. When tackling the design level, the method shows suitable for developing a processor which achieves a satisfying trade-off between time delay, area costs, and stability. The method is particularly suitable for the mathematical transforms used in signal processing applications. A generic calculation scheme is developed for the discrete fast Fourier transform (DFT and then applied to other integral transforms such as the discrete Hartley transform (DHT, the discrete cosine transform (DCT, and the discrete sine transform (DST. Some comparisons with other well-known proposals are also provided.

An upwind space-time conservation element and solution element scheme for solving dusty gas flow model

Science.gov (United States)

Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

An upwind space-time conservation element and solution element (CE/SE) scheme is extended to numerically approximate the dusty gas flow model. Unlike central CE/SE schemes, the current method uses the upwind procedure to derive the numerical fluxes through the inner boundary of conservation elements. These upwind fluxes are utilized to calculate the gradients of flow variables. For comparison and validation, the central upwind scheme is also applied to solve the same dusty gas flow model. The suggested upwind CE/SE scheme resolves the contact discontinuities more effectively and preserves the positivity of flow variables in low density flows. Several case studies are considered and the results of upwind CE/SE are compared with the solutions of central upwind scheme. The numerical results show better performance of the upwind CE/SE method as compared to the central upwind scheme.

An upwind space-time conservation element and solution element scheme for solving dusty gas flow model

Directory of Open Access Journals (Sweden)

Asad Rehman

Full Text Available An upwind space-time conservation element and solution element (CE/SE scheme is extended to numerically approximate the dusty gas flow model. Unlike central CE/SE schemes, the current method uses the upwind procedure to derive the numerical fluxes through the inner boundary of conservation elements. These upwind fluxes are utilized to calculate the gradients of flow variables. For comparison and validation, the central upwind scheme is also applied to solve the same dusty gas flow model. The suggested upwind CE/SE scheme resolves the contact discontinuities more effectively and preserves the positivity of flow variables in low density flows. Several case studies are considered and the results of upwind CE/SE are compared with the solutions of central upwind scheme. The numerical results show better performance of the upwind CE/SE method as compared to the central upwind scheme. Keywords: Dusty gas flow, Solid particles, Upwind schemes, Rarefaction wave, Shock wave, Contact discontinuity

Matrix albedo for discrete ordinates infinite-medium boundary condition

International Nuclear Information System (INIS)

Mathews, K.; Dishaw, J.

2007-01-01

Discrete ordinates problems with an infinite exterior medium (reflector) can be more efficiently computed by eliminating grid cells in the exterior medium and applying a matrix albedo boundary condition. The albedo matrix is a discretized bidirectional reflection distribution function (BRDF) that accounts for the angular quadrature set, spatial quadrature method, and spatial grid that would have been used to model a portion of the exterior medium. The method is exact in slab geometry, and could be used as an approximation in multiple dimensions or curvilinear coordinates. We present an adequate method for computing albedo matrices and demonstrate their use in verifying a discrete ordinates code in slab geometry by comparison with Ganapol's infinite medium semi-analytic TIEL benchmark. With sufficient resolution in the spatial and angular grids and iteration tolerance to yield solutions converged to 6 digits, the conventional (scalar) albedo boundary condition yielded 2-digit accuracy at the boundary, but the matrix albedo solution reproduced the benchmark scalar flux at the boundary to all 6 digits. (authors)

A scheme of hidden-structure attribute-based encryption with multiple authorities

Science.gov (United States)

Ling, J.; Weng, A. X.

2018-05-01

In the most of the CP-ABE schemes with hidden access structure, both all the user attributes and the key generation are managed by only one authority. The key generation efficiency will decrease as the number of user increases, and the data will encounter security issues as the only authority is attacked. We proposed a scheme of hidden-structure attribute-based encryption with multiple authorities, which introduces multiple semi-trusted attribute authorities, avoiding the threat even though one or more authorities are attacked. We also realized user revocation by managing a revocation list. Based on DBDH assumption, we proved that our scheme is of IND-CMA security. The analysis shows that our scheme improves the key generation efficiency.

Time-discrete higher order ALE formulations: a priori error analysis

KAUST Repository

Bonito, Andrea

2013-03-16

We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete schemes of any order applied to an advection-diffusion model defined on moving domains and written in the Arbitrary Lagrangian Eulerian (ALE) framework. Our estimates hold without any restrictions on the time steps for dG with exact integration or Reynolds\\' quadrature. They involve a mild restriction on the time steps for the practical Runge-Kutta-Radau methods of any order. The key ingredients are the stability results shown earlier in Bonito et al. (Time-discrete higher order ALE formulations: stability, 2013) along with a novel ALE projection. Numerical experiments illustrate and complement our theoretical results. © 2013 Springer-Verlag Berlin Heidelberg.

Finite element discretization of Darcy's equations with pressure dependent porosity

KAUST Repository

Girault, Vivette

2010-02-23

We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose a splitting scheme which involves solving two linear systems, but parts of the analysis of this method are still heuristic. Numerical tests are presented, which illustrate the introduced methods. © 2010 EDP Sciences, SMAI.

A discrete-ordinates solution for a radiation therapy problem

International Nuclear Information System (INIS)

Goldschmidt, Gustavo Brun; Reichert, Janice Teresinha; Barichello, Liliane Basso

2008-01-01

A concise and accurate procedure for evaluating dose distribution, in a radiation therapy planning, is presented. The analytical discrete-ordinates method (ADO method) is used to develop a complete solution for a spectral dependent radiative transfer equation, in a one-dimensional medium, according to a multigroup scheme. Numerical results are presented for test problems, where the Klein-Nishina scattering kernel was used to describe the interaction processes. (author)

Autonomous learning by simple dynamical systems with a discrete-time formulation

Science.gov (United States)

Bilen, Agustín M.; Kaluza, Pablo

2017-05-01

We present a discrete-time formulation for the autonomous learning conjecture. The main feature of this formulation is the possibility to apply the autonomous learning scheme to systems in which the errors with respect to target functions are not well-defined for all times. This restriction for the evaluation of functionality is a typical feature in systems that need a finite time interval to process a unit piece of information. We illustrate its application on an artificial neural network with feed-forward architecture for classification and a phase oscillator system with synchronization properties. The main characteristics of the discrete-time formulation are shown by constructing these systems with predefined functions.

Discrete element simulation of mill charge in 3D using the BLAZE-DEM GPU framework

CSIR Research Space (South Africa)

Govender, Nicolin

2015-08-01

Full Text Available The Discrete Element Method (DEM) simulation of charge motion in ball, semi autogenous (SAG) and autogenous mills has advanced to a stage where the effects of lifter design, power draft and product size can be evaluated with sufficient accuracy...

Novel Iris Biometric Watermarking Based on Singular Value Decomposition and Discrete Cosine Transform

Directory of Open Access Journals (Sweden)

Jinyu Lu

2014-01-01

Full Text Available A novel iris biometric watermarking scheme is proposed focusing on iris recognition instead of the traditional watermark for increasing the security of the digital products. The preprocess of iris image is to be done firstly, which generates the iris biometric template from person's eye images. And then the templates are to be on discrete cosine transform; the value of the discrete cosine is encoded to BCH error control coding. The host image is divided into four areas equally correspondingly. The BCH codes are embedded in the singular values of each host image's coefficients which are obtained through discrete cosine transform (DCT. Numerical results reveal that proposed method can extract the watermark effectively and illustrate its security and robustness.

A systematic method for constructing time discretizations of integrable lattice systems: local equations of motion

International Nuclear Information System (INIS)

Tsuchida, Takayuki

2010-01-01

We propose a new method for discretizing the time variable in integrable lattice systems while maintaining the locality of the equations of motion. The method is based on the zero-curvature (Lax pair) representation and the lowest-order 'conservation laws'. In contrast to the pioneering work of Ablowitz and Ladik, our method allows the auxiliary dependent variables appearing in the stage of time discretization to be expressed locally in terms of the original dependent variables. The time-discretized lattice systems have the same set of conserved quantities and the same structures of the solutions as the continuous-time lattice systems; only the time evolution of the parameters in the solutions that correspond to the angle variables is discretized. The effectiveness of our method is illustrated using examples such as the Toda lattice, the Volterra lattice, the modified Volterra lattice, the Ablowitz-Ladik lattice (an integrable semi-discrete nonlinear Schroedinger system) and the lattice Heisenberg ferromagnet model. For the modified Volterra lattice, we also present its ultradiscrete analogue.

Hybrid upwind discretization of nonlinear two-phase flow with gravity

Science.gov (United States)

Lee, S. H.; Efendiev, Y.; Tchelepi, H. A.

2015-08-01

Multiphase flow in porous media is described by coupled nonlinear mass conservation laws. For immiscible Darcy flow of multiple fluid phases, whereby capillary effects are negligible, the transport equations in the presence of viscous and buoyancy forces are highly nonlinear and hyperbolic. Numerical simulation of multiphase flow processes in heterogeneous formations requires the development of discretization and solution schemes that are able to handle the complex nonlinear dynamics, especially of the saturation evolution, in a reliable and computationally efficient manner. In reservoir simulation practice, single-point upwinding of the flux across an interface between two control volumes (cells) is performed for each fluid phase, whereby the upstream direction is based on the gradient of the phase-potential (pressure plus gravity head). This upwinding scheme, which we refer to as Phase-Potential Upwinding (PPU), is combined with implicit (backward-Euler) time discretization to obtain a Fully Implicit Method (FIM). Even though FIM suffers from numerical dispersion effects, it is widely used in practice. This is because of its unconditional stability and because it yields conservative, monotone numerical solutions. However, FIM is not unconditionally convergent. The convergence difficulties are particularly pronounced when the different immiscible fluid phases switch between co-current and counter-current states as a function of time, or (Newton) iteration. Whether the multiphase flow across an interface (between two control-volumes) is co-current, or counter-current, depends on the local balance between the viscous and buoyancy forces, and how the balance evolves in time. The sensitivity of PPU to small changes in the (local) pressure distribution exacerbates the problem. The common strategy to deal with these difficulties is to cut the timestep and try again. Here, we propose a Hybrid-Upwinding (HU) scheme for the phase fluxes, then HU is combined with implicit

Next to leading order semi-inclusive spin asymmetries

International Nuclear Information System (INIS)

Florian, D. de; Epele, L.N.; Fanchiotti, H.; Garcia C, C.A.; Sassot, R.

1996-04-01

We have computed semi-inclusive spin asymmetries for proton and deuteron targets including next to leading order (NLO) QCD corrections and contributions coming from the target fragmentation region. These corrections have been estimated using NLO fragmentation functions, parton distributions and also a model for spin dependent fracture functions which is proposed here. We have found that NLO corrections are small but non-negligible in a scheme where gluons are polarised and that our estimate for target fragmentation effects, which is in agreement with the available semi-inclusive data, does not modify significantly charged asymmetries but is non-negligible for the so called difference asymmetries. (author). 18 refs., 7 figs

Discontinuous nodal schemes applied to the bidimensional neutron transport equation

International Nuclear Information System (INIS)

Delfin L, A.; Valle G, E. Del; Hennart B, J.P.

1996-01-01

In this paper several strong discontinuous nodal schemes are described, starting from the one that has only two interpolation parameters per cell to the one having ten. Their application to the spatial discretization of the neutron transport equation in X-Y geometry is also described, giving, for each one of the nodal schemes, the approximation for the angular neutron flux that includes the set of interpolation parameters and the corresponding polynomial space. Numerical results were obtained for several test problems presenting here the problem with the highest degree of difficulty and their comparison with published results 1,2 . (Author)

An efficient and secure partial image encryption for wireless multimedia sensor networks using discrete wavelet transform, chaotic maps and substitution box

Science.gov (United States)

Khan, Muazzam A.; Ahmad, Jawad; Javaid, Qaisar; Saqib, Nazar A.

2017-03-01

Wireless Sensor Networks (WSN) is widely deployed in monitoring of some physical activity and/or environmental conditions. Data gathered from WSN is transmitted via network to a central location for further processing. Numerous applications of WSN can be found in smart homes, intelligent buildings, health care, energy efficient smart grids and industrial control systems. In recent years, computer scientists has focused towards findings more applications of WSN in multimedia technologies, i.e. audio, video and digital images. Due to bulky nature of multimedia data, WSN process a large volume of multimedia data which significantly increases computational complexity and hence reduces battery time. With respect to battery life constraints, image compression in addition with secure transmission over a wide ranged sensor network is an emerging and challenging task in Wireless Multimedia Sensor Networks. Due to the open nature of the Internet, transmission of data must be secure through a process known as encryption. As a result, there is an intensive demand for such schemes that is energy efficient as well as highly secure since decades. In this paper, discrete wavelet-based partial image encryption scheme using hashing algorithm, chaotic maps and Hussain's S-Box is reported. The plaintext image is compressed via discrete wavelet transform and then the image is shuffled column-wise and row wise-wise via Piece-wise Linear Chaotic Map (PWLCM) and Nonlinear Chaotic Algorithm, respectively. To get higher security, initial conditions for PWLCM are made dependent on hash function. The permuted image is bitwise XORed with random matrix generated from Intertwining Logistic map. To enhance the security further, final ciphertext is obtained after substituting all elements with Hussain's substitution box. Experimental and statistical results confirm the strength of the anticipated scheme.

Lecture Note on Discrete Mathematics: Predicates and Quantifiers

DEFF Research Database (Denmark)

Nordbjerg, Finn Ebertsen

2016-01-01

This lecture note supplements the treatment of predicates and quantifiers given in standard textbooks on Discrete Mathematics (e.g.: [1]) and introduces the notation used in this course. We will present central concepts that are important, when predicate logic is used for specification...

Discrete level schemes and their gamma radiation branching ratios (CENPL-DLS): Pt.2

Energy Technology Data Exchange (ETDEWEB)

Limin, Zhang; Zongdi, Su; Zhengjun, Sun [Chinese Nuclear Data Center, Beijing, BJ (China)

1996-06-01

The DLS data files contains the data and information of nuclear discrete levels and gamma rays. At present, it has 79461 levels and 93177 gamma rays for 1908 nuclides. The DLS sub-library has been set up at the CNDC, and widely used for nuclear model calculation and other field. the DLS management retrieval code DLS is introduced and an example is given for {sup 56}Fe. (1 tab.).

Controlling the chaotic discrete-Hénon system using a feedforward neural network with an adaptive learning rate

OpenAIRE

GÖKCE, Kürşad; UYAROĞLU, Yılmaz

2013-01-01

This paper proposes a feedforward neural network-based control scheme to control the chaotic trajectories of a discrete-Hénon map in order to stay within an acceptable distance from the stable fixed point. An adaptive learning back propagation algorithm with online training is employed to improve the effectiveness of the proposed method. The simulation study carried in the discrete-Hénon system verifies the validity of the proposed control system.

Phase-shift calculation using continuum-discretized states

International Nuclear Information System (INIS)

Suzuki, Y.; Horiuchi, W.; Arai, K.

2009-01-01

We present a method for calculating scattering phase shifts which utilizes continuum-discretized states obtained in a bound-state type calculation. The wrong asymptotic behavior of the discretized state is remedied by means of the Green's function formalism. Test examples confirm the accuracy of the method. The α+n scattering is described using realistic nucleon-nucleon potentials. The 3/2 - and 1/2 - phase shifts obtained in a single-channel calculation are too small in comparison with experiment. The 1/2 + phase shifts are in reasonable agreement with experiment, and gain contributions both from the tensor and central components of the nucleon-nucleon potential.

On the equivalence between the discrete ordinates and the spherical harmonics methods in radiative transfer

International Nuclear Information System (INIS)

Barichello, L.B.; Siewert, C.E.

1998-01-01

In this work concerning steady-state radiative-transfer calculations in plane-parallel media, the equivalence between the discrete ordinates method and the spherical harmonics method is proved. More specifically, it is shown that for standard radiative-transfer problems without the imposed restriction of azimuthal symmetry the two methods yield identical results for the radiation intensity when the quadrature scheme for the discrete ordinates method is defined by the zeros of the associated Legendre functions and when generalized Mark boundary conditions are used to define the spherical harmonics solution. It is also shown that, with these choices for a quadrature scheme and for the boundary conditions, the two methods can be formulated so as to require the same computational effort. Finally a justification for using the generalized Mark boundary conditions in the spherical harmonics solution is given

A novel grain cluster-based homogenization scheme

International Nuclear Information System (INIS)

Tjahjanto, D D; Eisenlohr, P; Roters, F

2010-01-01

An efficient homogenization scheme, termed the relaxed grain cluster (RGC), for elasto-plastic deformations of polycrystals is presented. The scheme is based on a generalization of the grain cluster concept. A volume element consisting of eight (= 2 × 2 × 2) hexahedral grains is considered. The kinematics of the RGC scheme is formulated within a finite deformation framework, where the relaxation of the local deformation gradient of each individual grain is connected to the overall deformation gradient by the, so-called, interface relaxation vectors. The set of relaxation vectors is determined by the minimization of the constitutive energy (or work) density of the overall cluster. An additional energy density associated with the mismatch at the grain boundaries due to relaxations is incorporated as a penalty term into the energy minimization formulation. Effectively, this penalty term represents the kinematical condition of deformation compatibility at the grain boundaries. Simulations have been performed for a dual-phase grain cluster loaded in uniaxial tension. The results of the simulations are presented and discussed in terms of the effective stress–strain response and the overall deformation anisotropy as functions of the penalty energy parameters. In addition, the prediction of the RGC scheme is compared with predictions using other averaging schemes, as well as to the result of direct finite element (FE) simulation. The comparison indicates that the present RGC scheme is able to approximate FE simulation results of relatively fine discretization at about three orders of magnitude lower computational cost

Cost-based droop scheme for DC microgrid

DEFF Research Database (Denmark)

Nutkani, Inam Ullah; Wang, Peng; Loh, Poh Chiang

2014-01-01

voltage level, less on optimized operation and control of generation sources. The latter theme is perused in this paper, where cost-based droop scheme is proposed for distributed generators (DGs) in DC microgrids. Unlike traditional proportional power sharing based droop scheme, the proposed scheme......-connected operation. Most importantly, the proposed scheme can reduce overall total generation cost in DC microgrids without centralized controller and communication links. The performance of the proposed scheme has been verified under different load conditions.......DC microgrids are gaining interest due to higher efficiencies of DC distribution compared with AC. The benefits of DC systems have been widely researched for data centers, IT facilities and residential applications. The research focus, however, has been more on system architecture and optimal...

Study and discretization of kinetic models and fluid models at low Mach number

International Nuclear Information System (INIS)

Dellacherie, Stephane

2011-01-01

This thesis summarizes our work between 1995 and 2010. It concerns the analysis and the discretization of Fokker-Planck or semi-classical Boltzmann kinetic models and of Euler or Navier-Stokes fluid models at low Mach number. The studied Fokker-Planck equation models the collisions between ions and electrons in a hot plasma, and is here applied to the inertial confinement fusion. The studied semi-classical Boltzmann equations are of two types. The first one models the thermonuclear reaction between a deuterium ion and a tritium ion producing an α particle and a neutron particle, and is also in our case used to describe inertial confinement fusion. The second one (known as the Wang-Chang and Uhlenbeck equations) models the transitions between electronic quantified energy levels of uranium and iron atoms in the AVLIS isotopic separation process. The basic properties of these two Boltzmann equations are studied, and, for the Wang-Chang and Uhlenbeck equations, a kinetic-fluid coupling algorithm is proposed. This kinetic-fluid coupling algorithm incited us to study the relaxation concept for gas and immiscible fluids mixtures, and to underline connections with classical kinetic theory. Then, a diphasic low Mach number model without acoustic waves is proposed to model the deformation of the interface between two immiscible fluids induced by high heat transfers at low Mach number. In order to increase the accuracy of the results without increasing computational cost, an AMR algorithm is studied on a simplified interface deformation model. These low Mach number studies also incited us to analyse on cartesian meshes the inaccuracy at low Mach number of Godunov schemes. Finally, the LBM algorithm applied to the heat equation is justified

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part II: numerical testing

Science.gov (United States)

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres; Zirk, Marko

2007-10-01

The semi-implicit semi-Lagrangian (SISL), two-time-level, non-hydrostatic numerical scheme, based on the non-hydrostatic, semi-elastic pressure-coordinate equations, is tested in model experiments with flow over given orography (elliptical hill, mountain ridge, system of successive ridges) in a rectangular domain with emphasis on the numerical accuracy and non-hydrostatic effect presentation capability. Comparison demonstrates good (in strong primary wave generation) to satisfactory (in weak secondary wave reproduction in some cases) consistency of the numerical modelling results with known stationary linear test solutions. Numerical stability of the developed model is investigated with respect to the reference state choice, modelling dynamics of a stationary front. The horizontally area-mean reference temperature proves to be the optimal stability warrant. The numerical scheme with explicit residual in the vertical forcing term becomes unstable for cross-frontal temperature differences exceeding 30 K. Stability is restored, if the vertical forcing is treated implicitly, which enables to use time steps, comparable with the hydrostatic SISL.

Simulation of coupled flow and mechanical deformation using IMplicit Pressure-Displacement Explicit Saturation (IMPDES) scheme

KAUST Repository

El-Amin, Mohamed; Negara, Ardiansyah; Salama, Amgad; Sun, Shuyu

2012-01-01

cell along the entire domain is given by the implicit difference equation. Also, the deformation equations are discretized implicitly. Using the obtained pressure, velocity is evaluated explicitly, while, using the upwind scheme, the saturation

Control of Discrete-Event Systems Automata and Petri Net Perspectives

CERN Document Server

Silva, Manuel; Schuppen, Jan

2013-01-01

Control of Discrete-event Systems provides a survey of the most important topics in the discrete-event systems theory with particular focus on finite-state automata, Petri nets and max-plus algebra. Coverage ranges from introductory material on the basic notions and definitions of discrete-event systems to more recent results. Special attention is given to results on supervisory control, state estimation and fault diagnosis of both centralized and distributed/decentralized systems developed in the framework of the Distributed Supervisory Control of Large Plants (DISC) project. Later parts of the text are devoted to the study of congested systems though fluidization, an over approximation allowing a much more efficient study of observation and control problems of timed Petri nets. Finally, the max-plus algebraic approach to the analysis and control of choice-free systems is also considered. Control of Discrete-event Systems provides an introduction to discrete-event systems for readers that are not familiar wi...

Calculation of the level density parameter using semi-classical approach

International Nuclear Information System (INIS)

Canbula, B.; Babacan, H.

2011-01-01

The level density parameters (level density parameter a and energy shift δ) for back-shifted Fermi gas model have been determined for 1136 nuclei for which complete level scheme is available. Level density parameter is calculated by using the semi-classical single particle level density, which can be obtained analytically through spherical harmonic oscillator potential. This method also enables us to analyze the Coulomb potential's effect on the level density parameter. The dependence of this parameter on energy has been also investigated. Another parameter, δ, is determined by fitting of the experimental level scheme and the average resonance spacings for 289 nuclei. Only level scheme is used for optimization procedure for remaining 847 nuclei. Level densities for some nuclei have been calculated by using these parameter values. Obtained results have been compared with the experimental level scheme and the resonance spacing data.

An explicit MOT-TDVIE scheme for analyzing electromagnetic field interactions on nonlinear scatterers

KAUST Repository

Ulku, Huseyin Arda

2015-02-01

An explicit marching on-in-time (MOT) based time domain electric field volume integral equation (TDVIE) solver for characterizing electromagnetic wave interactions on scatterers with nonlinear material properties is proposed. Discretization of the unknown electric field intensity and flux density is carried out by half and full Schaubert-Wilton-Glisson basis functions, respectively. Coupled system of spatially discretized TDVIE and the nonlinear constitutive relation between the field intensity and the flux density is integrated in time to compute the samples of the unknowns. An explicit PE(CE)m scheme is used for this purpose. Explicitness allows for \\'easy\\' incorporation of the nonlinearity as a function only to be evaluated on the right hand side of the coupled system of equations. A numerical example that demonstrates the applicability of the proposed MOT scheme to analyzing electromagnetic interactions on Kerr-nonlinear scatterers is presented. © 2015 IEEE.

A robust H.264/AVC video watermarking scheme with drift compensation.

Science.gov (United States)

Jiang, Xinghao; Sun, Tanfeng; Zhou, Yue; Wang, Wan; Shi, Yun-Qing

2014-01-01

A robust H.264/AVC video watermarking scheme for copyright protection with self-adaptive drift compensation is proposed. In our scheme, motion vector residuals of macroblocks with the smallest partition size are selected to hide copyright information in order to hold visual impact and distortion drift to a minimum. Drift compensation is also implemented to reduce the influence of watermark to the most extent. Besides, discrete cosine transform (DCT) with energy compact property is applied to the motion vector residual group, which can ensure robustness against intentional attacks. According to the experimental results, this scheme gains excellent imperceptibility and low bit-rate increase. Malicious attacks with different quantization parameters (QPs) or motion estimation algorithms can be resisted efficiently, with 80% accuracy on average after lossy compression.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

Science.gov (United States)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-03-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

Improved stochastic approximation methods for discretized parabolic partial differential equations

Science.gov (United States)

Guiaş, Flavius

2016-12-01

We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).