Numerical tilting compensation in microscopy based on wavefront sensing using transport of intensity equation method

NASA Astrophysics Data System (ADS)

Hu, Junbao; Meng, Xin; Wei, Qi; Kong, Yan; Jiang, Zhilong; Xue, Liang; Liu, Fei; Liu, Cheng; Wang, Shouyu

2018-03-01

Wide-field microscopy is commonly used for sample observations in biological research and medical diagnosis. However, the tilting error induced by the oblique location of the image recorder or the sample, as well as the inclination of the optical path often deteriorates the imaging quality. In order to eliminate the tilting in microscopy, a numerical tilting compensation technique based on wavefront sensing using transport of intensity equation method is proposed in this paper. Both the provided numerical simulations and practical experiments prove that the proposed technique not only accurately determines the tilting angle with simple setup and procedures, but also compensates the tilting error for imaging quality improvement even in the large tilting cases. Considering its simple systems and operations, as well as image quality improvement capability, it is believed the proposed method can be applied for tilting compensation in the optical microscopy.

Computation of rare transitions in the barotropic quasi-geostrophic equations

NASA Astrophysics Data System (ADS)

Laurie, Jason; Bouchet, Freddy

2015-01-01

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier-Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager-Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherwise. We adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.

Computing the optimal path in stochastic dynamical systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bauver, Martha; Forgoston, Eric, E-mail: eric.forgoston@montclair.edu; Billings, Lora

2016-08-15

In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensionalmore » system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.« less

Numerical analysis on the cutting and finishing efficiency of MRAFF process

NASA Astrophysics Data System (ADS)

Lih, F. L.

2016-03-01

The aim of the present research is to conduct a numerical study of the characteristic of a two-phase magnetorheological fluid with different operation conditions by the finite volume method called SIMPLE with an add-on MHD code.

On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rembiasz, Tomasz; Obergaulinger, Martin; Cerdá-Durán, Pablo

2017-06-01

We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD code Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, ofmore » the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle this problem properly, in particular, in three-dimensional simulations.« less

A SIMPLE, EFFICIENT SOLUTION OF FLUX-PROFILE RELATIONSHIPS IN THE ATMOSPHERIC SURFACE LAYER

EPA Science Inventory

This note describes a simple scheme for analytical estimation of the surface layer similarity functions from state variables. What distinguishes this note from the many previous papers on this topic is that this method is specifically targeted for numerical models where simplici...

Some observations on boundary conditions for numerical conservation laws

NASA Technical Reports Server (NTRS)

Kamowitz, David

1988-01-01

Four choices of outflow boundary conditions are considered for numerical conservation laws. All four methods are stable for linear problems, for which examples are presented where either a boundary layer forms or the numerical scheme, together with the boundary condition, is unstable due to the formation of a reflected shock. A simple heuristic argument is presented for determining the suitability of the boundary condition.

Numerical computation of linear instability of detonations

NASA Astrophysics Data System (ADS)

Kabanov, Dmitry; Kasimov, Aslan

2017-11-01

We propose a method to study linear stability of detonations by direct numerical computation. The linearized governing equations together with the shock-evolution equation are solved in the shock-attached frame using a high-resolution numerical algorithm. The computed results are processed by the Dynamic Mode Decomposition technique to generate dispersion relations. The method is applied to the reactive Euler equations with simple-depletion chemistry as well as more complex multistep chemistry. The results are compared with those known from normal-mode analysis. We acknowledge financial support from King Abdullah University of Science and Technology.

Reconstruction of local perturbations in periodic surfaces

NASA Astrophysics Data System (ADS)

Lechleiter, Armin; Zhang, Ruming

2018-03-01

This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce quasi-periodic fields in one periodic cell, are no longer available. Based on the Floquet-Bloch transform, a numerical method has been developed to solve the direct problem, that leads to a possibility to design an algorithm for the inverse problem. The numerical method introduced in this paper contains two steps. The first step is initialization, that is to locate the support of the perturbation by a simple method. This step reduces the inverse problem in an infinite domain into one periodic cell. The second step is to apply the Newton-CG method to solve the associated optimization problem. The perturbation is then approximated by a finite spline basis. Numerical examples are given at the end of this paper, showing the efficiency of the numerical method.

A study of numerical methods for hyperbolic conservation laws with stiff source terms

NASA Technical Reports Server (NTRS)

Leveque, R. J.; Yee, H. C.

1988-01-01

The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by using implicit methods, but other numerical difficulties are observed. The behavior of typical numerical methods on a simple advection equation with a parameter-dependent source term was studied. Two approaches to incorporate the source term were utilized: MacCormack type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. Various comparisons over a wide range of parameter values were made. In the stiff case where the solution contains discontinuities, incorrect numerical propagation speeds are observed with all of the methods considered. This phenomenon is studied and explained.

Designing ROW Methods

NASA Technical Reports Server (NTRS)

Freed, Alan D.

1996-01-01

There are many aspects to consider when designing a Rosenbrock-Wanner-Wolfbrandt (ROW) method for the numerical integration of ordinary differential equations (ODE's) solving initial value problems (IVP's). The process can be simplified by constructing ROW methods around good Runge-Kutta (RK) methods. The formulation of a new, simple, embedded, third-order, ROW method demonstrates this design approach.

Combustion and Magnetohydrodynamic Processes in Advanced Pulse Detonation Rocket Engines

DTIC Science & Technology

2012-10-01

use of high-order numerical methods can also be a powerful tool in the analysis of such complex flows, but we need to understand the interaction of...computational physics, 43(2):357372, 1981. [47] B. Einfeldt. On godunov-type methods for gas dynamics . SIAM Journal on Numerical Analysis , pages 294...dimensional effects with complex reaction kinetics, the simple one-dimensional detonation structure provides a rich spectrum of dynamical features which are

Stability analysis of multigrid acceleration methods for the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Fay, John F.

1990-01-01

A calculation is made of the stability of various relaxation schemes for the numerical solution of partial differential equations. A multigrid acceleration method is introduced, and its effects on stability are explored. A detailed stability analysis of a simple case is carried out and verified by numerical experiment. It is shown that the use of multigrids can speed convergence by several orders of magnitude without adversely affecting stability.

Numerical Polynomial Homotopy Continuation Method and String Vacua

DOE PAGES

Mehta, Dhagash

2011-01-01

Finding vmore » acua for the four-dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some simple toy models, it is, however, difficult to find all the vacua analytically. Recently developed algorithmic methods based on symbolic computer algebra can be of great help in the more realistic models. However, they suffer from serious algorithmic complexities and are limited to small system sizes. In this paper, we review a numerical method called the numerical polynomial homotopy continuation (NPHC) method, first used in the areas of lattice field theories, which by construction finds all of the vacua of a given potential that is known to have only isolated solutions. The NPHC method is known to suffer from no major algorithmic complexities and is embarrassingly parallelizable , and hence its applicability goes way beyond the existing symbolic methods. We first solve a simple toy model as a warm-up example to demonstrate the NPHC method at work. We then show that all the vacua of a more complicated model of a compactified M theory model, which has an S U ( 3 ) structure, can be obtained by using a desktop machine in just about an hour, a feat which was reported to be prohibitively difficult by the existing symbolic methods. Finally, we compare the various technicalities between the two methods.« less

Numerical Modeling of Ablation Heat Transfer

NASA Technical Reports Server (NTRS)

Ewing, Mark E.; Laker, Travis S.; Walker, David T.

2013-01-01

A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.

ULTRA-SHARP nonoscillatory convection schemes for high-speed steady multidimensional flow

NASA Technical Reports Server (NTRS)

Leonard, B. P.; Mokhtari, Simin

1990-01-01

For convection-dominated flows, classical second-order methods are notoriously oscillatory and often unstable. For this reason, many computational fluid dynamicists have adopted various forms of (inherently stable) first-order upwinding over the past few decades. Although it is now well known that first-order convection schemes suffer from serious inaccuracies attributable to artificial viscosity or numerical diffusion under high convection conditions, these methods continue to enjoy widespread popularity for numerical heat transfer calculations, apparently due to a perceived lack of viable high accuracy alternatives. But alternatives are available. For example, nonoscillatory methods used in gasdynamics, including currently popular TVD schemes, can be easily adapted to multidimensional incompressible flow and convective transport. This, in itself, would be a major advance for numerical convective heat transfer, for example. But, as is shown, second-order TVD schemes form only a small, overly restrictive, subclass of a much more universal, and extremely simple, nonoscillatory flux-limiting strategy which can be applied to convection schemes of arbitrarily high order accuracy, while requiring only a simple tridiagonal ADI line-solver, as used in the majority of general purpose iterative codes for incompressible flow and numerical heat transfer. The new universal limiter and associated solution procedures form the so-called ULTRA-SHARP alternative for high resolution nonoscillatory multidimensional steady state high speed convective modelling.

Numerical prediction of the energy efficiency of the three-dimensional fish school using the discretized Adomian decomposition method

NASA Astrophysics Data System (ADS)

Lin, Yinwei

2018-06-01

A three-dimensional modeling of fish school performed by a modified Adomian decomposition method (ADM) discretized by the finite difference method is proposed. To our knowledge, few studies of the fish school are documented due to expensive cost of numerical computing and tedious three-dimensional data analysis. Here, we propose a simple model replied on the Adomian decomposition method to estimate the efficiency of energy saving of the flow motion of the fish school. First, the analytic solutions of Navier-Stokes equations are used for numerical validation. The influences of the distance between the side-by-side two fishes are studied on the energy efficiency of the fish school. In addition, the complete error analysis for this method is presented.

Implementing a GPU-based numerical algorithm for modelling dynamics of a high-speed train

NASA Astrophysics Data System (ADS)

Sytov, E. S.; Bratus, A. S.; Yurchenko, D.

2018-04-01

This paper discusses the initiative of implementing a GPU-based numerical algorithm for studying various phenomena associated with dynamics of a high-speed railway transport. The proposed numerical algorithm for calculating a critical speed of the bogie is based on the first Lyapunov number. Numerical algorithm is validated by analytical results, derived for a simple model. A dynamic model of a carriage connected to a new dual-wheelset flexible bogie is studied for linear and dry friction damping. Numerical results obtained by CPU, MPU and GPU approaches are compared and appropriateness of these methods is discussed.

Reconstructing gravitational wave source parameters via direct comparisons to numerical relativity I: Method

NASA Astrophysics Data System (ADS)

Lange, Jacob; O'Shaughnessy, Richard; Healy, James; Lousto, Carlos; Shoemaker, Deirdre; Lovelace, Geoffrey; Scheel, Mark; Ossokine, Serguei

2016-03-01

In this talk, we describe a procedure to reconstruct the parameters of sufficiently massive coalescing compact binaries via direct comparison with numerical relativity simulations. For sufficiently massive sources, existing numerical relativity simulations are long enough to cover the observationally accessible part of the signal. Due to the signal's brevity, the posterior parameter distribution it implies is broad, simple, and easily reconstructed from information gained by comparing to only the sparse sample of existing numerical relativity simulations. We describe how followup simulations can corroborate and improve our understanding of a detected source. Since our method can include all physics provided by full numerical relativity simulations of coalescing binaries, it provides a valuable complement to alternative techniques which employ approximations to reconstruct source parameters. Supported by NSF Grant PHY-1505629.

Recursive least squares method of regression coefficients estimation as a special case of Kalman filter

NASA Astrophysics Data System (ADS)

Borodachev, S. M.

2016-06-01

The simple derivation of recursive least squares (RLS) method equations is given as special case of Kalman filter estimation of a constant system state under changing observation conditions. A numerical example illustrates application of RLS to multicollinearity problem.

The survey of preconditioners used for accelerating the rate of convergence in the Gauss-Seidel method

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Harada, Kyouji; Morimoto, Munenori; Sakakihara, Michio

2004-03-01

Several preconditioned iterative methods reported in the literature have been used for improving the convergence rate of the Gauss-Seidel method. In this article, on the basis of nonnegative matrix, comparisons between some splittings for such preconditioned matrices are derived. Simple numerical examples are also given.

A particle finite element method for machining simulations

NASA Astrophysics Data System (ADS)

Sabel, Matthias; Sator, Christian; Müller, Ralf

2014-07-01

The particle finite element method (PFEM) appears to be a convenient technique for machining simulations, since the geometry and topology of the problem can undergo severe changes. In this work, a short outline of the PFEM-algorithm is given, which is followed by a detailed description of the involved operations. The -shape method, which is used to track the topology, is explained and tested by a simple example. Also the kinematics and a suitable finite element formulation are introduced. To validate the method simple settings without topological changes are considered and compared to the standard finite element method for large deformations. To examine the performance of the method, when dealing with separating material, a tensile loading is applied to a notched plate. This investigation includes a numerical analysis of the different meshing parameters, and the numerical convergence is studied. With regard to the cutting simulation it is found that only a sufficiently large number of particles (and thus a rather fine finite element discretisation) leads to converged results of process parameters, such as the cutting force.

Meshless Solution of the Problem on the Static Behavior of Thin and Thick Laminated Composite Beams

NASA Astrophysics Data System (ADS)

Xiang, S.; Kang, G. W.

2018-03-01

For the first time, the static behavior of laminated composite beams is analyzed using the meshless collocation method based on a thin-plate-spline radial basis function. In the approximation of a partial differential equation by using a radial basis function, the shape parameter has an important role in ensuring the numerical accuracy. The choice of a shape parameter in the thin plate spline radial basis function is easier than in other radial basis functions. The governing differential equations are derived based on Reddy's third-order shear deformation theory. Numerical results are obtained for symmetric cross-ply laminated composite beams with simple-simple and cantilever boundary conditions under a uniform load. The results found are compared with available published ones and demonstrate the accuracy of the present method.

Fall in hematocrit per 1000 parasites cleared from peripheral blood: a simple method for estimating drug-related fall in hematocrit after treatment of malaria infections.

PubMed

Gbotosho, Grace Olusola; Okuboyejo, Titilope; Happi, Christian Tientcha; Sowunmi, Akintunde

2014-01-01

A simple method to estimate antimalarial drug-related fall in hematocrit (FIH) after treatment of Plasmodium falciparum infections in the field is described. The method involves numeric estimation of the relative difference in hematocrit at baseline (pretreatment) and the first 1 or 2 days after treatment begun as numerator and the corresponding relative difference in parasitemia as the denominator, and expressing it per 1000 parasites cleared from peripheral blood. Using the method showed that FIH/1000 parasites cleared from peripheral blood (cpb) at 24 or 48 hours were similar in artemether-lumefantrine and artesunate-amodiaquine-treated children (0.09; 95% confidence interval, 0.052-0.138 vs 0.10; 95% confidence interval, 0.069-0.139%; P = 0.75) FIH/1000 parasites cpb in patients with higher parasitemias were significantly (P < 0.0001) and five- to 10-fold lower than in patients with lower parasitemias suggesting conservation of hematocrit or red cells in patients with higher parasitemias treated with artesunate-amodiaquine or artemether-lumefantrine. FIH/1000 parasites cpb were similar in anemic and nonanemic children. Estimation of FIH/1000 parasites cpb is simple, allows estimation of relatively conserved hematocrit during treatment, and can be used in both observational studies and clinical trials involving antimalarial drugs.

The Schrodinger Eigenvalue March

ERIC Educational Resources Information Center

Tannous, C.; Langlois, J.

2011-01-01

A simple numerical method for the determination of Schrodinger equation eigenvalues is introduced. It is based on a marching process that starts from an arbitrary point, proceeds in two opposite directions simultaneously and stops after a tolerance criterion is met. The method is applied to solving several 1D potential problems including symmetric…

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules.

PubMed

Sun, Hui; Zhou, Shenggao; Moore, David K; Cheng, Li-Tien; Li, Bo

2016-05-01

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules

PubMed Central

Sun, Hui; Zhou, Shenggao; Moore, David K.; Cheng, Li-Tien; Li, Bo

2015-01-01

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems. PMID:27365866

Response of a Rotating Propeller to Aerodynamic Excitation

NASA Technical Reports Server (NTRS)

Arnoldi, Walter E.

1949-01-01

The flexural vibration of a rotating propeller blade with clamped shank is analyzed with the object of presenting, in matrix form, equations for the elastic bending moments in forced vibration resulting from aerodynamic forces applied at a fixed multiple of rotational speed. Matrix equations are also derived which define the critical speeds end mode shapes for any excitation order and the relation between critical speed and blade angle. Reference is given to standard works on the numerical solution of matrix equations of the forms derived. The use of a segmented blade as an approximation to a continuous blade provides a simple means for obtaining the matrix solution from the integral equation of equilibrium, so that, in the numerical application of the method presented, the several matrix arrays of the basic physical characteristics of the propeller blade are of simple form, end their simplicity is preserved until, with the solution in sight, numerical manipulations well-known in matrix algebra yield the desired critical speeds and mode shapes frame which the vibration at any operating condition may be synthesized. A close correspondence between the familiar Stodola method and the matrix method is pointed out, indicating that any features of novelty are characteristic not of the analytical procedure but only of the abbreviation, condensation, and efficient organization of the numerical procedure made possible by the use of classical matrix theory.

Robust and Simple Non-Reflecting Boundary Conditions for the Euler Equations: A New Approach Based on the Space-Time CE/SE Method

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Himansu, Ananda; Loh, Ching-Yuen; Wang, Xiao-Yen; Yu, Shang-Tao

2003-01-01

This paper reports on a significant advance in the area of non-reflecting boundary conditions (NRBCs) for unsteady flow computations. As a part of the development of the space-time conservation element and solution element (CE/SE) method, sets of NRBCs for 1D Euler problems are developed without using any characteristics-based techniques. These conditions are much simpler than those commonly reported in the literature, yet so robust that they are applicable to subsonic, transonic and supersonic flows even in the presence of discontinuities. In addition, the straightforward multidimensional extensions of the present 1D NRBCs have been shown numerically to be equally simple and robust. The paper details the theoretical underpinning of these NRBCs, and explains their unique robustness and accuracy in terms of the conservation of space-time fluxes. Some numerical results for an extended Sod's shock-tube problem, illustrating the effectiveness of the present NRBCs are included, together with an associated simple Fortran computer program. As a preliminary to the present development, a review of the basic CE/SE schemes is also included.

Spreadsheets in Science Teaching.

ERIC Educational Resources Information Center

Elliot, Chris

1988-01-01

Described is the use of a spreadsheet to model dynamic phenomena using numerical iterative methods. Uses the discharge of a capacitor, simple and damped harmonic motion, and the flow of heat along a bar as examples. (Author/CW)

Self-adjusting grid methods for one-dimensional hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Harten, A.; Hyman, J. M.

1983-01-01

The automatic adjustment of a grid which follows the dynamics of the numerical solution of hyperbolic conservation laws is given. The grid motion is determined by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals. The resulting algorithm is a simple extension of many currently popular Godunov-type methods. Computer codes using one of these methods can be easily modified to add the moving mesh as an option. Numerical examples are given that illustrate the improved accuracy of Godunov's and Roe's methods on a self-adjusting mesh. Previously announced in STAR as N83-15008

An implicit semianalytic numerical method for the solution of nonequilibrium chemistry problems

NASA Technical Reports Server (NTRS)

Graves, R. A., Jr.; Gnoffo, P. A.; Boughner, R. E.

1974-01-01

The first order differential equation form systems of equations. They are solved by a simple and relatively accurate implicit semianalytic technique which is derived from a quadrature solution of the governing equation. This method is mathematically simpler than most implicit methods and has the exponential nature of the problem embedded in the solution.

Random element method for numerical modeling of diffusional processes

NASA Technical Reports Server (NTRS)

Ghoniem, A. F.; Oppenheim, A. K.

1982-01-01

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

Measurement of Antenna Bore-Sight Gain

NASA Technical Reports Server (NTRS)

Fortinberry, Jarrod; Shumpert, Thomas

2016-01-01

The absolute or free-field gain of a simple antenna can be approximated using standard antenna theory formulae or for a more accurate prediction, numerical methods may be employed to solve for antenna parameters including gain. Both of these methods will result in relatively reasonable estimates but in practice antenna gain is usually verified and documented via measurements and calibration. In this paper, a relatively simple and low-cost, yet effective means of determining the bore-sight free-field gain of a VHF/UHF antenna is proposed by using the Brewster angle relationship.

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Ge, Fuying

1989-01-01

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

NASA Astrophysics Data System (ADS)

Witte, J. H.; Reisinger, C.

2010-09-01

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desireable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to an order of O(1/ρ), where ρ>0 is the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.

Simple numerical method for predicting steady compressible flows

NASA Technical Reports Server (NTRS)

Vonlavante, Ernst; Nelson, N. Duane

1986-01-01

A numerical method for solving the isenthalpic form of the governing equations for compressible viscous and inviscid flows was developed. The method was based on the concept of flux vector splitting in its implicit form. The method was tested on several demanding inviscid and viscous configurations. Two different forms of the implicit operator were investigated. The time marching to steady state was accelerated by the implementation of the multigrid procedure. Its various forms very effectively increased the rate of convergence of the present scheme. High quality steady state results were obtained in most of the test cases; these required only short computational times due to the relative efficiency of the basic method.

Pursuit and Evasion Strategies in Football.

ERIC Educational Resources Information Center

O'Connell, James

1995-01-01

Explores strategies in the situation of a runner trying to evade a tackler on a football field. Enables the student to test intuitive strategies in a familiar situation using simple graphical and numerical methods or direct experimentation. (JRH)

New method to evaluate the 7Li(p, n)7Be reaction near threshold

NASA Astrophysics Data System (ADS)

Herrera, María S.; Moreno, Gustavo A.; Kreiner, Andrés J.

2015-04-01

In this work a complete description of the 7Li(p, n)7Be reaction near threshold is given using center-of-mass and relative coordinates. It is shown that this standard approach, not used before in this context, leads to a simple mathematical representation which gives easy access to all relevant quantities in the reaction and allows a precise numerical implementation. It also allows in a simple way to include proton beam-energy spread affects. The method, implemented as a C++ code, was validated both with numerical and experimental data finding a good agreement. This tool is also used here to analyze scattered published measurements such as (p, n) cross sections, differential and total neutron yields for thick targets. Using these data we derive a consistent set of parameters to evaluate neutron production near threshold. Sensitivity of the results to data uncertainty and the possibility of incorporating new measurements are also discussed.

Crack Path Selection in Thermally Loaded Borosilicate/Steel Bibeam Specimen

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grutzik, Scott Joseph; Reedy, Jr., E. D.

Here, we have developed a novel specimen for studying crack paths in glass. Under certain conditions, the specimen reaches a state where the crack must select between multiple paths satisfying the K II = 0 condition. This path selection is a simple but challenging benchmark case for both analytical and numerical methods of predicting crack propagation. We document the development of the specimen, using an uncracked and instrumented test case to study the effect of adhesive choice and validate the accuracy of both a simple beam theory model and a finite element model. In addition, we present preliminary fracture testmore » results and provide a comparison to the path predicted by two numerical methods (mesh restructuring and XFEM). The directional stability of the crack path and differences in kink angle predicted by various crack kinking criteria is analyzed with a finite element model.« less

Variational Approach to Enhanced Sampling and Free Energy Calculations

NASA Astrophysics Data System (ADS)

Valsson, Omar; Parrinello, Michele

2014-08-01

The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo simulations, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks. A large number of solutions have been proposed to alleviate this problem. Many are based on the introduction of a bias potential which is a function of a small number of collective variables. However constructing such a bias is not simple. Here we introduce a functional of the bias potential and an associated variational principle. The bias that minimizes the functional relates in a simple way to the free energy surface. This variational principle can be turned into a practical, efficient, and flexible sampling method. A number of numerical examples are presented which include the determination of a three-dimensional free energy surface. We argue that, beside being numerically advantageous, our variational approach provides a convenient and novel standpoint for looking at the sampling problem.

Crack Path Selection in Thermally Loaded Borosilicate/Steel Bibeam Specimen

DOE PAGES

Grutzik, Scott Joseph; Reedy, Jr., E. D.

2017-08-04

Here, we have developed a novel specimen for studying crack paths in glass. Under certain conditions, the specimen reaches a state where the crack must select between multiple paths satisfying the K II = 0 condition. This path selection is a simple but challenging benchmark case for both analytical and numerical methods of predicting crack propagation. We document the development of the specimen, using an uncracked and instrumented test case to study the effect of adhesive choice and validate the accuracy of both a simple beam theory model and a finite element model. In addition, we present preliminary fracture testmore » results and provide a comparison to the path predicted by two numerical methods (mesh restructuring and XFEM). The directional stability of the crack path and differences in kink angle predicted by various crack kinking criteria is analyzed with a finite element model.« less

The Numerical Calculation and Experimental Measurement of the Inductance Parameters for Permanent Magnet Synchronous Motor in Electric Vehicle

NASA Astrophysics Data System (ADS)

Jiang, Chao; Qiao, Mingzhong; Zhu, Peng

2017-12-01

A permanent magnet synchronous motor with radial magnetic circuit and built-in permanent magnet is designed for the electric vehicle. Finite element numerical calculation and experimental measurement are adopted to obtain the direct axis and quadrature axis inductance parameters of the motor which are vital important for the motor control. The calculation method is simple, the measuring principle is clear, the results of numerical calculation and experimental measurement are mutual confirmation. A quick and effective method is provided to obtain the direct axis and quadrature axis inductance parameters of the motor, and then improve the design of motor or adjust the control parameters of the motor controller.

Time-dependent spectral renormalization method

NASA Astrophysics Data System (ADS)

Cole, Justin T.; Musslimani, Ziad H.

2017-11-01

The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

Determination of the transmission coefficients for quantum structures using FDTD method.

PubMed

Peng, Yangyang; Wang, Xiaoying; Sui, Wenquan

2011-12-01

The purpose of this work is to develop a simple method to incorporate quantum effect in traditional finite-difference time-domain (FDTD) simulators. Witch could make it possible to co-simulate systems include quantum structures and traditional components. In this paper, tunneling transmission coefficient is calculated by solving time-domain Schrödinger equation with a developed FDTD technique, called FDTD-S method. To validate the feasibility of the method, a simple resonant tunneling diode (RTD) structure model has been simulated using the proposed method. The good agreement between the numerical and analytical results proves its accuracy. The effectness and accuracy of this approach makes it a potential method for analysis and design of hybrid systems includes quantum structures and traditional components.

Numerical integration of discontinuous functions: moment fitting and smart octree

NASA Astrophysics Data System (ADS)

Hubrich, Simeon; Di Stolfo, Paolo; Kudela, László; Kollmannsberger, Stefan; Rank, Ernst; Schröder, Andreas; Düster, Alexander

2017-11-01

A fast and simple grid generation can be achieved by non-standard discretization methods where the mesh does not conform to the boundary or the internal interfaces of the problem. However, this simplification leads to discontinuous integrands for intersected elements and, therefore, standard quadrature rules do not perform well anymore. Consequently, special methods are required for the numerical integration. To this end, we present two approaches to obtain quadrature rules for arbitrary domains. The first approach is based on an extension of the moment fitting method combined with an optimization strategy for the position and weights of the quadrature points. In the second approach, we apply the smart octree, which generates curved sub-cells for the integration mesh. To demonstrate the performance of the proposed methods, we consider several numerical examples, showing that the methods lead to efficient quadrature rules, resulting in less integration points and in high accuracy.

A Family of Ellipse Methods for Solving Non-Linear Equations

ERIC Educational Resources Information Center

Gupta, K. C.; Kanwar, V.; Kumar, Sanjeev

2009-01-01

This note presents a method for the numerical approximation of simple zeros of a non-linear equation in one variable. In order to do so, the method uses an ellipse rather than a tangent approach. The main advantage of our method is that it does not fail even if the derivative of the function is either zero or very small in the vicinity of the…

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

NASA Astrophysics Data System (ADS)

Meyers, M. D.; Huang, C.-K.; Zeng, Y.; Yi, S. A.; Albright, B. J.

2015-09-01

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meyers, M.D., E-mail: mdmeyers@physics.ucla.edu; Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA 90095; Huang, C.-K., E-mail: huangck@lanl.gov

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTDmore » scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.« less

Valuation of financial models with non-linear state spaces

NASA Astrophysics Data System (ADS)

Webber, Nick

2001-02-01

A common assumption in valuation models for derivative securities is that the underlying state variables take values in a linear state space. We discuss numerical implementation issues in an interest rate model with a simple non-linear state space, formulating and comparing Monte Carlo, finite difference and lattice numerical solution methods. We conclude that, at least in low dimensional spaces, non-linear interest rate models may be viable.

A loop-counting method for covariate-corrected low-rank biclustering of gene-expression and genome-wide association study data.

PubMed

Rangan, Aaditya V; McGrouther, Caroline C; Kelsoe, John; Schork, Nicholas; Stahl, Eli; Zhu, Qian; Krishnan, Arjun; Yao, Vicky; Troyanskaya, Olga; Bilaloglu, Seda; Raghavan, Preeti; Bergen, Sarah; Jureus, Anders; Landen, Mikael

2018-05-14

A common goal in data-analysis is to sift through a large data-matrix and detect any significant submatrices (i.e., biclusters) that have a low numerical rank. We present a simple algorithm for tackling this biclustering problem. Our algorithm accumulates information about 2-by-2 submatrices (i.e., 'loops') within the data-matrix, and focuses on rows and columns of the data-matrix that participate in an abundance of low-rank loops. We demonstrate, through analysis and numerical-experiments, that this loop-counting method performs well in a variety of scenarios, outperforming simple spectral methods in many situations of interest. Another important feature of our method is that it can easily be modified to account for aspects of experimental design which commonly arise in practice. For example, our algorithm can be modified to correct for controls, categorical- and continuous-covariates, as well as sparsity within the data. We demonstrate these practical features with two examples; the first drawn from gene-expression analysis and the second drawn from a much larger genome-wide-association-study (GWAS).

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Yung, Chain Nan

1988-01-01

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

Highly accurate symplectic element based on two variational principles

NASA Astrophysics Data System (ADS)

Qing, Guanghui; Tian, Jia

2018-02-01

For the stability requirement of numerical resultants, the mathematical theory of classical mixed methods are relatively complex. However, generalized mixed methods are automatically stable, and their building process is simple and straightforward. In this paper, based on the seminal idea of the generalized mixed methods, a simple, stable, and highly accurate 8-node noncompatible symplectic element (NCSE8) was developed by the combination of the modified Hellinger-Reissner mixed variational principle and the minimum energy principle. To ensure the accuracy of in-plane stress results, a simultaneous equation approach was also suggested. Numerical experimentation shows that the accuracy of stress results of NCSE8 are nearly the same as that of displacement methods, and they are in good agreement with the exact solutions when the mesh is relatively fine. NCSE8 has advantages of the clearing concept, easy calculation by a finite element computer program, higher accuracy and wide applicability for various linear elasticity compressible and nearly incompressible material problems. It is possible that NCSE8 becomes even more advantageous for the fracture problems due to its better accuracy of stresses.

Monte Carlo investigation of transient acoustic fields in partially or completely bounded medium. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Thanedar, B. D.

1972-01-01

A simple repetitive calculation was used to investigate what happens to the field in terms of the signal paths of disturbances originating from the energy source. The computation allowed the field to be reconstructed as a function of space and time on a statistical basis. The suggested Monte Carlo method is in response to the need for a numerical method to supplement analytical methods of solution which are only valid when the boundaries have simple shapes, rather than for a medium that is bounded. For the analysis, a suitable model was created from which was developed an algorithm for the estimation of acoustic pressure variations in the region under investigation. The validity of the technique was demonstrated by analysis of simple physical models with the aid of a digital computer. The Monte Carlo method is applicable to a medium which is homogeneous and is enclosed by either rectangular or curved boundaries.

Fast Fourier transform-based solution of 2D and 3D magnetization problems in type-II superconductivity

NASA Astrophysics Data System (ADS)

Prigozhin, Leonid; Sokolovsky, Vladimir

2018-05-01

We consider the fast Fourier transform (FFT) based numerical method for thin film magnetization problems (Vestgården and Johansen 2012 Supercond. Sci. Technol. 25 104001), compare it with the finite element methods, and evaluate its accuracy. Proposed modifications of this method implementation ensure stable convergence of iterations and enhance its efficiency. A new method, also based on the FFT, is developed for 3D bulk magnetization problems. This method is based on a magnetic field formulation, different from the popular h-formulation of eddy current problems typically employed with the edge finite elements. The method is simple, easy to implement, and can be used with a general current–voltage relation; its efficiency is illustrated by numerical simulations.

Discrete exterior calculus approach for discretizing Maxwell's equations on face-centered cubic grids for FDTD

NASA Astrophysics Data System (ADS)

Salmasi, Mahbod; Potter, Michael

2018-07-01

Maxwell's equations are discretized on a Face-Centered Cubic (FCC) lattice instead of a simple cubic as an alternative to the standard Yee method for improvements in numerical dispersion characteristics and grid isotropy of the method. Explicit update equations and numerical dispersion expressions, and the stability criteria are derived. Also, several tools available to the standard Yee method such as PEC/PMC boundary conditions, absorbing boundary conditions, and scattered field formulation are extended to this method as well. A comparison between the FCC and the Yee formulations is made, showing that the FCC method exhibits better dispersion compared to its Yee counterpart. Simulations are provided to demonstrate both the accuracy and grid isotropy improvement of the method.

Asronomical refraction: Computational methods for all zenith angles

NASA Technical Reports Server (NTRS)

Auer, L. H.; Standish, E. M.

2000-01-01

It is shown that the problem of computing astronomical refraction for any value of the zenith angle may be reduced to a simple, nonsingular, numerical quadrature when the proper choice is made for the independent variable of integration.

3PE: A Tool for Estimating Groundwater Flow Vectors

EPA Science Inventory

Evaluation of hydraulic gradients and the associated groundwater flow rates and directions is a fundamental aspect of hydrogeologic characterization. Many methods, ranging in complexity from simple three-point solution techniques to complex numerical models of groundwater flow, ...

A numerical method for determination of source time functions for general three-dimensional rupture propagation

NASA Technical Reports Server (NTRS)

Das, S.

1979-01-01

A method to determine the displacement and the stress on the crack plane for a three-dimensional shear crack of arbitrary shape propagating in an infinite, homogeneous medium which is linearly elastic everywhere off the crack plane is presented. The main idea of the method is to use a representation theorem in which the displacement at any given point on the crack plane is written as an integral of the traction over the whole crack plane. As a test of the accuracy of the numerical technique, the results are compared with known solutions for two simple cases.

A simple strategy for varying the restart parameter in GMRES(m)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, A H; Jessup, E R; Kolev, T V

2007-10-02

When solving a system of linear equations with the restarted GMRES method, a fixed restart parameter is typically chosen. We present numerical experiments that demonstrate the beneficial effects of changing the value of the restart parameter in each restart cycle on the total time to solution. We propose a simple strategy for varying the restart parameter and provide some heuristic explanations for its effectiveness based on analysis of the symmetric case.

Comparison of a 3-D DEM simulation with MRI data

NASA Astrophysics Data System (ADS)

Ng, Tang-Tat; Wang, Changming

2001-04-01

This paper presents a comparison of a granular material studied experimentally and numerically. Simple shear tests were performed inside the magnetic core of magnetic resonance imaging (MRI) equipment. Spherical pharmaceutical pills were used as the granular material, with each pill's centre location determined by MRI. These centre locations in the initial assembly were then used as the initial configuration in the numerical simulation using the discrete element method. The contact properties between pharmaceutical pills used in the numerical simulation were obtained experimentally. The numerical predication was compared with experimental data at both macroscopic and microscopic levels. Good agreement was found at both levels.

The Zombie Plot: A Simple Graphic Method for Visualizing the Efficacy of a Diagnostic Test.

PubMed

Richardson, Michael L

2016-08-09

One of the most important jobs of a radiologist is to pick the most appropriate imaging test for a particular clinical situation. Making a proper selection sometimes requires statistical analysis. The objective of this article is to introduce a simple graphic technique, an ROC plot that has been divided into zones of mostly bad imaging efficacy (ZOMBIE, hereafter referred to as the "zombie plot"), that transforms information about imaging efficacy from the numeric domain into the visual domain. The numeric rationale for the use of zombie plots is given, as are several examples of the clinical use of these plots. Two online calculators are described that simplify the process of producing a zombie plot.

Multigrid methods for isogeometric discretization

PubMed Central

Gahalaut, K.P.S.; Kraus, J.K.; Tomar, S.K.

2013-01-01

We present (geometric) multigrid methods for isogeometric discretization of scalar second order elliptic problems. The smoothing property of the relaxation method, and the approximation property of the intergrid transfer operators are analyzed. These properties, when used in the framework of classical multigrid theory, imply uniform convergence of two-grid and multigrid methods. Supporting numerical results are provided for the smoothing property, the approximation property, convergence factor and iterations count for V-, W- and F-cycles, and the linear dependence of V-cycle convergence on the smoothing steps. For two dimensions, numerical results include the problems with variable coefficients, simple multi-patch geometry, a quarter annulus, and the dependence of convergence behavior on refinement levels ℓ, whereas for three dimensions, only the constant coefficient problem in a unit cube is considered. The numerical results are complete up to polynomial order p=4, and for C0 and Cp-1 smoothness. PMID:24511168

Extension of rezoned Eulerian-Lagrangian method to astrophysical plasma applications

NASA Technical Reports Server (NTRS)

Song, M. T.; Wu, S. T.; Dryer, Murray

1993-01-01

The rezoned Eulerian-Lagrangian procedure developed by Brackbill and Pracht (1973), which is limited to simple configurations of the magnetic fields, is modified in order to make it applicable to astrophysical plasma. For this purpose, two specific methods are introduced, which make it possible to determine the initial field topology for which no analytical expressions are available. Numerical examples illustrating these methods are presented.

Free boundary skin current MHD (magnetohydrodynamic) equilibria

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reusch, M.F.

1988-02-01

Function theoretic methods in the complex plane are used to develop simple parametric hodograph formulae which generate sharp boundary equilibria of arbitrary shape. The related method of Gorenflo and Merkel is discussed. A numerical technique for the construction of solutions, based on one of the methods is presented. A study is made of the bifurcations of an equilibrium of general form. 28 refs., 9 figs.

A Simple Geometrical Model for Calculation of the Effective Emissivity in Blackbody Cylindrical Cavities

NASA Astrophysics Data System (ADS)

De Lucas, Javier

2015-03-01

A simple geometrical model for calculating the effective emissivity in blackbody cylindrical cavities has been developed. The back ray tracing technique and the Monte Carlo method have been employed, making use of a suitable set of coordinates and auxiliary planes. In these planes, the trajectories of individual photons in the successive reflections between the cavity points are followed in detail. The theoretical model is implemented by using simple numerical tools, programmed in Microsoft Visual Basic for Application and Excel. The algorithm is applied to isothermal and non-isothermal diffuse cylindrical cavities with a lid; however, the basic geometrical structure can be generalized to a cylindro-conical shape and specular reflection. Additionally, the numerical algorithm and the program source code can be used, with minor changes, for determining the distribution of the cavity points, where photon absorption takes place. This distribution could be applied to the study of the influence of thermal gradients on the effective emissivity profiles, for example. Validation is performed by analyzing the convergence of the Monte Carlo method as a function of the number of trials and by comparison with published results of different authors.

Robust and Simple Non-Reflecting Boundary Conditions for the Euler Equations - A New Approach based on the Space-Time CE/SE Method

NASA Technical Reports Server (NTRS)

Chang, S.-C.; Himansu, A.; Loh, C.-Y.; Wang, X.-Y.; Yu, S.-T.J.

2005-01-01

This paper reports on a significant advance in the area of nonreflecting boundary conditions (NRBCs) for unsteady flow computations. As a part of t he development of t he space-time conservation element and solution element (CE/SE) method, sets of NRBCs for 1D Euler problems are developed without using any characteristics- based techniques. These conditions are much simpler than those commonly reported in the literature, yet so robust that they are applicable to subsonic, transonic and supersonic flows even in the presence of discontinuities. In addition, the straightforward multidimensional extensions of the present 1D NRBCs have been shown numerically to be equally simple and robust. The paper details the theoretical underpinning of these NRBCs, and explains t heir unique robustness and accuracy in terms of t he conservation of space-time fluxes. Some numerical results for an extended Sod's shock-tube problem, illustrating the effectiveness of the present NRBCs are included, together with an associated simple Fortran computer program. As a preliminary to the present development, a review of the basic CE/SE schemes is also included.

Solving transient acoustic boundary value problems with equivalent sources using a lumped parameter approach.

PubMed

Fahnline, John B

2016-12-01

An equivalent source method is developed for solving transient acoustic boundary value problems. The method assumes the boundary surface is discretized in terms of triangular or quadrilateral elements and that the solution is represented using the acoustic fields of discrete sources placed at the element centers. Also, the boundary condition is assumed to be specified for the normal component of the surface velocity as a function of time, and the source amplitudes are determined to match the known elemental volume velocity vector at a series of discrete time steps. Equations are given for marching-on-in-time schemes to solve for the source amplitudes at each time step for simple, dipole, and tripole source formulations. Several example problems are solved to illustrate the results and to validate the formulations, including problems with closed boundary surfaces where long-time numerical instabilities typically occur. A simple relationship between the simple and dipole source amplitudes in the tripole source formulation is derived so that the source radiates primarily in the direction of the outward surface normal. The tripole source formulation is shown to eliminate interior acoustic resonances and long-time numerical instabilities.

Simple Numerical Modelling for Gasdynamic Design of Wave Rotors

NASA Astrophysics Data System (ADS)

Okamoto, Koji; Nagashima, Toshio

The precise estimation of pressure waves generated in the passages is a crucial factor in wave rotor design. However, it is difficult to estimate the pressure wave analytically, e.g. by the method of characteristics, because the mechanism of pressure-wave generation and propagation in the passages is extremely complicated as compared to that in a shock tube. In this study, a simple numerical modelling scheme was developed to facilitate the design procedure. This scheme considers the three dominant factors in the loss mechanism —gradual passage opening, wall friction and leakage— for simulating the pressure waves precisely. The numerical scheme itself is based on the one-dimensional Euler equations with appropriate source terms to reduce the calculation time. The modelling of these factors was verified by comparing the results with those of a two-dimensional numerical simulation, which were previously validated by the experimental data in our previous study. Regarding wave rotor miniaturization, the leakage flow effect, which involves the interaction between adjacent cells, was investigated extensively. A port configuration principle was also examined and analyzed in detail to verify the applicability of the present numerical modelling scheme to the wave rotor design.

Numerical study of rotating detonation engine with an array of injection holes

NASA Astrophysics Data System (ADS)

Yao, S.; Han, X.; Liu, Y.; Wang, J.

2017-05-01

This paper aims to adopt the method of injection via an array of holes in three-dimensional numerical simulations of a rotating detonation engine (RDE). The calculation is based on the Euler equations coupled with a one-step Arrhenius chemistry model. A pre-mixed stoichiometric hydrogen-air mixture is used. The present study uses a more practical fuel injection method in RDE simulations, injection via an array of holes, which is different from the previous conventional simulations where a relatively simple full injection method is usually adopted. The computational results capture some important experimental observations and a transient period after initiation. These phenomena are usually absent in conventional RDE simulations due to the use of an idealistic injection approximation. The results are compared with those obtained from other numerical studies and experiments with RDEs.

A network thermodynamic method for numerical solution of the Nernst-Planck and Poisson equation system with application to ionic transport through membranes.

PubMed

Horno, J; González-Caballero, F; González-Fernández, C F

1990-01-01

Simple techniques of network thermodynamics are used to obtain the numerical solution of the Nernst-Planck and Poisson equation system. A network model for a particular physical situation, namely ionic transport through a thin membrane with simultaneous diffusion, convection and electric current, is proposed. Concentration and electric field profiles across the membrane, as well as diffusion potential, have been simulated using the electric circuit simulation program, SPICE. The method is quite general and extremely efficient, permitting treatments of multi-ion systems whatever the boundary and experimental conditions may be.

The numerical solution of linear multi-term fractional differential equations: systems of equations

NASA Astrophysics Data System (ADS)

Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

2002-11-01

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

Numerics made easy: solving the Navier-Stokes equation for arbitrary channel cross-sections using Microsoft Excel.

PubMed

Richter, Christiane; Kotz, Frederik; Giselbrecht, Stefan; Helmer, Dorothea; Rapp, Bastian E

2016-06-01

The fluid mechanics of microfluidics is distinctively simpler than the fluid mechanics of macroscopic systems. In macroscopic systems effects such as non-laminar flow, convection, gravity etc. need to be accounted for all of which can usually be neglected in microfluidic systems. Still, there exists only a very limited selection of channel cross-sections for which the Navier-Stokes equation for pressure-driven Poiseuille flow can be solved analytically. From these equations, velocity profiles as well as flow rates can be calculated. However, whenever a cross-section is not highly symmetric (rectangular, elliptical or circular) the Navier-Stokes equation can usually not be solved analytically. In all of these cases, numerical methods are required. However, in many instances it is not necessary to turn to complex numerical solver packages for deriving, e.g., the velocity profile of a more complex microfluidic channel cross-section. In this paper, a simple spreadsheet analysis tool (here: Microsoft Excel) will be used to implement a simple numerical scheme which allows solving the Navier-Stokes equation for arbitrary channel cross-sections.

High order filtering methods for approximating hyberbolic systems of conservation laws

NASA Technical Reports Server (NTRS)

Lafon, F.; Osher, S.

1990-01-01

In the computation of discontinuous solutions of hyperbolic systems of conservation laws, the recently developed essentially non-oscillatory (ENO) schemes appear to be very useful. However, they are computationally costly compared to simple central difference methods. A filtering method which is developed uses simple central differencing of arbitrarily high order accuracy, except when a novel local test indicates the development of spurious oscillations. At these points, the full ENO apparatus is used, maintaining the high order of accuracy, but removing spurious oscillations. Numerical results indicate the success of the method. High order of accuracy was obtained in regions of smooth flow without spurious oscillations for a wide range of problems and a significant speed up of generally a factor of almost three over the full ENO method.

Global Asymptotic Behavior of Iterative Implicit Schemes

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1994-01-01

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.

A numerical method for shock driven multiphase flow with evaporating particles

NASA Astrophysics Data System (ADS)

Dahal, Jeevan; McFarland, Jacob A.

2017-09-01

A numerical method for predicting the interaction of active, phase changing particles in a shock driven flow is presented in this paper. The Particle-in-Cell (PIC) technique was used to couple particles in a Lagrangian coordinate system with a fluid in an Eulerian coordinate system. The Piecewise Parabolic Method (PPM) hydrodynamics solver was used for solving the conservation equations and was modified with mass, momentum, and energy source terms from the particle phase. The method was implemented in the open source hydrodynamics software FLASH, developed at the University of Chicago. A simple validation of the methods is accomplished by comparing velocity and temperature histories from a single particle simulation with the analytical solution. Furthermore, simple single particle parcel simulations were run at two different sizes to study the effect of particle size on vorticity deposition in a shock-driven multiphase instability. Large particles were found to have lower enstrophy production at early times and higher enstrophy dissipation at late times due to the advection of the particle vorticity source term through the carrier gas. A 2D shock-driven instability of a circular perturbation is studied in simulations and compared to previous experimental data as further validation of the numerical methods. The effect of the particle size distribution and particle evaporation is examined further for this case. The results show that larger particles reduce the vorticity deposition, while particle evaporation increases it. It is also shown that for a distribution of particles sizes the vorticity deposition is decreased compared to single particle size case at the mean diameter.

A volume-of-fluid method for simulation of compressible axisymmetric multi-material flow

NASA Astrophysics Data System (ADS)

de Niem, D.; Kührt, E.; Motschmann, U.

2007-02-01

A two-dimensional Eulerian hydrodynamic method for the numerical simulation of inviscid compressible axisymmetric multi-material flow in external force fields for the situation of pure fluids separated by macroscopic interfaces is presented. The method combines an implicit Lagrangian step with an explicit Eulerian advection step. Individual materials obey separate energy equations, fulfill general equations of state, and may possess different temperatures. Material volume is tracked using a piecewise linear volume-of-fluid method. An overshoot-free logically simple and economic material advection algorithm for cylinder coordinates is derived, in an algebraic formulation. New aspects arising in the case of more than two materials such as the material ordering strategy during transport are presented. One- and two-dimensional numerical examples are given.

Conversion from Engineering Units to Telemetry Counts on Dryden Flight Simulators

NASA Technical Reports Server (NTRS)

Fantini, Jay A.

1998-01-01

Dryden real-time flight simulators encompass the simulation of pulse code modulation (PCM) telemetry signals. This paper presents a new method whereby the calibration polynomial (from first to sixth order), representing the conversion from counts to engineering units (EU), is numerically inverted in real time. The result is less than one-count error for valid EU inputs. The Newton-Raphson method is used to numerically invert the polynomial. A reverse linear interpolation between the EU limits is used to obtain an initial value for the desired telemetry count. The method presented here is not new. What is new is how classical numerical techniques are optimized to take advantage of modem computer power to perform the desired calculations in real time. This technique makes the method simple to understand and implement. There are no interpolation tables to store in memory as in traditional methods. The NASA F-15 simulation converts and transmits over 1000 parameters at 80 times/sec. This paper presents algorithm development, FORTRAN code, and performance results.

A stochastic vortex structure method for interacting particles in turbulent shear flows

NASA Astrophysics Data System (ADS)

Dizaji, Farzad F.; Marshall, Jeffrey S.; Grant, John R.

2018-01-01

In a recent study, we have proposed a new synthetic turbulence method based on stochastic vortex structures (SVSs), and we have demonstrated that this method can accurately predict particle transport, collision, and agglomeration in homogeneous, isotropic turbulence in comparison to direct numerical simulation results. The current paper extends the SVS method to non-homogeneous, anisotropic turbulence. The key element of this extension is a new inversion procedure, by which the vortex initial orientation can be set so as to generate a prescribed Reynolds stress field. After validating this inversion procedure for simple problems, we apply the SVS method to the problem of interacting particle transport by a turbulent planar jet. Measures of the turbulent flow and of particle dispersion, clustering, and collision obtained by the new SVS simulations are shown to compare well with direct numerical simulation results. The influence of different numerical parameters, such as number of vortices and vortex lifetime, on the accuracy of the SVS predictions is also examined.

Numerical detection of the Gardner transition in a mean-field glass former.

PubMed

Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Rainone, Corrado; Seoane, Beatriz; Zamponi, Francesco

2015-07-01

Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.

BOOK REVIEW: Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

NASA Astrophysics Data System (ADS)

Katsaounis, T. D.

2005-02-01

The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. The first chapter is an introduction to parallel processing. It covers fundamentals of parallel processing in a simple and concrete way and no prior knowledge of the subject is required. Examples of parallel implementation of basic linear algebra operations are presented using the Message Passing Interface (MPI) programming environment. Here, some knowledge of MPI routines is required by the reader. Examples solving in parallel simple PDEs using Diffpack and MPI are also presented. Chapter 2 presents the overlapping domain decomposition method for solving PDEs. It is well known that these methods are suitable for parallel processing. The first part of the chapter covers the mathematical formulation of the method as well as algorithmic and implementational issues. The second part presents a serial and a parallel implementational framework within the programming environment of Diffpack. The chapter closes by showing how to solve two application examples with the overlapping domain decomposition method using Diffpack. Chapter 3 is a tutorial about how to incorporate the multigrid solver in Diffpack. The method is illustrated by examples such as a Poisson solver, a general elliptic problem with various types of boundary conditions and a nonlinear Poisson type problem. In chapter 4 the mixed finite element is introduced. Technical issues concerning the practical implementation of the method are also presented. The main difficulties of the efficient implementation of the method, especially in two and three space dimensions on unstructured grids, are presented and addressed in the framework of Diffpack. The implementational process is illustrated by two examples, namely the system formulation of the Poisson problem and the Stokes problem. Chapter 5 is closely related to chapter 4 and addresses the problem of how to solve efficiently the linear systems arising by the application of the mixed finite element method. The proposed method is block preconditioning. Efficient techniques for implementing the method within Diffpack are presented. Optimal block preconditioners are used to solve the system formulation of the Poisson problem, the Stokes problem and the bidomain model for the electrical activity in the heart. The subject of chapter 6 is systems of PDEs. Linear and nonlinear systems are discussed. Fully implicit and operator splitting methods are presented. Special attention is paid to how existing solvers for scalar equations in Diffpack can be used to derive fully implicit solvers for systems. The proposed techniques are illustrated in terms of two applications, namely a system of PDEs modelling pipeflow and a two-phase porous media flow. Stochastic PDEs is the topic of chapter 7. The first part of the chapter is a simple introduction to stochastic PDEs; basic analytical properties are presented for simple models like transport phenomena and viscous drag forces. The second part considers the numerical solution of stochastic PDEs. Two basic techniques are presented, namely Monte Carlo and perturbation methods. The last part explains how to implement and incorporate these solvers into Diffpack. Chapter 8 describes how to operate Diffpack from Python scripts. The main goal here is to provide all the programming and technical details in order to glue the programming environment of Diffpack with visualization packages through Python and in general take advantage of the Python interfaces. Chapter 9 attempts to show how to use numerical experiments to measure the performance of various PDE solvers. The authors gathered a rather impressive list, a total of 14 PDE solvers. Solvers for problems like Poisson, Navier--Stokes, elasticity, two-phase flows and methods such as finite difference, finite element, multigrid, and gradient type methods are presented. The authors provide a series of numerical results combining various solvers with various methods in order to gain insight into their computational performance and efficiency. In Chapter 10 the authors consider a computationally challenging problem, namely the computation of the electrical activity of the human heart. After a brief introduction on the biology of the problem the authors present the mathematical models involved and a numerical method for solving them within the framework of Diffpack. Chapter 11 and 12 are closely related; actually they could have been combined in a single chapter. Chapter 11 introduces several mathematical models used in finance, based on the Black--Scholes equation. Chapter 12 considers several numerical methods like Monte Carlo, lattice methods, finite difference and finite element methods. Implementation of these methods within Diffpack is presented in the last part of the chapter. Chapter 13 presents how the finite element method is used for the modelling and analysis of elastic structures. The authors describe the structural elements of Diffpack which include popular elements such as beams and plates and examples are presented on how to use them to simulate elastic structures. Chapter 14 describes an application problem, namely the extrusion of aluminum. This is a rather\\endcolumn complicated process which involves non-Newtonian flow, heat transfer and elasticity. The authors describe the systems of PDEs modelling the underlying process and use a finite element method to obtain a numerical solution. The implementation of the numerical method in Diffpack is presented along with some applications. The last chapter, chapter 15, focuses on mathematical and numerical models of systems of PDEs governing geological processes in sedimentary basins. The underlying mathematical model is solved using the finite element method within a fully implicit scheme. The authors discuss the implementational issues involved within Diffpack and they present results from several examples. In summary, the book focuses on the computational and implementational issues involved in solving partial differential equations. The potential reader should have a basic knowledge of PDEs and the finite difference and finite element methods. The examples presented are solved within the programming framework of Diffpack and the reader should have prior experience with the particular software in order to take full advantage of the book. Overall the book is well written, the subject of each chapter is well presented and can serve as a reference for graduate students, researchers and engineers who are interested in the numerical solution of partial differential equations modelling various applications.

A numerical study of the axisymmetric Couette-Taylor problem using a fast high-resolution second-order central scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kupferman, R.

The author presents a numerical study of the axisymmetric Couette-Taylor problem using a finite difference scheme. The scheme is based on a staggered version of a second-order central-differencing method combined with a discrete Hodge projection. The use of central-differencing operators obviates the need to trace the characteristic flow associated with the hyperbolic terms. The result is a simple and efficient scheme which is readily adaptable to other geometries and to more complicated flows. The scheme exhibits competitive performance in terms of accuracy, resolution, and robustness. The numerical results agree accurately with linear stability theory and with previous numerical studies.

Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smooth particle hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Wenxiao; Daily, Michael D.; Baker, Nathan A.

2015-12-01

We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to an acetylcholinesterase monomer. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) boundary condition, is considered on the reactive boundaries. This new boundary condition treatment allows for the analysis of enzymes with "imperfect" reaction rates. Rates for inhibitor binding to mAChE are calculated atmore » various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.« less

Planet-disc interactions with Discontinuous Galerkin Methods using GPUs

NASA Astrophysics Data System (ADS)

Velasco Romero, David A.; Veiga, Maria Han; Teyssier, Romain; Masset, Frédéric S.

2018-05-01

We present a two-dimensional Cartesian code based on high order discontinuous Galerkin methods, implemented to run in parallel over multiple GPUs. A simple planet-disc setup is used to compare the behaviour of our code against the behaviour found using the FARGO3D code with a polar mesh. We make use of the time dependence of the torque exerted by the disc on the planet as a mean to quantify the numerical viscosity of the code. We find that the numerical viscosity of the Keplerian flow can be as low as a few 10-8r2Ω, r and Ω being respectively the local orbital radius and frequency, for fifth order schemes and resolution of ˜10-2r. Although for a single disc problem a solution of low numerical viscosity can be obtained at lower computational cost with FARGO3D (which is nearly an order of magnitude faster than a fifth order method), discontinuous Galerkin methods appear promising to obtain solutions of low numerical viscosity in more complex situations where the flow cannot be captured on a polar or spherical mesh concentric with the disc.

On some theoretical and practical aspects of multigrid methods. [to solve finite element systems from elliptic equations

NASA Technical Reports Server (NTRS)

Nicolaides, R. A.

1979-01-01

A description and explanation of a simple multigrid algorithm for solving finite element systems is given. Numerical results for an implementation are reported for a number of elliptic equations, including cases with singular coefficients and indefinite equations. The method shows the high efficiency, essentially independent of the grid spacing, predicted by the theory.

Nonlinear power spectrum from resummed perturbation theory: a leap beyond the BAO scale

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anselmi, Stefano; Pietroni, Massimo, E-mail: anselmi@ieec.uab.es, E-mail: massimo.pietroni@pd.infn.it

2012-12-01

A new computational scheme for the nonlinear cosmological matter power spectrum (PS) is presented. Our method is based on evolution equations in time, which can be cast in a form extremely convenient for fast numerical evaluations. A nonlinear PS is obtained in a time comparable to that needed for a simple 1-loop computation, and the numerical implementation is very simple. Our results agree with N-body simulations at the percent level in the BAO range of scales, and at the few-percent level up to k ≅ 1 h/Mpc at z∼>0.5, thereby opening the possibility of applying this tool to scales interestingmore » for weak lensing. We clarify the approximations inherent to this approach as well as its relations to previous ones, such as the Time Renormalization Group, and the multi-point propagator expansion. We discuss possible lines of improvements of the method and its intrinsic limitations by multi streaming at small scales and low redshifts.« less

Strain and vorticity analysis using small-scale faults and associated drag folds

NASA Astrophysics Data System (ADS)

Gomez-Rivas, Enrique; Bons, Paul D.; Griera, Albert; Carreras, Jordi; Druguet, Elena; Evans, Lynn

2007-12-01

Small-scale faults with associated drag folds in brittle-ductile rocks can retain detailed information on the kinematics and amount of deformation the host rock experienced. Measured fault orientation ( α), drag angle ( β) and the ratio of the thickness of deflected layers at the fault ( L) and further away ( T) can be compared with α, β and L/ T values that are calculated with a simple analytical model. Using graphs or a numerical best-fit routine, one can then determine the kinematic vorticity number and initial fault orientation that best fits the data. The proposed method was successfully tested on both analogue experiments and numerical simulations with BASIL. Using this method, a kinematic vorticity number of one (dextral simple shear) and a minimum finite strain of 2.5-3.8 was obtained for a population of antithetic faults with associated drag folds in a case study area at Mas Rabassers de Dalt on Cap de Creus in the Variscan of the easternmost Pyrenees, Spain.

Review of Thawing Time Prediction Models Depending
on Process Conditions and Product Characteristics

PubMed Central

Kluza, Franciszek; Spiess, Walter E. L.; Kozłowicz, Katarzyna

2016-01-01

Summary Determining thawing times of frozen foods is a challenging problem as the thermophysical properties of the product change during thawing. A number of calculation models and solutions have been developed. The proposed solutions range from relatively simple analytical equations based on a number of assumptions to a group of empirical approaches that sometimes require complex calculations. In this paper analytical, empirical and graphical models are presented and critically reviewed. The conditions of solution, limitations and possible applications of the models are discussed. The graphical and semi--graphical models are derived from numerical methods. Using the numerical methods is not always possible as running calculations takes time, whereas the specialized software and equipment are not always cheap. For these reasons, the application of analytical-empirical models is more useful for engineering. It is demonstrated that there is no simple, accurate and feasible analytical method for thawing time prediction. Consequently, simplified methods are needed for thawing time estimation of agricultural and food products. The review reveals the need for further improvement of the existing solutions or development of new ones that will enable accurate determination of thawing time within a wide range of practical conditions of heat transfer during processing. PMID:27904387

Eigenvalue assignment by minimal state-feedback gain in LTI multivariable systems

NASA Astrophysics Data System (ADS)

Ataei, Mohammad; Enshaee, Ali

2011-12-01

In this article, an improved method for eigenvalue assignment via state feedback in the linear time-invariant multivariable systems is proposed. This method is based on elementary similarity operations, and involves mainly utilisation of vector companion forms, and thus is very simple and easy to implement on a digital computer. In addition to the controllable systems, the proposed method can be applied for the stabilisable ones and also systems with linearly dependent inputs. Moreover, two types of state-feedback gain matrices can be achieved by this method: (1) the numerical one, which is unique, and (2) the parametric one, in which its parameters are determined in order to achieve a gain matrix with minimum Frobenius norm. The numerical examples are presented to demonstrate the advantages of the proposed method.

Field singularities at lossless metal-dielectric arbitrary-angle edges and their ramifications to the numerical modeling of gratings.

PubMed

Li, Lifeng

2012-04-01

I extend a previous work [J. Opt. Soc. Am. A, 738 (2011)] on field singularities at lossless metal-dielectric right-angle edges and their ramifications to the numerical modeling of gratings to the case of arbitrary metallic wedge angles. Simple criteria are given that allow one knowing the lossless permittivities and the arbitrary wedge angles to determine if the electric field at the edges is nonsingular, can be regularly singular, or can be irregularly singular without calculating the singularity exponent. Furthermore, the knowledge of the singularity type enables one to predict immediately if a numerical method that uses Fourier expansions of the transverse electric field components at the edges will converge or not without making any numerical tests. All conclusions of the previous work about the general relationships between field singularities, Fourier representation of singular fields, and convergence of numerical methods for modeling lossless metal-dielectric gratings have been reconfirmed.

Numerical noise prediction in fluid machinery

NASA Astrophysics Data System (ADS)

Pantle, Iris; Magagnato, Franco; Gabi, Martin

2005-09-01

Numerical methods successively became important in the design and optimization of fluid machinery. However, as noise emission is considered, one can hardly find standardized prediction methods combining flow and acoustical optimization. Several numerical field methods for sound calculations have been developed. Due to the complexity of the considered flow, approaches must be chosen to avoid exhaustive computing. In this contribution the noise of a simple propeller is investigated. The configurations of the calculations comply with an existing experimental setup chosen for evaluation. The used in-house CFD solver SPARC contains an acoustic module based on Ffowcs Williams-Hawkings Acoustic Analogy. From the flow results of the time dependent Large Eddy Simulation the time dependent acoustic sources are extracted and given to the acoustic module where relevant sound pressure levels are calculated. The difficulties, which arise while proceeding from open to closed rotors and from gas to liquid are discussed.

Two-way ANOVA Problems with Simple Numbers.

ERIC Educational Resources Information Center

Read, K. L. Q.; Shihab, L. H.

1998-01-01

Describes how to construct simple numerical examples in two-way ANOVAs, specifically randomized blocks, balanced two-way layouts, and Latin squares. Indicates that working through simple numerical problems is helpful to students meeting a technique for the first time and should be followed by computer-based analysis of larger, real datasets when…

Simple Numerical Analysis of Longboard Speedometer Data

ERIC Educational Resources Information Center

Hare, Jonathan

2013-01-01

Simple numerical data analysis is described, using a standard spreadsheet program, to determine distance, velocity (speed) and acceleration from voltage data generated by a skateboard/longboard speedometer (Hare 2012 "Phys. Educ." 47 409-17). This simple analysis is an introduction to data processing including scaling data as well as…

Numerical study of the shape parameter dependence of the local radial point interpolation method in linear elasticity.

PubMed

Moussaoui, Ahmed; Bouziane, Touria

2016-01-01

The method LRPIM is a Meshless method with properties of simple implementation of the essential boundary conditions and less costly than the moving least squares (MLS) methods. This method is proposed to overcome the singularity associated to polynomial basis by using radial basis functions. In this paper, we will present a study of a 2D problem of an elastic homogenous rectangular plate by using the method LRPIM. Our numerical investigations will concern the influence of different shape parameters on the domain of convergence,accuracy and using the radial basis function of the thin plate spline. It also will presents a comparison between numerical results for different materials and the convergence domain by precising maximum and minimum values as a function of distribution nodes number. The analytical solution of the deflection confirms the numerical results. The essential points in the method are: •The LRPIM is derived from the local weak form of the equilibrium equations for solving a thin elastic plate.•The convergence of the LRPIM method depends on number of parameters derived from local weak form and sub-domains.•The effect of distributions nodes number by varying nature of material and the radial basis function (TPS).

Making chaotic behavior in a damped linear harmonic oscillator

NASA Astrophysics Data System (ADS)

Konishi, Keiji

2001-06-01

The present Letter proposes a simple control method which makes chaotic behavior in a damped linear harmonic oscillator. This method is a modified scheme proposed in paper by Wang and Chen (IEEE CAS-I 47 (2000) 410) which presents an anti-control method for making chaotic behavior in discrete-time linear systems. We provide a systematic procedure to design parameters and sampling period of a feedback controller. Furthermore, we show that our method works well on numerical simulations.

Numerical Differentiation of Noisy, Nonsmooth Data

DOE PAGES

Chartrand, Rick

2011-01-01

We consider the problem of differentiating a function specified by noisy data. Regularizing the differentiation process avoids the noise amplification of finite-difference methods. We use total-variation regularization, which allows for discontinuous solutions. The resulting simple algorithm accurately differentiates noisy functions, including those which have a discontinuous derivative.

Spring constant of a tuning-fork sensor for dynamic force microscopy

PubMed Central

Lange, Manfred; Schmuck, Merlin; Schmidt, Nico; Möller, Rolf

2012-01-01

Summary We present an overview of experimental and numerical methods to determine the spring constant of a quartz tuning fork in qPlus configuration. The simple calculation for a rectangular cantilever is compared to the values obtained by the analysis of the thermal excitation and by the direct mechanical measurement of the force versus displacement. To elucidate the difference, numerical simulations were performed taking account of the real geometry including the glue that is used to mount the tuning fork. PMID:23365793

New developments in the method of space-time conservation element and solution element: Applications to the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1993-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods--i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to avoid several key limitations to the above traditional methods. An explicit model scheme for solving a simple 1-D unsteady convection-diffusion equation is constructed and used to illuminate major differences between the current method and those mentioned above. Unexpectedly, its amplification factors for the pure convection and pure diffusion cases are identical to those of the Leapfrog and the DuFort-Frankel schemes, respectively. Also, this explicit scheme and its Navier-Stokes extension have the unusual property that their stabilities are limited only by the CFL condition. Moreover, despite the fact that it does not use any flux-limiter or slope-limiter, the Navier-Stokes solver is capable of generating highly accurate shock tube solutions with shock discontinuities being resolved within one mesh interval. An accurate Euler solver also is constructed through another extension. It has many unusual properties, e.g., numerical diffusion at all mesh points can be controlled by a set of local parameters.

Free boundary skin current magnetohydrodynamic equilibria

NASA Astrophysics Data System (ADS)

Reusch, Michael F.

1988-10-01

Function theoretic methods in the complex plane are used to develop simple parametric hodograph formulas that generate sharp boundary equilibria of arbitrary shape. The related method of Gorenflo [Z. Angew. Math. Phys. 16, 279 (1965)] and Merkel (Ph.D. thesis, University of Munich, 1965) is discussed. A numerical technique for the construction of solutions, based on one of the methods, is presented. A study is made of the bifurcations of an equilibrium of general form.

Advantages of formulating an evolution equation directly for elastic distortional deformation in finite deformation plasticity

NASA Astrophysics Data System (ADS)

Rubin, M. B.; Cardiff, P.

2017-11-01

Simo (Comput Methods Appl Mech Eng 66:199-219, 1988) proposed an evolution equation for elastic deformation together with a constitutive equation for inelastic deformation rate in plasticity. The numerical algorithm (Simo in Comput Methods Appl Mech Eng 68:1-31, 1988) for determining elastic distortional deformation was simple. However, the proposed inelastic deformation rate caused plastic compaction. The corrected formulation (Simo in Comput Methods Appl Mech Eng 99:61-112, 1992) preserves isochoric plasticity but the numerical integration algorithm is complicated and needs special methods for calculation of the exponential map of a tensor. Alternatively, an evolution equation for elastic distortional deformation can be proposed directly with a simplified constitutive equation for inelastic distortional deformation rate. This has the advantage that the physics of inelastic distortional deformation is separated from that of dilatation. The example of finite deformation J2 plasticity with linear isotropic hardening is used to demonstrate the simplicity of the numerical algorithm.

K-means clustering for support construction in diffractive imaging.

PubMed

Hattanda, Shunsuke; Shioya, Hiroyuki; Maehara, Yosuke; Gohara, Kazutoshi

2014-03-01

A method for constructing an object support based on K-means clustering of the object-intensity distribution is newly presented in diffractive imaging. This releases the adjustment of unknown parameters in the support construction, and it is well incorporated with the Gerchberg and Saxton diagram. A simple numerical simulation reveals that the proposed method is effective for dynamically constructing the support without an initial prior support.

A simple and fast method for computing the relativistic Compton Scattering Kernel for radiative transfer

NASA Technical Reports Server (NTRS)

Kershaw, David S.; Prasad, Manoj K.; Beason, J. Douglas

1986-01-01

The Klein-Nishina differential cross section averaged over a relativistic Maxwellian electron distribution is analytically reduced to a single integral, which can then be rapidly evaluated in a variety of ways. A particularly fast method for numerically computing this single integral is presented. This is, to the authors' knowledge, the first correct computation of the Compton scattering kernel.

Confidence bands for measured economically optimal nitrogen rates

USDA-ARS?s Scientific Manuscript database

While numerous researchers have computed economically optimal N rate (EONR) values from measured yield – N rate data, nearly all have neglected to compute or estimate the statistical reliability of these EONR values. In this study, a simple method for computing EONR and its confidence bands is descr...

Current and state-of-the-art approaches for detecting mycotoxins in commodities

USDA-ARS?s Scientific Manuscript database

The tools that have been applied to detection of mycotoxins in commodities are numerous and powerful. These include everything from simple to use diagnostic test strips to complex, instrument intensive, methods such as ultra-high performance liquid chromatography-mass spectrometry (UPLC-MS). This wi...

The Instructional Cost Index. A Simplified Approach to Interinstitutional Cost Comparison.

ERIC Educational Resources Information Center

Beatty, George, Jr.; And Others

The paper describes a simple, yet effective method of computing a comparative index of instructional costs. The Instructional Cost Index identifies direct cost differentials among instructional programs. Cost differentials are described in terms of differences among numerical values of variables that reflect fundamental academic and resource…

A 1D radiative transfer benchmark with polarization via doubling and adding

NASA Astrophysics Data System (ADS)

Ganapol, B. D.

2017-11-01

Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic scattering in a 1D-slab medium with simple polarization. The 2-Stokes vector solution for the fully discretized radiative transfer equation in space and direction derives from the method of doubling and adding enhanced through convergence acceleration. Updates to benchmark solutions found in the literature to seven places for reflectance and transmittance as well as for angular flux follow. Finally, we conclude with the numerical solution in a partially randomly absorbing heterogeneous medium.

Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water flows in open channels

NASA Astrophysics Data System (ADS)

Qian, Shouguo; Li, Gang; Shao, Fengjing; Xing, Yulong

2018-05-01

We construct and study efficient high order discontinuous Galerkin methods for the shallow water flows in open channels with irregular geometry and a non-flat bottom topography in this paper. The proposed methods are well-balanced for the still water steady state solution, and can preserve the non-negativity of wet cross section numerically. The well-balanced property is obtained via a novel source term separation and discretization. A simple positivity-preserving limiter is employed to provide efficient and robust simulations near the wetting and drying fronts. Numerical examples are performed to verify the well-balanced property, the non-negativity of the wet cross section, and good performance for both continuous and discontinuous solutions.

Stochastic gradient ascent outperforms gamers in the Quantum Moves game

NASA Astrophysics Data System (ADS)

Sels, Dries

2018-04-01

In a recent work on quantum state preparation, Sørensen and co-workers [Nature (London) 532, 210 (2016), 10.1038/nature17620] explore the possibility of using video games to help design quantum control protocols. The authors present a game called "Quantum Moves" (https://www.scienceathome.org/games/quantum-moves/) in which gamers have to move an atom from A to B by means of optical tweezers. They report that, "players succeed where purely numerical optimization fails." Moreover, by harnessing the player strategies, they can "outperform the most prominent established numerical methods." The aim of this Rapid Communication is to analyze the problem in detail and show that those claims are untenable. In fact, without any prior knowledge and starting from a random initial seed, a simple stochastic local optimization method finds near-optimal solutions which outperform all players. Counterdiabatic driving can even be used to generate protocols without resorting to numeric optimization. The analysis results in an accurate analytic estimate of the quantum speed limit which, apart from zero-point motion, is shown to be entirely classical in nature. The latter might explain why gamers are reasonably good at the game. A simple modification of the BringHomeWater challenge is proposed to test this hypothesis.

Performance of some numerical Laplace inversion methods on American put option formula

NASA Astrophysics Data System (ADS)

Octaviano, I.; Yuniar, A. R.; Anisa, L.; Surjanto, S. D.; Putri, E. R. M.

2018-03-01

Numerical inversion approaches of Laplace transform is used to obtain a semianalytic solution. Some of the mathematical inversion methods such as Durbin-Crump, Widder, and Papoulis can be used to calculate American put options through the optimal exercise price in the Laplace space. The comparison of methods on some simple functions is aimed to know the accuracy and parameters which used in the calculation of American put options. The result obtained is the performance of each method regarding accuracy and computational speed. The Durbin-Crump method has an average error relative of 2.006e-004 with computational speed of 0.04871 seconds, the Widder method has an average error relative of 0.0048 with computational speed of 3.100181 seconds, and the Papoulis method has an average error relative of 9.8558e-004 with computational speed of 0.020793 seconds.

An Extended Lagrangian Method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1995-01-01

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the Lagrangian method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.

Optimized theory for simple and molecular fluids.

PubMed

Marucho, M; Montgomery Pettitt, B

2007-03-28

An optimized closure approximation for both simple and molecular fluids is presented. A smooth interpolation between Perkus-Yevick and hypernetted chain closures is optimized by minimizing the free energy self-consistently with respect to the interpolation parameter(s). The molecular version is derived from a refinement of the method for simple fluids. In doing so, a method is proposed which appropriately couples an optimized closure with the variant of the diagrammatically proper integral equation recently introduced by this laboratory [K. M. Dyer et al., J. Chem. Phys. 123, 204512 (2005)]. The simplicity of the expressions involved in this proposed theory has allowed the authors to obtain an analytic expression for the approximate excess chemical potential. This is shown to be an efficient tool to estimate, from first principles, the numerical value of the interpolation parameters defining the aforementioned closure. As a preliminary test, representative models for simple fluids and homonuclear diatomic Lennard-Jones fluids were analyzed, obtaining site-site correlation functions in excellent agreement with simulation data.

Simple method to set up low eccentricity initial data for moving puncture simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tichy, Wolfgang; Marronetti, Pedro

2011-01-15

We introduce two new eccentricity measures to analyze numerical simulations. Unlike earlier definitions these eccentricity measures do not involve any free parameters which makes them easy to use. We show how relatively inexpensive grid setups can be used to estimate the eccentricity during the early inspiral phase. Furthermore, we compare standard puncture data and post-Newtonian data in ADMTT gauge. We find that both use different coordinates. Thus low eccentricity initial momentum parameters for a certain separation measured in ADMTT coordinates are hard to use in puncture data, because it is not known how the separation in puncture coordinates is relatedmore » to the separation in ADMTT coordinates. As a remedy we provide a simple approach which allows us to iterate the momentum parameters until our numerical simulations result in acceptably low eccentricities.« less

Heat transfer coefficient of cryotop during freezing.

PubMed

Li, W J; Zhou, X L; Wang, H S; Liu, B L; Dai, J J

2013-01-01

Cryotop is an efficient vitrification method for cryopreservation of oocytes. It has been widely used owing to its simple operation and high freezing rate. Recently, the heat transfer performance of cryotop was studied by numerical simulation in several studies. However, the range of heat transfer coefficient in the simulation is uncertain. In this study, the heat transfer coefficient for cryotop during freezing process was analyzed. The cooling rates of 40 percent ethylene glycol (EG) droplet in cryotop during freezing were measured by ultra-fast measurement system and calculated by numerical simulation at different value of heat transfer coefficient. Compared with the results obtained by two methods, the range of the heat transfer coefficient necessary for the numerical simulation of cryotop was determined, which is between 9000 W/(m(2)·K) and 10000 W/(m (2)·K).

Numerical study of read scheme in one-selector one-resistor crossbar array

NASA Astrophysics Data System (ADS)

Kim, Sungho; Kim, Hee-Dong; Choi, Sung-Jin

2015-12-01

A comprehensive numerical circuit analysis of read schemes of a one selector-one resistance change memory (1S1R) crossbar array is carried out. Three schemes-the ground, V/2, and V/3 schemes-are compared with each other in terms of sensing margin and power consumption. Without the aid of a complex analytical approach or SPICE-based simulation, a simple numerical iteration method is developed to simulate entire current flows and node voltages within a crossbar array. Understanding such phenomena is essential in successfully evaluating the electrical specifications of selectors for suppressing intrinsic drawbacks of crossbar arrays, such as sneaky current paths and series line resistance problems. This method provides a quantitative tool for the accurate analysis of crossbar arrays and provides guidelines for developing an optimal read scheme, array configuration, and selector device specifications.

A study on the sensitivity of self-powered neutron detectors (SPNDs)

NASA Astrophysics Data System (ADS)

Lee, Wanno; Cho, Gyuseong; Kim, Kwanghyun; Kim, Hee Joon; choi, Yuseon; Park, Moon Chu; Kim, Soongpyung

2001-08-01

Self-powered neutron detectors (SPNDs) are widely used in reactors to monitor neutron flux, while they have several advantages such as small size, and relatively simple electronics required in conjunction with those usages, they have some intrinsic problems of the low level of output current-a slow response time and the rapid change of sensitivity-that make it difficult to use for a long term. Monte Carlo simulation was used to calculate the escape probability as a function of the birth position of emitted beta particle for geometry of rhodium-based SPNDs. A simple numerical method calculated the initial generation rate of beta particles and the change of generation rate due to rhodium burnup. Using results of the simulation and the simple numerical method, the burnup profile of rhodium number density and the neutron sensitivity were calculated as a function of burnup time in reactors. This method was verified by the comparison of this and other papers, and data of YGN3.4 (Young Gwang Nuclear plant 3, 4) about the initial sensitivity. In addition, for improvement of some properties of rhodium-based SPNDs, which are currently used, a modified geometry is proposed. The proposed geometry, which is tube-type, is able to increase the initial sensitivity due to increase of the escape probability. The escape probability was calculated by changing the thickness of the insulator and compared solid-type with tube-type about each insulator thickness. The method used here can be applied to the analysis and design of other types of SPNDs.

A simplified design of the staggered herringbone micromixer for practical applications

PubMed Central

Du, Yan; Zhang, Zhiyi; Yim, ChaeHo; Lin, Min; Cao, Xudong

2010-01-01

We demonstrated a simple method for the device design of a staggered herringbone micromixer (SHM) using numerical simulation. By correlating the simulated concentrations with channel length, we obtained a series of concentration versus channel length profiles, and used mixing completion length Lm as the only parameter to evaluate the performance of device structure on mixing. Fluorescence quenching experiments were subsequently conducted to verify the optimized SHM structure for a specific application. Good agreement was found between the optimization and the experimental data. Since Lm is straightforward, easily defined and calculated parameter for characterization of mixing performance, this method for designing micromixers is simple and effective for practical applications. PMID:20697584

A simplified design of the staggered herringbone micromixer for practical applications.

PubMed

Du, Yan; Zhang, Zhiyi; Yim, Chaeho; Lin, Min; Cao, Xudong

2010-05-07

We demonstrated a simple method for the device design of a staggered herringbone micromixer (SHM) using numerical simulation. By correlating the simulated concentrations with channel length, we obtained a series of concentration versus channel length profiles, and used mixing completion length L(m) as the only parameter to evaluate the performance of device structure on mixing. Fluorescence quenching experiments were subsequently conducted to verify the optimized SHM structure for a specific application. Good agreement was found between the optimization and the experimental data. Since L(m) is straightforward, easily defined and calculated parameter for characterization of mixing performance, this method for designing micromixers is simple and effective for practical applications.

Self-Care for Nurse Leaders in Acute Care Environment Reduces Perceived Stress: A Mixed-Methods Pilot Study Merits Further Investigation.

PubMed

Dyess, Susan Mac Leod; Prestia, Angela S; Marquit, Doren-Elyse; Newman, David

2018-03-01

Acute care practice settings are stressful. Nurse leaders face stressful demands of numerous competing priorities. Some nurse leaders experience unmanageable stress, but success requires self-care. This article presents a repeated measures intervention design study using mixed methods to investigate a self-care simple meditation practice for nurse leaders. Themes and subthemes emerged in association with the three data collection points: at baseline (pretest), after 6 weeks, and after 12 weeks (posttest) from introduction of the self-care simple meditation practice. An analysis of variance yielded a statistically significant drop in perceived stress at 6 weeks and again at 12 weeks. Conducting future research is merited.

Analysis of Discontinuities in a Rectangular Waveguide Using Dyadic Green's Function Approach in Conjunction with Method of Moments

NASA Technical Reports Server (NTRS)

Deshpande, M. D.

1997-01-01

The dyadic Green's function for an electric current source placed in a rectangular waveguide is derived using a magnetic vector potential approach. A complete solution for the electric and magnetic fields including the source location is obtained by simple differentiation of the vector potential around the source location. The simple differentiation approach which gives electric and magnetic fields identical to an earlier derivation is overlooked by the earlier workers in the derivation of the dyadic Green's function particularly around the source location. Numerical results obtained using the Green's function approach are compared with the results obtained using the Finite Element Method (FEM).

Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions

DOE PAGES

Lloyd, Jeffrey T.; Clayton, John D.; Austin, Ryan A.; ...

2015-07-10

Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes themore » rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide insight into the shock structure afforded by the numerical methods.« less

Design of ground test suspension systems for verification of flexible space structures

NASA Technical Reports Server (NTRS)

Cooley, V. M.; Juang, J. N.; Ghaemmaghami, P.

1988-01-01

A simple model demonstrates the frequency-increasing effects of a simple cable suspension on flexible test article/suspension systems. Two passive suspension designs, namely a negative spring mechanism and a rolling cart mechanism, are presented to alleviate the undesirable frequency-increasing effects. Analysis methods are provided for systems in which the augmentations are applied to both discrete and continuous representations of test articles. The damping analyses are based on friction equivalent viscous damping. Numerical examples are given for comparing the two augmentations with respect to minimizing frequency and damping increases.

Robust numerical solution of the reservoir routing equation

NASA Astrophysics Data System (ADS)

Fiorentini, Marcello; Orlandini, Stefano

2013-09-01

The robustness of numerical methods for the solution of the reservoir routing equation is evaluated. The methods considered in this study are: (1) the Laurenson-Pilgrim method, (2) the fourth-order Runge-Kutta method, and (3) the fixed order Cash-Karp method. Method (1) is unable to handle nonmonotonic outflow rating curves. Method (2) is found to fail under critical conditions occurring, especially at the end of inflow recession limbs, when large time steps (greater than 12 min in this application) are used. Method (3) is computationally intensive and it does not solve the limitations of method (2). The limitations of method (2) can be efficiently overcome by reducing the time step in the critical phases of the simulation so as to ensure that water level remains inside the domains of the storage function and the outflow rating curve. The incorporation of a simple backstepping procedure implementing this control into the method (2) yields a robust and accurate reservoir routing method that can be safely used in distributed time-continuous catchment models.

Numerical and Experimental Studies on Impact Loaded Concrete Structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saarenheimo, Arja; Hakola, Ilkka; Karna, Tuomo

2006-07-01

An experimental set-up has been constructed for medium scale impact tests. The main objective of this effort is to provide data for the calibration and verification of numerical models of a loading scenario where an aircraft impacts against a nuclear power plant. One goal is to develop and take in use numerical methods for predicting response of reinforced concrete structures to impacts of deformable projectiles that may contain combustible liquid ('fuel'). Loading, structural behaviour, like collapsing mechanism and the damage grade, will be predicted by simple analytical methods and using non-linear FE-method. In the so-called Riera method the behavior ofmore » the missile material is assumed to be rigid plastic or rigid visco-plastic. Using elastic plastic and elastic visco-plastic material models calculations are carried out by ABAQUS/Explicit finite element code, assuming axisymmetric deformation mode for the missile. With both methods, typically, the impact force time history, the velocity of the missile rear end and the missile shortening during the impact were recorded for comparisons. (authors)« less

Comparison of the convolution quadrature method and enhanced inverse FFT with application in elastodynamic boundary element method

NASA Astrophysics Data System (ADS)

Schanz, Martin; Ye, Wenjing; Xiao, Jinyou

2016-04-01

Transient problems can often be solved with transformation methods, where the inverse transformation is usually performed numerically. Here, the discrete Fourier transform in combination with the exponential window method is compared with the convolution quadrature method formulated as inverse transformation. Both are inverse Laplace transforms, which are formally identical but use different complex frequencies. A numerical study is performed, first with simple convolution integrals and, second, with a boundary element method (BEM) for elastodynamics. Essentially, when combined with the BEM, the discrete Fourier transform needs less frequency calculations, but finer mesh compared to the convolution quadrature method to obtain the same level of accuracy. If further fast methods like the fast multipole method are used to accelerate the boundary element method the convolution quadrature method is better, because the iterative solver needs much less iterations to converge. This is caused by the larger real part of the complex frequencies necessary for the calculation, which improves the conditions of system matrix.

Advances in Optical Fiber-Based Faraday Rotation Diagnostics

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, A D; McHale, G B; Goerz, D A

2009-07-27

In the past two years, we have used optical fiber-based Faraday Rotation Diagnostics (FRDs) to measure pulsed currents on several dozen capacitively driven and explosively driven pulsed power experiments. We have made simplifications to the necessary hardware for quadrature-encoded polarization analysis, including development of an all-fiber analysis scheme. We have developed a numerical model that is useful for predicting and quantifying deviations from the ideal diagnostic response. We have developed a method of analyzing quadrature-encoded FRD data that is simple to perform and offers numerous advantages over several existing methods. When comparison has been possible, we have seen good agreementmore » with our FRDs and other current sensors.« less

Numerical Simulation of the Detonation of Condensed Explosives

NASA Astrophysics Data System (ADS)

Wang, Cheng; Ye, Ting; Ning, Jianguo

Detonation process of a condensed explosive was simulated using a finite difference method. Euler equations were applied to describe the detonation flow field, an ignition and growth model for the chemical reaction and Jones-Wilkins-Lee (JWL) equations of state for the state of explosives and detonation products. Based on the simple mixture rule that assumes the reacting explosives to be a mixture of the reactant and product components, 1D and 2D codes were developed to simulate the detonation process of high explosive PBX9404. The numerical results are in good agreement with the experimental results, which demonstrates that the finite difference method, mixture rule and chemical reaction proposed in this paper are adequate and feasible.

Mathematical, Constitutive and Numerical Modelling of Catastrophic Landslides and Related Phenomena

NASA Astrophysics Data System (ADS)

Pastor, M.; Fernández Merodo, J. A.; Herreros, M. I.; Mira, P.; González, E.; Haddad, B.; Quecedo, M.; Tonni, L.; Drempetic, V.

2008-02-01

Mathematical and numerical models are a fundamental tool for predicting the behaviour of geostructures and their interaction with the environment. The term “mathematical model” refers to a mathematical description of the more relevant physical phenomena which take place in the problem being analyzed. It is indeed a wide area including models ranging from the very simple ones for which analytical solutions can be obtained to those more complicated requiring the use of numerical approximations such as the finite element method. During the last decades, mathematical, constitutive and numerical models have been very much improved and today their use is widespread both in industry and in research. One special case is that of fast catastrophic landslides, for which simplified methods are not able to provide accurate solutions in many occasions. Moreover, many finite element codes cannot be applied for propagation of the mobilized mass. The purpose of this work is to present an overview of the different alternative mathematical and numerical models which can be applied to both the initiation and propagation mechanisms of fast catastrophic landslides and other related problems such as waves caused by landslides.

A Materials Index--Its Storage, Retrieval, and Display

ERIC Educational Resources Information Center

Rosen, Carol Z.

1973-01-01

An experimental procedure for indexing physical materials based on simple syntactical rules was tested by encoding the materials in the journal, Applied Physics Letters,'' to produce a materials index. The syntax and numerous examples together with an indication of the method by which retrieval can be effected are presented. (5 references)…

Critical assessment of jet erosion test methodologies for cohesive soil and sediment

USDA-ARS?s Scientific Manuscript database

The submerged Jet Erosion Test (JET) is a commonly used technique to assess the erodibility of cohesive soil. Employing a linear excess shear stress equation and impinging jet theory, simple numerical methods have been developed to analyze data collected using a JET to determine the critical shear s...

Mathematical modelling of risk reduction in reinsurance

NASA Astrophysics Data System (ADS)

Balashov, R. B.; Kryanev, A. V.; Sliva, D. E.

2017-01-01

The paper presents a mathematical model of efficient portfolio formation in the reinsurance markets. The presented approach provides the optimal ratio between the expected value of return and the risk of yield values below a certain level. The uncertainty in the return values is conditioned by use of expert evaluations and preliminary calculations, which result in expected return values and the corresponding risk levels. The proposed method allows for implementation of computationally simple schemes and algorithms for numerical calculation of the numerical structure of the efficient portfolios of reinsurance contracts of a given insurance company.

Alternating Direction Implicit (ADI) schemes for a PDE-based image osmosis model

NASA Astrophysics Data System (ADS)

Calatroni, L.; Estatico, C.; Garibaldi, N.; Parisotto, S.

2017-10-01

We consider Alternating Direction Implicit (ADI) splitting schemes to compute efficiently the numerical solution of the PDE osmosis model considered by Weickert et al. in [10] for several imaging applications. The discretised scheme is shown to preserve analogous properties to the continuous model. The dimensional splitting strategy traduces numerically into the solution of simple tridiagonal systems for which standard matrix factorisation techniques can be used to improve upon the performance of classical implicit methods, even for large time steps. Applications to the shadow removal problem are presented.

(N+1)-dimensional fractional reduced differential transform method for fractional order partial differential equations

NASA Astrophysics Data System (ADS)

Arshad, Muhammad; Lu, Dianchen; Wang, Jun

2017-07-01

In this paper, we pursue the general form of the fractional reduced differential transform method (DTM) to (N+1)-dimensional case, so that fractional order partial differential equations (PDEs) can be resolved effectively. The most distinct aspect of this method is that no prescribed assumptions are required, and the huge computational exertion is reduced and round-off errors are also evaded. We utilize the proposed scheme on some initial value problems and approximate numerical solutions of linear and nonlinear time fractional PDEs are obtained, which shows that the method is highly accurate and simple to apply. The proposed technique is thus an influential technique for solving the fractional PDEs and fractional order problems occurring in the field of engineering, physics etc. Numerical results are obtained for verification and demonstration purpose by using Mathematica software.

Representing ductile damage with the dual domain material point method

DOE PAGES

Long, C. C.; Zhang, D. Z.; Bronkhorst, C. A.; ...

2015-12-14

In this study, we incorporate a ductile damage material model into a computational framework based on the Dual Domain Material Point (DDMP) method. As an example, simulations of a flyer plate experiment involving ductile void growth and material failure are performed. The results are compared with experiments performed on high purity tantalum. We also compare the numerical results obtained from the DDMP method with those obtained from the traditional Material Point Method (MPM). Effects of an overstress model, artificial viscosity, and physical viscosity are investigated. Our results show that a physical bulk viscosity and overstress model are important in thismore » impact and failure problem, while physical shear viscosity and artificial shock viscosity have negligible effects. A simple numerical procedure with guaranteed convergence is introduced to solve for the equilibrium plastic state from the ductile damage model.« less

Prediction and measurements of vibrations from a railway track lying on a peaty ground

NASA Astrophysics Data System (ADS)

Picoux, B.; Rotinat, R.; Regoin, J. P.; Le Houédec, D.

2003-10-01

This paper introduces a two-dimensional model for the response of the ground surface due to vibrations generated by a railway traffic. A semi-analytical wave propagation model is introduced which is subjected to a set of harmonic moving loads and based on a calculation method of the dynamic stiffness matrix of the ground. In order to model a complete railway system, the effect of a simple track model is taken into account including rails, sleepers and ballast especially designed for the study of low vibration frequencies. The priority has been given to a simple formulation based on the principle of spatial Fourier transforms compatible with good numerical efficiency and yet providing quick solutions. In addition, in situ measurements for a soft soil near a railway track were carried out and will be used to validate the numerical implementation. The numerical and experimental results constitute a significant body of useful data to, on the one hand, characterize the response of the environment of tracks and, on the other hand, appreciate the importance of the speed and weight on the behaviour of the structure.

Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smoothed particle hydrodynamics

DOE PAGES

Pan, Wenxiao; Daily, Michael; Baker, Nathan A.

2015-05-07

Background: The calculation of diffusion-controlled ligand binding rates is important for understanding enzyme mechanisms as well as designing enzyme inhibitors. Methods: We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) BC, is considered on the reactive boundaries. This new BC treatment allows for the analysis of enzymes with “imperfect” reaction rates. Results: The numerical method is first verified in simple systems and thenmore » applied to the calculation of ligand binding to a mouse acetylcholinesterase (mAChE) monomer. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Conclusions: Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.« less

Boby-Vortex Interaction, Sound Generation and Destructive Interference

NASA Technical Reports Server (NTRS)

Kao, Hsiao C.

2000-01-01

It is generally recognized that interaction of vortices with downstream blades is a major source of noise production. To analyze this problem numerically, a two-dimensional model of inviscid flow together with the method of matched asymptotic expansions is proposed. The method of matched asymptotic expansions is used to match the inner region of incompressible flow to the outer region of compressible flow. Because of incompressibility, relatively simple numerical methods are available to treat multiple vortices and multiple bodies of arbitrary shape. Disturbances from vortices and bodies propagate outward as sound waves. Due to their interactions, either constructive or destructive interference may result. When it is destructive, the combined sound intensity can be reduced, sometimes substantially. In addition, an analytical solution to sound generation by the cascade-vonex interaction is given.

A fast numerical scheme for causal relativistic hydrodynamics with dissipation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Takamoto, Makoto, E-mail: takamoto@tap.scphys.kyoto-u.ac.jp; Inutsuka, Shu-ichiro

2011-08-01

Highlights: {yields} We have developed a new multi-dimensional numerical scheme for causal relativistic hydrodynamics with dissipation. {yields} Our new scheme can calculate the evolution of dissipative relativistic hydrodynamics faster and more effectively than existing schemes. {yields} Since we use the Riemann solver for solving the advection steps, our method can capture shocks very accurately. - Abstract: In this paper, we develop a stable and fast numerical scheme for relativistic dissipative hydrodynamics based on Israel-Stewart theory. Israel-Stewart theory is a stable and causal description of dissipation in relativistic hydrodynamics although it includes relaxation process with the timescale for collision of constituentmore » particles, which introduces stiff equations and makes practical numerical calculation difficult. In our new scheme, we use Strang's splitting method, and use the piecewise exact solutions for solving the extremely short timescale problem. In addition, since we split the calculations into inviscid step and dissipative step, Riemann solver can be used for obtaining numerical flux for the inviscid step. The use of Riemann solver enables us to capture shocks very accurately. Simple numerical examples are shown. The present scheme can be applied to various high energy phenomena of astrophysics and nuclear physics.« less

On the Numerical Formulation of Parametric Linear Fractional Transformation (LFT) Uncertainty Models for Multivariate Matrix Polynomial Problems

NASA Technical Reports Server (NTRS)

Belcastro, Christine M.

1998-01-01

Robust control system analysis and design is based on an uncertainty description, called a linear fractional transformation (LFT), which separates the uncertain (or varying) part of the system from the nominal system. These models are also useful in the design of gain-scheduled control systems based on Linear Parameter Varying (LPV) methods. Low-order LFT models are difficult to form for problems involving nonlinear parameter variations. This paper presents a numerical computational method for constructing and LFT model for a given LPV model. The method is developed for multivariate polynomial problems, and uses simple matrix computations to obtain an exact low-order LFT representation of the given LPV system without the use of model reduction. Although the method is developed for multivariate polynomial problems, multivariate rational problems can also be solved using this method by reformulating the rational problem into a polynomial form.

Moving microphone arrays to reduce spatial aliasing in the beamforming technique: theoretical background and numerical investigation.

PubMed

Cigada, Alfredo; Lurati, Massimiliano; Ripamonti, Francesco; Vanali, Marcello

2008-12-01

This paper introduces a measurement technique aimed at reducing or possibly eliminating the spatial aliasing problem in the beamforming technique. Beamforming main disadvantages are a poor spatial resolution, at low frequency, and the spatial aliasing problem, at higher frequency, leading to the identification of false sources. The idea is to move the microphone array during the measurement operation. In this paper, the proposed approach is theoretically and numerically investigated by means of simple sound propagation models, proving its efficiency in reducing the spatial aliasing. A number of different array configurations are numerically investigated together with the most important parameters governing this measurement technique. A set of numerical results concerning the case of a planar rotating array is shown, together with a first experimental validation of the method.

Novel numerical and graphical representation of DNA sequences and proteins.

PubMed

Randić, M; Novic, M; Vikić-Topić, D; Plavsić, D

2006-12-01

We have introduced novel numerical and graphical representations of DNA, which offer a simple and unique characterization of DNA sequences. The numerical representation of a DNA sequence is given as a sequence of real numbers derived from a unique graphical representation of the standard genetic code. There is no loss of information on the primary structure of a DNA sequence associated with this numerical representation. The novel representations are illustrated with the coding sequences of the first exon of beta-globin gene of half a dozen species in addition to human. The method can be extended to proteins as is exemplified by humanin, a 24-aa peptide that has recently been identified as a specific inhibitor of neuronal cell death induced by familial Alzheimer's disease mutant genes.

An acoustic-convective splitting-based approach for the Kapila two-phase flow model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eikelder, M.F.P. ten, E-mail: m.f.p.teneikelder@tudelft.nl; Eindhoven University of Technology, Department of Mathematics and Computer Science, P.O. Box 513, 5600 MB Eindhoven; Daude, F.

In this paper we propose a new acoustic-convective splitting-based numerical scheme for the Kapila five-equation two-phase flow model. The splitting operator decouples the acoustic waves and convective waves. The resulting two submodels are alternately numerically solved to approximate the solution of the entire model. The Lagrangian form of the acoustic submodel is numerically solved using an HLLC-type Riemann solver whereas the convective part is approximated with an upwind scheme. The result is a simple method which allows for a general equation of state. Numerical computations are performed for standard two-phase shock tube problems. A comparison is made with a non-splittingmore » approach. The results are in good agreement with reference results and exact solutions.« less

Fast sweeping method for the factored eikonal equation

NASA Astrophysics Data System (ADS)

Fomel, Sergey; Luo, Songting; Zhao, Hongkai

2009-09-01

We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss-Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss-Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jing Yanfei, E-mail: yanfeijing@uestc.edu.c; Huang Tingzhu, E-mail: tzhuang@uestc.edu.c; Duan Yong, E-mail: duanyong@yahoo.c

This study is mainly focused on iterative solutions with simple diagonal preconditioning to two complex-valued nonsymmetric systems of linear equations arising from a computational chemistry model problem proposed by Sherry Li of NERSC. Numerical experiments show the feasibility of iterative methods to some extent when applied to the problems and reveal the competitiveness of our recently proposed Lanczos biconjugate A-orthonormalization methods to other classic and popular iterative methods. By the way, experiment results also indicate that application specific preconditioners may be mandatory and required for accelerating convergence.

Numerical approach for ECT by using boundary element method with Laplace transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Enokizono, M.; Todaka, T.; Shibao, K.

1997-03-01

This paper presents an inverse analysis by using BEM with Laplace transform. The method is applied to a simple problem in the eddy current testing (ECT). Some crack shapes in a conductive specimen are estimated from distributions of the transient eddy current on its sensing surface and magnetic flux density in the liftoff space. Because the transient behavior includes information on various frequency components, the method is applicable to the shape estimation of a comparative small crack.

Engineering topological edge states in two dimensional magnetic photonic crystal

NASA Astrophysics Data System (ADS)

Yang, Bing; Wu, Tong; Zhang, Xiangdong

2017-01-01

Based on a perturbative approach, we propose a simple and efficient method to engineer the topological edge states in two dimensional magnetic photonic crystals. The topological edge states in the microstructures can be constructed and varied by altering the parameters of the microstructure according to the field-energy distributions of the Bloch states at the related Bloch wave vectors. The validity of the proposed method has been demonstrated by exact numerical calculations through three concrete examples. Our method makes the topological edge states "designable."

Spectral editing of weakly coupled spins using variable flip angles in PRESS constant echo time difference spectroscopy: Application to GABA

NASA Astrophysics Data System (ADS)

Snyder, Jeff; Hanstock, Chris C.; Wilman, Alan H.

2009-10-01

A general in vivo magnetic resonance spectroscopy editing technique is presented to detect weakly coupled spin systems through subtraction, while preserving singlets through addition, and is applied to the specific brain metabolite γ-aminobutyric acid (GABA) at 4.7 T. The new method uses double spin echo localization (PRESS) and is based on a constant echo time difference spectroscopy approach employing subtraction of two asymmetric echo timings, which is normally only applicable to strongly coupled spin systems. By utilizing flip angle reduction of one of the two refocusing pulses in the PRESS sequence, we demonstrate that this difference method may be extended to weakly coupled systems, thereby providing a very simple yet effective editing process. The difference method is first illustrated analytically using a simple two spin weakly coupled spin system. The technique was then demonstrated for the 3.01 ppm resonance of GABA, which is obscured by the strong singlet peak of creatine in vivo. Full numerical simulations, as well as phantom and in vivo experiments were performed. The difference method used two asymmetric PRESS timings with a constant total echo time of 131 ms and a reduced 120° final pulse, providing 25% GABA yield upon subtraction compared to two short echo standard PRESS experiments. Phantom and in vivo results from human brain demonstrate efficacy of this method in agreement with numerical simulations.

A simple iterative independent component analysis algorithm for vibration source signal identification of complex structures

NASA Astrophysics Data System (ADS)

Lee, Dong-Sup; Cho, Dae-Seung; Kim, Kookhyun; Jeon, Jae-Jin; Jung, Woo-Jin; Kang, Myeng-Hwan; Kim, Jae-Ho

2015-01-01

Independent Component Analysis (ICA), one of the blind source separation methods, can be applied for extracting unknown source signals only from received signals. This is accomplished by finding statistical independence of signal mixtures and has been successfully applied to myriad fields such as medical science, image processing, and numerous others. Nevertheless, there are inherent problems that have been reported when using this technique: instability and invalid ordering of separated signals, particularly when using a conventional ICA technique in vibratory source signal identification of complex structures. In this study, a simple iterative algorithm of the conventional ICA has been proposed to mitigate these problems. The proposed method to extract more stable source signals having valid order includes an iterative and reordering process of extracted mixing matrix to reconstruct finally converged source signals, referring to the magnitudes of correlation coefficients between the intermediately separated signals and the signals measured on or nearby sources. In order to review the problems of the conventional ICA technique and to validate the proposed method, numerical analyses have been carried out for a virtual response model and a 30 m class submarine model. Moreover, in order to investigate applicability of the proposed method to real problem of complex structure, an experiment has been carried out for a scaled submarine mockup. The results show that the proposed method could resolve the inherent problems of a conventional ICA technique.

Rating of Dynamic Coefficient for Simple Beam Bridge Design on High-Speed Railways

NASA Astrophysics Data System (ADS)

Diachenko, Leonid; Benin, Andrey; Smirnov, Vladimir; Diachenko, Anastasia

2018-06-01

The aim of the work is to improve the methodology for the dynamic computation of simple beam spans during the impact of high-speed trains. Mathematical simulation utilizing numerical and analytical methods of structural mechanics is used in the research. The article analyses parameters of the effect of high-speed trains on simple beam spanning bridge structures and suggests a technique of determining of the dynamic index to the live load. Reliability of the proposed methodology is confirmed by results of numerical simulation of high-speed train passage over spans with different speeds. The proposed algorithm of dynamic computation is based on a connection between maximum acceleration of the span in the resonance mode of vibrations and the main factors of stress-strain state. The methodology allows determining maximum and also minimum values of the main efforts in the construction that makes possible to perform endurance tests. It is noted that dynamic additions for the components of the stress-strain state (bending moments, transverse force and vertical deflections) are different. This condition determines the necessity for differentiated approach to evaluation of dynamic coefficients performing design verification of I and II groups of limiting state. The practical importance: the methodology of determining the dynamic coefficients allows making dynamic calculation and determining the main efforts in split beam spans without numerical simulation and direct dynamic analysis that significantly reduces the labour costs for design.

Thermal radiation characteristics of nonisothermal cylindrical enclosures using a numerical ray tracing technique

NASA Technical Reports Server (NTRS)

Baumeister, Joseph F.

1990-01-01

Analysis of energy emitted from simple or complex cavity designs can lead to intricate solutions due to nonuniform radiosity and irradiation within a cavity. A numerical ray tracing technique was applied to simulate radiation propagating within and from various cavity designs. To obtain the energy balance relationships between isothermal and nonisothermal cavity surfaces and space, the computer code NEVADA was utilized for its statistical technique applied to numerical ray tracing. The analysis method was validated by comparing results with known theoretical and limiting solutions, and the electrical resistance network method. In general, for nonisothermal cavities the performance (apparent emissivity) is a function of cylinder length-to-diameter ratio, surface emissivity, and cylinder surface temperatures. The extent of nonisothermal conditions in a cylindrical cavity significantly affects the overall cavity performance. Results are presented over a wide range of parametric variables for use as a possible design reference.

The Space-Time Conservation Element and Solution Element Method-A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws. 2; Numerical Simulation of Shock Waves and Contact Discontinuities

NASA Technical Reports Server (NTRS)

Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung

1998-01-01

Without resorting to special treatment for each individual test case, the 1D and 2D CE/SE shock-capturing schemes described previously (in Part I) are used to simulate flows involving phenomena such as shock waves, contact discontinuities, expansion waves and their interactions. Five 1D and six 2D problems are considered to examine the capability and robustness of these schemes. Despite their simple logical structures and low computational cost (for the 2D CE/SE shock-capturing scheme, the CPU time is about 2 micro-secs per mesh point per marching step on a Cray C90 machine), the numerical results, when compared with experimental data, exact solutions or numerical solutions by other methods, indicate that these schemes can accurately resolve shock and contact discontinuities consistently.

Comment on “Symplectic integration of magnetic systems”: A proof that the Boris algorithm is not variational

DOE PAGES

Ellison, C. L.; Burby, J. W.; Qin, H.

2015-11-01

One popular technique for the numerical time advance of charged particles interacting with electric and magnetic fields according to the Lorentz force law [1], [2], [3] and [4] is the Boris algorithm. Its popularity stems from simple implementation, rapid iteration, and excellent long-term numerical fidelity [1] and [5]. Excellent long-term behavior strongly suggests the numerical dynamics exhibit conservation laws analogous to those governing the continuous Lorentz force system [6]. Moreover, without conserved quantities to constrain the numerical dynamics, algorithms typically dissipate or accumulate important observables such as energy and momentum over long periods of simulated time [6]. Identification of themore » conservative properties of an algorithm is important for establishing rigorous expectations on the long-term behavior; energy-preserving, symplectic, and volume-preserving methods each have particular implications for the qualitative numerical behavior [6], [7], [8], [9], [10] and [11].« less

New method for the extraction of bulk channel mobility and flat-band voltage in junctionless transistors

NASA Astrophysics Data System (ADS)

Jeon, Dae-Young; Park, So Jeong; Mouis, Mireille; Barraud, Sylvain; Kim, Gyu-Tae; Ghibaudo, Gérard

2013-11-01

A new and simple method for the extraction of electrical parameters in junctionless transistors (JLTs) is presented. The bulk channel mobility (μbulk) and flat-band voltage (Vfb) were successfully extracted from the new method, based on a linear dependence between the inverse of transconductance squared (1/gm2) vs gate voltage in the partially depleted operation regime (Vth < Vg < Vfb). The validity of the new method is also proved by 2D numerical simulation and newly defined Maserjian's-like function for gm of JLT devices.

Gradient optimization and nonlinear control

NASA Technical Reports Server (NTRS)

Hasdorff, L.

1976-01-01

The book represents an introduction to computation in control by an iterative, gradient, numerical method, where linearity is not assumed. The general language and approach used are those of elementary functional analysis. The particular gradient method that is emphasized and used is conjugate gradient descent, a well known method exhibiting quadratic convergence while requiring very little more computation than simple steepest descent. Constraints are not dealt with directly, but rather the approach is to introduce them as penalty terms in the criterion. General conjugate gradient descent methods are developed and applied to problems in control.

The meshless local Petrov-Galerkin method based on moving Kriging interpolation for solving the time fractional Navier-Stokes equations.

PubMed

Thamareerat, N; Luadsong, A; Aschariyaphotha, N

2016-01-01

In this paper, we present a numerical scheme used to solve the nonlinear time fractional Navier-Stokes equations in two dimensions. We first employ the meshless local Petrov-Galerkin (MLPG) method based on a local weak formulation to form the system of discretized equations and then we will approximate the time fractional derivative interpreted in the sense of Caputo by a simple quadrature formula. The moving Kriging interpolation which possesses the Kronecker delta property is applied to construct shape functions. This research aims to extend and develop further the applicability of the truly MLPG method to the generalized incompressible Navier-Stokes equations. Two numerical examples are provided to illustrate the accuracy and efficiency of the proposed algorithm. Very good agreement between the numerically and analytically computed solutions can be observed in the verification. The present MLPG method has proved its efficiency and reliability for solving the two-dimensional time fractional Navier-Stokes equations arising in fluid dynamics as well as several other problems in science and engineering.

An immersed boundary method for simulating vesicle dynamics in three dimensions

NASA Astrophysics Data System (ADS)

Seol, Yunchang; Hu, Wei-Fan; Kim, Yongsam; Lai, Ming-Chih

2016-10-01

We extend our previous immersed boundary (IB) method for 3D axisymmetric inextensible vesicle in Navier-Stokes flows (Hu et al., 2014 [17]) to general three dimensions. Despite a similar spirit in numerical algorithms to the axisymmetric case, the fully 3D numerical implementation is much more complicated and is far from straightforward. A vesicle membrane surface is known to be incompressible and exhibits bending resistance. As in 3D axisymmetric case, instead of keeping the vesicle locally incompressible, we adopt a modified elastic tension energy to make the vesicle surface patch nearly incompressible so that solving the unknown tension (Lagrange multiplier for the incompressible constraint) can be avoided. Nevertheless, the new elastic force derived from the modified tension energy has exactly the same mathematical form as the original one except the different definitions of tension. The vesicle surface is discretized on a triangular mesh where the elastic tension and bending force are calculated on each vertex (Lagrangian marker in the IB method) of the triangulation. A series of numerical tests on the present scheme are conducted to illustrate the robustness and applicability of the method. We perform the convergence study for the immersed boundary forces and the fluid velocity field. We then study the vesicle dynamics in various flows such as quiescent, simple shear, and gravitational flows. Our numerical results show good agreements with those obtained in previous theoretical, experimental and numerical studies.

Visual conspicuity: a new simple standard, its reliability, validity and applicability.

PubMed

Wertheim, A H

2010-03-01

A general standard for quantifying conspicuity is described. It derives from a simple and easy method to quantitatively measure the visual conspicuity of an object. The method stems from the theoretical view that the conspicuity of an object is not a property of that object, but describes the degree to which the object is perceptually embedded in, i.e. laterally masked by, its visual environment. First, three variations of a simple method to measure the strength of such lateral masking are described and empirical evidence for its reliability and its validity is presented, as are several tests of predictions concerning the effects of viewing distance and ambient light. It is then shown how this method yields a conspicuity standard, expressed as a number, which can be made part of a rule of law, and which can be used to test whether or not, and to what extent, the conspicuity of a particular object, e.g. a traffic sign, meets a predetermined criterion. An additional feature is that, when used under different ambient light conditions, the method may also yield an index of the amount of visual clutter in the environment. Taken together the evidence illustrates the methods' applicability in both the laboratory and in real-life situations. STATEMENT OF RELEVANCE: This paper concerns a proposal for a new method to measure visual conspicuity, yielding a numerical index that can be used in a rule of law. It is of importance to ergonomists and human factor specialists who are asked to measure the conspicuity of an object, such as a traffic or rail-road sign, or any other object. The new method is simple and circumvents the need to perform elaborate (search) experiments and thus has great relevance as a simple tool for applied research.

Simple and Accurate Method for Central Spin Problems

NASA Astrophysics Data System (ADS)

Lindoy, Lachlan P.; Manolopoulos, David E.

2018-06-01

We describe a simple quantum mechanical method that can be used to obtain accurate numerical results over long timescales for the spin correlation tensor of an electron spin that is hyperfine coupled to a large number of nuclear spins. This method does not suffer from the statistical errors that accompany a Monte Carlo sampling of the exact eigenstates of the central spin Hamiltonian obtained from the algebraic Bethe ansatz, or from the growth of the truncation error with time in the time-dependent density matrix renormalization group (TDMRG) approach. As a result, it can be applied to larger central spin problems than the algebraic Bethe ansatz, and for longer times than the TDMRG algorithm. It is therefore an ideal method to use to solve central spin problems, and we expect that it will also prove useful for a variety of related problems that arise in a number of different research fields.

Prediction of Sound Waves Propagating Through a Nozzle Without/With a Shock Wave Using the Space-Time CE/SE Method

NASA Technical Reports Server (NTRS)

Wang, Xiao-Yen; Chang, Sin-Chung; Jorgenson, Philip C. E.

2000-01-01

The benchmark problems in Category 1 (Internal Propagation) of the third Computational Aeroacoustics (CAA) Work-shop sponsored by NASA Glenn Research Center are solved using the space-time conservation element and solution element (CE/SE) method. The first problem addresses the propagation of sound waves through a nearly choked transonic nozzle. The second one concerns shock-sound interaction in a supersonic nozzle. A quasi one-dimension CE/SE Euler solver for a nonuniform mesh is developed and employed to solve both problems. Numerical solutions are compared with the analytical solution for both problems. It is demonstrated that the CE/SE method is capable of solving aeroacoustic problems with/without shock waves in a simple way. Furthermore, the simple nonreflecting boundary condition used in the CE/SE method which is not based on the characteristic theory works very well.

A fast and simple bonding method for low cost microfluidic chip fabrication

NASA Astrophysics Data System (ADS)

Yin, Zhifu; Zou, Helin

2018-01-01

With the development of the microstructure fabrication technique, microfluidic chips are widely used in biological and medical researchers. Future advances in their commercial applications depend on the mass bonding of microfluidic chip. In this study we are presenting a simple, low cost and fast way of bonding microfluidic chips at room temperature. The influence of the bonding pressure on the deformation of the microchannel and adhesive tape was analyzed by numerical simulation. By this method, the microfluidic chip can be fully sealed at low temperature and pressure without using any equipment. The dye water and gas leakage test indicated that the microfluidic chip can be bonded without leakage or block and its bonding strength can up to 0.84 MPa.

Implicitly solving phase appearance and disappearance problems using two-fluid six-equation model

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-01-25

Phase appearance and disappearance issue presents serious numerical challenges in two-phase flow simulations using the two-fluid six-equation model. Numerical challenges arise from the singular equation system when one phase is absent, as well as from the discontinuity in the solution space when one phase appears or disappears. In this work, a high-resolution spatial discretization scheme on staggered grids and fully implicit methods were applied for the simulation of two-phase flow problems using the two-fluid six-equation model. A Jacobian-free Newton-Krylov (JFNK) method was used to solve the discretized nonlinear problem. An improved numerical treatment was proposed and proved to be effectivemore » to handle the numerical challenges. The treatment scheme is conceptually simple, easy to implement, and does not require explicit truncations on solutions, which is essential to conserve mass and energy. Various types of phase appearance and disappearance problems relevant to thermal-hydraulics analysis have been investigated, including a sedimentation problem, an oscillating manometer problem, a non-condensable gas injection problem, a single-phase flow with heat addition problem and a subcooled flow boiling problem. Successful simulations of these problems demonstrate the capability and robustness of the proposed numerical methods and numerical treatments. As a result, volume fraction of the absent phase can be calculated effectively as zero.« less

The Space-Time Conservation Element and Solution Element Method: A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws. 1; The Two Dimensional Time Marching Schemes

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Wang, Xiao-Yen; Chow, Chuen-Yen

1998-01-01

A new high resolution and genuinely multidimensional numerical method for solving conservation laws is being, developed. It was designed to avoid the limitations of the traditional methods. and was built from round zero with extensive physics considerations. Nevertheless, its foundation is mathmatically simple enough that one can build from it a coherent, robust. efficient and accurate numerical framework. Two basic beliefs that set the new method apart from the established methods are at the core of its development. The first belief is that, in order to capture physics more efficiently and realistically, the modeling, focus should be placed on the original integral form of the physical conservation laws, rather than the differential form. The latter form follows from the integral form under the additional assumption that the physical solution is smooth, an assumption that is difficult to realize numerically in a region of rapid chance. such as a boundary layer or a shock. The second belief is that, with proper modeling of the integral and differential forms themselves, the resulting, numerical solution should automatically be consistent with the properties derived front the integral and differential forms, e.g., the jump conditions across a shock and the properties of characteristics. Therefore a much simpler and more robust method can be developed by not using the above derived properties explicitly.

Dimensional Analysis in Mathematical Modeling Systems: A Simple Numerical Method

DTIC Science & Technology

1991-02-01

US Army Ballistic Research Laboratories, Aberden Proving Ground , NID, August 1975. [18] Hi1irlimann, T., and .J. lKohlas "LPL: A Structured Language...such systems can prove that (a’ + ab + b2 + ba) = (a + b) 2 . With some effort, since the laws of physical algebra are a minor variant on those of

Heat simulation via Scilab programming

NASA Astrophysics Data System (ADS)

Hasan, Mohammad Khatim; Sulaiman, Jumat; Karim, Samsul Arifin Abdul

2014-07-01

This paper discussed the used of an open source sofware called Scilab to develop a heat simulator. In this paper, heat equation was used to simulate heat behavior in an object. The simulator was developed using finite difference method. Numerical experiment output show that Scilab can produce a good heat behavior simulation with marvellous visual output with only developing simple computer code.

Charge Transfer Inefficiency in Pinned Photodiode CMOS image sensors: Simple Montecarlo modeling and experimental measurement based on a pulsed storage-gate method

NASA Astrophysics Data System (ADS)

Pelamatti, Alice; Goiffon, Vincent; Chabane, Aziouz; Magnan, Pierre; Virmontois, Cédric; Saint-Pé, Olivier; de Boisanger, Michel Breart

2016-11-01

The charge transfer time represents the bottleneck in terms of temporal resolution in Pinned Photodiode (PPD) CMOS image sensors. This work focuses on the modeling and estimation of this key parameter. A simple numerical model of charge transfer in PPDs is presented. The model is based on a Montecarlo simulation and takes into account both charge diffusion in the PPD and the effect of potential obstacles along the charge transfer path. This work also presents a new experimental approach for the estimation of the charge transfer time, called pulsed Storage Gate (SG) method. This method, which allows reproduction of a ;worst-case; transfer condition, is based on dedicated SG pixel structures and is particularly suitable to compare transfer efficiency performances for different pixel geometries.

Multiplex SNaPshot-a new simple and efficient CYP2D6 and ADRB1 genotyping method.

PubMed

Ben, Songtao; Cooper-DeHoff, Rhonda M; Flaten, Hanna K; Evero, Oghenero; Ferrara, Tracey M; Spritz, Richard A; Monte, Andrew A

2016-04-23

Reliable, inexpensive, high-throughput genotyping methods are required for clinical trials. Traditional assays require numerous enzyme digestions or are too expensive for large sample volumes. Our objective was to develop an inexpensive, efficient, and reliable assay for CYP2D6 and ADRB1 accounting for numerous polymorphisms including gene duplications. We utilized the multiplex SNaPshot® custom genotype method to genotype CYP2D6 and ADRB1. We compared the method to reference standards genotyped using the Taqman Copy Number Variant Assay followed by pyrosequencing quantification and determined assigned genotype concordance. We genotyped 119 subjects. Seven (5.9 %) were found to be CYP2D6 poor metabolizers (PMs), 18 (15.1 %) intermediate metabolizers (IMs), 89 (74.8 %) extensive metabolizers (EMs), and 5 (4.2 %) ultra-rapid metabolizers (UMs). We genotyped two variants in the β1-adrenoreceptor, rs1801253 (Gly389Arg) and rs1801252 (Ser49Gly). The Gly389Arg genotype is Gly/Gly 18 (15.1 %), Gly/Arg 58 (48.7 %), and Arg/Arg 43 (36.1 %). The Ser49Gly genotype is Ser/Ser 82 (68.9 %), Ser/Gly 32 (26.9), and Gly/Gly 5 (4.2 %). The multiplex SNaPshot method was concordant with genotypes in reference samples. The multiplex SNaPshot method allows for specific and accurate detection of CYP2D6 genotypes and ADRB1 genotypes and haplotypes. This platform is simple and efficient and suited for high throughput.

On Numerical Heating

NASA Astrophysics Data System (ADS)

Liou, Meng-Sing

2013-11-01

The development of computational fluid dynamics over the last few decades has yielded enormous successes and capabilities that are being routinely employed today; however there remain some open problems to be properly resolved. One example is the so-called overheating problem, which can arise in two very different scenarios, from either colliding or receding streams. Common in both is a localized, numerically over-predicted temperature. Von Neumann reported the former, a compressive overheating, nearly 70 years ago and numerically smeared the temperature peak by introducing artificial diffusion. However, the latter is unphysical in an expansive (rarefying) situation; it still dogs every method known to the author. We will present a study aiming at resolving this overheating problem and we find that: (1) the entropy increase is one-to-one linked to the increase in the temperature rise and (2) the overheating is inevitable in the current computational fluid dynamics framework in practice. Finally we will show a simple hybrid method that fundamentally cures the overheating problem in a rarefying flow, but also retains the property of accurate shock capturing. Moreover, this remedy (enhancement of current numerical methods) can be included easily in the present Eulerian codes. This work is performed under NASA's Fundamental Aeronautics Program.

Bridges for Pedestrians with Random Parameters using the Stochastic Finite Elements Analysis

NASA Astrophysics Data System (ADS)

Szafran, J.; Kamiński, M.

2017-02-01

The main aim of this paper is to present a Stochastic Finite Element Method analysis with reference to principal design parameters of bridges for pedestrians: eigenfrequency and deflection of bridge span. They are considered with respect to random thickness of plates in boxed-section bridge platform, Young modulus of structural steel and static load resulting from crowd of pedestrians. The influence of the quality of the numerical model in the context of traditional FEM is shown also on the example of a simple steel shield. Steel structures with random parameters are discretized in exactly the same way as for the needs of traditional Finite Element Method. Its probabilistic version is provided thanks to the Response Function Method, where several numerical tests with random parameter values varying around its mean value enable the determination of the structural response and, thanks to the Least Squares Method, its final probabilistic moments.

Complex amplitude reconstruction by iterative amplitude-phase retrieval algorithm with reference

NASA Astrophysics Data System (ADS)

Shen, Cheng; Guo, Cheng; Tan, Jiubin; Liu, Shutian; Liu, Zhengjun

2018-06-01

Multi-image iterative phase retrieval methods have been successfully applied in plenty of research fields due to their simple but efficient implementation. However, there is a mismatch between the measurement of the first long imaging distance and the sequential interval. In this paper, an amplitude-phase retrieval algorithm with reference is put forward without additional measurements or priori knowledge. It gets rid of measuring the first imaging distance. With a designed update formula, it significantly raises the convergence speed and the reconstruction fidelity, especially in phase retrieval. Its superiority over the original amplitude-phase retrieval (APR) method is validated by numerical analysis and experiments. Furthermore, it provides a conceptual design of a compact holographic image sensor, which can achieve numerical refocusing easily.

Influence of the Numerical Scheme on the Solution Quality of the SWE for Tsunami Numerical Codes: The Tohoku-Oki, 2011Example.

NASA Astrophysics Data System (ADS)

Reis, C.; Clain, S.; Figueiredo, J.; Baptista, M. A.; Miranda, J. M. A.

2015-12-01

Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.

Numerical solution of the exact cavity equations of motion for an unstable optical resonator.

PubMed

Bowers, M S; Moody, S E

1990-09-20

We solve numerically, we believe for the first time, the exact cavity equations of motion for a realistic unstable resonator with a simple gain saturation model. The cavity equations of motion, first formulated by Siegman ["Exact Cavity Equations for Lasers with Large Output Coupling," Appl. Phys. Lett. 36, 412-414 (1980)], and which we term the dynamic coupled modes (DCM) method of solution, solve for the full 3-D time dependent electric field inside the optical cavity by expanding the field in terms of the actual diffractive transverse eigenmodes of the bare (gain free) cavity with time varying coefficients. The spatially varying gain serves to couple the bare cavity transverse modes and to scatter power from mode to mode. We show that the DCM method numerically converges with respect to the number of eigenmodes in the basis set. The intracavity intensity in the numerical example shown reaches a steady state, and this steady state distribution is compared with that computed from the traditional Fox and Li approach using a fast Fourier transform propagation algorithm. The output wavefronts from both methods are quite similar, and the computed output powers agree to within 10%. The usefulness and advantages of using this method for predicting the output of a laser, especially pulsed lasers used for coherent detection, are discussed.

Shift-connected SIMD array architectures for digital optical computing systems, with algorithms for numerical transforms and partial differential equations

NASA Astrophysics Data System (ADS)

Drabik, Timothy J.; Lee, Sing H.

1986-11-01

The intrinsic parallelism characteristics of easily realizable optical SIMD arrays prompt their present consideration in the implementation of highly structured algorithms for the numerical solution of multidimensional partial differential equations and the computation of fast numerical transforms. Attention is given to a system, comprising several spatial light modulators (SLMs), an optical read/write memory, and a functional block, which performs simple, space-invariant shifts on images with sufficient flexibility to implement the fastest known methods for partial differential equations as well as a wide variety of numerical transforms in two or more dimensions. Either fixed or floating-point arithmetic may be used. A performance projection of more than 1 billion floating point operations/sec using SLMs with 1000 x 1000-resolution and operating at 1-MHz frame rates is made.

Ancient numerical daemons of conceptual hydrological modeling: 1. Fidelity and efficiency of time stepping schemes

NASA Astrophysics Data System (ADS)

Clark, Martyn P.; Kavetski, Dmitri

2010-10-01

A major neglected weakness of many current hydrological models is the numerical method used to solve the governing model equations. This paper thoroughly evaluates several classes of time stepping schemes in terms of numerical reliability and computational efficiency in the context of conceptual hydrological modeling. Numerical experiments are carried out using 8 distinct time stepping algorithms and 6 different conceptual rainfall-runoff models, applied in a densely gauged experimental catchment, as well as in 12 basins with diverse physical and hydroclimatic characteristics. Results show that, over vast regions of the parameter space, the numerical errors of fixed-step explicit schemes commonly used in hydrology routinely dwarf the structural errors of the model conceptualization. This substantially degrades model predictions, but also, disturbingly, generates fortuitously adequate performance for parameter sets where numerical errors compensate for model structural errors. Simply running fixed-step explicit schemes with shorter time steps provides a poor balance between accuracy and efficiency: in some cases daily-step adaptive explicit schemes with moderate error tolerances achieved comparable or higher accuracy than 15 min fixed-step explicit approximations but were nearly 10 times more efficient. From the range of simple time stepping schemes investigated in this work, the fixed-step implicit Euler method and the adaptive explicit Heun method emerge as good practical choices for the majority of simulation scenarios. In combination with the companion paper, where impacts on model analysis, interpretation, and prediction are assessed, this two-part study vividly highlights the impact of numerical errors on critical performance aspects of conceptual hydrological models and provides practical guidelines for robust numerical implementation.

Power-law behaviour evaluation from foreign exchange market data using a wavelet transform method

NASA Astrophysics Data System (ADS)

Wei, H. L.; Billings, S. A.

2009-09-01

Numerous studies in the literature have shown that the dynamics of many time series including observations in foreign exchange markets exhibit scaling behaviours. A simple new statistical approach, derived from the concept of the continuous wavelet transform correlation function (WTCF), is proposed for the evaluation of power-law properties from observed data. The new method reveals that foreign exchange rates obey power-laws and thus belong to the class of self-similarity processes.

Implementation of Preconditioned Dual-Time Procedures in OVERFLOW

NASA Technical Reports Server (NTRS)

Pandya, Shishir A.; Venkateswaran, Sankaran; Pulliam, Thomas H.; Kwak, Dochan (Technical Monitor)

2003-01-01

Preconditioning methods have become the method of choice for the solution of flowfields involving the simultaneous presence of low Mach and transonic regions. It is well known that these methods are important for insuring accurate numerical discretization as well as convergence efficiency over various operating conditions such as low Mach number, low Reynolds number and high Strouhal numbers. For unsteady problems, the preconditioning is introduced within a dual-time framework wherein the physical time-derivatives are used to march the unsteady equations and the preconditioned time-derivatives are used for purposes of numerical discretization and iterative solution. In this paper, we describe the implementation of the preconditioned dual-time methodology in the OVERFLOW code. To demonstrate the performance of the method, we employ both simple and practical unsteady flowfields, including vortex propagation in a low Mach number flow, flowfield of an impulsively started plate (Stokes' first problem) arid a cylindrical jet in a low Mach number crossflow with ground effect. All the results demonstrate that the preconditioning algorithm is responsible for improvements to both numerical accuracy and convergence efficiency and, thereby, enables low Mach number unsteady computations to be performed at a fraction of the cost of traditional time-marching methods.

Simple, accurate formula for the average bit error probability of multiple-input multiple-output free-space optical links over negative exponential turbulence channels.

PubMed

Peppas, Kostas P; Lazarakis, Fotis; Alexandridis, Antonis; Dangakis, Kostas

2012-08-01

In this Letter we investigate the error performance of multiple-input multiple-output free-space optical communication systems employing intensity modulation/direct detection and operating over strong atmospheric turbulence channels. Atmospheric-induced strong turbulence fading is modeled using the negative exponential distribution. For the considered system, an approximate yet accurate analytical expression for the average bit error probability is derived and an efficient method for its numerical evaluation is proposed. Numerically evaluated and computer simulation results are further provided to demonstrate the validity of the proposed mathematical analysis.

Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2

NASA Technical Reports Server (NTRS)

Karki, K. C.; Patankar, S. V.; Runchal, A. K.; Mongia, H. C.

1988-01-01

The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially.

Triangle based TVD schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Durlofsky, Louis J.; Osher, Stanley; Engquist, Bjorn

1990-01-01

A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second order accuracy. Numerical results for linear advection and Burgers' equation are presented.

Linking species abundance distributions in numerical abundance and biomass through simple assumptions about community structure.

PubMed

Henderson, Peter A; Magurran, Anne E

2010-05-22

Species abundance distributions (SADs) are widely used as a tool for summarizing ecological communities but may have different shapes, depending on the currency used to measure species importance. We develop a simple plotting method that links SADs in the alternative currencies of numerical abundance and biomass and is underpinned by testable predictions about how organisms occupy physical space. When log numerical abundance is plotted against log biomass, the species lie within an approximately triangular region. Simple energetic and sampling constraints explain the triangular form. The dispersion of species within this triangle is the key to understanding why SADs of numerical abundance and biomass can differ. Given regular or random species dispersion, we can predict the shape of the SAD for both currencies under a variety of sampling regimes. We argue that this dispersion pattern will lie between regular and random for the following reasons. First, regular dispersion patterns will result if communities are comprised groups of organisms that use different components of the physical space (e.g. open water, the sea bed surface or rock crevices in a marine fish assemblage), and if the abundance of species in each of these spatial guilds is linked to the way individuals of varying size use the habitat. Second, temporal variation in abundance and sampling error will tend to randomize this regular pattern. Data from two intensively studied marine ecosystems offer empirical support for these predictions. Our approach also has application in environmental monitoring and the recognition of anthropogenic disturbance, which may change the shape of the triangular region by, for example, the loss of large body size top predators that occur at low abundance.

Linking species abundance distributions in numerical abundance and biomass through simple assumptions about community structure

PubMed Central

Henderson, Peter A.; Magurran, Anne E.

2010-01-01

Species abundance distributions (SADs) are widely used as a tool for summarizing ecological communities but may have different shapes, depending on the currency used to measure species importance. We develop a simple plotting method that links SADs in the alternative currencies of numerical abundance and biomass and is underpinned by testable predictions about how organisms occupy physical space. When log numerical abundance is plotted against log biomass, the species lie within an approximately triangular region. Simple energetic and sampling constraints explain the triangular form. The dispersion of species within this triangle is the key to understanding why SADs of numerical abundance and biomass can differ. Given regular or random species dispersion, we can predict the shape of the SAD for both currencies under a variety of sampling regimes. We argue that this dispersion pattern will lie between regular and random for the following reasons. First, regular dispersion patterns will result if communities are comprised groups of organisms that use different components of the physical space (e.g. open water, the sea bed surface or rock crevices in a marine fish assemblage), and if the abundance of species in each of these spatial guilds is linked to the way individuals of varying size use the habitat. Second, temporal variation in abundance and sampling error will tend to randomize this regular pattern. Data from two intensively studied marine ecosystems offer empirical support for these predictions. Our approach also has application in environmental monitoring and the recognition of anthropogenic disturbance, which may change the shape of the triangular region by, for example, the loss of large body size top predators that occur at low abundance. PMID:20071388

Chemical composition of igneous rocks expressed by means of diagrams, with reference to rock classification on a quantitative chemico-mineralogical basis

USGS Publications Warehouse

Iddings, J.P.

1903-01-01

The value of graphical methods for expressing relative quantities has been well established in all kinds of statistical exposition and discussion. Their use in conveying definite conceptions of relative quantities of chemical and mineral components of rocks is becoming more and more frequent, and the value of the results in some cases can not be overestimated. This is especially true when a series or group of rocks is being considered. The intricate variations in the amounts of numerous mineral components, or of chemical components, baffle most attempts to comprehend their interrelationships by simple contemplation or by study of the numbers in which they may be expressed. Many facts and relations are overlooked which arc readily observed when diagrams are used to represent numerical figures. Moreover, visual memory is sufficiently developed in most persons to enable them to carry in mind simple geometrical forms, where it does not permit them to recollect manifold assemblages of oft-repeated numbers. Mental impressions of simple diagrams are, therefore, more definite and lasting and enable the student to store up a much greater amount of quantitative data than he could otherwise acquire.

On the error propagation of semi-Lagrange and Fourier methods for advection problems☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2015-01-01

In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation (semi-Lagrangian methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-Lagrangian approach (which is conservative and has to store more than a single value per cell). We demonstrate, by carrying out numerical experiments, that the worst case error estimates given in the literature provide a good explanation for the error propagation of the interpolation-based semi-Lagrangian methods. For the discontinuous Galerkin semi-Lagrangian method, however, we find that the characteristic property of semi-Lagrangian error estimates (namely the fact that the error increases proportionally to the number of time steps) is not observed. We provide an explanation for this behavior and conduct numerical simulations that corroborate the different qualitative features of the error in the two respective types of semi-Lagrangian methods. The method based on the fast Fourier transform is exact but, due to round-off errors, susceptible to a linear increase of the error in the number of time steps. We show how to modify the Cooley–Tukey algorithm in order to obtain an error growth that is proportional to the square root of the number of time steps. Finally, we show, for a simple model, that our conclusions hold true if the advection solver is used as part of a splitting scheme. PMID:25844018

A fast numerical solution of scattering by a cylinder: Spectral method for the boundary integral equations

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.

Horizontal lifelines - review of regulations and simple design method considering anchorage rigidity.

PubMed

Galy, Bertrand; Lan, André

2018-03-01

Among the many occupational risks construction workers encounter every day falling from a height is the most dangerous. The objective of this article is to propose a simple analytical design method for horizontal lifelines (HLLs) that considers anchorage flexibility. The article presents a short review of the standards and regulations/acts/codes concerning HLLs in Canada the USA and Europe. A static analytical approach is proposed considering anchorage flexibility. The analytical results are compared with a series of 42 dynamic fall tests and a SAP2000 numerical model. The experimental results show that the analytical method is a little conservative and overestimates the line tension in most cases with a maximum of 17%. The static SAP2000 results show a maximum 2.1% difference with the analytical method. The analytical method is accurate enough to safely design HLLs and quick design abaci are provided to allow the engineer to make quick on-site verification if needed.

A robust collagen scoring method for human liver fibrosis by second harmonic microscopy.

PubMed

Guilbert, Thomas; Odin, Christophe; Le Grand, Yann; Gailhouste, Luc; Turlin, Bruno; Ezan, Frédérick; Désille, Yoann; Baffet, Georges; Guyader, Dominique

2010-12-06

Second Harmonic Generation (SHG) microscopy offers the opportunity to image collagen of type I without staining. We recently showed that a simple scoring method, based on SHG images of histological human liver biopsies, correlates well with the Metavir assessment of fibrosis level (Gailhouste et al., J. Hepatol., 2010). In this article, we present a detailed study of this new scoring method with two different objective lenses. By using measurements of the objectives point spread functions and of the photomultiplier gain, and a simple model of the SHG intensity, we show that our scoring method, applied to human liver biopsies, is robust to the objective's numerical aperture (NA) for low NA, the choice of the reference sample and laser power, and the spatial sampling rate. The simplicity and robustness of our collagen scoring method may open new opportunities in the quantification of collagen content in different organs, which is of main importance in providing diagnostic information and evaluation of therapeutic efficiency.

A Double Perturbation Method for Reducing Dynamical Degradation of the Digital Baker Map

NASA Astrophysics Data System (ADS)

Liu, Lingfeng; Lin, Jun; Miao, Suoxia; Liu, Bocheng

2017-06-01

The digital Baker map is widely used in different kinds of cryptosystems, especially for image encryption. However, any chaotic map which is realized on the finite precision device (e.g. computer) will suffer from dynamical degradation, which refers to short cycle lengths, low complexity and strong correlations. In this paper, a novel double perturbation method is proposed for reducing the dynamical degradation of the digital Baker map. Both state variables and system parameters are perturbed by the digital logistic map. Numerical experiments show that the perturbed Baker map can achieve good statistical and cryptographic properties. Furthermore, a new image encryption algorithm is provided as a simple application. With a rather simple algorithm, the encrypted image can achieve high security, which is competitive to the recently proposed image encryption algorithms.

A Partially-Stirred Batch Reactor Model for Under-Ventilated Fire Dynamics

NASA Astrophysics Data System (ADS)

McDermott, Randall; Weinschenk, Craig

2013-11-01

A simple discrete quadrature method is developed for closure of the mean chemical source term in large-eddy simulations (LES) and implemented in the publicly available fire model, Fire Dynamics Simulator (FDS). The method is cast as a partially-stirred batch reactor model for each computational cell. The model has three distinct components: (1) a subgrid mixing environment, (2) a mixing model, and (3) a set of chemical rate laws. The subgrid probability density function (PDF) is described by a linear combination of Dirac delta functions with quadrature weights set to satisfy simple integral constraints for the computational cell. It is shown that under certain limiting assumptions, the present method reduces to the eddy dissipation concept (EDC). The model is used to predict carbon monoxide concentrations in direct numerical simulation (DNS) of a methane slot burner and in LES of an under-ventilated compartment fire.

Spatiotemporal video deinterlacing using control grid interpolation

NASA Astrophysics Data System (ADS)

Venkatesan, Ragav; Zwart, Christine M.; Frakes, David H.; Li, Baoxin

2015-03-01

With the advent of progressive format display and broadcast technologies, video deinterlacing has become an important video-processing technique. Numerous approaches exist in the literature to accomplish deinterlacing. While most earlier methods were simple linear filtering-based approaches, the emergence of faster computing technologies and even dedicated video-processing hardware in display units has allowed higher quality but also more computationally intense deinterlacing algorithms to become practical. Most modern approaches analyze motion and content in video to select different deinterlacing methods for various spatiotemporal regions. We introduce a family of deinterlacers that employs spectral residue to choose between and weight control grid interpolation based spatial and temporal deinterlacing methods. The proposed approaches perform better than the prior state-of-the-art based on peak signal-to-noise ratio, other visual quality metrics, and simple perception-based subjective evaluations conducted by human viewers. We further study the advantages of using soft and hard decision thresholds on the visual performance.

Vibration based algorithm for crack detection in cantilever beam containing two different types of cracks

NASA Astrophysics Data System (ADS)

Behzad, Mehdi; Ghadami, Amin; Maghsoodi, Ameneh; Michael Hale, Jack

2013-11-01

In this paper, a simple method for detection of multiple edge cracks in Euler-Bernoulli beams having two different types of cracks is presented based on energy equations. Each crack is modeled as a massless rotational spring using Linear Elastic Fracture Mechanics (LEFM) theory, and a relationship among natural frequencies, crack locations and stiffness of equivalent springs is demonstrated. In the procedure, for detection of m cracks in a beam, 3m equations and natural frequencies of healthy and cracked beam in two different directions are needed as input to the algorithm. The main accomplishment of the presented algorithm is the capability to detect the location, severity and type of each crack in a multi-cracked beam. Concise and simple calculations along with accuracy are other advantages of this method. A number of numerical examples for cantilever beams including one and two cracks are presented to validate the method.

Simple Method to Generate Terawatt-Attosecond X-Ray Free-Electron-Laser Pulses.

PubMed

Prat, Eduard; Reiche, Sven

2015-06-19

X-ray free-electron lasers (XFELs) are cutting-edge research tools that produce almost fully coherent radiation with high power and short-pulse length with applications in multiple science fields. There is a strong demand to achieve even shorter pulses and higher radiation powers than the ones obtained at state-of-the-art XFEL facilities. In this context we propose a novel method to generate terawatt-attosecond XFEL pulses, where an XFEL pulse is pushed through several short good-beam regions of the electron bunch. In addition to the elements of conventional XFEL facilities, the method uses only a multiple-slotted foil and small electron delays between undulator sections. Our scheme is thus simple, compact, and easy to implement both in already operating as well as future XFEL projects. We present numerical simulations that confirm the feasibility and validity of our proposal.

Dynamic motion of red blood cells in simple shear flow

NASA Astrophysics Data System (ADS)

Sui, Y.; Chew, Y. T.; Roy, P.; Cheng, Y. P.; Low, H. T.

2008-11-01

A three-dimensional numerical model is proposed to simulate the dynamic motion of red blood cells (RBCs) in simple shear flow. The RBCs are approximated by ghost cells consisting of Newtonian liquid drops enclosed by Skalak membranes which take into account the membrane shear elasticity and the membrane area incompressibility. The RBCs have an initially biconcave discoid resting shape, and the internal liquid is assumed to have the same physical properties as the matrix fluid. The simulation is based on a hybrid method, in which the immersed boundary concept is introduced into the framework of the lattice Boltzmann method, and a finite element model is incorporated to obtain the forces acting on the nodes of the cell membrane which is discretized into flat triangular elements. The dynamic motion of RBCs is investigated in simple shear flow under a broad range of shear rates. At large shear rates, the cells are found to carry out a swinging motion, in which periodic inclination oscillation and shape deformation superimpose on the membrane tank treading motion. With the shear rate decreasing, the swinging amplitude of the cell increases, and finally triggers a transition to tumbling motion. This is the first direct numerical simulation that predicts both the swinging motion of the RBCs and the shear rate induced transition, which have been observed in a recent experiment. It is also found that as the mode changes from swinging to tumbling, the apparent viscosity of the suspension increases monotonically.

Numerical solution of the Hele-Shaw equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Whitaker, N.

1987-04-01

An algorithm is presented for approximating the motion of the interface between two immiscible fluids in a Hele-Shaw cell. The interface is represented by a set of volume fractions. We use the Simple Line Interface Calculation method along with the method of fractional steps to transport the interface. The equation of continuity leads to a Poisson equation for the pressure. The Poisson equation is discretized. Near the interface where the velocity field is discontinuous, the discretization is based on a weak formulation of the continuity equation. Interpolation is used on each side of the interface to increase the accuracy ofmore » the algorithm. The weak formulation as well as the interpolation are based on the computed volume fractions. This treatment of the interface is new. The discretized equations are solved by a modified conjugate gradient method. Surface tension is included and the curvature is computed through the use of osculating circles. For perturbations of small amplitude, a surprisingly good agreement is found between the numerical results and linearized perturbation theory. Numerical results are presented for the finite amplitude growth of unstable fingers. 62 refs., 13 figs.« less

An efficient transport solver for tokamak plasmas

DOE PAGES

Park, Jin Myung; Murakami, Masanori; St. John, H. E.; ...

2017-01-03

A simple approach to efficiently solve a coupled set of 1-D diffusion-type transport equations with a stiff transport model for tokamak plasmas is presented based on the 4th order accurate Interpolated Differential Operator scheme along with a nonlinear iteration method derived from a root-finding algorithm. Here, numerical tests using the Trapped Gyro-Landau-Fluid model show that the presented high order method provides an accurate transport solution using a small number of grid points with robust nonlinear convergence.

Numerical solution for the interaction of shock wave with laminar boundary layer in two-dimensional flow on a flat plate. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Landau, U.

1984-01-01

The finite difference computation method was investigated for solving problems of interaction between a shock wave and a laminar boundary layer, through solution of the complete Navier-Stokes equations. This method provided excellent solutions, was simple to perform and needed a relatively short solution time. A large number of runs for various flow conditions could be carried out from which the interaction characteristics and principal factors that influence interaction could be studied.

Gauge-independent decoherence models for solids in external fields

NASA Astrophysics Data System (ADS)

Wismer, Michael S.; Yakovlev, Vladislav S.

2018-04-01

We demonstrate gauge-invariant modeling of an open system of electrons in a periodic potential interacting with an optical field. For this purpose, we adapt the covariant derivative to the case of mixed states and put forward a decoherence model that has simple analytical forms in the length and velocity gauges. We demonstrate our methods by calculating harmonic spectra in the strong-field regime and numerically verifying the equivalence of the deterministic master equation to the stochastic Monte Carlo wave-function method.

Untangling Slab Dynamics Using 3-D Numerical and Analytical Models

NASA Astrophysics Data System (ADS)

Holt, A. F.; Royden, L.; Becker, T. W.

2016-12-01

Increasingly sophisticated numerical models have enabled us to make significant strides in identifying the key controls on how subducting slabs deform. For example, 3-D models have demonstrated that subducting plate width, and the related strength of toroidal flow around the plate edge, exerts a strong control on both the curvature and the rate of migration of the trench. However, the results of numerical subduction models can be difficult to interpret, and many first order dynamics issues remain at least partially unresolved. Such issues include the dominant controls on trench migration, the interdependence of asthenospheric pressure and slab dynamics, and how nearby slabs influence each other's dynamics. We augment 3-D, dynamically evolving finite element models with simple, analytical force-balance models to distill the physics associated with subduction into more manageable parts. We demonstrate that for single, isolated subducting slabs much of the complexity of our fully numerical models can be encapsulated by simple analytical expressions. Rates of subduction and slab dip correlate strongly with the asthenospheric pressure difference across the subducting slab. For double subduction, an additional slab gives rise to more complex mantle pressure and flow fields, and significantly extends the range of plate kinematics (e.g., convergence rate, trench migration rate) beyond those present in single slab models. Despite these additional complexities, we show that much of the dynamics of such multi-slab systems can be understood using the physics illuminated by our single slab study, and that a force-balance method can be used to relate intra-plate stress to viscous pressure in the asthenosphere and coupling forces at plate boundaries. This method has promise for rapid modeling of large systems of subduction zones on a global scale.

Numerical slope stability simulations of chasma walls in Valles Marineris/Mars using a distinct element method (dem).

NASA Astrophysics Data System (ADS)

Imre, B.

2003-04-01

NUMERICAL SLOPE STABILITY SIMULATIONS OF CHASMA WALLS IN VALLES MARINERIS/MARS USING A DISTINCT ELEMENT METHOD (DEM). B. Imre (1) (1) German Aerospace Center, Berlin Adlershof, bernd.imre@gmx.net The 8- to 10-km depths of Valles Marineris (VM) offer excellent views into the upper Martian crust. Layering, fracturing, lithology, stratigraphy and the content of volatiles have influenced the evolution of the Valles Marineris wallslopes. But these parameters also reflect the development of VM and its wall slopes. The scope of this work is to gain understanding in these parameters by back-simulating the development of wall slopes. For that purpose, the two dimensional Particle Flow Code PFC2D has been chosen (ITASCA, version 2.00-103). PFC2D is a distinct element code for numerical modelling of movements and interactions of assemblies of arbitrarily sized circular particles. Particles may be bonded together to represent a solid material. Movements of particles are unlimited. That is of importance because results of open systems with numerous unknown variables are non-unique and therefore highly path dependent. This DEM allows the simulation of whole development paths of VM walls what makes confirmation of the model more complete (e.g. Oreskes et al., Science 263, 1994). To reduce the number of unknown variables a proper (that means as simple as possible) field-site had to be selected. The northern wall of eastern Candor Chasma has been chosen. This wall is up to 8-km high and represents a significant outcrop of the upper Martian crust. It is quite uncomplex, well-aligned and of simple morphology. Currently the work on the model is at the stage of performing the parameter study. Results will be presented via poster by the EGS-Meeting.

Experimental study and finite element analysis based on equivalent load method for laser ultrasonic measurement of elastic constants.

PubMed

Zhan, Yu; Liu, Changsheng; Zhang, Fengpeng; Qiu, Zhaoguo

2016-07-01

The laser ultrasonic generation of Rayleigh surface wave and longitudinal wave in an elastic plate is studied by experiment and finite element method. In order to eliminate the measurement error and the time delay of the experimental system, the linear fitting method of experimental data is applied. The finite element analysis software ABAQUS is used to simulate the propagation of Rayleigh surface wave and longitudinal wave caused by laser excitation on a sheet metal sample surface. The equivalent load method is proposed and applied. The pulsed laser is equivalent to the surface load in time and space domain to meet the Gaussian profile. The relationship between the physical parameters of the laser and the load is established by the correction factor. The numerical solution is in good agreement with the experimental result. The simple and effective numerical and experimental methods for laser ultrasonic measurement of the elastic constants are demonstrated. Copyright © 2016. Published by Elsevier B.V.

A compressible multiphase framework for simulating supersonic atomization

NASA Astrophysics Data System (ADS)

Regele, Jonathan D.; Garrick, Daniel P.; Hosseinzadeh-Nik, Zahra; Aslani, Mohamad; Owkes, Mark

2016-11-01

The study of atomization in supersonic combustors is critical in designing efficient and high performance scramjets. Numerical methods incorporating surface tension effects have largely focused on the incompressible regime as most atomization applications occur at low Mach numbers. Simulating surface tension effects in high speed compressible flow requires robust numerical methods that can handle discontinuities caused by both material interfaces and shocks. A shock capturing/diffused interface method is developed to simulate high-speed compressible gas-liquid flows with surface tension effects using the five-equation model. This includes developments that account for the interfacial pressure jump that occurs in the presence of surface tension. A simple and efficient method for computing local interface curvature is developed and an acoustic non-dimensional scaling for the surface tension force is proposed. The method successfully captures a variety of droplet breakup modes over a range of Weber numbers and demonstrates the impact of surface tension in countering droplet deformation in both subsonic and supersonic cross flows.

Modeling reactive transport processes in fractured rock using the time domain random walk approach within a dual-porosity framework

NASA Astrophysics Data System (ADS)

Roubinet, D.; Russian, A.; Dentz, M.; Gouze, P.

2017-12-01

Characterizing and modeling hydrodynamic reactive transport in fractured rock are critical challenges for various research fields and applications including environmental remediation, geological storage, and energy production. To this end, we consider a recently developed time domain random walk (TDRW) approach, which is adapted to reproduce anomalous transport behaviors and capture heterogeneous structural and physical properties. This method is also very well suited to optimize numerical simulations by memory-shared massive parallelization and provide numerical results at various scales. So far, the TDRW approach has been applied for modeling advective-diffusive transport with mass transfer between mobile and immobile regions and simple (theoretical) reactions in heterogeneous porous media represented as single continuum domains. We extend this approach to dual-continuum representations considering a highly permeable fracture network embedded into a poorly permeable rock matrix with heterogeneous geochemical reactions occurring in both geological structures. The resulting numerical model enables us to extend the range of the modeled heterogeneity scales with an accurate representation of solute transport processes and no assumption on the Fickianity of these processes. The proposed model is compared to existing particle-based methods that are usually used to model reactive transport in fractured rocks assuming a homogeneous surrounding matrix, and is used to evaluate the impact of the matrix heterogeneity on the apparent reaction rates for different 2D and 3D simple-to-complex fracture network configurations.

Robust and Accurate Shock Capturing Method for High-Order Discontinuous Galerkin Methods

NASA Technical Reports Server (NTRS)

Atkins, Harold L.; Pampell, Alyssa

2011-01-01

A simple yet robust and accurate approach for capturing shock waves using a high-order discontinuous Galerkin (DG) method is presented. The method uses the physical viscous terms of the Navier-Stokes equations as suggested by others; however, the proposed formulation of the numerical viscosity is continuous and compact by construction, and does not require the solution of an auxiliary diffusion equation. This work also presents two analyses that guided the formulation of the numerical viscosity and certain aspects of the DG implementation. A local eigenvalue analysis of the DG discretization applied to a shock containing element is used to evaluate the robustness of several Riemann flux functions, and to evaluate algorithm choices that exist within the underlying DG discretization. A second analysis examines exact solutions to the DG discretization in a shock containing element, and identifies a "model" instability that will inevitably arise when solving the Euler equations using the DG method. This analysis identifies the minimum viscosity required for stability. The shock capturing method is demonstrated for high-speed flow over an inviscid cylinder and for an unsteady disturbance in a hypersonic boundary layer. Numerical tests are presented that evaluate several aspects of the shock detection terms. The sensitivity of the results to model parameters is examined with grid and order refinement studies.

A numerical study of transient heat and mass transfer in crystal growth

NASA Technical Reports Server (NTRS)

Han, Samuel Bang-Moo

1987-01-01

A numerical analysis of transient heat and solute transport across a rectangular cavity is performed. Five nonlinear partial differential equations which govern the conservation of mass, momentum, energy and solute concentration related to crystal growth in solution, are simultaneously integrated by a numerical method based on the SIMPLE algorithm. Numerical results showed that the flow, temperature and solute fields are dependent on thermal and solutal Grashoff number, Prandtl number, Schmidt number and aspect ratio. The average Nusselt and Sherwood numbers evaluated at the center of the cavity decrease markedly when the solutal buoyancy force acts in the opposite direction to the thermal buoyancy force. When the solutal and thermal buoyancy forces act in the same direction, however, Sherwood number increases significantly and yet Nusselt number decreases. Overall effects of convection on the crystal growth are seen to be an enhancement of growth rate as expected but with highly nonuniform spatial growth variations.

Electron-phonon scattering rates in complex polar crystals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prange, M. P.; Campbell, L. W.; Kerisit, S.

2017-09-01

The thermalization of fast electrons by phonons is studied in CsI, NaI, SrI2, and YAP. This numerical study uses an improvement to a recently developed ab initio method based on a density functional perturbation theoretical description of the phonon modes that provides a way to go beyond widely used phonon models based on binary crystals. Improvements to this method are described, and scattering rates are presented and discussed. The results here treat polar and nonpolar scattering on equal footing and allow an assessment of the relative importance of the two types of scattering. The relative activity of the numerous phononmore » modes in materials with complicated structures is discussed, and a simple criterion for finding the modes that scatter strongly is presented.« less

A new potential for the numerical simulations of electrolyte solutions on a hypersphere

NASA Astrophysics Data System (ADS)

Caillol, Jean-Michel

1993-12-01

We propose a new way of performing numerical simulations of the restricted primitive model of electrolytes—and related models—on a hypersphere. In this new approach, the system is viewed as a single component fluid of charged bihard spheres constrained to move at the surface of a four dimensional sphere. A charged bihard sphere is defined as the rigid association of two antipodal charged hard spheres of opposite signs. These objects interact via a simple analytical potential obtained by solving the Poisson-Laplace equation on the hypersphere. This new technique of simulation enables a precise determination of the chemical potential of the charged species in the canonical ensemble by a straightforward application of Widom's insertion method. Comparisons with previous simulations demonstrate the efficiency and the reliability of the method.

Concrete ensemble Kalman filters with rigorous catastrophic filter divergence

PubMed Central

Kelly, David; Majda, Andrew J.; Tong, Xin T.

2015-01-01

The ensemble Kalman filter and ensemble square root filters are data assimilation methods used to combine high-dimensional, nonlinear dynamical models with observed data. Ensemble methods are indispensable tools in science and engineering and have enjoyed great success in geophysical sciences, because they allow for computationally cheap low-ensemble-state approximation for extremely high-dimensional turbulent forecast models. From a theoretical perspective, the dynamical properties of these methods are poorly understood. One of the central mysteries is the numerical phenomenon known as catastrophic filter divergence, whereby ensemble-state estimates explode to machine infinity, despite the true state remaining in a bounded region. In this article we provide a breakthrough insight into the phenomenon, by introducing a simple and natural forecast model that transparently exhibits catastrophic filter divergence under all ensemble methods and a large set of initializations. For this model, catastrophic filter divergence is not an artifact of numerical instability, but rather a true dynamical property of the filter. The divergence is not only validated numerically but also proven rigorously. The model cleanly illustrates mechanisms that give rise to catastrophic divergence and confirms intuitive accounts of the phenomena given in past literature. PMID:26261335

Full-degrees-of-freedom frequency based substructuring

NASA Astrophysics Data System (ADS)

Drozg, Armin; Čepon, Gregor; Boltežar, Miha

2018-01-01

Dividing the whole system into multiple subsystems and a separate dynamic analysis is common practice in the field of structural dynamics. The substructuring process improves the computational efficiency and enables an effective realization of the local optimization, modal updating and sensitivity analyses. This paper focuses on frequency-based substructuring methods using experimentally obtained data. An efficient substructuring process has already been demonstrated using numerically obtained frequency-response functions (FRFs). However, the experimental process suffers from several difficulties, among which, many of them are related to the rotational degrees of freedom. Thus, several attempts have been made to measure, expand or combine numerical correction methods in order to obtain a complete response model. The proposed methods have numerous limitations and are not yet generally applicable. Therefore, in this paper an alternative approach based on experimentally obtained data only, is proposed. The force-excited part of the FRF matrix is measured with piezoelectric translational and rotational direct accelerometers. The incomplete moment-excited part of the FRF matrix is expanded, based on the modal model. The proposed procedure is integrated in a Lagrange Multiplier Frequency Based Substructuring method and demonstrated on a simple beam structure, where the connection coordinates are mainly associated with the rotational degrees of freedom.

The method of space-time conservation element and solution element-applications to one-dimensional and two-dimensional time-marching flow problems

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Wang, Xiao-Yen; Chow, Chuen-Yen

1995-01-01

A nontraditional numerical method for solving conservation laws is being developed. The new method is designed from a physicist's perspective, i.e., its development is based more on physics than numerics. Even though it uses only the simplest approximation techniques, a 2D time-marching Euler solver developed recently using the new method is capable of generating nearly perfect solutions for a 2D shock reflection problem used by Helen Yee and others. Moreover, a recent application of this solver to computational aeroacoustics (CAA) problems reveals that: (1) accuracy of its results is comparable to that of a 6th order compact difference scheme even though nominally the current solver is only of 2nd-order accuracy; (2) generally, the non-reflecting boundary condition can be implemented in a simple way without involving characteristic variables; and (3) most importantly, the current solver is capable of handling both continuous and discontinuous flows very well and thus provides a unique numerical tool for solving those flow problems where the interactions between sound waves and shocks are important, such as the noise field around a supersonic over- or under-expansion jet.

Concrete ensemble Kalman filters with rigorous catastrophic filter divergence.

PubMed

Kelly, David; Majda, Andrew J; Tong, Xin T

2015-08-25

The ensemble Kalman filter and ensemble square root filters are data assimilation methods used to combine high-dimensional, nonlinear dynamical models with observed data. Ensemble methods are indispensable tools in science and engineering and have enjoyed great success in geophysical sciences, because they allow for computationally cheap low-ensemble-state approximation for extremely high-dimensional turbulent forecast models. From a theoretical perspective, the dynamical properties of these methods are poorly understood. One of the central mysteries is the numerical phenomenon known as catastrophic filter divergence, whereby ensemble-state estimates explode to machine infinity, despite the true state remaining in a bounded region. In this article we provide a breakthrough insight into the phenomenon, by introducing a simple and natural forecast model that transparently exhibits catastrophic filter divergence under all ensemble methods and a large set of initializations. For this model, catastrophic filter divergence is not an artifact of numerical instability, but rather a true dynamical property of the filter. The divergence is not only validated numerically but also proven rigorously. The model cleanly illustrates mechanisms that give rise to catastrophic divergence and confirms intuitive accounts of the phenomena given in past literature.

Visualization of flow separation and control by vortex generators on an single flap in landing configuration

NASA Astrophysics Data System (ADS)

Součková, Natálie; Kuklová, Jana; Popelka, Lukáš; Matějka, Milan

2012-04-01

This paper focuses on a suppression of the flow separation, which occurs on a deflected flap, by means of vortex generators (VG's). An airfoil NACA 63A421 with a simple flap and vane-type vortex generators were used. The investigation was carried out by using experimental and numerical methods. The data from the numerical simulation of the flapped airfoil without VG's control were used for the vortex generator design. Two sizes, two different shapes and various spacing of the vortex generators were tested. The flow past the airfoil was visualized through three methods, namely tuft filaments technique, oil and thermo camera visualization. The experiments were performed in closed circuit wind tunnels with closed and open test sections. The lift curves for both cases without and with vortex generators were acquired for a lift coefficient improvement determination. The improvement was achieved for several cases by means all of the applied methods.

Numerical modeling of zero-offset laboratory data in a strong topographic environment: results for a spectral-element method and a discretized Kirchhoff integral method

NASA Astrophysics Data System (ADS)

Favretto-Cristini, Nathalie; Tantsereva, Anastasiya; Cristini, Paul; Ursin, Bjørn; Komatitsch, Dimitri; Aizenberg, Arkady M.

2014-08-01

Accurate simulation of seismic wave propagation in complex geological structures is of particular interest nowadays. However conventional methods may fail to simulate realistic wavefields in environments with great and rapid structural changes, due for instance to the presence of shadow zones, diffractions and/or edge effects. Different methods, developed to improve seismic modeling, are typically tested on synthetic configurations against analytical solutions for simple canonical problems or reference methods, or via direct comparison with real data acquired in situ. Such approaches have limitations, especially if the propagation occurs in a complex environment with strong-contrast reflectors and surface irregularities, as it can be difficult to determine the method which gives the best approximation of the "real" solution, or to interpret the results obtained without an a priori knowledge of the geologic environment. An alternative approach for seismics consists in comparing the synthetic data with high-quality data collected in laboratory experiments under controlled conditions for a known configuration. In contrast with numerical experiments, laboratory data possess many of the characteristics of field data, as real waves propagate through models with no numerical approximations. We thus present a comparison of laboratory-scaled measurements of 3D zero-offset wave reflection of broadband pulses from a strong topographic environment immersed in a water tank with numerical data simulated by means of a spectral-element method and a discretized Kirchhoff integral method. The results indicate a good quantitative fit in terms of time arrivals and acceptable fit in amplitudes for all datasets.

An Investigation of the Tensile Strength of a Composite-To-Metal Adhesive Joint

NASA Astrophysics Data System (ADS)

Tsouvalis, Nicholas G.; Karatzas, Vassilios A.

2011-04-01

The present study examines the feasibility of a simple concept composite-to-metal butt joint through the performance of both numerical and experimental studies. The composite part is made of glass/epoxy unidirectional layers made with the vacuum bag method. The geometry of the joint is typical for marine applications and corresponds to a low stiffness ratio. Two major parameters are investigated, namely the overlap length and the surface preparation of the steel adherent. Manufacturing of specimens and the procedure of the tensile tests are described in detail, giving hints for obtaining a better quality joint. Axial elongation and strains at various places of the joint were monitored and also numerically calculated. The tests revealed that the joint is quite effective, irrespectively of the steel surface preparation method. The failure loads are comparable and in some cases superior to other corresponding values found in the literature. The numerical models proved to adequately predict the structural response of the joint up to the loading where debonding starts.

Numerical simulation of water hammer in low pressurized pipe: comparison of SimHydraulics and Lax-Wendroff method with experiment

NASA Astrophysics Data System (ADS)

Himr, D.

2013-04-01

Article describes simulation of unsteady flow during water hammer with two programs, which use different numerical approaches to solve ordinary one dimensional differential equations describing the dynamics of hydraulic elements and pipes. First one is Matlab-Simulink-SimHydraulics, which is a commercial software developed to solve the dynamics of general hydraulic systems. It defines them with block elements. The other software is called HYDRA and it is based on the Lax-Wendrff numerical method, which serves as a tool to solve the momentum and continuity equations. This program was developed in Matlab by Brno University of Technology. Experimental measurements were performed on a simple test rig, which consists of an elastic pipe with strong damping connecting two reservoirs. Water hammer is induced with fast closing the valve. Physical properties of liquid and pipe elasticity parameters were considered in both simulations, which are in very good agreement and differences in comparison with experimental data are minimal.

Space Group Symmetry Fractionalization in a Chiral Kagome Heisenberg Antiferromagnet.

PubMed

Zaletel, Michael P; Zhu, Zhenyue; Lu, Yuan-Ming; Vishwanath, Ashvin; White, Steven R

2016-05-13

The anyonic excitations of a spin liquid can feature fractional quantum numbers under space group symmetries. Detecting these fractional quantum numbers, which are analogs of the fractional charge of Laughlin quasiparticles, may prove easier than the direct observation of anyonic braiding and statistics. Motivated by the recent numerical discovery of spin-liquid phases in the kagome Heisenberg antiferromagnet, we theoretically predict the pattern of space group symmetry fractionalization in the kagome lattice SO(3)-symmetric chiral spin liquid. We provide a method to detect these fractional quantum numbers in finite-size numerics which is simple to implement in the density matrix renormalization group. Applying these developments to the chiral spin liquid phase of a kagome Heisenberg model, we find perfect agreement between our theoretical prediction and numerical observations.

Simple Numerical Simulation of Strain Measurement

NASA Technical Reports Server (NTRS)

Tai, H.

2002-01-01

By adopting the basic principle of the reflection (and transmission) of a plane polarized electromagnetic wave incident normal to a stack of films of alternating refractive index, a simple numerical code was written to simulate the maximum reflectivity (transmittivity) of a fiber optic Bragg grating corresponding to various non-uniform strain conditions including photo-elastic effect in certain cases.

The method of space-time and conservation element and solution element: A new approach for solving the Navier-Stokes and Euler equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1995-01-01

A new numerical framework for solving conservation laws is being developed. This new framework differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to overcome several key limitations of the above traditional methods. A two-level scheme for solving the convection-diffusion equation is constructed and used to illuminate the major differences between the present method and those previously mentioned. This explicit scheme, referred to as the a-mu scheme, has two independent marching variables.

Geometrically derived difference formulae for the numerical integration of trajectory problems

NASA Technical Reports Server (NTRS)

Mcleod, R. J. Y.; Sanz-Serna, J. M.

1981-01-01

The term 'trajectory problem' is taken to include problems that can arise, for instance, in connection with contour plotting, or in the application of continuation methods, or during phase-plane analysis. Geometrical techniques are used to construct difference methods for these problems to produce in turn explicit and implicit circularly exact formulae. Based on these formulae, a predictor-corrector method is derived which, when compared with a closely related standard method, shows improved performance. It is found that this latter method produces spurious limit cycles, and this behavior is partly analyzed. Finally, a simple variable-step algorithm is constructed and tested.

Least Squares Moving-Window Spectral Analysis.

PubMed

Lee, Young Jong

2017-08-01

Least squares regression is proposed as a moving-windows method for analysis of a series of spectra acquired as a function of external perturbation. The least squares moving-window (LSMW) method can be considered an extended form of the Savitzky-Golay differentiation for nonuniform perturbation spacing. LSMW is characterized in terms of moving-window size, perturbation spacing type, and intensity noise. Simulation results from LSMW are compared with results from other numerical differentiation methods, such as single-interval differentiation, autocorrelation moving-window, and perturbation correlation moving-window methods. It is demonstrated that this simple LSMW method can be useful for quantitative analysis of nonuniformly spaced spectral data with high frequency noise.

A benchmark study of the sea-level equation in GIA modelling

NASA Astrophysics Data System (ADS)

Martinec, Zdenek; Klemann, Volker; van der Wal, Wouter; Riva, Riccardo; Spada, Giorgio; Simon, Karen; Blank, Bas; Sun, Yu; Melini, Daniele; James, Tom; Bradley, Sarah

2017-04-01

The sea-level load in glacial isostatic adjustment (GIA) is described by the so called sea-level equation (SLE), which represents the mass redistribution between ice sheets and oceans on a deforming earth. Various levels of complexity of SLE have been proposed in the past, ranging from a simple mean global sea level (the so-called eustatic sea level) to the load with a deforming ocean bottom, migrating coastlines and a changing shape of the geoid. Several approaches to solve the SLE have been derived, from purely analytical formulations to fully numerical methods. Despite various teams independently investigating GIA, there has been no systematic intercomparison amongst the solvers through which the methods may be validated. The goal of this paper is to present a series of benchmark experiments designed for testing and comparing numerical implementations of the SLE. Our approach starts with simple load cases even though the benchmark will not result in GIA predictions for a realistic loading scenario. In the longer term we aim for a benchmark with a realistic loading scenario, and also for benchmark solutions with rotational feedback. The current benchmark uses an earth model for which Love numbers have been computed and benchmarked in Spada et al (2011). In spite of the significant differences in the numerical methods employed, the test computations performed so far show a satisfactory agreement between the results provided by the participants. The differences found can often be attributed to the different approximations inherent to the various algorithms. Literature G. Spada, V. R. Barletta, V. Klemann, R. E. M. Riva, Z. Martinec, P. Gasperini, B. Lund, D. Wolf, L. L. A. Vermeersen, and M. A. King, 2011. A benchmark study for glacial isostatic adjustment codes. Geophys. J. Int. 185: 106-132 doi:10.1111/j.1365-

A fast method for finding bound systems in numerical simulations: Results from the formation of asteroid binaries

NASA Astrophysics Data System (ADS)

Leinhardt, Zoë M.; Richardson, Derek C.

2005-08-01

We present a new code ( companion) that identifies bound systems of particles in O(NlogN) time. Simple binaries consisting of pairs of mutually bound particles and complex hierarchies consisting of collections of mutually bound particles are identifiable with this code. In comparison, brute force binary search methods scale as O(N) while full hierarchy searches can be as expensive as O(N), making analysis highly inefficient for multiple data sets with N≳10. A simple test case is provided to illustrate the method. Timing tests demonstrating O(NlogN) scaling with the new code on real data are presented. We apply our method to data from asteroid satellite simulations [Durda et al., 2004. Icarus 167, 382-396; Erratum: Icarus 170, 242; reprinted article: Icarus 170, 243-257] and note interesting multi-particle configurations. The code is available at http://www.astro.umd.edu/zoe/companion/ and is distributed under the terms and conditions of the GNU Public License.

Effect of curvature on the backscattering from leaves

NASA Technical Reports Server (NTRS)

Sarabandi, K.; Senior, T. B. A.; Ulaby, F. T.

1988-01-01

Using a model previously developed for the backscattering cross section of a planar leaf at X-band frequencies and above, the effect of leaf curvature is examined. For normal incidence on a rectangular section of a leaf curved in one and two dimensions, an integral expression for the backscattered field is evaluated numerically and by a stationary phase approximation, leading to a simple analytical expression for the cross section reduction produced by the curvature. Numerical results based on the two methods are virtually identical, and in excellent agreement with measured data for rectangular sections of coleus leaves applied to the surfaces of styrofoam cylinders and spheres of different radii.

Effect of curvature on the backscattering from a leaf

NASA Technical Reports Server (NTRS)

Sarabandi, K.; Senior, T. B. A.; Ulaby, F. T.

1988-01-01

Using a model previously developed for the backscattering cross section of a planar leaf at X-band frequencies and above, the effect of leaf curvature is examined. For normal incidence on a rectangular section of a leaf curved in one and two dimensions, an integral expression for the backscattered field is evaluated numerically and by a stationary phase approximation, leading to a simple analytical expression for the cross-section reduction produced by the curvature. Numerical results based on the two methods are virtually identical, and in excellent agreement with measured data for rectangular sections of coleus leaves applied to the surfaces of styrofoam cylinders and spheres of different radii.

Neuronal Correlation Parameter and the Idea of Thermodynamic Entropy of an N-Body Gravitationally Bounded System.

PubMed

Haranas, Ioannis; Gkigkitzis, Ioannis; Kotsireas, Ilias; Austerlitz, Carlos

2017-01-01

Understanding how the brain encodes information and performs computation requires statistical and functional analysis. Given the complexity of the human brain, simple methods that facilitate the interpretation of statistical correlations among different brain regions can be very useful. In this report we introduce a numerical correlation measure that may serve the interpretation of correlational neuronal data, and may assist in the evaluation of different brain states. The description of the dynamical brain system, through a global numerical measure may indicate the presence of an action principle which may facilitate a application of physics principles in the study of the human brain and cognition.

Dislocation-induced stress in polycrystalline materials: mesoscopic simulations in the dislocation density formalism

NASA Astrophysics Data System (ADS)

Berkov, D. V.; Gorn, N. L.

2018-06-01

In this paper we present a simple and effective numerical method which allows a fast Fourier transformation-based evaluation of stress generated by dislocations with arbitrary directions and Burgers vectors if the (site-dependent) dislocation density is known. Our method allows the evaluation of the dislocation stress using a rectangular grid with shape-anisotropic discretization cells without employing higher multipole moments of the dislocation interaction coefficients. Using the proposed method, we first simulate the stress created by relatively simple non-homogeneous distributions of vertical edge and so-called ‘mixed’ dislocations in a disk-shaped sample, which is necessary to understand the dislocation behavior in more complicated systems. The main part of our research is devoted to the stress distribution in polycrystalline layers with the dislocation density rapidly varying with the distance to the layer bottom. Considering GaN as a typical example of such systems, we investigate dislocation-induced stress for edge and mixed dislocations, having random orientations of Burgers vectors among crystal grains. We show that the rapid decay of the dislocation density leads to many highly non-trivial features of the stress distributions in such layers and study in detail the dependence of these features on the average grain size. Finally we develop an analytical approach which allows us to predict the evolution of the stress variance with the grain size and compare analytical predictions with numerical results.

A novel method of utilizing permeable reactive kiddle (PRK) for the remediation of acid mine drainage.

PubMed

Lee, Woo-Chun; Lee, Sang-Woo; Yun, Seong-Taek; Lee, Pyeong-Koo; Hwang, Yu Sik; Kim, Soon-Oh

2016-01-15

Numerous technologies have been developed and applied to remediate AMD, but each has specific drawbacks. To overcome the limitations of existing methods and improve their effectiveness, we propose a novel method utilizing permeable reactive kiddle (PRK). This manuscript explores the performance of the PRK method. In line with the concept of green technology, the PRK method recycles industrial waste, such as steel slag and waste cast iron. Our results demonstrate that the PRK method can be applied to remediate AMD under optimal operational conditions. Especially, this method allows for simple installation and cheap expenditure, compared with established technologies. Copyright © 2015 Elsevier B.V. All rights reserved.

Hybrid Upwind Splitting (HUS) by a Field-by-Field Decomposition

NASA Technical Reports Server (NTRS)

Coquel, Frederic; Liou, Meng-Sing

1995-01-01

We introduce and develop a new approach for upwind biasing: the hybrid upwind splitting (HUS) method. This original procedure is based on a suitable hybridization of current prominent flux vector splitting (FVS) and flux difference splitting (FDS) methods. The HUS method is designed to naturally combine the respective strengths of the above methods while excluding their main deficiencies. Specifically, the HUS strategy yields a family of upwind methods that exhibit the robustness of FVS schemes in the capture of nonlinear waves and the accuracy of some FDS schemes in the resolution of linear waves. We give a detailed construction of the HUS methods following a general and systematic procedure directly performed at the basic level of the field by field (i.e. waves) decomposition involved in FDS methods. For such a given decomposition, each field is endowed either with FVS or FDS numerical fluxes, depending on the nonlinear nature of the field under consideration. Such a design principle is made possible thanks to the introduction of a convenient formalism that provides us with a unified framework for upwind methods. The HUS methods we propose bring significant improvements over current methods in terms of accuracy and robustness. They yield entropy-satisfying approximate solutions as they are strongly supported in numerical experiments. Field by field hybrid numerical fluxes also achieve fairly simple and explicit expressions and hence require a computational effort between that of the FVS and FDS. Several numerical experiments ranging from stiff 1D shock-tube to high speed viscous flows problems are displayed, intending to illustrate the benefits of the present approach. We assess in particular the relevance of our HUS schemes to viscous flow calculations.

A variational approach to multi-phase motion of gas, liquid and solid based on the level set method

NASA Astrophysics Data System (ADS)

Yokoi, Kensuke

2009-07-01

We propose a simple and robust numerical algorithm to deal with multi-phase motion of gas, liquid and solid based on the level set method [S. Osher, J.A. Sethian, Front propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulation, J. Comput. Phys. 79 (1988) 12; M. Sussman, P. Smereka, S. Osher, A level set approach for capturing solution to incompressible two-phase flow, J. Comput. Phys. 114 (1994) 146; J.A. Sethian, Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999; S. Osher, R. Fedkiw, Level Set Methods and Dynamics Implicit Surface, Applied Mathematical Sciences, vol. 153, Springer, 2003]. In Eulerian framework, to simulate interaction between a moving solid object and an interfacial flow, we need to define at least two functions (level set functions) to distinguish three materials. In such simulations, in general two functions overlap and/or disagree due to numerical errors such as numerical diffusion. In this paper, we resolved the problem using the idea of the active contour model [M. Kass, A. Witkin, D. Terzopoulos, Snakes: active contour models, International Journal of Computer Vision 1 (1988) 321; V. Caselles, R. Kimmel, G. Sapiro, Geodesic active contours, International Journal of Computer Vision 22 (1997) 61; G. Sapiro, Geometric Partial Differential Equations and Image Analysis, Cambridge University Press, 2001; R. Kimmel, Numerical Geometry of Images: Theory, Algorithms, and Applications, Springer-Verlag, 2003] introduced in the field of image processing.

A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

DOE PAGES

Gao, Kai; Chung, Eric T.; Gibson, Richard L.; ...

2015-06-05

The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elasticmore » wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.« less

Prediction of the interaction between a simple moving vehicle and an infinite periodically supported rail - Green's functions approach

NASA Astrophysics Data System (ADS)

Mazilu, Traian

2010-09-01

This paper herein describes the interaction between a simple moving vehicle and an infinite periodically supported rail, in order to signalise the basic features of the vehicle/track vibration behaviour in general, and wheel/rail vibration, in particular. The rail is modelled as an infinite Timoshenko beam resting on semi-sleepers via three-directional rail pads and ballast. The time-domain analysis was performed applying Green's matrix of the track method. This method allows taking into account the nonlinearities of the wheel/rail contact and the Doppler effect. The numerical analysis is dedicated to the wheel/rail response due to two types of excitation: the steady-state interaction and rail irregularities. The study points out to certain aspects regarding the parametric resonance, the amplitude-modulated vibration due to corrugation and the Doppler effect.

A Quick Method for Estimating Vehicle Characteristics Appropriate for Continuous Thrust Round Trip Missions Within the Solar System

NASA Technical Reports Server (NTRS)

Emrich, Bill

2006-01-01

A simple method of estimating vehicle parameters appropriate for interplanetary travel can provide a useful tool for evaluating the suitability of particular propulsion systems to various space missions. Although detailed mission analyses for interplanetary travel can be quite complex, it is possible to derive hirly simple correlations which will provide reasonable trip time estimates to the planets. In the present work, it is assumed that a constant thrust propulsion system propels a spacecraft on a round trip mission having equidistant outbound and inbound legs in which the spacecraft accelerates during the first portion of each leg of the journey and decelerates during the last portion of each leg of the journey. Comparisons are made with numerical calculations from low thrust trajectory codes to estimate the range of applicability of the simplified correlations.

A simple method to calculate first-passage time densities with arbitrary initial conditions

NASA Astrophysics Data System (ADS)

Nyberg, Markus; Ambjörnsson, Tobias; Lizana, Ludvig

2016-06-01

Numerous applications all the way from biology and physics to economics depend on the density of first crossings over a boundary. Motivated by the lack of general purpose analytical tools for computing first-passage time densities (FPTDs) for complex problems, we propose a new simple method based on the independent interval approximation (IIA). We generalise previous formulations of the IIA to include arbitrary initial conditions as well as to deal with discrete time and non-smooth continuous time processes. We derive a closed form expression for the FPTD in z and Laplace-transform space to a boundary in one dimension. Two classes of problems are analysed in detail: discrete time symmetric random walks (Markovian) and continuous time Gaussian stationary processes (Markovian and non-Markovian). Our results are in good agreement with Langevin dynamics simulations.

Simple adaptive control system design for a quadrotor with an internal PFC

NASA Astrophysics Data System (ADS)

Mizumoto, Ikuro; Nakamura, Takuto; Kumon, Makoto; Takagi, Taro

2014-12-01

The paper deals with an adaptive control system design problem for a four rotor helicopter or quadrotor. A simple adaptive control design scheme with a parallel feedforward compensator (PFC) in the internal loop of the considered quadrotor will be proposed based on the backstepping strategy. As is well known, the backstepping control strategy is one of the advanced control strategy for nonlinear systems. However, the control algorithm will become complex if the system has higher order relative degrees. We will show that one can skip some design steps of the backstepping method by introducing a PFC in the inner loop of the considered quadrotor, so that the structure of the obtained controller will be simplified and a high gain based adaptive feedback control system will be designed. The effectiveness of the proposed method will be confirmed through numerical simulations.

The Oceanographic Multipurpose Software Environment (OMUSE v1.0)

NASA Astrophysics Data System (ADS)

Pelupessy, Inti; van Werkhoven, Ben; van Elteren, Arjen; Viebahn, Jan; Candy, Adam; Portegies Zwart, Simon; Dijkstra, Henk

2017-08-01

In this paper we present the Oceanographic Multipurpose Software Environment (OMUSE). OMUSE aims to provide a homogeneous environment for existing or newly developed numerical ocean simulation codes, simplifying their use and deployment. In this way, numerical experiments that combine ocean models representing different physics or spanning different ranges of physical scales can be easily designed. Rapid development of simulation models is made possible through the creation of simple high-level scripts. The low-level core of the abstraction in OMUSE is designed to deploy these simulations efficiently on heterogeneous high-performance computing resources. Cross-verification of simulation models with different codes and numerical methods is facilitated by the unified interface that OMUSE provides. Reproducibility in numerical experiments is fostered by allowing complex numerical experiments to be expressed in portable scripts that conform to a common OMUSE interface. Here, we present the design of OMUSE as well as the modules and model components currently included, which range from a simple conceptual quasi-geostrophic solver to the global circulation model POP (Parallel Ocean Program). The uniform access to the codes' simulation state and the extensive automation of data transfer and conversion operations aids the implementation of model couplings. We discuss the types of couplings that can be implemented using OMUSE. We also present example applications that demonstrate the straightforward model initialization and the concurrent use of data analysis tools on a running model. We give examples of multiscale and multiphysics simulations by embedding a regional ocean model into a global ocean model and by coupling a surface wave propagation model with a coastal circulation model.

The Complex-Step-Finite-Difference method

NASA Astrophysics Data System (ADS)

Abreu, Rafael; Stich, Daniel; Morales, Jose

2015-07-01

We introduce the Complex-Step-Finite-Difference method (CSFDM) as a generalization of the well-known Finite-Difference method (FDM) for solving the acoustic and elastic wave equations. We have found a direct relationship between modelling the second-order wave equation by the FDM and the first-order wave equation by the CSFDM in 1-D, 2-D and 3-D acoustic media. We present the numerical methodology in order to apply the introduced CSFDM and show an example for wave propagation in simple homogeneous and heterogeneous models. The CSFDM may be implemented as an extension into pre-existing numerical techniques in order to obtain fourth- or sixth-order accurate results with compact three time-level stencils. We compare advantages of imposing various types of initial motion conditions of the CSFDM and demonstrate its higher-order accuracy under the same computational cost and dispersion-dissipation properties. The introduced method can be naturally extended to solve different partial differential equations arising in other fields of science and engineering.

Efficient solution of parabolic equations by Krylov approximation methods

NASA Technical Reports Server (NTRS)

Gallopoulos, E.; Saad, Y.

1990-01-01

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

A numerical method for computing unsteady 2-D boundary layer flows

NASA Technical Reports Server (NTRS)

Krainer, Andreas

1988-01-01

A numerical method for computing unsteady two-dimensional boundary layers in incompressible laminar and turbulent flows is described and applied to a single airfoil changing its incidence angle in time. The solution procedure adopts a first order panel method with a simple wake model to solve for the inviscid part of the flow, and an implicit finite difference method for the viscous part of the flow. Both procedures integrate in time in a step-by-step fashion, in the course of which each step involves the solution of the elliptic Laplace equation and the solution of the parabolic boundary layer equations. The Reynolds shear stress term of the boundary layer equations is modeled by an algebraic eddy viscosity closure. The location of transition is predicted by an empirical data correlation originating from Michel. Since transition and turbulence modeling are key factors in the prediction of viscous flows, their accuracy will be of dominant influence to the overall results.

An engineering study of hybrid adaptation of wind tunnel walls for three-dimensional testing

NASA Technical Reports Server (NTRS)

Brown, Clinton; Kalumuck, Kenneth; Waxman, David

1987-01-01

Solid wall tunnels having only upper and lower walls flexing are described. An algorithm for selecting the wall contours for both 2 and 3 dimensional wall flexure is presented and numerical experiments are used to validate its applicability to the general test case of 3 dimensional lifting aircraft models in rectangular cross section wind tunnels. The method requires an initial approximate representation of the model flow field at a given lift with wallls absent. The numerical methods utilized are derived by use of Green's source solutions obtained using the method of images; first order linearized flow theory is employed with Prandtl-Glauert compressibility transformations. Equations are derived for the flexed shape of a simple constant thickness plate wall under the influence of a finite number of jacks in an axial row along the plate centerline. The Green's source methods are developed to provide estimations of residual flow distortion (interferences) with measured wall pressures and wall flow inclinations as inputs.

A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pelanti, Marica, E-mail: marica.pelanti@ensta-paristech.fr; Shyue, Keh-Ming, E-mail: shyue@ntu.edu.tw

2014-02-15

We model liquid–gas flows with cavitation by a variant of the six-equation single-velocity two-phase model with stiff mechanical relaxation of Saurel–Petitpas–Berry (Saurel et al., 2009) [9]. In our approach we employ phasic total energy equations instead of the phasic internal energy equations of the classical six-equation system. This alternative formulation allows us to easily design a simple numerical method that ensures consistency with mixture total energy conservation at the discrete level and agreement of the relaxed pressure at equilibrium with the correct mixture equation of state. Temperature and Gibbs free energy exchange terms are included in the equations as relaxationmore » terms to model heat and mass transfer and hence liquid–vapor transition. The algorithm uses a high-resolution wave propagation method for the numerical approximation of the homogeneous hyperbolic portion of the model. In two dimensions a fully-discretized scheme based on a hybrid HLLC/Roe Riemann solver is employed. Thermo-chemical terms are handled numerically via a stiff relaxation solver that forces thermodynamic equilibrium at liquid–vapor interfaces under metastable conditions. We present numerical results of sample tests in one and two space dimensions that show the ability of the proposed model to describe cavitation mechanisms and evaporation wave dynamics.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hewett, D.W.; Yu-Jiuan Chen

The authors describe how they hold onto orthogonal mesh discretization when dealing with curved boundaries. Special difference operators were constructed to approximate numerical zones split by the domain boundary; the operators are particularly simple for this rectangular mesh. The authors demonstrated that this simple numerical approach, termed Dynamic Alternating Direction Implicit, turned out to be considerably more efficient than more complex grid-adaptive algorithms that were tried previously.

Numerical study of centrifugal compressor stage vaneless diffusers

NASA Astrophysics Data System (ADS)

Galerkin, Y.; Soldatova, K.; Solovieva, O.

2015-08-01

The authors analyzed CFD calculations of flow in vaneless diffusers with relative width in range from 0.014 to 0.100 at inlet flow angles in range from 100 to 450 with different inlet velocity coefficients, Reynolds numbers and surface roughness. The aim is to simulate calculated performances by simple algebraic equations. The friction coefficient that represents head losses as friction losses is proposed for simulation. The friction coefficient and loss coefficient are directly connected by simple equation. The advantage is that friction coefficient changes comparatively little in range of studied parameters. Simple equations for this coefficient are proposed by the authors. The simulation accuracy is sufficient for practical calculations. To create the complete algebraic model of the vaneless diffuser the authors plan to widen this method of modeling to diffusers with different relative length and for wider range of Reynolds numbers.

Periodic Pulay method for robust and efficient convergence acceleration of self-consistent field iterations

DOE PAGES

Banerjee, Amartya S.; Suryanarayana, Phanish; Pask, John E.

2016-01-21

Pulay's Direct Inversion in the Iterative Subspace (DIIS) method is one of the most widely used mixing schemes for accelerating the self-consistent solution of electronic structure problems. In this work, we propose a simple generalization of DIIS in which Pulay extrapolation is performed at periodic intervals rather than on every self-consistent field iteration, and linear mixing is performed on all other iterations. Lastly, we demonstrate through numerical tests on a wide variety of materials systems in the framework of density functional theory that the proposed generalization of Pulay's method significantly improves its robustness and efficiency.

A discontinuous Galerkin method for two-dimensional PDE models of Asian options

NASA Astrophysics Data System (ADS)

Hozman, J.; Tichý, T.; Cvejnová, D.

2016-06-01

In our previous research we have focused on the problem of plain vanilla option valuation using discontinuous Galerkin method for numerical PDE solution. Here we extend a simple one-dimensional problem into two-dimensional one and design a scheme for valuation of Asian options, i.e. options with payoff depending on the average of prices collected over prespecified horizon. The algorithm is based on the approach combining the advantages of the finite element methods together with the piecewise polynomial generally discontinuous approximations. Finally, an illustrative example using DAX option market data is provided.

Application of the probabilistic approximate analysis method to a turbopump blade analysis. [for Space Shuttle Main Engine

NASA Technical Reports Server (NTRS)

Thacker, B. H.; Mcclung, R. C.; Millwater, H. R.

1990-01-01

An eigenvalue analysis of a typical space propulsion system turbopump blade is presented using an approximate probabilistic analysis methodology. The methodology was developed originally to investigate the feasibility of computing probabilistic structural response using closed-form approximate models. This paper extends the methodology to structures for which simple closed-form solutions do not exist. The finite element method will be used for this demonstration, but the concepts apply to any numerical method. The results agree with detailed analysis results and indicate the usefulness of using a probabilistic approximate analysis in determining efficient solution strategies.

A simple mass-conserved level set method for simulation of multiphase flows

NASA Astrophysics Data System (ADS)

Yuan, H.-Z.; Shu, C.; Wang, Y.; Shu, S.

2018-04-01

In this paper, a modified level set method is proposed for simulation of multiphase flows with large density ratio and high Reynolds number. The present method simply introduces a source or sink term into the level set equation to compensate the mass loss or offset the mass increase. The source or sink term is derived analytically by applying the mass conservation principle with the level set equation and the continuity equation of flow field. Since only a source term is introduced, the application of the present method is as simple as the original level set method, but it can guarantee the overall mass conservation. To validate the present method, the vortex flow problem is first considered. The simulation results are compared with those from the original level set method, which demonstrates that the modified level set method has the capability of accurately capturing the interface and keeping the mass conservation. Then, the proposed method is further validated by simulating the Laplace law, the merging of two bubbles, a bubble rising with high density ratio, and Rayleigh-Taylor instability with high Reynolds number. Numerical results show that the mass is a well-conserved by the present method.

Simple optical method of qualitative assessment of sperm motility: preliminary results

NASA Astrophysics Data System (ADS)

Sozanska, Agnieszka; Kolwas, Krystyna; Galas, Jacek; Blocki, Narcyz; Czyzewski, Adam

2005-09-01

The examination of quality of the sperm ejaculate is one of the most important steps in artificial fertilization procedure. The main aim of semen storage centres is to characterise the best semen quality for fertilization. Reliable information about sperm motility is also one the most important parameters for in vitro laboratory procedures. There exist very expensive automated methods for semen analysis but they are unachievable for most of laboratories and semen storage centres. Motivation for this study is to elaborate a simple, cheap, objective and repeatable method for semen motility assessment. The method enables to detect even small changes in motility introduced by medical, physical or chemical factors. To test the reliability of the method we used cryopreserved bull semen from Lowicz Semen Storage Centre. The examined sperm specimen was warmed in water bath and then centrifuged. The best semen was collected by the swim-up technique and diluted to a proper concentration. Several semen concentrations and dilutions were tested in order to find the best probe parameters giving repeatable results. For semen visualization we used the phase-contrast microscope with a CCD camera. A PC computer was used to acquire and to analyse the data. The microscope table equipped with a microscope glass pool 0.7mm deep instead of some conventional plane microscope slides was stabilised at the temperature of 37°C. The main idea of our method is based on a numerical processing of the optical contrast of the sperm images which illustrates the dynamics of the sperm cells movement and on appropriate analysis of a grey scale level of the superimposed images. An elaborated numerical algorithm allows us to find the relative amount of motile sperm cells. The proposed method of sperm motility assessment seems to be objective and repeatable.

Regimes of stability and scaling relations for the removal time in the asteroid belt: a simple kinetic model and numerical tests

NASA Astrophysics Data System (ADS)

Cubrovic, Mihailo

2005-02-01

We report on our theoretical and numerical results concerning the transport mechanisms in the asteroid belt. We first derive a simple kinetic model of chaotic diffusion and show how it gives rise to some simple correlations (but not laws) between the removal time (the time for an asteroid to experience a qualitative change of dynamical behavior and enter a wide chaotic zone) and the Lyapunov time. The correlations are shown to arise in two different regimes, characterized by exponential and power-law scalings. We also show how is the so-called “stable chaos” (exponential regime) related to anomalous diffusion. Finally, we check our results numerically and discuss their possible applications in analyzing the motion of particular asteroids.

A simple method to eliminate shielding currents for magnetization perpendicular to superconducting tapes wound into coils

NASA Astrophysics Data System (ADS)

Kajikawa, Kazuhiro; Funaki, Kazuo

2011-12-01

Application of an external AC magnetic field parallel to superconducting tapes helps in eliminating the magnetization caused by the shielding current induced in the flat faces of the tapes. This method helps in realizing a magnet system with high-temperature superconducting tapes for magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR) applications. The effectiveness of the proposed method is validated by numerical calculations carried out using the finite-element method and experiments performed using a commercially available superconducting tape. The field uniformity for a single-layer solenoid coil after the application of an AC field is also estimated by a theoretical consideration.

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

Point-particle method to compute diffusion-limited cellular uptake.

PubMed

Sozza, A; Piazza, F; Cencini, M; De Lillo, F; Boffetta, G

2018-02-01

We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used to calibrate the method, linking the numerical parameters to the physical particle radius and uptake rate. We study the configurations of multiple absorbers of increasing complexity to examine the performance of the method by comparing our simulations with available exact analytical or numerical results. We demonstrate the potential of the method to resolve the complex diffusive interactions, here quantified by the Sherwood number, measuring the uptake rate in terms of that of isolated absorbers. We implement the method in a pseudospectral solver that can be generalized to include fluid motion and fluid-particle interactions. As a test case of the presence of a flow, we consider the uptake rate by a particle in a linear shear flow. Overall, our method represents a powerful and flexible computational tool that can be employed to investigate many complex situations in biology, chemistry, and related sciences.

Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) Collocation Method for Solving Linear and Nonlinear Fokker-Planck Equations

NASA Astrophysics Data System (ADS)

Parand, K.; Latifi, S.; Moayeri, M. M.; Delkhosh, M.

2018-05-01

In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective, reliable and does not require any restrictive assumptions for nonlinear terms.

Numerical simulation of failure behavior of granular debris flows based on flume model tests.

PubMed

Zhou, Jian; Li, Ye-xun; Jia, Min-cai; Li, Cui-na

2013-01-01

In this study, the failure behaviors of debris flows were studied by flume model tests with artificial rainfall and numerical simulations (PFC(3D)). Model tests revealed that grain sizes distribution had profound effects on failure mode, and the failure in slope of medium sand started with cracks at crest and took the form of retrogressive toe sliding failure. With the increase of fine particles in soil, the failure mode of the slopes changed to fluidized flow. The discrete element method PFC(3D) can overcome the hypothesis of the traditional continuous medium mechanic and consider the simple characteristics of particle. Thus, a numerical simulations model considering liquid-solid coupled method has been developed to simulate the debris flow. Comparing the experimental results, the numerical simulation result indicated that the failure mode of the failure of medium sand slope was retrogressive toe sliding, and the failure of fine sand slope was fluidized sliding. The simulation result is consistent with the model test and theoretical analysis, and grain sizes distribution caused different failure behavior of granular debris flows. This research should be a guide to explore the theory of debris flow and to improve the prevention and reduction of debris flow.

An improved version of NCOREL: A computer program for 3-D nonlinear supersonic potential flow computations

NASA Technical Reports Server (NTRS)

Siclari, Michael J.

1988-01-01

A computer code called NCOREL (for Nonconical Relaxation) has been developed to solve for supersonic full potential flows over complex geometries. The method first solves for the conical at the apex and then marches downstream in a spherical coordinate system. Implicit relaxation techniques are used to numerically solve the full potential equation at each subsequent crossflow plane. Many improvements have been made to the original code including more reliable numerics for computing wing-body flows with multiple embedded shocks, inlet flow through simulation, wake model and entropy corrections. Line relaxation or approximate factorization schemes are optionally available. Improved internal grid generation using analytic conformal mappings, supported by a simple geometric Harris wave drag input that was originally developed for panel methods and internal geometry package are some of the new features.

Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse

NASA Astrophysics Data System (ADS)

Lusso, Christelle; Ern, Alexandre; Bouchut, François; Mangeney, Anne; Farin, Maxime; Roche, Olivier

2017-03-01

This work is devoted to numerical modeling and simulation of granular flows relevant to geophysical flows such as avalanches and debris flows. We consider an incompressible viscoplastic fluid, described by a rheology with pressure-dependent yield stress, in a 2D setting with a free surface. We implement a regularization method to deal with the singularity of the rheological law, using a mixed finite element approximation of the momentum and incompressibility equations, and an arbitrary Lagrangian Eulerian (ALE) formulation for the displacement of the domain. The free surface is evolved by taking care of its deposition onto the bottom and of preventing it from folding over itself. Several tests are performed to assess the efficiency of our method. The first test is dedicated to verify its accuracy and cost on a one-dimensional simple shear plug flow. On this configuration we setup rules for the choice of the numerical parameters. The second test aims to compare the results of our numerical method to those predicted by an augmented Lagrangian formulation in the case of the collapse and spreading of a granular column over a horizontal rigid bed. Finally we show the reliability of our method by comparing numerical predictions to data from experiments of granular collapse of both trapezoidal and rectangular columns over horizontal rigid or erodible granular bed made of the same material. We compare the evolution of the free surface, the velocity profiles, and the static-flowing interface. The results show the ability of our method to deal numerically with the front behavior of granular collapses over an erodible bed.

Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics

NASA Astrophysics Data System (ADS)

Rangan, Aaditya V.; Cai, David; Tao, Louis

2007-02-01

Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear boundary conditions. The PDEs themselves are self-consistently specified by parameters which are functions of the boundary values of the solution. The moment equations can be stiff in space and time. Numerical methods are presented here for efficiently and accurately solving these moment equations. The essential ingredients in our numerical methods include: (i) the system is discretized in time with an implicit Euler method within a spectral deferred correction framework, therefore, the PDEs of the kinetic theory are reduced to a sequence, in time, of boundary value problems (BVPs) with nonlinear boundary conditions; (ii) a set of auxiliary parameters is introduced to recast the original BVP with nonlinear boundary conditions as BVPs with linear boundary conditions - with additional algebraic constraints on the auxiliary parameters; (iii) a careful combination of two Newton's iterates for the nonlinear BVP with linear boundary condition, interlaced with a Newton's iterate for solving the associated algebraic constraints is constructed to achieve quadratic convergence for obtaining the solutions with self-consistent parameters. It is shown that a simple fixed-point iteration can only achieve a linear convergence for the self-consistent parameters. The practicability and efficiency of our numerical methods for solving the moment equations of the kinetic theory are illustrated with numerical examples. It is further demonstrated that the moment equations derived from the kinetic theory of neuronal network dynamics can very well capture the coarse-grained dynamical properties of integrate-and-fire neuronal networks.

State relations for a two-phase mixture of reacting explosives and applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kubota, Shiro; Saburi, Tei; Ogata, Yuji

2007-10-15

To assess the assumptions behind the two phase mixture rule for reacting explosives, the shock-to-detonation transition process was calculated for high explosives using a finite difference method. An ignition and growth model and the Jones-Wilkins-Lee (JWL) equations of state were employed. The simple mixture rule assumes that the reacting explosive is a simple mixture of the reactant and product components. Four different assumptions, such as that of thermal equilibrium and isotropy, were adopted to calculate the pressure. The main purpose of this paper is to present the answer to the question of why the numerical results of shock-initiation are insensitivemore » to the assumptions adopted. The equations of state for reactants and products were assessed by considering plots of the specific internal energy E and specific volume V. If the slopes of the constant-pressure lines for both components in the E-V plane are almost the same, it is demonstrated that the numerical results are insensitive to the assumptions adopted. We have found that the relation for the specific volumes of the two components can be approximately expressed by a single curve of the specific volume of the reactant vs that of the products. We discuss this relationship in terms of the results of the numerical simulation. (author)« less

A Dynamic Approach to Monitoring Particle Fallout in a Cleanroom Environment

NASA Technical Reports Server (NTRS)

Perry, Radford L., III

2010-01-01

This slide presentation discusses a mathematical model to monitor particle fallout in a cleanroom. "Cleanliness levels" do not lead to increases with regards to cleanroom type or time because the levels are not linear. Activity level, impacts the cleanroom class. The numerical method presented leads to a simple Class-hour formulation, that allows for dynamic monitoring of the particle using a standard air particle counter.

Proposal for a quantitative index of flood disasters.

PubMed

Feng, Lihua; Luo, Gaoyuan

2010-07-01

Drawing on calculations of wind scale and earthquake magnitude, this paper develops a new quantitative method for measuring flood magnitude and disaster intensity. Flood magnitude is the quantitative index that describes the scale of a flood; the flood's disaster intensity is the quantitative index describing the losses caused. Both indices have numerous theoretical and practical advantages with definable concepts and simple applications, which lend them key practical significance.

Simple and fast spectral domain algorithm for quantitative phase imaging of living cells with digital holographic microscopy

NASA Astrophysics Data System (ADS)

Min, Junwei; Yao, Baoli; Ketelhut, Steffi; Kemper, Björn

2017-02-01

The modular combination of optical microscopes with digital holographic microscopy (DHM) has been proven to be a powerful tool for quantitative live cell imaging. The introduction of condenser and different microscope objectives (MO) simplifies the usage of the technique and makes it easier to measure different kinds of specimens with different magnifications. However, the high flexibility of illumination and imaging also causes variable phase aberrations that need to be eliminated for high resolution quantitative phase imaging. The existent phase aberrations compensation methods either require add additional elements into the reference arm or need specimen free reference areas or separate reference holograms to build up suitable digital phase masks. These inherent requirements make them unpractical for usage with highly variable illumination and imaging systems and prevent on-line monitoring of living cells. In this paper, we present a simple numerical method for phase aberration compensation based on the analysis of holograms in spatial frequency domain with capabilities for on-line quantitative phase imaging. From a single shot off-axis hologram, the whole phase aberration can be eliminated automatically without numerical fitting or pre-knowledge of the setup. The capabilities and robustness for quantitative phase imaging of living cancer cells are demonstrated.

Trajectory optimization for an asymmetric launch vehicle. M.S. Thesis - MIT

NASA Technical Reports Server (NTRS)

Sullivan, Jeanne Marie

1990-01-01

A numerical optimization technique is used to fully automate the trajectory design process for an symmetric configuration of the proposed Advanced Launch System (ALS). The objective of the ALS trajectory design process is the maximization of the vehicle mass when it reaches the desired orbit. The trajectories used were based on a simple shape that could be described by a small set of parameters. The use of a simple trajectory model can significantly reduce the computation time required for trajectory optimization. A predictive simulation was developed to determine the on-orbit mass given an initial vehicle state, wind information, and a set of trajectory parameters. This simulation utilizes an idealized control system to speed computation by increasing the integration time step. The conjugate gradient method is used for the numerical optimization of on-orbit mass. The method requires only the evaluation of the on-orbit mass function using the predictive simulation, and the gradient of the on-orbit mass function with respect to the trajectory parameters. The gradient is approximated with finite differencing. Prelaunch trajectory designs were carried out using the optimization procedure. The predictive simulation is used in flight to redesign the trajectory to account for trajectory deviations produced by off-nominal conditions, e.g., stronger than expected head winds.

Nanocrystal synthesis in microfluidic reactors: where next?

PubMed

Phillips, Thomas W; Lignos, Ioannis G; Maceiczyk, Richard M; deMello, Andrew J; deMello, John C

2014-09-07

The past decade has seen a steady rise in the use of microfluidic reactors for nanocrystal synthesis, with numerous studies reporting improved reaction control relative to conventional batch chemistry. However, flow synthesis procedures continue to lag behind batch methods in terms of chemical sophistication and the range of accessible materials, with most reports having involved simple one- or two-step chemical procedures directly adapted from proven batch protocols. Here we examine the current status of microscale methods for nanocrystal synthesis, and consider what role microreactors might ultimately play in laboratory-scale research and industrial production.

Finding all solutions of nonlinear equations using the dual simplex method

NASA Astrophysics Data System (ADS)

Yamamura, Kiyotaka; Fujioka, Tsuyoshi

2003-03-01

Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming. This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations using the dual simplex method. In this letter, an improved version of the LP test algorithm is proposed. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 300 nonlinear equations in practical computation time.

Discrete is it enough? The revival of Piola-Hencky keynotes to analyze three-dimensional Elastica

NASA Astrophysics Data System (ADS)

Turco, Emilio

2018-04-01

Complex problems such as those concerning the mechanics of materials can be confronted only by considering numerical simulations. Analytical methods are useful to build guidelines or reference solutions but, for general cases of technical interest, they have to be solved numerically, especially in the case of large displacements and deformations. Probably continuous models arose for producing inspiring examples and stemmed from homogenization techniques. These techniques allowed for the solution of some paradigmatic examples but, in general, always require a discretization method for solving problems dictated by the applications. Therefore, and also by taking into account that computing powers are nowadays more largely available and cheap, the question arises: why not using directly a discrete model for 3D beams? In other words, it could be interesting to formulate a discrete model without using an intermediate continuum one, as this last, at the end, has to be discretized in any case. These simple considerations immediately evoke some very basic models developed many years ago when the computing powers were practically inexistent but the problem of finding simple solutions to beam deformation problem was already an emerging one. Actually, in recent years, the keynotes of Hencky and Piola attracted a renewed attention [see, one for all, the work (Turco et al. in Zeitschrift für Angewandte Mathematik und Physik 67(4):1-28, 2016)]: generalizing their results, in the present paper, a novel directly discrete three-dimensional beam model is presented and discussed, in the framework of geometrically nonlinear analysis. Using a stepwise algorithm based essentially on Newton's method to compute the extrapolations and on the Riks' arc-length method to perform the corrections, we could obtain some numerical simulations showing the computational effectiveness of presented model: Indeed, it presents a convenient balance between accuracy and computational cost.

A matrix-inversion method for gamma-source mapping from gamma-count data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adsley, Ian; Burgess, Claire; Bull, Richard K

In a previous paper it was proposed that a simple matrix inversion method could be used to extract source distributions from gamma-count maps, using simple models to calculate the response matrix. The method was tested using numerically generated count maps. In the present work a 100 kBq Co{sup 60} source has been placed on a gridded surface and the count rate measured using a NaI scintillation detector. The resulting map of gamma counts was used as input to the matrix inversion procedure and the source position recovered. A multi-source array was simulated by superposition of several single-source count maps andmore » the source distribution was again recovered using matrix inversion. The measurements were performed for several detector heights. The effects of uncertainties in source-detector distances on the matrix inversion method are also examined. The results from this work give confidence in the application of the method to practical applications, such as the segregation of highly active objects amongst fuel-element debris. (authors)« less

Numerical simulation of a shear-thinning fluid through packed spheres

NASA Astrophysics Data System (ADS)

Liu, Hai Long; Moon, Jong Sin; Hwang, Wook Ryol

2012-12-01

Flow behaviors of a non-Newtonian fluid in spherical microstructures have been studied by a direct numerical simulation. A shear-thinning (power-law) fluid through both regular and randomly packed spheres has been numerically investigated in a representative unit cell with the tri-periodic boundary condition, employing a rigorous three-dimensional finite-element scheme combined with fictitious-domain mortar-element methods. The present scheme has been validated for the classical spherical packing problems with literatures. The flow mobility of regular packing structures, including simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC), as well as randomly packed spheres, has been investigated quantitatively by considering the amount of shear-thinning, the pressure gradient and the porosity as parameters. Furthermore, the mechanism leading to the main flow path in a highly shear-thinning fluid through randomly packed spheres has been discussed.

Supercomputer use in orthopaedic biomechanics research: focus on functional adaptation of bone.

PubMed

Hart, R T; Thongpreda, N; Van Buskirk, W C

1988-01-01

The authors describe two biomechanical analyses carried out using numerical methods. One is an analysis of the stress and strain in a human mandible, and the other analysis involves modeling the adaptive response of a sheep bone to mechanical loading. The computing environment required for the two types of analyses is discussed. It is shown that a simple stress analysis of a geometrically complex mandible can be accomplished using a minicomputer. However, more sophisticated analyses of the same model with dynamic loading or nonlinear materials would require supercomputer capabilities. A supercomputer is also required for modeling the adaptive response of living bone, even when simple geometric and material models are use.

Numerical solutions to the time-dependent Bloch equations revisited.

PubMed

Murase, Kenya; Tanki, Nobuyoshi

2011-01-01

The purpose of this study was to demonstrate a simple and fast method for solving the time-dependent Bloch equations. First, the time-dependent Bloch equations were reduced to a homogeneous linear differential equation, and then a simple equation was derived to solve it using a matrix operation. The validity of this method was investigated by comparing with the analytical solutions in the case of constant radiofrequency irradiation. There was a good agreement between them, indicating the validity of this method. As a further example, this method was applied to the time-dependent Bloch equations in the two-pool exchange model for chemical exchange saturation transfer (CEST) or amide proton transfer (APT) magnetic resonance imaging (MRI), and the Z-spectra and asymmetry spectra were calculated from their solutions. They were also calculated using the fourth/fifth-order Runge-Kutta-Fehlberg (RKF) method for comparison. There was also a good agreement between them, and this method was much faster than the RKF method. In conclusion, this method will be useful for analyzing the complex CEST or APT contrast mechanism and/or investigating the optimal conditions for CEST or APT MRI. Copyright © 2011 Elsevier Inc. All rights reserved.

Zombie states for description of structure and dynamics of multi-electron systems

NASA Astrophysics Data System (ADS)

Shalashilin, Dmitrii V.

2018-05-01

Canonical Coherent States (CSs) of Harmonic Oscillator have been extensively used as a basis in a number of computational methods of quantum dynamics. However, generalising such techniques for fermionic systems is difficult because Fermionic Coherent States (FCSs) require complicated algebra of Grassmann numbers not well suited for numerical calculations. This paper introduces a coherent antisymmetrised superposition of "dead" and "alive" electronic states called here Zombie State (ZS), which can be used in a manner of FCSs but without Grassmann algebra. Instead, for Zombie States, a very simple sign-changing rule is used in the definition of creation and annihilation operators. Then, calculation of electronic structure Hamiltonian matrix elements between two ZSs becomes very simple and a straightforward technique for time propagation of fermionic wave functions can be developed. By analogy with the existing methods based on Canonical Coherent States of Harmonic Oscillator, fermionic wave functions can be propagated using a set of randomly selected Zombie States as a basis. As a proof of principles, the proposed Coupled Zombie States approach is tested on a simple example showing that the technique is exact.

Electromagnetic Field Penetration Studies

NASA Technical Reports Server (NTRS)

Deshpande, M.D.

2000-01-01

A numerical method is presented to determine electromagnetic shielding effectiveness of rectangular enclosure with apertures on its wall used for input and output connections, control panels, visual-access windows, ventilation panels, etc. Expressing EM fields in terms of cavity Green's function inside the enclosure and the free space Green's function outside the enclosure, integral equations with aperture tangential electric fields as unknown variables are obtained by enforcing the continuity of tangential electric and magnetic fields across the apertures. Using the Method of Moments, the integral equations are solved for unknown aperture fields. From these aperture fields, the EM field inside a rectangular enclosure due to external electromagnetic sources are determined. Numerical results on electric field shielding of a rectangular cavity with a thin rectangular slot obtained using the present method are compared with the results obtained using simple transmission line technique for code validation. The present technique is applied to determine field penetration inside a Boeing-757 by approximating its passenger cabin as a rectangular cavity filled with a homogeneous medium and its passenger windows by rectangular apertures. Preliminary results for, two windows, one on each side of fuselage were considered. Numerical results for Boeing-757 at frequencies 26 MHz, 171-175 MHz, and 428-432 MHz are presented.

A new adaptive estimation method of spacecraft thermal mathematical model with an ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Akita, T.; Takaki, R.; Shima, E.

2012-04-01

An adaptive estimation method of spacecraft thermal mathematical model is presented. The method is based on the ensemble Kalman filter, which can effectively handle the nonlinearities contained in the thermal model. The state space equations of the thermal mathematical model is derived, where both temperature and uncertain thermal characteristic parameters are considered as the state variables. In the method, the thermal characteristic parameters are automatically estimated as the outputs of the filtered state variables, whereas, in the usual thermal model correlation, they are manually identified by experienced engineers using trial-and-error approach. A numerical experiment of a simple small satellite is provided to verify the effectiveness of the presented method.

Models of convection-driven tectonic plates - A comparison of methods and results

NASA Technical Reports Server (NTRS)

King, Scott D.; Gable, Carl W.; Weinstein, Stuart A.

1992-01-01

Recent numerical studies of convection in the earth's mantle have included various features of plate tectonics. This paper describes three methods of modeling plates: through material properties, through force balance, and through a thin power-law sheet approximation. The results obtained are compared using each method on a series of simple calculations. From these results, scaling relations between the different parameterizations are developed. While each method produces different degrees of deformation within the surface plate, the surface heat flux and average plate velocity agree to within a few percent. The main results are not dependent upon the plate modeling method and herefore are representative of the physical system modeled.

Solid oxide fuel cell simulation and design optimization with numerical adjoint techniques

NASA Astrophysics Data System (ADS)

Elliott, Louie C.

This dissertation reports on the application of numerical optimization techniques as applied to fuel cell simulation and design. Due to the "multi-physics" inherent in a fuel cell, which results in a highly coupled and non-linear behavior, an experimental program to analyze and improve the performance of fuel cells is extremely difficult. This program applies new optimization techniques with computational methods from the field of aerospace engineering to the fuel cell design problem. After an overview of fuel cell history, importance, and classification, a mathematical model of solid oxide fuel cells (SOFC) is presented. The governing equations are discretized and solved with computational fluid dynamics (CFD) techniques including unstructured meshes, non-linear solution methods, numerical derivatives with complex variables, and sensitivity analysis with adjoint methods. Following the validation of the fuel cell model in 2-D and 3-D, the results of the sensitivity analysis are presented. The sensitivity derivative for a cost function with respect to a design variable is found with three increasingly sophisticated techniques: finite difference, direct differentiation, and adjoint. A design cycle is performed using a simple optimization method to improve the value of the implemented cost function. The results from this program could improve fuel cell performance and lessen the world's dependence on fossil fuels.

On some variational acceleration techniques and related methods for local refinement

NASA Astrophysics Data System (ADS)

Teigland, Rune

1998-10-01

This paper shows that the well-known variational acceleration method described by Wachspress (E. Wachspress, Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics, Prentice-Hall, Englewood Cliffs, NJ, 1966) and later generalized to multilevels (known as the additive correction multigrid method (B.R Huthchinson and G.D. Raithby, Numer. Heat Transf., 9, 511-537 (1986))) is similar to the FAC method of McCormick and Thomas (S.F McCormick and J.W. Thomas, Math. Comput., 46, 439-456 (1986)) and related multilevel methods. The performance of the method is demonstrated for some simple model problems using local refinement and suggestions for improving the performance of the method are given.

THE SYSTEMATIC ERROR TEST FOR PSF CORRECTION IN WEAK GRAVITATIONAL LENSING SHEAR MEASUREMENT BY THE ERA METHOD BY IDEALIZING PSF

DOE Office of Scientific and Technical Information (OSTI.GOV)

Okura, Yuki; Futamase, Toshifumi, E-mail: yuki.okura@riken.jp

We improve the ellipticity of re-smeared artificial image (ERA) method of point-spread function (PSF) correction in a weak lensing shear analysis in order to treat the realistic shape of galaxies and the PSF. This is done by re-smearing the PSF and the observed galaxy image using a re-smearing function (RSF) and allows us to use a new PSF with a simple shape and to correct the PSF effect without any approximations or assumptions. We perform a numerical test to show that the method applied for galaxies and PSF with some complicated shapes can correct the PSF effect with a systematicmore » error of less than 0.1%. We also apply the ERA method for real data of the Abell 1689 cluster to confirm that it is able to detect the systematic weak lensing shear pattern. The ERA method requires less than 0.1 or 1 s to correct the PSF for each object in a numerical test and a real data analysis, respectively.« less

Three-dimensional Diffusive Strip Method

NASA Astrophysics Data System (ADS)

Martinez-Ruiz, Daniel; Meunier, Patrice; Duchemin, Laurent; Villermaux, Emmanuel

2016-11-01

The Diffusive Strip Method (DSM) is a near-exact numerical method developed for mixing computations at large Péclet number in two-dimensions. The method consists in following stretched material lines to compute a-posteriori the resulting scalar field is extended here to three-dimensional flows, following surfaces. We describe its 3D peculiarities, and show how it applies to a simple Taylor-Couette configuration with non-rotating boundary conditions at the top end, bottom and outer cylinder. This flow produces an elaborate, although controlled, steady 3D flow which relies on the Ekman pumping arising from the rotation of the inner cylinder is both studied experimentally, and numerically modeled. A recurrent two-cells structure appears formed by stream tubes shaped as nested tori. A scalar blob in the flow experiences a Lagrangian oscillating dynamics with stretchings and compressions, driving the mixing process, and yielding both rapidly-mixed and nearly pure-diffusive regions. A triangulated-surface method is developed to calculate the blob elongation and scalar concentration PDFs through a single variable computation along the advected blob surface, capturing the rich evolution observed in the experiments.

Burton-Miller-type singular boundary method for acoustic radiation and scattering

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Gu, Yan

2014-08-01

This paper proposes the singular boundary method (SBM) in conjunction with Burton and Miller's formulation for acoustic radiation and scattering. The SBM is a strong-form collocation boundary discretization technique using the singular fundamental solutions, which is mathematically simple, easy-to-program, meshless and introduces the concept of source intensity factors (SIFs) to eliminate the singularities of the fundamental solutions. Therefore, it avoids singular numerical integrals in the boundary element method (BEM) and circumvents the troublesome placement of the fictitious boundary in the method of fundamental solutions (MFS). In the present method, we derive the SIFs of exterior Helmholtz equation by means of the SIFs of exterior Laplace equation owing to the same order of singularities between the Laplace and Helmholtz fundamental solutions. In conjunction with the Burton-Miller formulation, the SBM enhances the quality of the solution, particularly in the vicinity of the corresponding interior eigenfrequencies. Numerical illustrations demonstrate efficiency and accuracy of the present scheme on some benchmark examples under 2D and 3D unbounded domains in comparison with the analytical solutions, the boundary element solutions and Dirichlet-to-Neumann finite element solutions.

Hirarchical emotion calculation model for virtual human modellin - biomed 2010.

PubMed

Zhao, Yue; Wright, David

2010-01-01

This paper introduces a new emotion generation method for virtual human modelling. The method includes a novel hierarchical emotion structure, a group of emotion calculation equations and a simple heuristics decision making mechanism, which enables virtual humans to perform emotionally in real-time according to their internal and external factors. Emotion calculation equations used in this research were derived from psychologic emotion measurements. Virtual humans can utilise the information in virtual memory and emotion calculation equations to generate their own numerical emotion states within the hierarchical emotion structure. Those emotion states are important internal references for virtual humans to adopt appropriate behaviours and also key cues for their decision making. A simple heuristics theory is introduced and integrated into decision making process in order to make the virtual humans decision making more like a real human. A data interface which connects the emotion calculation and the decision making structure together has also been designed and simulated to test the method in Virtools environment.

Effective Algorithm for Detection and Correction of the Wave Reconstruction Errors Caused by the Tilt of Reference Wave in Phase-shifting Interferometry

NASA Astrophysics Data System (ADS)

Xu, Xianfeng; Cai, Luzhong; Li, Dailin; Mao, Jieying

2010-04-01

In phase-shifting interferometry (PSI) the reference wave is usually supposed to be an on-axis plane wave. But in practice a slight tilt of reference wave often occurs, and this tilt will introduce unexpected errors of the reconstructed object wave-front. Usually the least-square method with iterations, which is time consuming, is employed to analyze the phase errors caused by the tilt of reference wave. Here a simple effective algorithm is suggested to detect and then correct this kind of errors. In this method, only some simple mathematic operation is used, avoiding using least-square equations as needed in most methods reported before. It can be used for generalized phase-shifting interferometry with two or more frames for both smooth and diffusing objects, and the excellent performance has been verified by computer simulations. The numerical simulations show that the wave reconstruction errors can be reduced by 2 orders of magnitude.

Large eddy simulations and direct numerical simulations of high speed turbulent reacting flows

NASA Technical Reports Server (NTRS)

Givi, Peyman; Madnia, Cyrus K.; Steinberger, Craig J.

1990-01-01

This research is involved with the implementation of advanced computational schemes based on large eddy simulations (LES) and direct numerical simulations (DNS) to study the phenomenon of mixing and its coupling with chemical reactions in compressible turbulent flows. In the efforts related to LES, a research program to extend the present capabilities of this method was initiated for the treatment of chemically reacting flows. In the DNS efforts, the focus is on detailed investigations of the effects of compressibility, heat release, and non-equilibrium kinetics modelings in high speed reacting flows. Emphasis was on the simulations of simple flows, namely homogeneous compressible flows, and temporally developing high speed mixing layers.

Estimation of the curvature of the solid liquid interface during Bridgman crystal growth

NASA Astrophysics Data System (ADS)

Barat, Catherine; Duffar, Thierry; Garandet, Jean-Paul

1998-11-01

An approximate solution for the solid/liquid interface curvature due to the crucible effect in crystal growth is derived from simple heat flux considerations. The numerical modelling of the problem carried out with the help of the finite element code FIDAP supports the predictions of our analytical expression and allows to identify its range of validity. Experimental interface curvatures, measured in gallium antimonide samples grown by the vertical Bridgman method, are seen to compare satisfactorily to analytical and numerical results. Other literature data are also in fair agreement with the predictions of our models in the case where the amount of heat carried by the crucible is small compared to the overall heat flux.

Numerical Solution of the Extended Nernst-Planck Model.

PubMed

Samson; Marchand

1999-07-01

The main features of a numerical model aiming at predicting the drift of ions in an electrolytic solution upon a chemical potential gradient are presented. The mechanisms of ionic diffusion are described by solving the extended Nernst-Planck system of equations. The electrical coupling between the various ionic fluxes is accounted for by the Poisson equation. Furthermore, chemical activity effects are considered in the model. The whole system of nonlinear equations is solved using the finite-element method. Results yielded by the model for simple test cases are compared to those obtained using an analytical solution. Applications of the model to more complex problems are also presented and discussed. Copyright 1999 Academic Press.

Numerical simulation of transmission coefficient using c-number Langevin equation

NASA Astrophysics Data System (ADS)

Barik, Debashis; Bag, Bidhan Chandra; Ray, Deb Shankar

2003-12-01

We numerically implement the reactive flux formalism on the basis of a recently proposed c-number Langevin equation [Barik et al., J. Chem. Phys. 119, 680 (2003); Banerjee et al., Phys. Rev. E 65, 021109 (2002)] to calculate transmission coefficient. The Kramers' turnover, the T2 enhancement of the rate at low temperatures and other related features of temporal behavior of the transmission coefficient over a range of temperature down to absolute zero, noise correlation, and friction are examined for a double well potential and compared with other known results. This simple method is based on canonical quantization and Wigner quasiclassical phase space function and takes care of quantum effects due to the system order by order.

Numerical Modeling in Geodynamics: Success, Failure and Perspective

NASA Astrophysics Data System (ADS)

Ismail-Zadeh, A.

2005-12-01

A real success in numerical modeling of dynamics of the Earth can be achieved only by multidisciplinary research teams of experts in geodynamics, applied and pure mathematics, and computer science. The success in numerical modeling is based on the following basic, but simple, rules. (i) People need simplicity most, but they understand intricacies best (B. Pasternak, writer). Start from a simple numerical model, which describes basic physical laws by a set of mathematical equations, and move then to a complex model. Never start from a complex model, because you cannot understand the contribution of each term of the equations to the modeled geophysical phenomenon. (ii) Study the numerical methods behind your computer code. Otherwise it becomes difficult to distinguish true and erroneous solutions to the geodynamic problem, especially when your problem is complex enough. (iii) Test your model versus analytical and asymptotic solutions, simple 2D and 3D model examples. Develop benchmark analysis of different numerical codes and compare numerical results with laboratory experiments. Remember that the numerical tool you employ is not perfect, and there are small bugs in every computer code. Therefore the testing is the most important part of your numerical modeling. (iv) Prove (if possible) or learn relevant statements concerning the existence, uniqueness and stability of the solution to the mathematical and discrete problems. Otherwise you can solve an improperly-posed problem, and the results of the modeling will be far from the true solution of your model problem. (v) Try to analyze numerical models of a geological phenomenon using as less as possible tuning model variables. Already two tuning variables give enough possibilities to constrain your model well enough with respect to observations. The data fitting sometimes is quite attractive and can take you far from a principal aim of your numerical modeling: to understand geophysical phenomena. (vi) If the number of tuning model variables are greater than two, test carefully the effect of each of the variables on the modeled phenomenon. Remember: With four exponents I can fit an elephant (E. Fermi, physicist). (vii) Make your numerical model as accurate as possible, but never put the aim to reach a great accuracy: Undue precision of computations is the first symptom of mathematical illiteracy (N. Krylov, mathematician). How complex should be a numerical model? A model which images any detail of the reality is as useful as a map of scale 1:1 (J. Robinson, economist). This message is quite important for geoscientists, who study numerical models of complex geodynamical processes. I believe that geoscientists will never create a model of the real Earth dynamics, but we should try to model the dynamics such a way to simulate basic geophysical processes and phenomena. Does a particular model have a predictive power? Each numerical model has a predictive power, otherwise the model is useless. The predictability of the model varies with its complexity. Remember that a solution to the numerical model is an approximate solution to the equations, which have been chosen in believe that they describe dynamic processes of the Earth. Hence a numerical model predicts dynamics of the Earth as well as the mathematical equations describe this dynamics. What methodological advances are still needed for testable geodynamic modeling? Inverse (time-reverse) numerical modeling and data assimilation are new methodologies in geodynamics. The inverse modeling can allow to test geodynamic models forward in time using restored (from present-day observations) initial conditions instead of unknown conditions.

Algorithms for computing the geopotential using a simple density layer

NASA Technical Reports Server (NTRS)

Morrison, F.

1976-01-01

Several algorithms have been developed for computing the potential and attraction of a simple density layer. These are numerical cubature, Taylor series, and a mixed analytic and numerical integration using a singularity-matching technique. A computer program has been written to combine these techniques for computing the disturbing acceleration on an artificial earth satellite. A total of 1640 equal-area, constant surface density blocks on an oblate spheroid are used. The singularity-matching algorithm is used in the subsatellite region, Taylor series in the surrounding zone, and numerical cubature on the rest of the earth.

The Lyapunov dimension and its estimation via the Leonov method

NASA Astrophysics Data System (ADS)

Kuznetsov, N. V.

2016-06-01

Along with widely used numerical methods for estimating and computing the Lyapunov dimension there is an effective analytical approach, proposed by G.A. Leonov in 1991. The Leonov method is based on the direct Lyapunov method with special Lyapunov-like functions. The advantage of the method is that it allows one to estimate the Lyapunov dimension of invariant sets without localization of the set in the phase space and, in many cases, to get effectively an exact Lyapunov dimension formula. In this work the invariance of the Lyapunov dimension with respect to diffeomorphisms and its connection with the Leonov method are discussed. For discrete-time dynamical systems an analog of Leonov method is suggested. In a simple but rigorous way, here it is presented the connection between the Leonov method and the key related works: Kaplan and Yorke (the concept of the Lyapunov dimension, 1979), Douady and Oesterlé (upper bounds of the Hausdorff dimension via the Lyapunov dimension of maps, 1980), Constantin, Eden, Foiaş, and Temam (upper bounds of the Hausdorff dimension via the Lyapunov exponents and Lyapunov dimension of dynamical systems, 1985-90), and the numerical calculation of the Lyapunov exponents and dimension.

One-pot synthesis of monodisperse CoFe2O4@Ag core-shell nanoparticles and their characterization.

PubMed

Hara, Shuta; Aisu, Jumpei; Kato, Masahiro; Aono, Takashige; Sugawa, Kosuke; Takase, Kouichi; Otsuki, Joe; Shimizu, Shigeru; Ikake, Hiroki

2018-06-08

In recent years, monodispersed magnetic nanoparticles with a core/shell structure are expected for their wide applications including magnetic fluid, recoverable catalysts, and biological analysis. However, their synthesis method needs numerous processes such as solvent substitution, exchange of protective agents, and centrifugation. A simple and rapid method for the synthesis of monodispersed core-shell nanoparticles makes it possible to accelerate their further applications. This paper describes a simple and rapid one-pot synthesis of core (CoFe 2 O 4 )-shell (Ag) nanoparticles with high monodispersity. The synthesized nanoparticles showed plasmonic light absorption owing to the Ag shell. Moreover, the magnetic property of the nanoparticles had a soft magnetic behavior at room temperature and a hard magnetic behavior at 5 K. In addition, the nanoparticles showed high monodispersity with a low polydispersity index (PDI) value of 0.083 in hexane.

Phase-and-amplitude recovery from a single phase-contrast image using partially spatially coherent x-ray radiation

NASA Astrophysics Data System (ADS)

Beltran, Mario A.; Paganin, David M.; Pelliccia, Daniele

2018-05-01

A simple method of phase-and-amplitude extraction is derived that corrects for image blurring induced by partially spatially coherent incident illumination using only a single intensity image as input. The method is based on Fresnel diffraction theory for the case of high Fresnel number, merged with the space-frequency description formalism used to quantify partially coherent fields and assumes the object under study is composed of a single-material. A priori knowledge of the object’s complex refractive index and information obtained by characterizing the spatial coherence of the source is required. The algorithm was applied to propagation-based phase-contrast data measured with a laboratory-based micro-focus x-ray source. The blurring due to the finite spatial extent of the source is embedded within the algorithm as a simple correction term to the so-called Paganin algorithm and is also numerically stable in the presence of noise.

One-pot synthesis of monodisperse CoFe2O4@Ag core-shell nanoparticles and their characterization

NASA Astrophysics Data System (ADS)

Hara, Shuta; Aisu, Jumpei; Kato, Masahiro; Aono, Takashige; Sugawa, Kosuke; Takase, Kouichi; Otsuki, Joe; Shimizu, Shigeru; Ikake, Hiroki

2018-06-01

In recent years, monodispersed magnetic nanoparticles with a core/shell structure are expected for their wide applications including magnetic fluid, recoverable catalysts, and biological analysis. However, their synthesis method needs numerous processes such as solvent substitution, exchange of protective agents, and centrifugation. A simple and rapid method for the synthesis of monodispersed core-shell nanoparticles makes it possible to accelerate their further applications. This paper describes a simple and rapid one-pot synthesis of core (CoFe2O4)-shell (Ag) nanoparticles with high monodispersity. The synthesized nanoparticles showed plasmonic light absorption owing to the Ag shell. Moreover, the magnetic property of the nanoparticles had a soft magnetic behavior at room temperature and a hard magnetic behavior at 5 K. In addition, the nanoparticles showed high monodispersity with a low polydispersity index (PDI) value of 0.083 in hexane.

Simple adaptive control system design for a quadrotor with an internal PFC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mizumoto, Ikuro; Nakamura, Takuto; Kumon, Makoto

2014-12-10

The paper deals with an adaptive control system design problem for a four rotor helicopter or quadrotor. A simple adaptive control design scheme with a parallel feedforward compensator (PFC) in the internal loop of the considered quadrotor will be proposed based on the backstepping strategy. As is well known, the backstepping control strategy is one of the advanced control strategy for nonlinear systems. However, the control algorithm will become complex if the system has higher order relative degrees. We will show that one can skip some design steps of the backstepping method by introducing a PFC in the inner loopmore » of the considered quadrotor, so that the structure of the obtained controller will be simplified and a high gain based adaptive feedback control system will be designed. The effectiveness of the proposed method will be confirmed through numerical simulations.« less

Numerical and Experimental Study of a Cooling for Vanes in a Small Turbine Engine

NASA Astrophysics Data System (ADS)

Šimák, Jan; Michálek, Jan

2016-03-01

This paper is concerned with a cooling system for inlet guide vanes of a small turbine engine which are exposed to a high temperature gas leaving a combustion chamber. Because of small dimensions of the vanes, only a simple internal cavity and cooling holes can be realized. The idea was to utilize a film cooling technique. The proposed solution was simulated by means of a numerical method based on a coupling of CFD and heat transfer solvers. The numerical results of various scenarios (different coolant temperature, heat transfer to surroundings) showed a desired decrease of the temperature, especially on the most critical part - the trailing edge. The numerical data are compared to results obtained by experimental measurements performed in a test facility in our institute. A quarter segment model of the inlet guide vanes wheel was equipped with thermocouples in order to verify an effect of cooling. Despite some uncertainty in the results, a verifiable decrease of the vane temperature was observed.

Large calculation of the flow over a hypersonic vehicle using a GPU

NASA Astrophysics Data System (ADS)

Elsen, Erich; LeGresley, Patrick; Darve, Eric

2008-12-01

Graphics processing units are capable of impressive computing performance up to 518 Gflops peak performance. Various groups have been using these processors for general purpose computing; most efforts have focussed on demonstrating relatively basic calculations, e.g. numerical linear algebra, or physical simulations for visualization purposes with limited accuracy. This paper describes the simulation of a hypersonic vehicle configuration with detailed geometry and accurate boundary conditions using the compressible Euler equations. To the authors' knowledge, this is the most sophisticated calculation of this kind in terms of complexity of the geometry, the physical model, the numerical methods employed, and the accuracy of the solution. The Navier-Stokes Stanford University Solver (NSSUS) was used for this purpose. NSSUS is a multi-block structured code with a provably stable and accurate numerical discretization which uses a vertex-based finite-difference method. A multi-grid scheme is used to accelerate the solution of the system. Based on a comparison of the Intel Core 2 Duo and NVIDIA 8800GTX, speed-ups of over 40× were demonstrated for simple test geometries and 20× for complex geometries.

Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical electromagnetism techniques

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rodriguez, Alejandro; Ibanescu, Mihai; Joannopoulos, J. D.

2007-09-15

We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green's function for imaginary frequencies (equivalently, real frequencies in imaginary time). We develop the approach by systematically examining various formulations of Casimir forces from the previous decades and evaluating them according to their suitability for numerical computation. We illustratemore » our approach with a simple finite-difference frequency-domain implementation, test it for known geometries such as a cylinder and a plate, and apply it to new geometries. In particular, we show that a pistonlike geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising nonmonotonic ''lateral'' force from the walls.« less

Experimental study of the oscillation of spheres in an acoustic levitator.

PubMed

Andrade, Marco A B; Pérez, Nicolás; Adamowski, Julio C

2014-10-01

The spontaneous oscillation of solid spheres in a single-axis acoustic levitator is experimentally investigated by using a high speed camera to record the position of the levitated sphere as a function of time. The oscillations in the axial and radial directions are systematically studied by changing the sphere density and the acoustic pressure amplitude. In order to interpret the experimental results, a simple model based on a spring-mass system is applied in the analysis of the sphere oscillatory behavior. This model requires the knowledge of the acoustic pressure distribution, which was obtained numerically by using a linear finite element method (FEM). Additionally, the linear acoustic pressure distribution obtained by FEM was compared with that measured with a laser Doppler vibrometer. The comparison between numerical and experimental pressure distributions shows good agreement for low values of pressure amplitude. When the pressure amplitude is increased, the acoustic pressure distribution becomes nonlinear, producing harmonics of the fundamental frequency. The experimental results of the spheres oscillations for low pressure amplitudes are consistent with the results predicted by the simple model based on a spring-mass system.

Rotation of a spheroid in a Couette flow at moderate Reynolds numbers.

PubMed

Yu, Zhaosheng; Phan-Thien, Nhan; Tanner, Roger I

2007-08-01

The rotation of a single spheroid in a planar Couette flow as a model for simple shear flow is numerically simulated with the distributed Lagrangian multiplier based fictitious domain method. The study is focused on the effects of inertia on the orbital behavior of prolate and oblate spheroids. The numerical orbits are found to be well described by a simple empirical model, which states that the rate of the spheroid rotation about the vorticity axis is a sinusoidal function of the corresponding projection angle in the flow-gradient plane, and that the exponential growth rate of the orbit function is a constant. The following transitions in the steady state with increasing Reynolds number are identified: Jeffery orbit, tumbling, quasi-Jeffery orbit, log rolling, and inclined rolling for a prolate spheroid; and Jeffery orbit, log rolling, inclined rolling, and motionless state for an oblate spheroid. In addition, it is shown that the orbit behavior is sensitive to the initial orientation in the case of strong inertia and there exist different steady states for certain shear Reynolds number regimes.

Experimental investigation and numerical simulation of 3He gas diffusion in simple geometries: implications for analytical models of 3He MR lung morphometry.

PubMed

Parra-Robles, J; Ajraoui, S; Deppe, M H; Parnell, S R; Wild, J M

2010-06-01

Models of lung acinar geometry have been proposed to analytically describe the diffusion of (3)He in the lung (as measured with pulsed gradient spin echo (PGSE) methods) as a possible means of characterizing lung microstructure from measurement of the (3)He ADC. In this work, major limitations in these analytical models are highlighted in simple diffusion weighted experiments with (3)He in cylindrical models of known geometry. The findings are substantiated with numerical simulations based on the same geometry using finite difference representation of the Bloch-Torrey equation. The validity of the existing "cylinder model" is discussed in terms of the physical diffusion regimes experienced and the basic reliance of the cylinder model and other ADC-based approaches on a Gaussian diffusion behaviour is highlighted. The results presented here demonstrate that physical assumptions of the cylinder model are not valid for large diffusion gradient strengths (above approximately 15 mT/m), which are commonly used for (3)He ADC measurements in human lungs. (c) 2010 Elsevier Inc. All rights reserved.

A tutorial solution to scattering of radiation in a thin atmosphere bounded below by a diffusely reflecting, absorbing surface

NASA Technical Reports Server (NTRS)

Buglia, J. J.

1982-01-01

A simple tutorial method, based on a photon tracking procedure, is described to determine the spherical albedo for a thin atmosphere overlying a reflecting surface. This procedure is used to provide a physical structure with which to interpret the more detailed but highly mathematical analyses presented. The final equations are shown to be in good numerical agreement with more exact solutions for thin atmospheres.

A Facile Preparation of Imidazolinium Chlorides

PubMed Central

Kuhn, Kevin M.; Grubbs, Robert H.

2009-01-01

A process for the preparation of symmetric and unsymmetric imidazolinium chlorides that involves reaction of a formamidine with dichloroethane and a base (a) is described. This method makes it possible to obtain numerous imidazolinium chlorides under solvent-free reaction conditions and in excellent yields with purification by simple filtration. Alternatively, symmetric imidazolinium chlorides can be prepared directly in moderate yields from substituted anilines by utilizing half of the formamidine intermediate as sacrificial base (b). PMID:18412354

Usefulness of Wave Data Assimilation to the WAVE WATCH III Modeling System

NASA Astrophysics Data System (ADS)

Choi, J. K.; Dykes, J. D.; Yaremchuk, M.; Wittmann, P.

2017-12-01

In-situ and remote-sensed wave data are more abundant currently than in years past, with excellent accuracy at global scales. Forecast skill of the WAVE WATCH III model is improved by assimilation of these measurements and they are also useful for model validation and calibration. It has been known that the impact of assimilation in wind-sea conditions is not large, but spectra that result in large swell with long term propagation are identified and assimilated, the improved accuracy of the initial conditions improve the long-term forecasts. The Navy's assimilation method started with the simple Optimal Interpolation (OI) method. Operationally, Fleet Numerical Meteorology and Oceanography Center uses the sequential 2DVar scheme, but a new approach has been tested based on an adjoint-free method to variational assimilation in WAVE WATCH III. We will present the status of wave data assimilation into the WAVE WATCH III numerical model and upcoming development of this new adjoint-free variational approach.

Orthogonal polynomial projectors for the Projector Augmented Wave (PAW) formalism.

NASA Astrophysics Data System (ADS)

Holzwarth, N. A. W.; Matthews, G. E.; Tackett, A. R.; Dunning, R. B.

1998-03-01

The PAW method for density functional electronic structure calculations developed by Blöchl(Phys. Rev. B 50), 17953 (1994) and also used by our group(Phys. Rev. B 55), 2005 (1997) has numerical advantages of a pseudopotential technique while retaining the physics of an all-electron formalism. We describe a new method for generating the necessary set of atom-centered projector and basis functions, based on choosing the projector functions from a set of orthogonal polynomials multiplied by a localizing weight factor. Numerical benefits of the new scheme result from having direct control of the shape of the projector functions and from the use of a simple repulsive local potential term to eliminate ``ghost state" problems, which can haunt calculations of this kind. We demonstrate the method by calculating the cohesive energies of CaF2 and Mo and the density of states of CaMoO4 which shows detailed agreement with LAPW results over a 66 eV range of energy including upper core, valence, and conduction band states.

Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils

NASA Astrophysics Data System (ADS)

Soranzo, Enrico; Wu, Wei

2013-04-01

Excavation of shallow tunnels with the New Austrian Tunnelling Method (NATM) requires proper assessing of the tunnel face stability, to enable an open-face excavation, and the estimation of the correspondent surface settlements. Soils in a partially saturated condition exhibit a higher cohesion than in a fully saturated state, which can be taken into account when assessing the stability of the tunnel face. For the assessment of the face support pressure, different methods are used in engineering practice, varying from simple empirical and analytical formulations to advanced finite element analysis. Such procedures can be modified to account for the unsaturated state of soils. In this study a method is presented to incorporate the effect of partial saturation in the numerical analysis. The results are then compared with a simple analytical formulation derived from parametric studies. As to the numerical analysis, the variation of cohesion and of Young's modulus with saturation can be considered when the water table lies below the tunnel in a soil exhibiting a certain capillary rise, so that the tunnel is driven in a partially saturated layer. The linear elastic model with Mohr-Coulomb failure criterion can be extended to partially saturated states and calibrated with triaxial tests on unsaturated. In order to model both positive and negative pore water pressure (suction), Bishop's effective stress is incorporated into Mohr-Coulomb's failure criterion. The effective stress parameter in Bishop's formulation is related to the degree of saturation as suggested by Fredlund. If a linear suction distribution is assumed, the degree of saturation can be calculated from the Soil Water Characteristic Curve (SWCC). Expressions exist that relate the Young's modulus of unsaturated soils to the net mean stress and the matric suction. The results of the numerical computation can be compared to Vermeer & Ruse's closed-form formula that expresses the limit support pressure of the tunnel face. The expression is derived from parametric studies and predicts stability of the tunnel face when negative values are returned, suggesting that open-face tunnelling can be performed. The formula can be modified to account for the variation of cohesion along the tunnel face. The results obtained from both the numerical analysis and the analytical formulation are well in agreement and show that the stability of the tunnel face can greatly benefit from the enhanced cohesion of partially saturated soils.

Incorporating the gas analyzer response time in gas exchange computations.

PubMed

Mitchell, R R

1979-11-01

A simple method for including the gas analyzer response time in the breath-by-breath computation of gas exchange rates is described. The method uses a difference equation form of a model for the gas analyzer in the computation of oxygen uptake and carbon dioxide production and avoids a numerical differentiation required to correct the gas fraction wave forms. The effect of not accounting for analyzer response time is shown to be a 20% underestimation in gas exchange rate. The present method accurately measures gas exchange rate, is relatively insensitive to measurement errors in the analyzer time constant, and does not significantly increase the computation time.

Simple method for the generation of multiple homogeneous field volumes inside the bore of superconducting magnets.

PubMed

Chou, Ching-Yu; Ferrage, Fabien; Aubert, Guy; Sakellariou, Dimitris

2015-07-17

Standard Magnetic Resonance magnets produce a single homogeneous field volume, where the analysis is performed. Nonetheless, several modern applications could benefit from the generation of multiple homogeneous field volumes along the axis and inside the bore of the magnet. In this communication, we propose a straightforward method using a combination of ring structures of permanent magnets in order to cancel the gradient of the stray field in a series of distinct volumes. These concepts were demonstrated numerically on an experimentally measured magnetic field profile. We discuss advantages and limitations of our method and present the key steps required for an experimental validation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kang, Hyun-Ju; Chung, Chin-Wook, E-mail: joykang@hanyang.ac.kr; Choi, Hyeok

A modified central difference method (MCDM) is proposed to obtain the electron energy distribution functions (EEDFs) in single Langmuir probes. Numerical calculation of the EEDF with MCDM is simple and has less noise. This method provides the second derivatives at a given point as the weighted average of second order central difference derivatives calculated at different voltage intervals, weighting each by the square of the interval. In this paper, the EEDFs obtained from MCDM are compared to those calculated via the averaged central difference method. It is found that MCDM effectively suppresses the noises in the EEDF, while the samemore » number of points are used to calculate of the second derivative.« less

Finite difference elastic wave modeling with an irregular free surface using ADER scheme

NASA Astrophysics Data System (ADS)

Almuhaidib, Abdulaziz M.; Nafi Toksöz, M.

2015-06-01

In numerical modeling of seismic wave propagation in the earth, we encounter two important issues: the free surface and the topography of the surface (i.e. irregularities). In this study, we develop a 2D finite difference solver for the elastic wave equation that combines a 4th- order ADER scheme (Arbitrary high-order accuracy using DERivatives), which is widely used in aeroacoustics, with the characteristic variable method at the free surface boundary. The idea is to treat the free surface boundary explicitly by using ghost values of the solution for points beyond the free surface to impose the physical boundary condition. The method is based on the velocity-stress formulation. The ultimate goal is to develop a numerical solver for the elastic wave equation that is stable, accurate and computationally efficient. The solver treats smooth arbitrary-shaped boundaries as simple plane boundaries. The computational cost added by treating the topography is negligible compared to flat free surface because only a small number of grid points near the boundary need to be computed. In the presence of topography, using 10 grid points per shortest shear-wavelength, the solver yields accurate results. Benchmark numerical tests using several complex models that are solved by our method and other independent accurate methods show an excellent agreement, confirming the validity of the method for modeling elastic waves with an irregular free surface.

Effect of atmospheric scattering and surface reflection on upwelling solar radiation

NASA Technical Reports Server (NTRS)

Suttles, J. T.; Barkstrom, B. R.; Tiwari, S. N.

1981-01-01

A study is presented of the solar radiation transfer in the complete earth-atmosphere system, and numerical results are compared with satellite data obtained during the Earth Radiation Budget Experiment on Nimbus 6, in August, 1975. Emphasis is placed on the upwelling radiance distribution at the top of the atmosphere, assumed to be at 50 km. The numerical technique is based on the finite difference method, which includes azimuth and spectral variations for the entire solar wavelength range. Detailed solar properties, atmospheric physical properties, and optical properties are used. However, since the property descriptions are based on a trade-off between accuracy and computational realities, aerosol and cloud optical properties are treated with simple approximations. The radiative transfer model is in good agreement with the satellite radiance observations. The method provides a valuable tool in analyzing satellite- and ground-based radiation budget measurements and in designing instrumentation.

Finite element solution of optimal control problems with inequality constraints

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.

1990-01-01

A finite-element method based on a weak Hamiltonian form of the necessary conditions is summarized for optimal control problems. Very crude shape functions (so simple that element numerical quadrature is not necessary) can be used to develop an efficient procedure for obtaining candidate solutions (i.e., those which satisfy all the necessary conditions) even for highly nonlinear problems. An extension of the formulation allowing for discontinuities in the states and derivatives of the states is given. A theory that includes control inequality constraints is fully developed. An advanced launch vehicle (ALV) model is presented. The model involves staging and control constraints, thus demonstrating the full power of the weak formulation to date. Numerical results are presented along with total elapsed computer time required to obtain the results. The speed and accuracy in obtaining the results make this method a strong candidate for a real-time guidance algorithm.

Prediction of sound absorption in rigid porous media with the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

da Silva, Andrey Ricardo; Mareze, Paulo; Brandão, Eric

2016-02-01

In this work, sound absorption phenomena associated with the viscous shear stress within rigid porous media is investigated with a simple isothermal lattice Boltzmann BGK model. Simulations are conducted for different macroscopic material properties such as sample thickness and porosity and the results are compared with the exact analytical solution for materials with slit-like structure in terms of acoustic impedance and sound absorption coefficient. The numerical results agree very well with the exact solution, particularly for the sound absorption coefficient. The small deviations found in the low frequency limit for the real part of the acoustic impedance are attributed to the ratio between the thicknesses of the slit and the viscous boundary layer. The results suggest that the lattice Boltzmann method can be a very compelling numerical tool for simulating viscous sound absorption phenomena in the time domain, particularly due to its computational simplicity when compared to traditional continuum based techniques.

Zero-multipole summation method for efficiently estimating electrostatic interactions in molecular system.

PubMed

Fukuda, Ikuo

2013-11-07

The zero-multipole summation method has been developed to efficiently evaluate the electrostatic Coulombic interactions of a point charge system. This summation prevents the electrically non-neutral multipole states that may artificially be generated by a simple cutoff truncation, which often causes large amounts of energetic noise and significant artifacts. The resulting energy function is represented by a constant term plus a simple pairwise summation, using a damped or undamped Coulombic pair potential function along with a polynomial of the distance between each particle pair. Thus, the implementation is straightforward and enables facile applications to high-performance computations. Any higher-order multipole moment can be taken into account in the neutrality principle, and it only affects the degree and coefficients of the polynomial and the constant term. The lowest and second moments correspond respectively to the Wolf zero-charge scheme and the zero-dipole summation scheme, which was previously proposed. Relationships with other non-Ewald methods are discussed, to validate the current method in their contexts. Good numerical efficiencies were easily obtained in the evaluation of Madelung constants of sodium chloride and cesium chloride crystals.

Direct simulation Monte Carlo modeling of relaxation processes in polyatomic gases

NASA Astrophysics Data System (ADS)

Pfeiffer, M.; Nizenkov, P.; Mirza, A.; Fasoulas, S.

2016-02-01

Relaxation processes of polyatomic molecules are modeled and implemented in an in-house Direct Simulation Monte Carlo code in order to enable the simulation of atmospheric entry maneuvers at Mars and Saturn's Titan. The description of rotational and vibrational relaxation processes is derived from basic quantum-mechanics using a rigid rotator and a simple harmonic oscillator, respectively. Strategies regarding the vibrational relaxation process are investigated, where good agreement for the relaxation time according to the Landau-Teller expression is found for both methods, the established prohibiting double relaxation method and the new proposed multi-mode relaxation. Differences and applications areas of these two methods are discussed. Consequently, two numerical methods used for sampling of energy values from multi-dimensional distribution functions are compared. The proposed random-walk Metropolis algorithm enables the efficient treatment of multiple vibrational modes within a time step with reasonable computational effort. The implemented model is verified and validated by means of simple reservoir simulations and the comparison to experimental measurements of a hypersonic, carbon-dioxide flow around a flat-faced cylinder.

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

Numerical modeling of an enhanced very early time electromagnetic (VETEM) prototype system

USGS Publications Warehouse

Cui, T.J.; Chew, W.C.; Aydiner, A.A.; Wright, D.L.; Smith, D.V.; Abraham, J.D.

2000-01-01

In this paper, two numerical models are presented to simulate an enhanced very early time electromagnetic (VETEM) prototype system, which is used for buried-object detection and environmental problems. Usually, the VETEM system contains a transmitting loop antenna and a receiving loop antenna, which run on a lossy ground to detect buried objects. In the first numerical model, the loop antennas are accurately analyzed using the Method of Moments (MoM) for wire antennas above or buried in lossy ground. Then, Conjugate Gradient (CG) methods, with the use of the fast Fourier transform (FFT) or MoM, are applied to investigate the scattering from buried objects. Reflected and scattered magnetic fields are evaluated at the receiving loop to calculate the output electric current. However, the working frequency for the VETEM system is usually low and, hence, two magnetic dipoles are used to replace the transmitter and receiver in the second numerical model. Comparing these two models, the second one is simple, but only valid for low frequency or small loops, while the first modeling is more general. In this paper, all computations are performed in the frequency domain, and the FFT is used to obtain the time-domain responses. Numerical examples show that simulation results from these two models fit very well when the frequency ranges from 10 kHz to 10 MHz, and both results are close to the measured data.

Computation of Sound Propagation by Boundary Element Method

NASA Technical Reports Server (NTRS)

Guo, Yueping

2005-01-01

This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which are used to compare the BEM solutions. The comparisons show very good agreements and validate the accuracy of the BEM approach implemented here.

Hemodynamic effect of bypass geometry on intracranial aneurysm: A numerical investigation.

PubMed

Kurşun, Burak; Uğur, Levent; Keskin, Gökhan

2018-05-01

Hemodynamic analyzes are used in the clinical investigation and treatment of cardiovascular diseases. In the present study, the effect of bypass geometry on intracranial aneurysm hemodynamics was investigated numerically. Pressure, wall shear stress (WSS) and velocity distribution causing the aneurysm to grow and rupture were investigated and the best conditions were tried to be determined in case of bypassing between basilar (BA) and left/right posterior arteries (LPCA/RPCA) for different values of parameters. The finite volume method was used for numerical solutions and calculations were performed with the ANSYS-Fluent software. The SIMPLE algorithm was used to solve the discretized conservation equations. Second Order Upwind method was preferred for finding intermediate point values in the computational domain. As the blood flow velocity changes with time, the blood viscosity value also changes. For this reason, the Carreu model was used in determining the viscosity depending on the velocity. Numerical study results showed that when bypassed, pressure and wall shear stresses reduced in the range of 40-70% in the aneurysm. Numerical results obtained are presented in graphs including the variation of pressure, wall shear stress and velocity streamlines in the aneurysm. Considering the numerical results for all parameter values, it is seen that the most important factors affecting the pressure and WSS values in bypassing are the bypass position on the basilar artery (L b ) and the diameter of the bypass vessel (d). Pressure and wall shear stress reduced in the range of 40-70% in the aneurysm in the case of bypass for all parameters. This demonstrates that pressure and WSS values can be greatly reduced in aneurysm treatment by bypassing in cases where clipping or coil embolization methods can not be applied. Copyright © 2018 Elsevier B.V. All rights reserved.

A simple but precise method for quantitative measurement of the quality of the laser focus in a scanning optical microscope

PubMed Central

MACRAE, K.; TRAVIS, C.; AMOR, R.; NORRIS, G.; WILSON, S.H.; OPPO, G.‐L.; MCCONNELL, G.

2015-01-01

Summary We report a method for characterizing the focussing laser beam exiting the objective in a laser scanning microscope. This method provides the size of the optical focus, the divergence of the beam, the ellipticity and the astigmatism. We use a microscopic‐scale knife edge in the form of a simple transmission electron microscopy grid attached to a glass microscope slide, and a light‐collecting optical fibre and photodiode underneath the specimen. By scanning the laser spot from a reflective to a transmitting part of the grid, a beam profile in the form of an error function can be obtained and by repeating this with the knife edge at different axial positions relative to the beam waist, the divergence and astigmatism of the postobjective laser beam can be obtained. The measured divergence can be used to quantify how much of the full numerical aperture of the lens is used in practice. We present data of the beam radius, beam divergence, ellipticity and astigmatism obtained with low (0.15, 0.7) and high (1.3) numerical aperture lenses and lasers commonly used in confocal and multiphoton laser scanning microscopy. Our knife‐edge method has several advantages over alternative knife‐edge methods used in microscopy including that the knife edge is easy to prepare, that the beam can be characterized also directly under a cover slip, as necessary to reduce spherical aberrations for objectives designed to be used with a cover slip, and it is suitable for use with commercial laser scanning microscopes where access to the laser beam can be limited. PMID:25864964

Numerical convergence of the self-diffusion coefficient and viscosity obtained with Thomas-Fermi-Dirac molecular dynamics.

PubMed

Danel, J-F; Kazandjian, L; Zérah, G

2012-06-01

Computations of the self-diffusion coefficient and viscosity in warm dense matter are presented with an emphasis on obtaining numerical convergence and a careful evaluation of the standard deviation. The transport coefficients are computed with the Green-Kubo relation and orbital-free molecular dynamics at the Thomas-Fermi-Dirac level. The numerical parameters are varied until the Green-Kubo integral is equal to a constant in the t→+∞ limit; the transport coefficients are deduced from this constant and not by extrapolation of the Green-Kubo integral. The latter method, which gives rise to an unknown error, is tested for the computation of viscosity; it appears that it should be used with caution. In the large domain of coupling constant considered, both the self-diffusion coefficient and viscosity turn out to be well approximated by simple analytical laws using a single effective atomic number calculated in the average-atom model.

Numerical convergence of the self-diffusion coefficient and viscosity obtained with Thomas-Fermi-Dirac molecular dynamics

NASA Astrophysics Data System (ADS)

Danel, J.-F.; Kazandjian, L.; Zérah, G.

2012-06-01

Computations of the self-diffusion coefficient and viscosity in warm dense matter are presented with an emphasis on obtaining numerical convergence and a careful evaluation of the standard deviation. The transport coefficients are computed with the Green-Kubo relation and orbital-free molecular dynamics at the Thomas-Fermi-Dirac level. The numerical parameters are varied until the Green-Kubo integral is equal to a constant in the t→+∞ limit; the transport coefficients are deduced from this constant and not by extrapolation of the Green-Kubo integral. The latter method, which gives rise to an unknown error, is tested for the computation of viscosity; it appears that it should be used with caution. In the large domain of coupling constant considered, both the self-diffusion coefficient and viscosity turn out to be well approximated by simple analytical laws using a single effective atomic number calculated in the average-atom model.

Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg; Zhou, Yu

2016-07-15

Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonantmore » frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.« less

Effect of load eccentricity on the buckling of thin-walled laminated C-columns

NASA Astrophysics Data System (ADS)

Wysmulski, Pawel; Teter, Andrzej; Debski, Hubert

2018-01-01

The study investigates the behaviour of short, thin-walled laminated C-columns under eccentric compression. The tested columns are simple-supported. The effect of load inaccuracy on the critical and post-critical (local buckling) states is examined. A numerical analysis by the finite element method and experimental tests on a test stand are performed. The samples were produced from a carbon-epoxy prepreg by the autoclave technique. The experimental tests rest on the assumption that compressive loads are 1.5 higher than the theoretical critical force. Numerical modelling is performed using the commercial software package ABAQUS®. The critical load is determined by solving an eigen problem using the Subspace algorithm. The experimental critical loads are determined based on post-buckling paths. The numerical and experimental results show high agreement, thus demonstrating a significant effect of load inaccuracy on the critical load corresponding to the column's local buckling.

Effect of Forcing Function on Nonlinear Acoustic Standing Waves

NASA Technical Reports Server (NTRS)

Finkheiner, Joshua R.; Li, Xiao-Fan; Raman, Ganesh; Daniels, Chris; Steinetz, Bruce

2003-01-01

Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.

Numerical simulations of sessile droplet evaporating on heated substrate

NASA Astrophysics Data System (ADS)

Chen, Xue; Chen, Paul G.; Ouazzani, Jalil; Liu, Qiusheng

2017-04-01

Motivated by the space project EFILE, a 2D axisymmetric numerical model in the framework of ALE method is developed to investigate the coupled physical mechanism during the evaporation of a pinned drop that partially wets on a heated substrate. The model accounts for mass transport in surrounding air, Marangoni convection inside the drop and heat conduction in the substrate as well as moving interface. Numerical results predict simple scaling laws for the evaporation rate which scales linearly with drop radius but follows a power-law with substrate temperature. It is highlighted that thermal effect of the substrate has a great impact on the temperature profile at the drop surface, which leads to a multicellular thermocapillary flow pattern. In particular, the structure of the multicellular flow behavior induced within a heated drop is mainly controlled by a geometric parameter (aspect ratio). A relationship between the number of thermal cells and the aspect ratio is proposed.

Review of FD-TD numerical modeling of electromagnetic wave scattering and radar cross section

NASA Technical Reports Server (NTRS)

Taflove, Allen; Umashankar, Korada R.

1989-01-01

Applications of the finite-difference time-domain (FD-TD) method for numerical modeling of electromagnetic wave interactions with structures are reviewed, concentrating on scattering and radar cross section (RCS). A number of two- and three-dimensional examples of FD-TD modeling of scattering and penetration are provided. The objects modeled range in nature from simple geometric shapes to extremely complex aerospace and biological systems. Rigorous analytical or experimental validatons are provided for the canonical shapes, and it is shown that FD-TD predictive data for near fields and RCS are in excellent agreement with the benchmark data. It is concluded that with continuing advances in FD-TD modeling theory for target features relevant to the RCS problems and in vector and concurrent supercomputer technology, it is likely that FD-TD numerical modeling will occupy an important place in RCS technology in the 1990s and beyond.

MUSTA fluxes for systems of conservation laws

NASA Astrophysics Data System (ADS)

Toro, E. F.; Titarev, V. A.

2006-08-01

This paper is about numerical fluxes for hyperbolic systems and we first present a numerical flux, called GFORCE, that is a weighted average of the Lax-Friedrichs and Lax-Wendroff fluxes. For the linear advection equation with constant coefficient, the new flux reduces identically to that of the Godunov first-order upwind method. Then we incorporate GFORCE in the framework of the MUSTA approach [E.F. Toro, Multi-Stage Predictor-Corrector Fluxes for Hyperbolic Equations. Technical Report NI03037-NPA, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK, 17th June, 2003], resulting in a version that we call GMUSTA. For non-linear systems this gives results that are comparable to those of the Godunov method in conjunction with the exact Riemann solver or complete approximate Riemann solvers, noting however that in our approach, the solution of the Riemann problem in the conventional sense is avoided. Both the GFORCE and GMUSTA fluxes are extended to multi-dimensional non-linear systems in a straightforward unsplit manner, resulting in linearly stable schemes that have the same stability regions as the straightforward multi-dimensional extension of Godunov's method. The methods are applicable to general meshes. The schemes of this paper share with the family of centred methods the common properties of being simple and applicable to a large class of hyperbolic systems, but the schemes of this paper are distinctly more accurate. Finally, we proceed to the practical implementation of our numerical fluxes in the framework of high-order finite volume WENO methods for multi-dimensional non-linear hyperbolic systems. Numerical results are presented for the Euler equations and for the equations of magnetohydrodynamics.

Respiratory Artefact Removal in Forced Oscillation Measurements: A Machine Learning Approach.

PubMed

Pham, Thuy T; Thamrin, Cindy; Robinson, Paul D; McEwan, Alistair L; Leong, Philip H W

2017-08-01

Respiratory artefact removal for the forced oscillation technique can be treated as an anomaly detection problem. Manual removal is currently considered the gold standard, but this approach is laborious and subjective. Most existing automated techniques used simple statistics and/or rejected anomalous data points. Unfortunately, simple statistics are insensitive to numerous artefacts, leading to low reproducibility of results. Furthermore, rejecting anomalous data points causes an imbalance between the inspiratory and expiratory contributions. From a machine learning perspective, such methods are unsupervised and can be considered simple feature extraction. We hypothesize that supervised techniques can be used to find improved features that are more discriminative and more highly correlated with the desired output. Features thus found are then used for anomaly detection by applying quartile thresholding, which rejects complete breaths if one of its features is out of range. The thresholds are determined by both saliency and performance metrics rather than qualitative assumptions as in previous works. Feature ranking indicates that our new landmark features are among the highest scoring candidates regardless of age across saliency criteria. F1-scores, receiver operating characteristic, and variability of the mean resistance metrics show that the proposed scheme outperforms previous simple feature extraction approaches. Our subject-independent detector, 1IQR-SU, demonstrated approval rates of 80.6% for adults and 98% for children, higher than existing methods. Our new features are more relevant. Our removal is objective and comparable to the manual method. This is a critical work to automate forced oscillation technique quality control.

A SIMPLE METHOD FOR MEASURING THE ELECTRON-BEAM MAGNETIZATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Halavanau, A.; Qiang, G.; Wisniewski, E.

2016-10-18

There are a number of projects that require magnetized beams, such as electron cooling or aiding in “flat” beam transforms. Here we explore a simple technique to characterize the magnetization, observed through the angular momentum of magnetized beams. These beams are produced through photoemission. The generating drive laser first passes through microlens arrays (fly-eye light condensers) to form a transversely modulated pulse incident on the photocathode surface [1]. The resulting charge distribution is then accelerated from the photocathode. We explore the evolution of the pattern via the relative shearing of the beamlets, providing information about the angular momentum. This methodmore » is illustrated through numerical simulations and preliminary measurements carried out at the Argonne Wakefield Accelerator (AWA) facility are presented.« less

Mode Identification of High-Amplitude Pressure Waves in Liquid Rocket Engines

NASA Astrophysics Data System (ADS)

EBRAHIMI, R.; MAZAHERI, K.; GHAFOURIAN, A.

2000-01-01

Identification of existing instability modes from experimental pressure measurements of rocket engines is difficult, specially when steep waves are present. Actual pressure waves are often non-linear and include steep shocks followed by gradual expansions. It is generally believed that interaction of these non-linear waves is difficult to analyze. A method of mode identification is introduced. After presumption of constituent modes, they are superposed by using a standard finite difference scheme for solution of the classical wave equation. Waves are numerically produced at each end of the combustion tube with different wavelengths, amplitudes, and phases with respect to each other. Pressure amplitude histories and phase diagrams along the tube are computed. To determine the validity of the presented method for steep non-linear waves, the Euler equations are numerically solved for non-linear waves, and negligible interactions between these waves are observed. To show the applicability of this method, other's experimental results in which modes were identified are used. Results indicate that this simple method can be used in analyzing complicated pressure signal measurements.

Magnetic Field Suppression of Flow in Semiconductor Melt

NASA Technical Reports Server (NTRS)

Fedoseyev, A. I.; Kansa, E. J.; Marin, C.; Volz, M. P.; Ostrogorsky, A. G.

2000-01-01

One of the most promising approaches for the reduction of convection during the crystal growth of conductive melts (semiconductor crystals) is the application of magnetic fields. Current technology allows the experimentation with very intense static fields (up to 80 KGauss) for which nearly convection free results are expected from simple scaling analysis in stabilized systems (vertical Bridgman method with axial magnetic field). However, controversial experimental results were obtained. The computational methods are, therefore, a fundamental tool in the understanding of the phenomena accounting during the solidification of semiconductor materials. Moreover, effects like the bending of the isomagnetic lines, different aspect ratios and misalignments between the direction of the gravity and magnetic field vectors can not be analyzed with analytical methods. The earliest numerical results showed controversial conclusions and are not able to explain the experimental results. Although the generated flows are extremely low, the computational task is a complicated because of the thin boundary layers. That is one of the reasons for the discrepancy in the results that numerical studies reported. Modeling of these magnetically damped crystal growth experiments requires advanced numerical methods. We used, for comparison, three different approaches to obtain the solution of the problem of thermal convection flows: (1) Spectral method in spectral superelement implementation, (2) Finite element method with regularization for boundary layers, (3) Multiquadric method, a novel method with global radial basis functions, that is proven to have exponential convergence. The results obtained by these three methods are presented for a wide region of Rayleigh and Hartman numbers. Comparison and discussion of accuracy, efficiency, reliability and agreement with experimental results will be presented as well.

A Gaussian quadrature method for total energy analysis in electronic state calculations

NASA Astrophysics Data System (ADS)

Fukushima, Kimichika

This article reports studies by Fukushima and coworkers since 1980 concerning their highly accurate numerical integral method using Gaussian quadratures to evaluate the total energy in electronic state calculations. Gauss-Legendre and Gauss-Laguerre quadratures were used for integrals in the finite and infinite regions, respectively. Our previous article showed that, for diatomic molecules such as CO and FeO, elliptic coordinates efficiently achieved high numerical integral accuracy even with a numerical basis set including transition metal atomic orbitals. This article will generalize straightforward details for multiatomic systems with direct integrals in each decomposed elliptic coordinate determined from the nuclear positions of picked-up atom pairs. Sample calculations were performed for the molecules O3 and H2O. This article will also try to present, in another coordinate, a numerical integral by partially using the Becke's decomposition published in 1988, but without the Becke's fuzzy cell generated by the polynomials of internuclear distance between the pair atoms. Instead, simple nuclear weights comprising exponential functions around nuclei are used. The one-center integral is performed with a Gaussian quadrature pack in a spherical coordinate, included in the author's original program in around 1980. As for this decomposition into one-center integrals, sample calculations are carried out for Li2.

Quantum Mechanics, Path Integrals and Option Pricing:. Reducing the Complexity of Finance

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.; Corianò, Claudio; Srikant, Marakani

2003-04-01

Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of options. The ideas are sketched out for simple models, such as the Black-Scholes model, where analytical and numerical results are compared. Application of the method to nonlinear systems is also briefly overviewed. More general models, for exotic or path-dependent options are discussed.

The exact eigenfunctions and eigenvalues of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

NASA Technical Reports Server (NTRS)

Reimers, J. R.; Heller, E. J.

1985-01-01

Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eigenstates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon-Heller spectral quantization method.

Investigation of ODE integrators using interactive graphics. [Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Brown, R. L.

1978-01-01

Two FORTRAN programs using an interactive graphic terminal to generate accuracy and stability plots for given multistep ordinary differential equation (ODE) integrators are described. The first treats the fixed stepsize linear case with complex variable solutions, and generates plots to show accuracy and error response to step driving function of a numerical solution, as well as the linear stability region. The second generates an analog to the stability region for classes of non-linear ODE's as well as accuracy plots. Both systems can compute method coefficients from a simple specification of the method. Example plots are given.

Modeling the surface evapotranspiration over the southern Great Plains

NASA Technical Reports Server (NTRS)

Liljegren, J. C.; Doran, J. C.; Hubbe, J. M.; Shaw, W. J.; Zhong, S.; Collatz, G. J.; Cook, D. R.; Hart, R. L.

1996-01-01

We have developed a method to apply the Simple Biosphere Model of Sellers et al to calculate the surface fluxes of sensible heat and water vapor at high spatial resolution over the domain of the US DOE's Cloud and Radiation Testbed (CART) in Kansas and Oklahoma. The CART, which is within the GCIP area of interest for the Mississippi River Basin, is an extensively instrumented facility operated as part of the DOE's Atmospheric Radiation Measurement (ARM) program. Flux values calculated with our method will be used to provide lower boundary conditions for numerical models to study the atmosphere over the CART domain.

Combustion Control System Design of Diesel Engine via ASPR based Output Feedback Control Strategy with a PFC

NASA Astrophysics Data System (ADS)

Mizumoto, Ikuro; Tsunematsu, Junpei; Fujii, Seiya

2016-09-01

In this paper, a design method of an output feedback control system with a simple feedforward input for a combustion model of diesel engine will be proposed based on the almost strictly positive real-ness (ASPR-ness) of the controlled system for a combustion control of diesel engines. A parallel feedforward compensator (PFC) design scheme which renders the resulting augmented controlled system ASPR will also be proposed in order to design a stable output feedback control system for the considered combustion model. The effectiveness of our proposed method will be confirmed through numerical simulations.

Towards standard testbeds for numerical relativity

NASA Astrophysics Data System (ADS)

Alcubierre, Miguel; Allen, Gabrielle; Bona, Carles; Fiske, David; Goodale, Tom; Guzmán, F. Siddhartha; Hawke, Ian; Hawley, Scott H.; Husa, Sascha; Koppitz, Michael; Lechner, Christiane; Pollney, Denis; Rideout, David; Salgado, Marcelo; Schnetter, Erik; Seidel, Edward; Shinkai, Hisa-aki; Shoemaker, Deirdre; Szilágyi, Béla; Takahashi, Ryoji; Winicour, Jeff

2004-01-01

In recent years, many different numerical evolution schemes for Einstein's equations have been proposed to address stability and accuracy problems that have plagued the numerical relativity community for decades. Some of these approaches have been tested on different spacetimes, and conclusions have been drawn based on these tests. However, differences in results originate from many sources, including not only formulations of the equations, but also gauges, boundary conditions, numerical methods and so on. We propose to build up a suite of standardized testbeds for comparing approaches to the numerical evolution of Einstein's equations that are designed to both probe their strengths and weaknesses and to separate out different effects, and their causes, seen in the results. We discuss general design principles of suitable testbeds, and we present an initial round of simple tests with periodic boundary conditions. This is a pivotal first step towards building a suite of testbeds to serve the numerical relativists and researchers from related fields who wish to assess the capabilities of numerical relativity codes. We present some examples of how these tests can be quite effective in revealing various limitations of different approaches, and illustrating their differences. The tests are presently limited to vacuum spacetimes, can be run on modest computational resources and can be used with many different approaches used in the relativity community.

Constant pressure and temperature discrete-time Langevin molecular dynamics

NASA Astrophysics Data System (ADS)

Grønbech-Jensen, Niels; Farago, Oded

2014-11-01

We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems—a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.

Asynchronous collision integrators: Explicit treatment of unilateral contact with friction and nodal restraints

PubMed Central

Wolff, Sebastian; Bucher, Christian

2013-01-01

This article presents asynchronous collision integrators and a simple asynchronous method treating nodal restraints. Asynchronous discretizations allow individual time step sizes for each spatial region, improving the efficiency of explicit time stepping for finite element meshes with heterogeneous element sizes. The article first introduces asynchronous variational integration being expressed by drift and kick operators. Linear nodal restraint conditions are solved by a simple projection of the forces that is shown to be equivalent to RATTLE. Unilateral contact is solved by an asynchronous variant of decomposition contact response. Therein, velocities are modified avoiding penetrations. Although decomposition contact response is solving a large system of linear equations (being critical for the numerical efficiency of explicit time stepping schemes) and is needing special treatment regarding overconstraint and linear dependency of the contact constraints (for example from double-sided node-to-surface contact or self-contact), the asynchronous strategy handles these situations efficiently and robust. Only a single constraint involving a very small number of degrees of freedom is considered at once leading to a very efficient solution. The treatment of friction is exemplified for the Coulomb model. Special care needs the contact of nodes that are subject to restraints. Together with the aforementioned projection for restraints, a novel efficient solution scheme can be presented. The collision integrator does not influence the critical time step. Hence, the time step can be chosen independently from the underlying time-stepping scheme. The time step may be fixed or time-adaptive. New demands on global collision detection are discussed exemplified by position codes and node-to-segment integration. Numerical examples illustrate convergence and efficiency of the new contact algorithm. Copyright © 2013 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons, Ltd. PMID:23970806

Electromagnetic Launch Technology Assessment. Scientific Basis and Unified Treatment: Forces and Electromechanical Power Conversion (Analytical and Numerical Methods),

DTIC Science & Technology

1990-06-01

on simple railgun accelerators andI homopolar generators. Complex rotating flux compressors would drastically improve the performance of EM launchers...velocities. If this is the direction of improvement, then energies stored in the electric trains built with linear electric motors in Japan and Western I...laboratories which had power supplies 3 already built for other programs ( homopolar generators in conjunction with an inductor and an opening switch

Carcinogenicity and Immunotoxicity of Embedded Depleted Uranium and Heavy-Metal Tungsten Alloy in Rodents

DTIC Science & Technology

2006-10-01

local metal- induced toxicity daily for two weeks following surgery and weekly thereafter for the duration of the study. Task 1 - Determine whether...A quick and simple method for the quantitation of lactate dehydrogenase release in measurements of cellular cytotoxicity and tumor necrosis factor...4 months, no signs of local or systemic toxic- ity were observed (Peuster et al. 2003). Studies on health effects of Ni and Co are more numerous

Direction of Coupling from Phases of Interacting Oscillators: A Permutation Information Approach

NASA Astrophysics Data System (ADS)

Bahraminasab, A.; Ghasemi, F.; Stefanovska, A.; McClintock, P. V. E.; Kantz, H.

2008-02-01

We introduce a directionality index for a time series based on a comparison of neighboring values. It can distinguish unidirectional from bidirectional coupling, as well as reveal and quantify asymmetry in bidirectional coupling. It is tested on a numerical model of coupled van der Pol oscillators, and applied to cardiorespiratory data from healthy subjects. There is no need for preprocessing and fine-tuning the parameters, which makes the method very simple, computationally fast and robust.

Assessing the capability of continuum and discrete particle methods to simulate gas-solids flow using DNS predictions as a benchmark

DOE PAGES

Lu, Liqiang; Liu, Xiaowen; Li, Tingwen; ...

2017-08-12

For this study, gas–solids flow in a three-dimension periodic domain was numerically investigated by direct numerical simulation (DNS), computational fluid dynamic-discrete element method (CFD-DEM) and two-fluid model (TFM). DNS data obtained by finely resolving the flow around every particle are used as a benchmark to assess the validity of coarser DEM and TFM approaches. The CFD-DEM predicts the correct cluster size distribution and under-predicts the macro-scale slip velocity even with a grid size as small as twice the particle diameter. The TFM approach predicts larger cluster size and lower slip velocity with a homogeneous drag correlation. Although the slip velocitymore » can be matched by a simple modification to the drag model, the predicted voidage distribution is still different from DNS: Both CFD-DEM and TFM over-predict the fraction of particles in dense regions and under-predict the fraction of particles in regions of intermediate void fractions. Also, the cluster aspect ratio of DNS is smaller than CFD-DEM and TFM. Since a simple correction to the drag model can predict a correct slip velocity, it is hopeful that drag corrections based on more elaborate theories that consider voidage gradient and particle fluctuations may be able to improve the current predictions of cluster distribution.« less

Hierarchical modeling for reliability analysis using Markov models. B.S./M.S. Thesis - MIT

NASA Technical Reports Server (NTRS)

Fagundo, Arturo

1994-01-01

Markov models represent an extremely attractive tool for the reliability analysis of many systems. However, Markov model state space grows exponentially with the number of components in a given system. Thus, for very large systems Markov modeling techniques alone become intractable in both memory and CPU time. Often a particular subsystem can be found within some larger system where the dependence of the larger system on the subsystem is of a particularly simple form. This simple dependence can be used to decompose such a system into one or more subsystems. A hierarchical technique is presented which can be used to evaluate these subsystems in such a way that their reliabilities can be combined to obtain the reliability for the full system. This hierarchical approach is unique in that it allows the subsystem model to pass multiple aggregate state information to the higher level model, allowing more general systems to be evaluated. Guidelines are developed to assist in the system decomposition. An appropriate method for determining subsystem reliability is also developed. This method gives rise to some interesting numerical issues. Numerical error due to roundoff and integration are discussed at length. Once a decomposition is chosen, the remaining analysis is straightforward but tedious. However, an approach is developed for simplifying the recombination of subsystem reliabilities. Finally, a real world system is used to illustrate the use of this technique in a more practical context.

Assessing the capability of continuum and discrete particle methods to simulate gas-solids flow using DNS predictions as a benchmark

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, Liqiang; Liu, Xiaowen; Li, Tingwen

For this study, gas–solids flow in a three-dimension periodic domain was numerically investigated by direct numerical simulation (DNS), computational fluid dynamic-discrete element method (CFD-DEM) and two-fluid model (TFM). DNS data obtained by finely resolving the flow around every particle are used as a benchmark to assess the validity of coarser DEM and TFM approaches. The CFD-DEM predicts the correct cluster size distribution and under-predicts the macro-scale slip velocity even with a grid size as small as twice the particle diameter. The TFM approach predicts larger cluster size and lower slip velocity with a homogeneous drag correlation. Although the slip velocitymore » can be matched by a simple modification to the drag model, the predicted voidage distribution is still different from DNS: Both CFD-DEM and TFM over-predict the fraction of particles in dense regions and under-predict the fraction of particles in regions of intermediate void fractions. Also, the cluster aspect ratio of DNS is smaller than CFD-DEM and TFM. Since a simple correction to the drag model can predict a correct slip velocity, it is hopeful that drag corrections based on more elaborate theories that consider voidage gradient and particle fluctuations may be able to improve the current predictions of cluster distribution.« less

Efficient O(N) integration for all-electron electronic structure calculation using numeric basis functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Havu, V.; Fritz Haber Institute of the Max Planck Society, Berlin; Blum, V.

2009-12-01

We consider the problem of developing O(N) scaling grid-based operations needed in many central operations when performing electronic structure calculations with numeric atom-centered orbitals as basis functions. We outline the overall formulation of localized algorithms, and specifically the creation of localized grid batches. The choice of the grid partitioning scheme plays an important role in the performance and memory consumption of the grid-based operations. Three different top-down partitioning methods are investigated, and compared with formally more rigorous yet much more expensive bottom-up algorithms. We show that a conceptually simple top-down grid partitioning scheme achieves essentially the same efficiency as themore » more rigorous bottom-up approaches.« less

Large eddy simulations and direct numerical simulations of high speed turbulent reacting flows

NASA Technical Reports Server (NTRS)

Givi, Peyman; Madnia, C. K.; Steinberger, C. J.; Tsai, A.

1991-01-01

This research is involved with the implementations of advanced computational schemes based on large eddy simulations (LES) and direct numerical simulations (DNS) to study the phenomenon of mixing and its coupling with chemical reactions in compressible turbulent flows. In the efforts related to LES, a research program was initiated to extend the present capabilities of this method for the treatment of chemically reacting flows, whereas in the DNS efforts, focus was on detailed investigations of the effects of compressibility, heat release, and nonequilibrium kinetics modeling in high speed reacting flows. The efforts to date were primarily focussed on simulations of simple flows, namely, homogeneous compressible flows and temporally developing hign speed mixing layers. A summary of the accomplishments is provided.

Similarity solution of the Boussinesq equation

NASA Astrophysics Data System (ADS)

Lockington, D. A.; Parlange, J.-Y.; Parlange, M. B.; Selker, J.

Similarity transforms of the Boussinesq equation in a semi-infinite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial differential equation to a boundary-value problem. Chen et al. [Trans Porous Media 1995;18:15-36] use a hodograph method to derive an integral equation formulation of the new differential equation which they solve by numerical iteration. In the present paper, the convergence of their scheme is improved such that numerical iteration can be avoided for all practical purposes. However, a simpler analytical approach is also presented which is based on Shampine's transformation of the boundary value problem to an initial value problem. This analytical approximation is remarkably simple and yet more accurate than the analytical hodograph approximations.

Cognitive Strategy Use and Measured Numeric Ability in Immediate- and Long-Term Recall of Everyday Numeric Information

PubMed Central

Bermingham, Douglas; Hill, Robert D.; Woltz, Dan; Gardner, Michael K.

2013-01-01

The goals of this study were to assess the primary effects of the use of cognitive strategy and a combined measure of numeric ability on recall of every-day numeric information (i.e. prices). Additionally, numeric ability was assessed as a moderator in the relationship between strategy use and memory for prices. One hundred participants memorized twelve prices that varied from 1 to 6 digits; they recalled these immediately and after 7 days. The use of strategies, assessed through self-report, was associated with better overall recall, but not forgetting. Numeric ability was not associated with either better overall recall or forgetting. A small moderating interaction was found, in which higher levels of numeric ability enhanced the beneficial effects of strategy use on overall recall. Exploratory analyses found two further small moderating interactions: simple strategy use enhanced overall recall at higher levels of numeric ability, compared to complex strategy use; and complex strategy use was associated with lower levels of forgetting, but only at higher levels of numeric ability, compared to the simple strategy use. These results provide support for an objective measure of numeric ability, as well as adding to the literature on memory and the benefits of cognitive strategy use. PMID:23483964

Cognitive strategy use and measured numeric ability in immediate- and long-term recall of everyday numeric information.

PubMed

Bermingham, Douglas; Hill, Robert D; Woltz, Dan; Gardner, Michael K

2013-01-01

The goals of this study were to assess the primary effects of the use of cognitive strategy and a combined measure of numeric ability on recall of every-day numeric information (i.e. prices). Additionally, numeric ability was assessed as a moderator in the relationship between strategy use and memory for prices. One hundred participants memorized twelve prices that varied from 1 to 6 digits; they recalled these immediately and after 7 days. The use of strategies, assessed through self-report, was associated with better overall recall, but not forgetting. Numeric ability was not associated with either better overall recall or forgetting. A small moderating interaction was found, in which higher levels of numeric ability enhanced the beneficial effects of strategy use on overall recall. Exploratory analyses found two further small moderating interactions: simple strategy use enhanced overall recall at higher levels of numeric ability, compared to complex strategy use; and complex strategy use was associated with lower levels of forgetting, but only at higher levels of numeric ability, compared to the simple strategy use. These results provide support for an objective measure of numeric ability, as well as adding to the literature on memory and the benefits of cognitive strategy use.

Modeling of diatomic molecule using the Morse potential and the Verlet algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fidiani, Elok

Performing molecular modeling usually uses special software for Molecular Dynamics (MD) such as: GROMACS, NAMD, JMOL etc. Molecular dynamics is a computational method to calculate the time dependent behavior of a molecular system. In this work, MATLAB was used as numerical method for a simple modeling of some diatomic molecules: HCl, H{sub 2} and O{sub 2}. MATLAB is a matrix based numerical software, in order to do numerical analysis, all the functions and equations describing properties of atoms and molecules must be developed manually in MATLAB. In this work, a Morse potential was generated to describe the bond interaction betweenmore » the two atoms. In order to analyze the simultaneous motion of molecules, the Verlet Algorithm derived from Newton’s Equations of Motion (classical mechanics) was operated. Both the Morse potential and the Verlet algorithm were integrated using MATLAB to derive physical properties and the trajectory of the molecules. The data computed by MATLAB is always in the form of a matrix. To visualize it, Visualized Molecular Dynamics (VMD) was performed. Such method is useful for development and testing some types of interaction on a molecular scale. Besides, this can be very helpful for describing some basic principles of molecular interaction for educational purposes.« less

Numerical investigations on mapping permeability heterogeneity in coal seam gas reservoirs using seismo-electric methods

NASA Astrophysics Data System (ADS)

Gross, L.; Shaw, S.

2016-04-01

Mapping the horizontal distribution of permeability is a key problem for the coal seam gas industry. Poststack seismic data with anisotropy attributes provide estimates for fracture density and orientation which are then interpreted in terms of permeability. This approach delivers an indirect measure of permeability and can fail if other sources of anisotropy (for instance stress) come into play. Seismo-electric methods, based on recording the electric signal from pore fluid movements stimulated through a seismic wave, measure permeability directly. In this paper we use numerical simulations to demonstrate that the seismo-electric method is potentially suitable to map the horizontal distribution of permeability changes across coal seams. We propose the use of an amplitude to offset (AVO) analysis of the electrical signal in combination with poststack seismic data collected during the exploration phase. Recording of electrical signals from a simple seismic source can be closer to production planning and operations. The numerical model is based on a sonic wave propagation model under the low frequency, saturated media assumption and uses a coupled high order spectral element and low order finite element solver. We investigate the impact of seam thickness, coal seam layering, layering in the overburden and horizontal heterogeneity of permeability.

A hybrid interface tracking - level set technique for multiphase flow with soluble surfactant

NASA Astrophysics Data System (ADS)

Shin, Seungwon; Chergui, Jalel; Juric, Damir; Kahouadji, Lyes; Matar, Omar K.; Craster, Richard V.

2018-04-01

A formulation for soluble surfactant transport in multiphase flows recently presented by Muradoglu and Tryggvason (JCP 274 (2014) 737-757) [17] is adapted to the context of the Level Contour Reconstruction Method, LCRM, (Shin et al. IJNMF 60 (2009) 753-778, [8]) which is a hybrid method that combines the advantages of the Front-tracking and Level Set methods. Particularly close attention is paid to the formulation and numerical implementation of the surface gradients of surfactant concentration and surface tension. Various benchmark tests are performed to demonstrate the accuracy of different elements of the algorithm. To verify surfactant mass conservation, values for surfactant diffusion along the interface are compared with the exact solution for the problem of uniform expansion of a sphere. The numerical implementation of the discontinuous boundary condition for the source term in the bulk concentration is compared with the approximate solution. Surface tension forces are tested for Marangoni drop translation. Our numerical results for drop deformation in simple shear are compared with experiments and results from previous simulations. All benchmarking tests compare well with existing data thus providing confidence that the adapted LCRM formulation for surfactant advection and diffusion is accurate and effective in three-dimensional multiphase flows with a structured mesh. We also demonstrate that this approach applies easily to massively parallel simulations.

A probabilistic method for constructing wave time-series at inshore locations using model scenarios

USGS Publications Warehouse

Long, Joseph W.; Plant, Nathaniel G.; Dalyander, P. Soupy; Thompson, David M.

2014-01-01

Continuous time-series of wave characteristics (height, period, and direction) are constructed using a base set of model scenarios and simple probabilistic methods. This approach utilizes an archive of computationally intensive, highly spatially resolved numerical wave model output to develop time-series of historical or future wave conditions without performing additional, continuous numerical simulations. The archive of model output contains wave simulations from a set of model scenarios derived from an offshore wave climatology. Time-series of wave height, period, direction, and associated uncertainties are constructed at locations included in the numerical model domain. The confidence limits are derived using statistical variability of oceanographic parameters contained in the wave model scenarios. The method was applied to a region in the northern Gulf of Mexico and assessed using wave observations at 12 m and 30 m water depths. Prediction skill for significant wave height is 0.58 and 0.67 at the 12 m and 30 m locations, respectively, with similar performance for wave period and direction. The skill of this simplified, probabilistic time-series construction method is comparable to existing large-scale, high-fidelity operational wave models but provides higher spatial resolution output at low computational expense. The constructed time-series can be developed to support a variety of applications including climate studies and other situations where a comprehensive survey of wave impacts on the coastal area is of interest.

Differences in arithmetic performance between Chinese and German adults are accompanied by differences in processing of non-symbolic numerical magnitude

PubMed Central

Lonnemann, Jan; Li, Su; Zhao, Pei; Li, Peng; Linkersdörfer, Janosch; Lindberg, Sven; Hasselhorn, Marcus; Yan, Song

2017-01-01

Human beings are assumed to possess an approximate number system (ANS) dedicated to extracting and representing approximate numerical magnitude information. The ANS is assumed to be fundamental to arithmetic learning and has been shown to be associated with arithmetic performance. It is, however, still a matter of debate whether better arithmetic skills are reflected in the ANS. To address this issue, Chinese and German adults were compared regarding their performance in simple arithmetic tasks and in a non-symbolic numerical magnitude comparison task. Chinese participants showed a better performance in solving simple arithmetic tasks and faster reaction times in the non-symbolic numerical magnitude comparison task without making more errors than their German peers. These differences in performance could not be ascribed to differences in general cognitive abilities. Better arithmetic skills were thus found to be accompanied by a higher speed of retrieving non-symbolic numerical magnitude knowledge but not by a higher precision of non-symbolic numerical magnitude representations. The group difference in the speed of retrieving non-symbolic numerical magnitude knowledge was fully mediated by the performance in arithmetic tasks, suggesting that arithmetic skills shape non-symbolic numerical magnitude processing skills. PMID:28384191

On simulating flow with multiple time scales using a method of averages

DOE Office of Scientific and Technical Information (OSTI.GOV)

Margolin, L.G.

1997-12-31

The author presents a new computational method based on averaging to efficiently simulate certain systems with multiple time scales. He first develops the method in a simple one-dimensional setting and employs linear stability analysis to demonstrate numerical stability. He then extends the method to multidimensional fluid flow. His method of averages does not depend on explicit splitting of the equations nor on modal decomposition. Rather he combines low order and high order algorithms in a generalized predictor-corrector framework. He illustrates the methodology in the context of a shallow fluid approximation to an ocean basin circulation. He finds that his newmore » method reproduces the accuracy of a fully explicit second-order accurate scheme, while costing less than a first-order accurate scheme.« less

Theoretical Basis for Dynamic Label Propagation in Stationary Metabolic Networks under Step and Periodic Inputs

PubMed Central

Sokol, Serguei; Portais, Jean-Charles

2015-01-01

The dynamics of label propagation in a stationary metabolic network during an isotope labeling experiment can provide highly valuable information on the network topology, metabolic fluxes, and on the size of metabolite pools. However, major issues, both in the experimental set-up and in the accompanying numerical methods currently limit the application of this approach. Here, we propose a method to apply novel types of label inputs, sinusoidal or more generally periodic label inputs, to address both the practical and numerical challenges of dynamic labeling experiments. By considering a simple metabolic system, i.e. a linear, non-reversible pathway of arbitrary length, we develop mathematical descriptions of label propagation for both classical and novel label inputs. Theoretical developments and computer simulations show that the application of rectangular periodic pulses has both numerical and practical advantages over other approaches. We applied the strategy to estimate fluxes in a simulated experiment performed on a complex metabolic network (the central carbon metabolism of Escherichia coli), to further demonstrate its value in conditions which are close to those in real experiments. This study provides a theoretical basis for the rational interpretation of label propagation curves in real experiments, and will help identify the strengths, pitfalls and limitations of such experiments. The cases described here can also be used as test cases for more general numerical methods aimed at identifying network topology, analyzing metabolic fluxes or measuring concentrations of metabolites. PMID:26641860

A reliable algorithm for optimal control synthesis

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1992-01-01

In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2003-01-01

A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the hyperbolicity of the Euler equation system and the first principle of plane (simple) wave propagation. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in ID, 2D and 3D space are illustrated to demonstrate its robustness in practical computations.

The CE/SE Method: a CFD Framework for the Challenges of the New Millennium

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Yu, Sheng-Tao

2001-01-01

The space-time conservation element and solution element (CE/SE) method, which was originated and is continuously being developed at NASA Glenn Research Center, is a high-resolution, genuinely multidimensional and unstructured-mesh compatible numerical method for solving conservation laws. Since its inception in 1991, the CE/SE method has been used to obtain highly accurate numerical solutions for 1D, 2D and 3D flow problems involving shocks, contact discontinuities, acoustic waves, vortices, shock/acoustic waves/vortices interactions, shock/boundary layers interactions and chemical reactions. Without the aid of preconditioning or other special techniques, it has been applied to both steady and unsteady flows with speeds ranging from Mach number = 0.00288 to 10. In addition, the method has unique features that allow for (i) the use of very simple non-reflecting boundary conditions, and (ii) a unified wall boundary treatment for viscous and inviscid flows. The CE/SE method was developed with the conviction that, with a solid foundation in physics, a robust, coherent and accurate numerical framework can be built without involving overly complex mathematics. As a result, the method was constructed using a set of design principles that facilitate simplicity, robustness and accuracy. The most important among them are: (i) enforcing both local and global flux conservation in space and time, with flux evaluation at an interface being an integral part of the solution procedure and requiring no interpolation or extrapolation; (ii) unifying space and time and treating them as a single entity; and (iii) requiring that a numerical scheme be built from a nondissipative core scheme such that the numerical dissipation can be effectively controlled and, as a result, will not overwhelm the physical dissipation. Part I of the workshop will be devoted to a discussion of these principles along with a description of how the ID, 2D and 3D CE/SE schemes are constructed. In Part II, various applications of the CE/SE method, particularly those involving chemical reactions and acoustics, will be presented. The workshop will be concluded with a sketch of the future research directions.

Simple method for the generation of multiple homogeneous field volumes inside the bore of superconducting magnets

PubMed Central

Chou, Ching-Yu; Ferrage, Fabien; Aubert, Guy; Sakellariou, Dimitris

2015-01-01

Standard Magnetic Resonance magnets produce a single homogeneous field volume, where the analysis is performed. Nonetheless, several modern applications could benefit from the generation of multiple homogeneous field volumes along the axis and inside the bore of the magnet. In this communication, we propose a straightforward method using a combination of ring structures of permanent magnets in order to cancel the gradient of the stray field in a series of distinct volumes. These concepts were demonstrated numerically on an experimentally measured magnetic field profile. We discuss advantages and limitations of our method and present the key steps required for an experimental validation. PMID:26182891

Optimal nonlinear filtering using the finite-volume method

NASA Astrophysics Data System (ADS)

Fox, Colin; Morrison, Malcolm E. K.; Norton, Richard A.; Molteno, Timothy C. A.

2018-01-01

Optimal sequential inference, or filtering, for the state of a deterministic dynamical system requires simulation of the Frobenius-Perron operator, that can be formulated as the solution of a continuity equation. For low-dimensional, smooth systems, the finite-volume numerical method provides a solution that conserves probability and gives estimates that converge to the optimal continuous-time values, while a Courant-Friedrichs-Lewy-type condition assures that intermediate discretized solutions remain positive density functions. This method is demonstrated in an example of nonlinear filtering for the state of a simple pendulum, with comparison to results using the unscented Kalman filter, and for a case where rank-deficient observations lead to multimodal probability distributions.

Two-dimensional fourier transform spectrometer

DOEpatents

DeFlores, Lauren; Tokmakoff, Andrei

2016-10-25

The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

Two-dimensional fourier transform spectrometer

DOEpatents

DeFlores, Lauren; Tokmakoff, Andrei

2013-09-03

The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo

DOE PAGES

White, Alexander J.; Gorshkov, Vyacheslav N.; Tretiak, Sergei; ...

2015-07-07

Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficientmore » as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In many cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.« less

A moment projection method for population balance dynamics with a shrinkage term

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Shaohua; Yapp, Edward K.Y.; Akroyd, Jethro

A new method of moments for solving the population balance equation is developed and presented. The moment projection method (MPM) is numerically simple and easy to implement and attempts to address the challenge of particle shrinkage due to processes such as oxidation, evaporation or dissolution. It directly solves the moment transport equation for the moments and tracks the number of the smallest particles using the algorithm by Blumstein and Wheeler (1973) . The performance of the new method is measured against the method of moments (MOM) and the hybrid method of moments (HMOM). The results suggest that MPM performs muchmore » better than MOM and HMOM where shrinkage is dominant. The new method predicts mean quantities which are almost as accurate as a high-precision stochastic method calculated using the established direct simulation algorithm (DSA).« less

Wigner phase space distribution via classical adiabatic switching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bose, Amartya; Makri, Nancy; Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, Illinois 61801

2015-09-21

Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if themore » perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.« less

An empirical method for approximating stream baseflow time series using groundwater table fluctuations

NASA Astrophysics Data System (ADS)

Meshgi, Ali; Schmitter, Petra; Babovic, Vladan; Chui, Ting Fong May

2014-11-01

Developing reliable methods to estimate stream baseflow has been a subject of interest due to its importance in catchment response and sustainable watershed management. However, to date, in the absence of complex numerical models, baseflow is most commonly estimated using statistically derived empirical approaches that do not directly incorporate physically-meaningful information. On the other hand, Artificial Intelligence (AI) tools such as Genetic Programming (GP) offer unique capabilities to reduce the complexities of hydrological systems without losing relevant physical information. This study presents a simple-to-use empirical equation to estimate baseflow time series using GP so that minimal data is required and physical information is preserved. A groundwater numerical model was first adopted to simulate baseflow for a small semi-urban catchment (0.043 km2) located in Singapore. GP was then used to derive an empirical equation relating baseflow time series to time series of groundwater table fluctuations, which are relatively easily measured and are physically related to baseflow generation. The equation was then generalized for approximating baseflow in other catchments and validated for a larger vegetation-dominated basin located in the US (24 km2). Overall, this study used GP to propose a simple-to-use equation to predict baseflow time series based on only three parameters: minimum daily baseflow of the entire period, area of the catchment and groundwater table fluctuations. It serves as an alternative approach for baseflow estimation in un-gauged systems when only groundwater table and soil information is available, and is thus complementary to other methods that require discharge measurements.

Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2007-06-01

In [P.K. Moore, Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for higher-order methods in three space dimensions, Int. J. Numer. Anal. Mod. 3 (2006) 21-51] a fixed, high-order h-refinement finite element algorithm, Href, was introduced for solving reaction-diffusion equations in three space dimensions. In this paper Href is coupled with continuation creating an automatic method for solving regularly and singularly perturbed reaction-diffusion equations. The simple quasilinear Newton solver of Moore, (2006) is replaced by the nonlinear solver NITSOL [M. Pernice, H.F. Walker, NITSOL: a Newton iterative solver for nonlinear systems, SIAM J. Sci. Comput. 19 (1998) 302-318]. Good initial guesses for the nonlinear solver are obtained using continuation in the small parameter ɛ. Two strategies allow adaptive selection of ɛ. The first depends on the rate of convergence of the nonlinear solver and the second implements backtracking in ɛ. Finally a simple method is used to select the initial ɛ. Several examples illustrate the effectiveness of the algorithm.

Structural dynamics and vibrations of damped, aircraft-type structures

NASA Technical Reports Server (NTRS)

Young, Maurice I.

1992-01-01

Engineering preliminary design methods for approximating and predicting the effects of viscous or equivalent viscous-type damping treatments on the free and forced vibration of lightly damped aircraft-type structures are developed. Similar developments are presented for dynamic hysteresis viscoelastic-type damping treatments. It is shown by both engineering analysis and numerical illustrations that the intermodal coupling of the undamped modes arising from the introduction of damping may be neglected in applying these preliminary design methods, except when dissimilar modes of these lightly damped, complex aircraft-type structures have identical or nearly identical natural frequencies. In such cases, it is shown that a relatively simple, additional interaction calculation between pairs of modes exhibiting this 'modal response' phenomenon suffices in the prediction of interacting modal damping fractions. The accuracy of the methods is shown to be very good to excellent, depending on the normal natural frequency separation of the system modes, thereby permitting a relatively simple preliminary design approach. This approach is shown to be a natural precursor to elaborate finite element, digital computer design computations in evaluating the type, quantity, and location of damping treatment.

Direct simulation Monte Carlo modeling of relaxation processes in polyatomic gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pfeiffer, M., E-mail: mpfeiffer@irs.uni-stuttgart.de; Nizenkov, P., E-mail: nizenkov@irs.uni-stuttgart.de; Mirza, A., E-mail: mirza@irs.uni-stuttgart.de

2016-02-15

Relaxation processes of polyatomic molecules are modeled and implemented in an in-house Direct Simulation Monte Carlo code in order to enable the simulation of atmospheric entry maneuvers at Mars and Saturn’s Titan. The description of rotational and vibrational relaxation processes is derived from basic quantum-mechanics using a rigid rotator and a simple harmonic oscillator, respectively. Strategies regarding the vibrational relaxation process are investigated, where good agreement for the relaxation time according to the Landau-Teller expression is found for both methods, the established prohibiting double relaxation method and the new proposed multi-mode relaxation. Differences and applications areas of these two methodsmore » are discussed. Consequently, two numerical methods used for sampling of energy values from multi-dimensional distribution functions are compared. The proposed random-walk Metropolis algorithm enables the efficient treatment of multiple vibrational modes within a time step with reasonable computational effort. The implemented model is verified and validated by means of simple reservoir simulations and the comparison to experimental measurements of a hypersonic, carbon-dioxide flow around a flat-faced cylinder.« less

An immersed-boundary method for flow–structure interaction in biological systems with application to phonation

PubMed Central

Luo, Haoxiang; Mittal, Rajat; Zheng, Xudong; Bielamowicz, Steven A.; Walsh, Raymond J.; Hahn, James K.

2008-01-01

A new numerical approach for modeling a class of flow–structure interaction problems typically encountered in biological systems is presented. In this approach, a previously developed, sharp-interface, immersed-boundary method for incompressible flows is used to model the fluid flow and a new, sharp-interface Cartesian grid, immersed boundary method is devised to solve the equations of linear viscoelasticity that governs the solid. The two solvers are coupled to model flow–structure interaction. This coupled solver has the advantage of simple grid generation and efficient computation on simple, single-block structured grids. The accuracy of the solid-mechanics solver is examined by applying it to a canonical problem. The solution methodology is then applied to the problem of laryngeal aerodynamics and vocal fold vibration during human phonation. This includes a three-dimensional eigen analysis for a multi-layered vocal fold prototype as well as two-dimensional, flow-induced vocal fold vibration in a modeled larynx. Several salient features of the aerodynamics as well as vocal-fold dynamics are presented. PMID:19936017

An efficient higher order family of root finders

NASA Astrophysics Data System (ADS)

Petkovic, Ljiljana D.; Rancic, Lidija; Petkovic, Miodrag S.

2008-06-01

A one parameter family of iterative methods for the simultaneous approximation of simple complex zeros of a polynomial, based on a cubically convergent Hansen-Patrick's family, is studied. We show that the convergence of the basic family of the fourth order can be increased to five and six using Newton's and Halley's corrections, respectively. Since these corrections use the already calculated values, the computational efficiency of the accelerated methods is significantly increased. Further acceleration is achieved by applying the Gauss-Seidel approach (single-step mode). One of the most important problems in solving nonlinear equations, the construction of initial conditions which provide both the guaranteed and fast convergence, is considered for the proposed accelerated family. These conditions are computationally verifiable; they depend only on the polynomial coefficients, its degree and initial approximations, which is of practical importance. Some modifications of the considered family, providing the computation of multiple zeros of polynomials and simple zeros of a wide class of analytic functions, are also studied. Numerical examples demonstrate the convergence properties of the presented family of root-finding methods.

Color TV: total variation methods for restoration of vector-valued images.

PubMed

Blomgren, P; Chan, T F

1998-01-01

We propose a new definition of the total variation (TV) norm for vector-valued functions that can be applied to restore color and other vector-valued images. The new TV norm has the desirable properties of 1) not penalizing discontinuities (edges) in the image, 2) being rotationally invariant in the image space, and 3) reducing to the usual TV norm in the scalar case. Some numerical experiments on denoising simple color images in red-green-blue (RGB) color space are presented.

Accelerating wave propagation modeling in the frequency domain using Python

NASA Astrophysics Data System (ADS)

Jo, Sang Hoon; Park, Min Jun; Ha, Wan Soo

2017-04-01

Python is a dynamic programming language adopted in many science and engineering areas. We used Python to simulate wave propagation in the frequency domain. We used the Pardiso matrix solver to solve the impedance matrix of the wave equation. Numerical examples shows that Python with numpy consumes longer time to construct the impedance matrix using the finite element method when compared with Fortran; however we could reduce the time significantly to be comparable to that of Fortran using a simple Numba decorator.

Thermodynamics and kinetics of reactions in protective coating systems

NASA Technical Reports Server (NTRS)

Gupta, B.; Sarkhel, A.; Shankar, S.; Seigle, L.

1975-01-01

A study of the aluminization of Ni from packs containing various percentages of unalloyed Al confirmed that the surface aluminum content of specimens aluminized tends to decrease with time and consequently a simple parabolic law for the weight-gain vs. time relationship is not obeyed. The diffusivity-composition relationship in NiAl was examined, and a set of curves is presented. A numerical method for the calculation of coating dissolution rates was developed and applied to NiAl-Ni3Al type of coatings.

BPERM version 3.0: A 2-D wakepotential/impedance code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barts, T.; Chou, W.

1996-10-01

BPERM 3.0 is an improved version of a previous release. The main purpose of this version is to make it more user friendly. Following a simple 1-2-3 procedure, one obtains both text and graphical output of the wakepotential and impedance for a given geometry. The calculation is based on a boundary perturbation method, which is significantly faster than numerical simulations. It is accurate when the discontinuities are small. In particular, it works well for tapered structures. 5 refs., 3 figs.

Theoretical study on some plasma parameters and thermophysical properties of various gas mixtures in gas-discharge lasers

NASA Astrophysics Data System (ADS)

Temelkov, K. A.; Slaveeva, S. I.; Fedchenko, Yu I.; Chernogorova, T. P.

2018-03-01

Using the well-known Wassiljewa equation and a new simple method, the thermal conductivities of various 2- and 3-component gas mixtures were calculated and compared under gas-discharge conditions optimal for two prospective lasers excited in a nanosecond pulsed longitudinal discharge. By solving the non-stationary heat-conduction equation for electrons, a 2D numerical model was also developed for determination of the radial and temporal dependences of the electron temperature Te (r, t).

A return mapping algorithm for isotropic and anisotropic plasticity models using a line search method

DOE PAGES

Scherzinger, William M.

2016-05-01

The numerical integration of constitutive models in computational solid mechanics codes allows for the solution of boundary value problems involving complex material behavior. Metal plasticity models, in particular, have been instrumental in the development of these codes. Here, most plasticity models implemented in computational codes use an isotropic von Mises yield surface. The von Mises, of J 2, yield surface has a simple predictor-corrector algorithm - the radial return algorithm - to integrate the model.

THE FIRST FERMI IN A HIGH ENERGY NUCLEAR COLLISION.

DOE Office of Scientific and Technical Information (OSTI.GOV)

KRASNITZ,A.

1999-08-09

At very high energies, weak coupling, non-perturbative methods can be used to study classical gluon production in nuclear collisions. One observes in numerical simulations that after an initial formation time, the produced partons are on shell, and their subsequent evolution can be studied using transport theory. At the initial formation time, a simple non-perturbative relation exists between the energy and number densities of the produced partons, and a scale determined by the saturated parton density in the nucleus.

Synthesis markers in illegally manufactured 3,4-methylenedioxyamphetamine and 3,4-methylenedioxymethamphetamine.

PubMed

Bohn, M; Bohn, G; Blaschke, G

1993-01-01

In this paper the isolation and identification of 12 compounds as impurities in illicit 3,4-methylenedioxyamphetamine (MDA) and 3,4-methylenedioxymethamphetamine (MDMA) is reported. Isolation of these substances is performed by preparative TLC, while identification is performed by using mass spectrometry and 1H-NMR spectroscopy. A simple and rapid method for detection of these impurities in seized MDA and MDMA samples is described. The identification of the impurities can provide numerous points on which to base comparative analysis of different exhibits.

High-order centered difference methods with sharp shock resolution

NASA Technical Reports Server (NTRS)

Gustafsson, Bertil; Olsson, Pelle

1994-01-01

In this paper we consider high-order centered finite difference approximations of hyperbolic conservation laws. We propose different ways of adding artificial viscosity to obtain sharp shock resolution. For the Riemann problem we give simple explicit formulas for obtaining stationary one and two-point shocks. This can be done for any order of accuracy. It is shown that the addition of artificial viscosity is equivalent to ensuring the Lax k-shock condition. We also show numerical experiments that verify the theoretical results.

Queueing Network Models for Parallel Processing of Task Systems: an Operational Approach

NASA Technical Reports Server (NTRS)

Mak, Victor W. K.

1986-01-01

Computer performance modeling of possibly complex computations running on highly concurrent systems is considered. Earlier works in this area either dealt with a very simple program structure or resulted in methods with exponential complexity. An efficient procedure is developed to compute the performance measures for series-parallel-reducible task systems using queueing network models. The procedure is based on the concept of hierarchical decomposition and a new operational approach. Numerical results for three test cases are presented and compared to those of simulations.

Consistent three-equation model for thin films

NASA Astrophysics Data System (ADS)

Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

2017-11-01

Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

Analytic Formulation and Numerical Implementation of an Acoustic Pressure Gradient Prediction

NASA Technical Reports Server (NTRS)

Lee, Seongkyu; Brentner, Kenneth S.; Farassat, Fereidoun

2007-01-01

The scattering of rotor noise is an area that has received little attention over the years, yet the limited work that has been done has shown that both the directivity and intensity of the acoustic field may be significantly modified by the presence of scattering bodies. One of the inputs needed to compute the scattered acoustic field is the acoustic pressure gradient on a scattering surface. Two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the PSU-WOPWOP rotor noise prediction code. These formulations are presented in this paper. The first formulation is derived by taking the gradient of Farassat's retarded-time Formulation 1A. Although this formulation is relatively simple, it requires numerical time differentiation of the acoustic integrals. In the second formulation, the time differentiation is taken inside the integrals analytically. The acoustic pressure gradient predicted by these new formulations is validated through comparison with the acoustic pressure gradient determined by a purely numerical approach for two model rotors. The agreement between analytic formulations and numerical method is excellent for both stationary and moving observers case.

A comprehensive fluvial geomorphology study of riverbank erosion on the Red River in Winnipeg, Manitoba, Canada

NASA Astrophysics Data System (ADS)

Kimiaghalam, Navid; Goharrokhi, Masoud; Clark, Shawn P.; Ahmari, Habib

2015-10-01

Riverbank erosion on the Red River in Winnipeg, Manitoba has raised concerns over the last 20 years and more. Although several recent studies have shown that fluvial erosion can reduce riverbank stability and promote geotechnical slope failure, there are too few that have focused on this phenomenon. The present study includes field measurements, experimental testing, and numerical modelling to quantify fluvial erosion through a 10 km reach of the Red River. Results have shown that seasonal freeze-thaw processes can dramatically reduce the critical shear stress and increase erodibility of the riverbanks. Moreover, a simple method has been employed using hydrodynamic numerical models to define the applied shear stresses on the river banks based on the river water level, which will be useful for further research and design purposes. The TEMP/W numerical model was used to define seasonal frost depth to estimate freeze-thaw effects. Finally all field measurements, experimental and numerical models results were used to predict annual fluvial erosion through this reach of the river.

Let Us Look After the Veins of the Earth: The Sonification of Time-series Field Data by Analog Methods

NASA Astrophysics Data System (ADS)

Rivera, V. A.; Amaya, L. F.

2017-12-01

In 2016, graduate students from Northwestern University's Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) initiated the Science Sonification and Composition Project, which pairs scientists with student composers to create original music inspired by and utilizing the products of scientific research. In 2017, these pieces were performed at Northwestern for a mixed audience of scientists, musicians, and community members. Sonification of data, or the representation of data as sound, is an increasingly popular method of examining data in the geosciences, especially in astrophysics, where sonification of gravitational waves has recently made major news. Numerical time-series data are often excellent candidates for sonification, as the data can be modified by simple algorithmic means to convert numerical values which represent physical measurements to numerical values representing musical "variables" like volume, pitch, or timbre. Our collaboration, a result of the CIERA initiative, explores methods of sonification that do not involve a simple conversion of data to sound, instead attempting to create sound from data by analog methods. The piece uses both time-series groundwater elevation data and physical soil samples from the locations where the water table measurements were collected. The field site from which both data and samples were collected is Gensburg Markham Prairie, an urban nature preserve on Chicago's south side which hosts a long-term study on the collateral benefits of urban greenspace for stormwater management and storage. Our aim was to combine physical, living elements with technology to mirror the research, where we examine flows and cycles in nature by "taking the pulse" of the landscape using sensing networks. Soil samples were placed in metal vessels outfitted with contact microphones and manipulated by hand and with water, using time-series data as a guide, much like sheet music. This was repeated for samples and sensors at different physical locations throughout the prairie, with each recording comprising an audible representation of soil properties and water dynamics at each location. The resulting sound was processed to create electronic music, which was paired with live instrumental performance.

A simple method to predict body temperature of small reptiles from environmental temperature.

PubMed

Vickers, Mathew; Schwarzkopf, Lin

2016-05-01

To study behavioral thermoregulation, it is useful to use thermal sensors and physical models to collect environmental temperatures that are used to predict organism body temperature. Many techniques involve expensive or numerous types of sensors (cast copper models, or temperature, humidity, radiation, and wind speed sensors) to collect the microhabitat data necessary to predict body temperatures. Expense and diversity of requisite sensors can limit sampling resolution and accessibility of these methods. We compare body temperature predictions of small lizards from iButtons, DS18B20 sensors, and simple copper models, in both laboratory and natural conditions. Our aim was to develop an inexpensive yet accurate method for body temperature prediction. Either method was applicable given appropriate parameterization of the heat transfer equation used. The simplest and cheapest method was DS18B20 sensors attached to a small recording computer. There was little if any deficit in precision or accuracy compared to other published methods. We show how the heat transfer equation can be parameterized, and it can also be used to predict body temperature from historically collected data, allowing strong comparisons between current and previous environmental temperatures using the most modern techniques. Our simple method uses very cheap sensors and loggers to extensively sample habitat temperature, improving our understanding of microhabitat structure and thermal variability with respect to small ectotherms. While our method was quite precise, we feel any potential loss in accuracy is offset by the increase in sample resolution, important as it is increasingly apparent that, particularly for small ectotherms, habitat thermal heterogeneity is the strongest influence on transient body temperature.

Numerical study of droplet evaporation in an acoustic levitator

NASA Astrophysics Data System (ADS)

Bänsch, Eberhard; Götz, Michael

2018-03-01

We present a finite element method for the simulation of all relevant processes of the evaporation of a liquid droplet suspended in an acoustic levitation device. The mathematical model and the numerical implementation take into account heat and mass transfer across the interface between the liquid and gaseous phase and the influence of acoustic streaming on this process, as well as the displacement and deformation of the droplet due to acoustic radiation pressure. We apply this numerical method to several theoretical and experimental examples and compare our results with the well-known d2-law for the evaporation of spherical droplets and with theoretical predictions for the acoustic streaming velocity. We study the influence of acoustic streaming on the distribution of water vapor and temperature in the levitation device, with special attention to the vapor distribution in the emerging toroidal vortices. We also compare the evaporation rate of a droplet with and without acoustic streaming, as well as the evaporation rates in dependence of different temperatures and sound pressure levels. Finally, a simple model of protein inactivation due to heat damage is considered and studied for different evaporation settings and their respective influence on protein damage.

Numerical Simulation of Dynamic Contact Angles and Contact Lines in Multiphase Flows using Level Set Method

NASA Astrophysics Data System (ADS)

Pendota, Premchand

Many physical phenomena and industrial applications involve multiphase fluid flows and hence it is of high importance to be able to simulate various aspects of these flows accurately. The Dynamic Contact Angles (DCA) and the contact lines at the wall boundaries are a couple of such important aspects. In the past few decades, many mathematical models were developed for predicting the contact angles of the inter-face with the wall boundary under various flow conditions. These models are used to incorporate the physics of DCA and contact line motion in numerical simulations using various interface capturing/tracking techniques. In the current thesis, a simple approach to incorporate the static and dynamic contact angle boundary conditions using the level set method is developed and implemented in multiphase CFD codes, LIT (Level set Interface Tracking) (Herrmann (2008)) and NGA (flow solver) (Desjardins et al (2008)). Various DCA models and associated boundary conditions are reviewed. In addition, numerical aspects such as the occurrence of a stress singularity at the contact lines and grid convergence of macroscopic interface shape are dealt with in the context of the level set approach.

A numerical approach to finding general stationary vacuum black holes

NASA Astrophysics Data System (ADS)

Adam, Alexander; Kitchen, Sam; Wiseman, Toby

2012-08-01

The Harmonic Einstein equation is the vacuum Einstein equation supplemented by a gauge fixing term which we take to be that of DeTurck. For static black holes analytically continued to Riemannian manifolds without boundary at the horizon, this equation has previously been shown to be elliptic, and Ricci flow and Newton’s method provide good numerical algorithms to solve it. Here we extend these techniques to the arbitrary cohomogeneity stationary case which must be treated in Lorentzian signature. For stationary spacetimes with globally timelike Killing vector the Harmonic Einstein equation is elliptic. In the presence of horizons and ergo-regions it is less obviously so. Motivated by the Rigidity theorem we study a class of stationary black hole spacetimes which is general enough to include many interesting higher dimensional solutions. We argue the Harmonic Einstein equation consistently truncates to this class of spacetimes giving an elliptic problem. The Killing horizons and axes of rotational symmetry are boundaries for this problem and we determine boundary conditions there. As a simple example we numerically construct 4D rotating black holes in a cavity using Anderson’s boundary conditions. We demonstrate both Newton’s method and Ricci flow to find these Lorentzian solutions.

Numerical Simulation of the Layer-Bylayer Destruction of Cylindrical Shells Under Explosive Loading

NASA Astrophysics Data System (ADS)

Abrosimov, N. A.; Novoseltseva, N. A.

2015-09-01

A technique of numerical analysis of the influence of reinforcement structure on the nature of the dynamic response and the process of layer-by-layer destruction of layered fiberglass cylindrical shells under an axisymmetric internal explosive loading is elaborated. The kinematic model of deformation of the laminate package is based on a nonclassical theory of shells. The geometric dependences are based on simple quadratic relations of the nonlinear theory of elasticity. The relationship between the stress and strain tensors are established by using Hooke's law for orthotropic bodies with account of degradation of stiffness characteristics of the multilayer composite due to the local destruction of some its elementary layers. An energetically consistent system of dynamic equations for composite cylindrical shells is obtained by minimizing the functional of total energy of the shell as a three-dimensional body. The numerical method for solving the formulated initial boundary-value problem is based on an explicit variational-difference scheme. Results confirming the reliability of the method used to analyze the influence of reinforcement structure on the character of destruction and the bearing capacity of pulse-loaded cylindrical shells are presented.

Symmetry, stability, and computation of degenerate lasing modes

NASA Astrophysics Data System (ADS)

Liu, David; Zhen, Bo; Ge, Li; Hernandez, Felipe; Pick, Adi; Burkhardt, Stephan; Liertzer, Matthias; Rotter, Stefan; Johnson, Steven G.

2017-02-01

We present a general method to obtain the stable lasing solutions for the steady-state ab initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2D). We find that under most regimes (with one pathological exception), the stable solutions are clockwise and counterclockwise circulating modes, generalizing previously known results of ring lasers to all 2D rotational symmetry groups. Our method uses a combination of semianalytical solutions close to lasing threshold and numerical solvers to track the lasing modes far above threshold. Near threshold, we find closed-form expressions for both circulating modes and other types of lasing solutions as well as for their linearized Maxwell-Bloch eigenvalues, providing a simple way to determine their stability without having to do a full nonlinear numerical calculation. Above threshold, we show that a key feature of the circulating mode is its "chiral" intensity pattern, which arises from spontaneous symmetry breaking of mirror symmetry, and whose symmetry group requires that the degeneracy persists even when nonlinear effects become important. Finally, we introduce a numerical technique to solve the degenerate SALT equations far above threshold even when spatial discretization artificially breaks the degeneracy.

Recommendations for Achieving Accurate Numerical Simulation of Tip Clearance Flows in Transonic Compressor Rotors

NASA Technical Reports Server (NTRS)

VanZante, Dale E.; Strazisar, Anthony J.; Wood, Jerry R,; Hathaway, Michael D.; Okiishi, Theodore H.

2000-01-01

The tip clearance flows of transonic compressor rotors are important because they have a significant impact on rotor and stage performance. While numerical simulations of these flows are quite sophisticated. they are seldom verified through rigorous comparisons of numerical and measured data because these kinds of measurements are rare in the detail necessary to be useful in high-speed machines. In this paper we compare measured tip clearance flow details (e.g. trajectory and radial extent) with corresponding data obtained from a numerical simulation. Recommendations for achieving accurate numerical simulation of tip clearance flows are presented based on this comparison. Laser Doppler Velocimeter (LDV) measurements acquired in a transonic compressor rotor, NASA Rotor 35, are used. The tip clearance flow field of this transonic rotor was simulated using a Navier-Stokes turbomachinery solver that incorporates an advanced k-epsilon turbulence model derived for flows that are not in local equilibrium. Comparison between measured and simulated results indicates that simulation accuracy is primarily dependent upon the ability of the numerical code to resolve important details of a wall-bounded shear layer formed by the relative motion between the over-tip leakage flow and the shroud wall. A simple method is presented for determining the strength of this shear layer.

Identification of source velocities on 3D structures in non-anechoic environments: Theoretical background and experimental validation of the inverse patch transfer functions method

NASA Astrophysics Data System (ADS)

Aucejo, M.; Totaro, N.; Guyader, J.-L.

2010-08-01

In noise control, identification of the source velocity field remains a major problem open to investigation. Consequently, methods such as nearfield acoustical holography (NAH), principal source projection, the inverse frequency response function and hybrid NAH have been developed. However, these methods require free field conditions that are often difficult to achieve in practice. This article presents an alternative method known as inverse patch transfer functions, designed to identify source velocities and developed in the framework of the European SILENCE project. This method is based on the definition of a virtual cavity, the double measurement of the pressure and particle velocity fields on the aperture surfaces of this volume, divided into elementary areas called patches and the inversion of impedances matrices, numerically computed from a modal basis obtained by FEM. Theoretically, the method is applicable to sources with complex 3D geometries and measurements can be carried out in a non-anechoic environment even in the presence of other stationary sources outside the virtual cavity. In the present paper, the theoretical background of the iPTF method is described and the results (numerical and experimental) for a source with simple geometry (two baffled pistons driven in antiphase) are presented and discussed.

A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation

PubMed Central

Wang, Jinfeng; Li, Hong; Fang, Zhichao

2014-01-01

We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen's expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates in L 2-norm for the scalar unknown u and a priori error estimates in (L 2)2-norm for its gradient λ and its flux σ. Moreover, we obtain the optimal a priori error estimates in H 1-norm for the scalar unknown u. Finally, we obtained some numerical results to illustrate efficiency of the new method. PMID:24701153

Using Fisher information to track stability in multivariate ...

EPA Pesticide Factsheets

With the current proliferation of data, the proficient use of statistical and mining techniques offer substantial benefits to capture useful information from any dataset. As numerous approaches make use of information theory concepts, here, we discuss how Fisher information (FI) can be applied to sustainability science problems and used in data mining applications by analyzing patterns in data. FI was developed as a measure of information content in data, and it has been adapted to assess order in complex system behaviors. The main advantage of the approach is the ability to collapse multiple variables into an index that can be used to assess stability and track overall trends in a system, including its regimes and regime shifts. Here, we provide a brief overview of FI theory, followed by a simple step-by-step numerical example on how to compute FI. Furthermore, we introduce an open source Python library that can be freely downloaded from GitHub and we use it in a simple case study to evaluate the evolution of FI for the global-mean temperature from 1880 to 2015. Results indicate significant declines in FI starting in 1978, suggesting a possible regime shift. Demonstrate Fisher information as a useful method for assessing patterns in big data.

Heat Transfer to Surfaces of Finite Catalytic Activity in Frozen Dissociated Hypersonic Flow

NASA Technical Reports Server (NTRS)

Chung, Paul M.; Anderson, Aemer D.

1961-01-01

The heat transfer due to catalytic recombination of a partially dissociated diatomic gas along the surfaces of two-dimensional and axisymmetric bodies with finite catalytic efficiencies is studied analytically. An integral method is employed resulting in simple yet relatively complete solutions for the particular configurations considered. A closed form solution is derived which enables one to calculate atom mass-fraction distribution, therefore catalytic heat transfer distribution, along the surface of a flat plate in frozen compressible flow with and without transpiration. Numerical calculations are made to determine the atom mass-fraction distribution along an axisymmetric conical body with spherical nose in frozen hypersonic compressible flow. A simple solution based on a local similarity concept is found to be in good agreement with these numerical calculations. The conditions are given for which the local similarity solution is expected to be satisfactory. The limitations on the practical application of the analysis to the flight of the blunt bodies in the atmosphere are discussed. The use of boundary-layer theory and the assumption of frozen flow restrict application of the analysis to altitudes between about 150,000 and 250,000 feet.

Use of paired simple and complex models to reduce predictive bias and quantify uncertainty

NASA Astrophysics Data System (ADS)

Doherty, John; Christensen, Steen

2011-12-01

Modern environmental management and decision-making is based on the use of increasingly complex numerical models. Such models have the advantage of allowing representation of complex processes and heterogeneous system property distributions inasmuch as these are understood at any particular study site. The latter are often represented stochastically, this reflecting knowledge of the character of system heterogeneity at the same time as it reflects a lack of knowledge of its spatial details. Unfortunately, however, complex models are often difficult to calibrate because of their long run times and sometimes questionable numerical stability. Analysis of predictive uncertainty is also a difficult undertaking when using models such as these. Such analysis must reflect a lack of knowledge of spatial hydraulic property details. At the same time, it must be subject to constraints on the spatial variability of these details born of the necessity for model outputs to replicate observations of historical system behavior. In contrast, the rapid run times and general numerical reliability of simple models often promulgates good calibration and ready implementation of sophisticated methods of calibration-constrained uncertainty analysis. Unfortunately, however, many system and process details on which uncertainty may depend are, by design, omitted from simple models. This can lead to underestimation of the uncertainty associated with many predictions of management interest. The present paper proposes a methodology that attempts to overcome the problems associated with complex models on the one hand and simple models on the other hand, while allowing access to the benefits each of them offers. It provides a theoretical analysis of the simplification process from a subspace point of view, this yielding insights into the costs of model simplification, and into how some of these costs may be reduced. It then describes a methodology for paired model usage through which predictive bias of a simplified model can be detected and corrected, and postcalibration predictive uncertainty can be quantified. The methodology is demonstrated using a synthetic example based on groundwater modeling environments commonly encountered in northern Europe and North America.

Determination of point of incidence for the case of reflection or refraction at spherical surface knowing two points lying on the ray.

PubMed

Mikš, Antonín; Novák, Pavel

2017-09-01

The paper is focused on the problem of determination of the point of incidence of a light ray for the case of reflection or refraction at the spherical optical surface, assuming that two fixed points in space that the sought light ray should go through are given. The requirement is that one of these points lies on the incident ray and the other point on the reflected/refracted ray. Although at first glance it seems to be a simple problem, it will be shown that it has no simple analytical solution. The basic idea of the solution is given, and it is shown that the problem leads to a nonlinear equation in one variable. The roots of the resulting nonlinear equation can be found by numerical methods of mathematical optimization. The proposed methods were implemented in MATLAB, and the proper function of these algorithms was verified on several examples.

The Logic of Reachability

NASA Technical Reports Server (NTRS)

Smith, David E.; Jonsson, Ari K.; Clancy, Daniel (Technical Monitor)

2001-01-01

In recent years, Graphplan style reachability analysis and mutual exclusion reasoning have been used in many high performance planning systems. While numerous refinements and extensions have been developed, the basic plan graph structure and reasoning mechanisms used in these systems are tied to the very simple STRIPS model of action. In 1999, Smith and Weld generalized the Graphplan methods for reachability and mutex reasoning to allow actions to have differing durations. However, the representation of actions still has some severe limitations that prevent the use of these techniques for many real-world planning systems. In this paper, we 1) separate the logic of reachability from the particular representation and inference methods used in Graphplan, and 2) extend the notions of reachability and mutual exclusion to more general notions of time and action. As it turns out, the general rules for mutual exclusion reasoning take on a remarkably clean and simple form. However, practical instantiations of them turn out to be messy, and require that we make representation and reasoning choices.

Non-planar vibrations of slightly curved pipes conveying fluid in simple and combination parametric resonances

NASA Astrophysics Data System (ADS)

Czerwiński, Andrzej; Łuczko, Jan

2018-01-01

The paper summarises the experimental investigations and numerical simulations of non-planar parametric vibrations of a statically deformed pipe. Underpinning the theoretical analysis is a 3D dynamic model of curved pipe. The pipe motion is governed by four non-linear partial differential equations with periodically varying coefficients. The Galerkin method was applied, the shape function being that governing the beam's natural vibrations. Experiments were conducted in the range of simple and combination parametric resonances, evidencing the possibility of in-plane and out-of-plane vibrations as well as fully non-planar vibrations in the combination resonance range. It is demonstrated that sub-harmonic and quasi-periodic vibrations are likely to be excited. The method suggested allows the spatial modes to be determined basing on results registered at selected points in the pipe. Results are summarised in the form of time histories, phase trajectory plots and spectral diagrams. Dedicated video materials give us a better insight into the investigated phenomena.

Helmholtz-Smoluchowski velocity for viscoelastic electroosmotic flows.

PubMed

Park, H M; Lee, W M

2008-01-15

Many biofluids such as blood and DNA solutions are viscoelastic and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. Adopting appropriate constitutive equations these exotic flow behaviors can be modeled and predicted reasonably using various numerical methods. However, the governing equations for viscoelastic flows are not easily solvable, especially for electroosmotic flows where the streamwise velocity varies rapidly from zero at the wall to a nearly uniform velocity at the outside of the very thin electric double layer. In the present investigation, we have devised a simple method to find the volumetric flow rate of viscoelastic electroosmotic flows through microchannels. It is based on the concept of the Helmholtz-Smoluchowski velocity which is widely adopted in the electroosmotic flows of Newtonian fluids. It is shown that the Helmholtz-Smoluchowski velocity for viscoelastic fluids can be found by solving a simple cubic algebraic equation. The volumetric flow rate obtained using this Helmholtz-Smoluchowski velocity is found to be almost the same as that obtained by solving the governing partial differential equations for various viscoelastic fluids.

Artificial Boundary Conditions Based on the Difference Potentials Method

NASA Technical Reports Server (NTRS)

Tsynkov, Semyon V.

1996-01-01

While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensive. The methods from the second group (local ABC's) are, as a rule, algorithmically simple, numerically cheap, and geometrically universal; however, they usually lack accuracy of computations. In this paper we first present a survey and provide a comparative assessment of different existing methods for constructing the ABC's. Then, we describe a relatively new ABC's technique of ours and review the corresponding results. This new technique, in our opinion, is currently one of the most promising in the field. It enables one to construct such ABC's that combine the advantages relevant to the two aforementioned classes of existing methods. Our approach is based on application of the difference potentials method attributable to V. S. Ryaben'kii. This approach allows us to obtain highly accurate ABC's in the form of certain (nonlocal) boundary operator equations. The operators involved are analogous to the pseudodifferential boundary projections first introduced by A. P. Calderon and then also studied by R. T. Seeley. The apparatus of the boundary pseudodifferential equations, which has formerly been used mostly in the qualitative theory of integral equations and PDE'S, is now effectively employed for developing numerical methods in the different fields of scientific computing.

A sensitivity analysis method for the body segment inertial parameters based on ground reaction and joint moment regressor matrices.

PubMed

Futamure, Sumire; Bonnet, Vincent; Dumas, Raphael; Venture, Gentiane

2017-11-07

This paper presents a method allowing a simple and efficient sensitivity analysis of dynamics parameters of complex whole-body human model. The proposed method is based on the ground reaction and joint moment regressor matrices, developed initially in robotics system identification theory, and involved in the equations of motion of the human body. The regressor matrices are linear relatively to the segment inertial parameters allowing us to use simple sensitivity analysis methods. The sensitivity analysis method was applied over gait dynamics and kinematics data of nine subjects and with a 15 segments 3D model of the locomotor apparatus. According to the proposed sensitivity indices, 76 segments inertial parameters out the 150 of the mechanical model were considered as not influent for gait. The main findings were that the segment masses were influent and that, at the exception of the trunk, moment of inertia were not influent for the computation of the ground reaction forces and moments and the joint moments. The same method also shows numerically that at least 90% of the lower-limb joint moments during the stance phase can be estimated only from a force-plate and kinematics data without knowing any of the segment inertial parameters. Copyright © 2017 Elsevier Ltd. All rights reserved.

Large-scale computation of incompressible viscous flow by least-squares finite element method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, T. L.; Povinelli, Louis A.

1993-01-01

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.

A General-applications Direct Global Matrix Algorithm for Rapid Seismo-acoustic Wavefield Computations

NASA Technical Reports Server (NTRS)

Schmidt, H.; Tango, G. J.; Werby, M. F.

1985-01-01

A new matrix method for rapid wave propagation modeling in generalized stratified media, which has recently been applied to numerical simulations in diverse areas of underwater acoustics, solid earth seismology, and nondestructive ultrasonic scattering is explained and illustrated. A portion of recent efforts jointly undertaken at NATOSACLANT and NORDA Numerical Modeling groups in developing, implementing, and testing a new fast general-applications wave propagation algorithm, SAFARI, formulated at SACLANT is summarized. The present general-applications SAFARI program uses a Direct Global Matrix Approach to multilayer Green's function calculation. A rapid and unconditionally stable solution is readily obtained via simple Gaussian ellimination on the resulting sparsely banded block system, precisely analogous to that arising in the Finite Element Method. The resulting gains in accuracy and computational speed allow consideration of much larger multilayered air/ocean/Earth/engineering material media models, for many more source-receiver configurations than previously possible. The validity and versatility of the SAFARI-DGM method is demonstrated by reviewing three practical examples of engineering interest, drawn from ocean acoustics, engineering seismology and ultrasonic scattering.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jo, J.C.; Shin, W.K.; Choi, C.Y.

Transient heat transfer problems with phase changes (Stefan problems) occur in many engineering situations, including potential core melting and solidification during pressurized-water-reactor severe accidents, ablation of thermal shields, melting and solidification of alloys, and many others. This article addresses the numerical analysis of nonlinear transient heat transfer with melting or solidification. An effective and simple procedure is presented for the simulation of the motion of the boundary and the transient temperature field during the phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual-reciprocity boundary-element method. The dual-reciprocity boundary-element approach providedmore » in this article is much simpler than the usual boundary-element method in applying a reciprocity principle and an available technique for dealing with the domain integral of the boundary element formulation simultaneously. In this article, attention is focused on two-dimensional melting (ablation)/solidification problems for simplicity. The accuracy and effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of some examples of one-phase ablation/solidification problems with their known semianalytical or numerical solutions where available.« less

A boundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in two dimensions.

PubMed

Yang, S A

2002-10-01

This paper presents an effective solution method for predicting acoustic radiation and scattering fields in two dimensions. The difficulty of the fictitious characteristic frequency is overcome by incorporating an auxiliary interior surface that satisfies certain boundary condition into the body surface. This process gives rise to a set of uniquely solvable boundary integral equations. Distributing monopoles with unknown strengths over the body and interior surfaces yields the simple source formulation. The modified boundary integral equations are further transformed to ordinary ones that contain nonsingular kernels only. This implementation allows direct application of standard quadrature formulas over the entire integration domain; that is, the collocation points are exactly the positions at which the integration points are located. Selecting the interior surface is an easy task. Moreover, only a few corresponding interior nodal points are sufficient for the computation. Numerical calculations consist of the acoustic radiation and scattering by acoustically hard elliptic and rectangular cylinders. Comparisons with analytical solutions are made. Numerical results demonstrate the efficiency and accuracy of the current solution method.

Solution of mixed convection heat transfer from isothermal in-line fins

NASA Technical Reports Server (NTRS)

Khalilollahi, Amir

1993-01-01

Transient and steady state combined natural and forced convective flows over two in-line finite thickness fins (louvers) in a vertical channel are numerically solved using two methods. The first method of solution is based on the 'Simple Arbitrary Lagrangian Eulerian' (SALE) technique which incorporates mainly two computational phases: (1) a Lagrangian phase in which the velocity field is updated by the effects of all forces, and (2) an Eulerian phase that executes all advective fluxes of mass, momentum and energy. The second method of solution uses the finite element code entitled FIDAP. In the first part, comparison of the results by FIDAP, SALE, and available experimental work were done and discussed for steady state forced convection over louvered fins. Good agreements were deduced between the three sets of results especially for the flow over a single fin. In the second part and in the absence of experimental literature, the numerical predictions were extended to the transient transports and to the opposing flow where pressure drop is reversed. Results are presented and discussed for heat transfer and pressure drop in assisting and opposing mixed convection flows.

A numerical model of two-phase flow at the micro-scale using the volume-of-fluid method

NASA Astrophysics Data System (ADS)

Shams, Mosayeb; Raeini, Ali Q.; Blunt, Martin J.; Bijeljic, Branko

2018-03-01

This study presents a simple and robust numerical scheme to model two-phase flow in porous media where capillary forces dominate over viscous effects. The volume-of-fluid method is employed to capture the fluid-fluid interface whose dynamics is explicitly described based on a finite volume discretization of the Navier-Stokes equations. Interfacial forces are calculated directly on reconstructed interface elements such that the total curvature is preserved. The computed interfacial forces are explicitly added to the Navier-Stokes equations using a sharp formulation which effectively eliminates spurious currents. The stability and accuracy of the implemented scheme is validated on several two- and three-dimensional test cases, which indicate the capability of the method to model two-phase flow processes at the micro-scale. In particular we show how the co-current flow of two viscous fluids leads to greatly enhanced flow conductance for the wetting phase in corners of the pore space, compared to a case where the non-wetting phase is an inviscid gas.

A deterministic Lagrangian particle separation-based method for advective-diffusion problems

NASA Astrophysics Data System (ADS)

Wong, Ken T. M.; Lee, Joseph H. W.; Choi, K. W.

2008-12-01

A simple and robust Lagrangian particle scheme is proposed to solve the advective-diffusion transport problem. The scheme is based on relative diffusion concepts and simulates diffusion by regulating particle separation. This new approach generates a deterministic result and requires far less number of particles than the random walk method. For the advection process, particles are simply moved according to their velocity. The general scheme is mass conservative and is free from numerical diffusion. It can be applied to a wide variety of advective-diffusion problems, but is particularly suited for ecological and water quality modelling when definition of particle attributes (e.g., cell status for modelling algal blooms or red tides) is a necessity. The basic derivation, numerical stability and practical implementation of the NEighborhood Separation Technique (NEST) are presented. The accuracy of the method is demonstrated through a series of test cases which embrace realistic features of coastal environmental transport problems. Two field application examples on the tidal flushing of a fish farm and the dynamics of vertically migrating marine algae are also presented.

Rules of Thumb for Depth of Investigation, Pseudo-Position and Resolution of the Electrical Resistivity Method from Analysis of the Moments of the Sensitivity Function for a Homogeneous Half-Space

NASA Astrophysics Data System (ADS)

Butler, S. L.

2017-12-01

The electrical resistivity method is now highly developed with 2D and even 3D surveys routinely performed and with available fast inversion software. However, rules of thumb, based on simple mathematical formulas, for important quantities like depth of investigation, horizontal position and resolution have not previously been available and would be useful for survey planning, preliminary interpretation and general education about the method. In this contribution, I will show that the sensitivity function for the resistivity method for a homogeneous half-space can be analyzed in terms of its first and second moments which yield simple mathematical formulas. The first moment gives the sensitivity-weighted center of an apparent resistivity measurement with the vertical center being an estimate of the depth of investigation. I will show that this depth of investigation estimate works at least as well as previous estimates based on the peak and median of the depth sensitivity function which must be calculated numerically for a general four electrode array. The vertical and horizontal first moments can also be used as pseudopositions when plotting 1, 2 and 3D pseudosections. The appropriate horizontal plotting point for a pseudosection was not previously obvious for nonsymmetric arrays. The second moments of the sensitivity function give estimates of the spatial extent of the region contributing to an apparent resistivity measurement and hence are measures of the resolution. These also have simple mathematical formulas.

A simple formulation for deriving effective atomic numbers via electron density calibration from dual-energy CT data in the human body.

PubMed

Saito, Masatoshi; Sagara, Shota

2017-06-01

The main objective of this study is to propose a simple formulation (which we called DEEDZ) for deriving effective atomic numbers (Z eff ) via electron density (ρ e ) calibration from dual-energy (DE) CT data. We carried out numerical analysis of this DEEDZ method for a large variety of materials with known elemental compositions and mass densities using an available photon cross sections database. The new conversion approach was also applied to previously published experimental DECT data to validate its practical feasibility. We performed numerical analysis of the DEEDZ conversion method for tissue surrogates that have the same chemical compositions and mass densities as a commercial tissue-characterization phantom in order to determine the parameters necessary for the ρ e and Z eff calibrations in the DEEDZ conversion. These parameters were then applied to the human-body-equivalent tissues of ICRU Report 46 as objects of interest with unknown ρ e and Z eff . The attenuation coefficients of these materials were calculated using the XCOM photon cross sections database. We also applied the DEEDZ conversion to experimental DECT data available in the literature, which was measured for two commercial phantoms of different shapes and sizes using a dual-source CT scanner at 80 kV and 140 kV/Sn. The simulated Z eff 's were in excellent agreement with the reference values for almost all of the ICRU-46 human tissues over the Z eff range from 5.83 (gallstones-cholesterol) to 16.11 (bone mineral-hydroxyapatite). The relative deviations from the reference Z eff were within ± 0.3% for all materials, except for one outlier that presented a -3.1% deviation, namely, the thyroid. The reason for this discrepancy is that the thyroid contains a small amount of iodine, an element with a large atomic number (Z = 53). In the experimental case, we confirmed that the simple formulation with less fit parameters enable to calibrate Z eff as accurately as the existing calibration procedure. The DEEDZ conversion method based on the simple formulation proposed could facilitate the construction of ρ e and Z eff images from acquired DECT data. © 2017 American Association of Physicists in Medicine.

Direct Measurement of the Topological Charge in Elliptical Beams Using Diffraction by a Triangular Aperture.

PubMed

Melo, Leandro A; Jesus-Silva, Alcenísio J; Chávez-Cerda, Sabino; Ribeiro, Paulo H Souto; Soares, Willamys C

2018-04-23

We introduce a simple method to characterize the topological charge associated with the orbital angular momentum of a m-order elliptic light beam. This method consists in the observation of the far field pattern of the beam carrying orbital angular momentum, diffracted from a triangular aperture. We show numerically and experimentally, for Mathieu, Ince-Gaussian, and vortex Hermite-Gaussian beams, that only isosceles triangular apertures allow us to determine in a precise and direct way, the magnitude m of the order and the number and sign of unitary topological charges of isolated vortices inside the core of these beams.

On the joint inversion of geophysical data for models of the coupled core-mantle system

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1991-01-01

Joint inversion of magnetic, earth rotation, geoid, and seismic data for a unified model of the coupled core-mantle system is proposed and shown to be possible. A sample objective function is offered and simplified by targeting results from independent inversions and summary travel time residuals instead of original observations. These data are parameterized in terms of a very simple, closed model of the topographically coupled core-mantle system. Minimization of the simplified objective function leads to a nonlinear inverse problem; an iterative method for solution is presented. Parameterization and method are emphasized; numerical results are not presented.

A recurrent neural network for solving bilevel linear programming problem.

PubMed

He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie; Huang, Junjian

2014-04-01

In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.

A new statistical method for transfer coefficient calculations in the framework of the general multiple-compartment model of transport for radionuclides in biological systems.

PubMed

Garcia, F; Arruda-Neto, J D; Manso, M V; Helene, O M; Vanin, V R; Rodriguez, O; Mesa, J; Likhachev, V P; Filho, J W; Deppman, A; Perez, G; Guzman, F; de Camargo, S P

1999-10-01

A new and simple statistical procedure (STATFLUX) for the calculation of transfer coefficients of radionuclide transport to animals and plants is proposed. The method is based on the general multiple-compartment model, which uses a system of linear equations involving geometrical volume considerations. By using experimentally available curves of radionuclide concentrations versus time, for each animal compartment (organs), flow parameters were estimated by employing a least-squares procedure, whose consistency is tested. Some numerical results are presented in order to compare the STATFLUX transfer coefficients with those from other works and experimental data.

Photoacoustic spectroscopy of condensed matter

NASA Technical Reports Server (NTRS)

Somoano, R. B.

1978-01-01

Photoacoustic spectroscopy is a new analytical tool that provides a simple nondestructive technique for obtaining information about the electronic absorption spectrum of samples such as powders, semisolids, gels, and liquids. It can also be applied to samples which cannot be examined by conventional optical methods. Numerous applications of this technique in the field of inorganic and organic semiconductors, biology, and catalysis have been described. Among the advantages of photoacoustic spectroscopy, the signal is almost insensitive to light scattering by the sample and information can be obtained about nonradiative deactivation processes. Signal saturation, which can modify the intensity of individual absorption bands in special cases, is a drawback of the method.

Fast and simple acquisition of solid-state 14N NMR spectra with signal enhancement via population transfer.

PubMed

O'Dell, Luke A; Schurko, Robert W

2009-05-20

A new approach for the acquisition of static, wideline (14)N NMR powder patterns is outlined. The method involves the use of frequency-swept pulses which serve two simultaneous functions: (1) broad-band excitation of magnetization and (2) signal enhancement via population transfer. The signal enhancement mechanism is described using numerical simulations and confirmed experimentally. This approach, which we call DEISM (Direct Enhancement of Integer Spin Magnetization), allows high-quality (14)N spectra to be acquired at intermediate field strengths in an uncomplicated way and in a fraction of the time required for previously reported methods.

Can a numerically stable subgrid-scale model for turbulent flow computation be ideally accurate?: a preliminary theoretical study for the Gaussian filtered Navier-Stokes equations.

PubMed

Ida, Masato; Taniguchi, Nobuyuki

2003-09-01

This paper introduces a candidate for the origin of the numerical instabilities in large eddy simulation repeatedly observed in academic and practical industrial flow computations. Without resorting to any subgrid-scale modeling, but based on a simple assumption regarding the streamwise component of flow velocity, it is shown theoretically that in a channel-flow computation, the application of the Gaussian filtering to the incompressible Navier-Stokes equations yields a numerically unstable term, a cross-derivative term, which is similar to one appearing in the Gaussian filtered Vlasov equation derived by Klimas [J. Comput. Phys. 68, 202 (1987)] and also to one derived recently by Kobayashi and Shimomura [Phys. Fluids 15, L29 (2003)] from the tensor-diffusivity subgrid-scale term in a dynamic mixed model. The present result predicts that not only the numerical methods and the subgrid-scale models employed but also only the applied filtering process can be a seed of this numerical instability. An investigation concerning the relationship between the turbulent energy scattering and the unstable term shows that the instability of the term does not necessarily represent the backscatter of kinetic energy which has been considered a possible origin of numerical instabilities in large eddy simulation. The present findings raise the question whether a numerically stable subgrid-scale model can be ideally accurate.

Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bobylev, A.V., E-mail: alexander.bobylev@kau.se; Potapenko, I.F., E-mail: firena@yandex.ru

2013-08-01

Highlights: •A general approach to Monte Carlo methods for multicomponent plasmas is proposed. •We show numerical tests for the two-component (electrons and ions) case. •An optimal choice of parameters for speeding up the computations is discussed. •A rigorous estimate of the error of approximation is proved. -- Abstract: A general approach to Monte Carlo methods for Coulomb collisions is proposed. Its key idea is an approximation of Landau–Fokker–Planck equations by Boltzmann equations of quasi-Maxwellian kind. It means that the total collision frequency for the corresponding Boltzmann equation does not depend on the velocities. This allows to make the simulation processmore » very simple since the collision pairs can be chosen arbitrarily, without restriction. It is shown that this approach includes the well-known methods of Takizuka and Abe (1977) [12] and Nanbu (1997) as particular cases, and generalizes the approach of Bobylev and Nanbu (2000). The numerical scheme of this paper is simpler than the schemes by Takizuka and Abe [12] and by Nanbu. We derive it for the general case of multicomponent plasmas and show some numerical tests for the two-component (electrons and ions) case. An optimal choice of parameters for speeding up the computations is also discussed. It is also proved that the order of approximation is not worse than O(√(ε)), where ε is a parameter of approximation being equivalent to the time step Δt in earlier methods. A similar estimate is obtained for the methods of Takizuka and Abe and Nanbu.« less

A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods

NASA Astrophysics Data System (ADS)

Syrakos, Alexandros; Varchanis, Stylianos; Dimakopoulos, Yannis; Goulas, Apostolos; Tsamopoulos, John

2017-12-01

Finite volume methods (FVMs) constitute a popular class of methods for the numerical simulation of fluid flows. Among the various components of these methods, the discretisation of the gradient operator has received less attention despite its fundamental importance with regards to the accuracy of the FVM. The most popular gradient schemes are the divergence theorem (DT) (or Green-Gauss) scheme and the least-squares (LS) scheme. Both are widely believed to be second-order accurate, but the present study shows that in fact the common variant of the DT gradient is second-order accurate only on structured meshes whereas it is zeroth-order accurate on general unstructured meshes, and the LS gradient is second-order and first-order accurate, respectively. This is explained through a theoretical analysis and is confirmed by numerical tests. The schemes are then used within a FVM to solve a simple diffusion equation on unstructured grids generated by several methods; the results reveal that the zeroth-order accuracy of the DT gradient is inherited by the FVM as a whole, and the discretisation error does not decrease with grid refinement. On the other hand, use of the LS gradient leads to second-order accurate results, as does the use of alternative, consistent, DT gradient schemes, including a new iterative scheme that makes the common DT gradient consistent at almost no extra cost. The numerical tests are performed using both an in-house code and the popular public domain partial differential equation solver OpenFOAM.

On the formation of fold-type oscillation marks in the continuous casting of steel.

PubMed

Vynnycky, M; Saleem, S; Devine, K M; Florio, B J; Mitchell, S L; O'Brien, S B G

2017-06-01

Asymptotic methods are employed to revisit an earlier model for oscillation-mark formation in the continuous casting of steel. A systematic non-dimensionalization of the governing equations, which was not carried out previously, leads to a model with 12 dimensionless parameters. Analysis is provided in the same parameter regime as for the earlier model, and surprisingly simple analytical solutions are found for the oscillation-mark profiles; these are found to agree reasonably well with the numerical solution in the earlier model and very well with fold-type oscillation marks that have been obtained in more recent experimental work. The benefits of this approach, when compared with time-consuming numerical simulations, are discussed in the context of auxiliary models for macrosegregation and thermomechanical stresses and strains.

Analytic algorithms for determining radiative transfer optical properties of ocean waters.

PubMed

Kaskas, Ayse; Güleçyüz, Mustafa C; Tezcan, Cevdet; McCormick, Norman J

2006-10-10

A synthetic model for the scattering phase function is used to develop simple algebraic equations, valid for any water type, for evaluating the ratio of the backscattering to absorption coefficients of spatially uniform, very deep waters with data from upward and downward planar irradiances and the remotely sensed reflectance. The phase function is a variable combination of a forward-directed Dirac delta function plus isotropic scattering, which is an elementary model for strongly forward scattering such as that encountered in oceanic optics applications. The incident illumination at the surface is taken to be diffuse plus a collimated beam. The algorithms are compared with other analytic correlations that were previously derived from extensive numerical simulations, and they are also numerically tested with forward problem results computed with a modified FN method.

A computer code for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1986-01-01

In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.

An interative solution of an integral equation for radiative transfer by using variational technique

NASA Technical Reports Server (NTRS)

Yoshikawa, K. K.

1973-01-01

An effective iterative technique is introduced to solve a nonlinear integral equation frequently associated with radiative transfer problems. The problem is formulated in such a way that each step of an iterative sequence requires the solution of a linear integral equation. The advantage of a previously introduced variational technique which utilizes a stepwise constant trial function is exploited to cope with the nonlinear problem. The method is simple and straightforward. Rapid convergence is obtained by employing a linear interpolation of the iterative solutions. Using absorption coefficients of the Milne-Eddington type, which are applicable to some planetary atmospheric radiation problems. Solutions are found in terms of temperature and radiative flux. These solutions are presented numerically and show excellent agreement with other numerical solutions.

On the formation of fold-type oscillation marks in the continuous casting of steel

PubMed Central

Saleem, S.; Devine, K. M.; Florio, B. J.; Mitchell, S. L.; O’Brien, S. B. G.

2017-01-01

Asymptotic methods are employed to revisit an earlier model for oscillation-mark formation in the continuous casting of steel. A systematic non-dimensionalization of the governing equations, which was not carried out previously, leads to a model with 12 dimensionless parameters. Analysis is provided in the same parameter regime as for the earlier model, and surprisingly simple analytical solutions are found for the oscillation-mark profiles; these are found to agree reasonably well with the numerical solution in the earlier model and very well with fold-type oscillation marks that have been obtained in more recent experimental work. The benefits of this approach, when compared with time-consuming numerical simulations, are discussed in the context of auxiliary models for macrosegregation and thermomechanical stresses and strains. PMID:28680666

A Simple and Accurate Rate-Driven Infiltration Model

NASA Astrophysics Data System (ADS)

Cui, G.; Zhu, J.

2017-12-01

In this study, we develop a novel Rate-Driven Infiltration Model (RDIMOD) for simulating infiltration into soils. Unlike traditional methods, RDIMOD avoids numerically solving the highly non-linear Richards equation or simply modeling with empirical parameters. RDIMOD employs infiltration rate as model input to simulate one-dimensional infiltration process by solving an ordinary differential equation. The model can simulate the evolutions of wetting front, infiltration rate, and cumulative infiltration on any surface slope including vertical and horizontal directions. Comparing to the results from the Richards equation for both vertical infiltration and horizontal infiltration, RDIMOD simply and accurately predicts infiltration processes for any type of soils and soil hydraulic models without numerical difficulty. Taking into account the accuracy, capability, and computational effectiveness and stability, RDIMOD can be used in large-scale hydrologic and land-atmosphere modeling.

Poisson's ratio of fiber-reinforced composites

NASA Astrophysics Data System (ADS)

Christiansson, Henrik; Helsing, Johan

1996-05-01

Poisson's ratio flow diagrams, that is, the Poisson's ratio versus the fiber fraction, are obtained numerically for hexagonal arrays of elastic circular fibers in an elastic matrix. High numerical accuracy is achieved through the use of an interface integral equation method. Questions concerning fixed point theorems and the validity of existing asymptotic relations are investigated and partially resolved. Our findings for the transverse effective Poisson's ratio, together with earlier results for random systems by other authors, make it possible to formulate a general statement for Poisson's ratio flow diagrams: For composites with circular fibers and where the phase Poisson's ratios are equal to 1/3, the system with the lowest stiffness ratio has the highest Poisson's ratio. For other choices of the elastic moduli for the phases, no simple statement can be made.

ParaExp Using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations

NASA Astrophysics Data System (ADS)

Merkel, M.; Niyonzima, I.; Schöps, S.

2017-12-01

Recently, ParaExp was proposed for the time integration of linear hyperbolic problems. It splits the time interval of interest into subintervals and computes the solution on each subinterval in parallel. The overall solution is decomposed into a particular solution defined on each subinterval with zero initial conditions and a homogeneous solution propagated by the matrix exponential applied to the initial conditions. The efficiency of the method depends on fast approximations of this matrix exponential based on recent results from numerical linear algebra. This paper deals with the application of ParaExp in combination with Leapfrog to electromagnetic wave problems in time domain. Numerical tests are carried out for a simple toy problem and a realistic spiral inductor model discretized by the Finite Integration Technique.

Improved Multi-Axial, Temperature and Time Dependent (MATT) Failure Model

NASA Technical Reports Server (NTRS)

Richardson, D. E.; Anderson, G. L.; Macon, D. J.

2002-01-01

An extensive effort has recently been completed by the Space Shuttle's Reusable Solid Rocket Motor (RSRM) nozzle program to completely characterize the effects of multi-axial loading, temperature and time on the failure characteristics of three filled epoxy adhesives (TIGA 321, EA913NA, EA946). As part of this effort, a single general failure criterion was developed that accounted for these effects simultaneously. This model was named the Multi- Axial, Temperature, and Time Dependent or MATT failure criterion. Due to the intricate nature of the failure criterion, some parameters were required to be calculated using complex equations or numerical methods. This paper documents some simple but accurate modifications to the failure criterion to allow for calculations of failure conditions without complex equations or numerical techniques.

Determining ecoregional numeric nutrient criteria by stressor-response models in Yungui ecoregion lakes, China.

PubMed

Huo, Shouliang; Ma, Chunzi; Xi, Beidou; Tong, Zhonghua; He, Zhuoshi; Su, Jing; Wu, Fengchang

2014-01-01

The importance of developing numeric nutrient criteria has been recognized to protect the designated uses of water bodies from nutrient enrichment that is associated with broadly occurring levels of nitrogen/phosphorus pollution. The identification and estimation of stressor-response models in aquatic ecosystems has been shown to be useful in the determination of nutrient criteria. In this study, three methods based on stressor-response relationships were applied to determine nutrient criteria for Yungui ecoregion lakes with respect to total phosphorus (TP), total nitrogen (TN), and planktonic chlorophyll a (Chl a). Simple linear regression (SLR) models were established to provide an estimate of the relationship between a response variable and a stressor. Multiple linear regressions were used to simultaneously estimate the effect of TP and TN on Chl a. A morphoedaphic index (MEI) was applied to derive nutrient criteria using data from Yungui ecoregion lakes, which were considered as areas with less anthropogenic influences. Nutrient criteria, as determined by these three methods, showed broad agreement for all parameters. The ranges of numeric nutrient criteria for Yungui ecoregion lakes were determined as follows: TP 0.008-0.010 mg/L and TN 0.140-0.178 mg/L. The stressor-response analysis described will be of benefit to support countries in their numeric criteria development programs and to further the goal of reducing nitrogen/phosphorus pollution in China.

Experimental validation of a numerical 3-D finite model applied to wind turbines design under vibration constraints: TREVISE platform

NASA Astrophysics Data System (ADS)

Sellami, Takwa; Jelassi, Sana; Darcherif, Abdel Moumen; Berriri, Hanen; Mimouni, Med Faouzi

2018-04-01

With the advancement of wind turbines towards complex structures, the requirement of trusty structural models has become more apparent. Hence, the vibration characteristics of the wind turbine components, like the blades and the tower, have to be extracted under vibration constraints. Although extracting the modal properties of blades is a simple task, calculating precise modal data for the whole wind turbine coupled to its tower/foundation is still a perplexing task. In this framework, this paper focuses on the investigation of the structural modeling approach of modern commercial micro-turbines. Thus, the structural model a complex designed wind turbine, which is Rutland 504, is established based on both experimental and numerical methods. A three-dimensional (3-D) numerical model of the structure was set up based on the finite volume method (FVM) using the academic finite element analysis software ANSYS. To validate the created model, experimental vibration tests were carried out using the vibration test system of TREVISE platform at ECAM-EPMI. The tests were based on the experimental modal analysis (EMA) technique, which is one of the most efficient techniques for identifying structures parameters. Indeed, the poles and residues of the frequency response functions (FRF), between input and output spectra, were calculated to extract the mode shapes and the natural frequencies of the structure. Based on the obtained modal parameters, the numerical designed model was up-dated.

Low Reynolds number two-equation modeling of turbulent flows

NASA Technical Reports Server (NTRS)

Michelassi, V.; Shih, T.-H.

1991-01-01

A k-epsilon model that accounts for viscous and wall effects is presented. The proposed formulation does not contain the local wall distance thereby making very simple the application to complex geometries. The formulation is based on an existing k-epsilon model that proved to fit very well with the results of direct numerical simulation. The new form is compared with nine different two-equation models and with direct numerical simulation for a fully developed channel flow at Re = 3300. The simple flow configuration allows a comparison free from numerical inaccuracies. The computed results prove that few of the considered forms exhibit a satisfactory agreement with the channel flow data. The model shows an improvement with respect to the existing formulations.

A diffusion model of protected population on bilocal habitat with generalized resource

NASA Astrophysics Data System (ADS)

Vasilyev, Maxim D.; Trofimtsev, Yuri I.; Vasilyeva, Natalya V.

2017-11-01

A model of population distribution in a two-dimensional area divided by an ecological barrier, i.e. the boundaries of natural reserve, is considered. Distribution of the population is defined by diffusion, directed migrations and areal resource. The exchange of specimens occurs between two parts of the habitat. The mathematical model is presented in the form of a boundary value problem for a system of non-linear parabolic equations with variable parameters of diffusion and growth function. The splitting space variables, sweep method and simple iteration methods were used for the numerical solution of a system. A set of programs was coded in Python. Numerical simulation results for the two-dimensional unsteady non-linear problem are analyzed in detail. The influence of migration flow coefficients and functions of natural birth/death ratio on the distributions of population densities is investigated. The results of the research would allow to describe the conditions of the stable and sustainable existence of populations in bilocal habitat containing the protected and non-protected zones.

Three-wave resonant interactions: Multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics

NASA Astrophysics Data System (ADS)

Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong

2018-03-01

We investigate three-wave resonant interactions through both the generalized Darboux transformation method and numerical simulations. Firstly, we derive a simple multi-dark-dark-dark-soliton formula through the generalized Darboux transformation. Secondly, we use the matrix analysis method to avoid the singularity of transformed potential functions and to find the general nonsingular breather solutions. Moreover, through a limit process, we deduce the general rogue wave solutions and give a classification by their dynamics including bright, dark, four-petals, and two-peaks rogue waves. Ever since the coexistence of dark soliton and rogue wave in non-zero background, their interactions naturally become a quite appealing topic. Based on the N-fold Darboux transformation, we can derive the explicit solutions to depict their interactions. Finally, by performing extensive numerical simulations we can predict whether these dark solitons and rogue waves are stable enough to propagate. These results can be available for several physical subjects such as fluid dynamics, nonlinear optics, solid state physics, and plasma physics.

Eigenstates and dynamics of Hooke's atom: Exact results and path integral simulations

NASA Astrophysics Data System (ADS)

Gholizadehkalkhoran, Hossein; Ruokosenmäki, Ilkka; Rantala, Tapio T.

2018-05-01

The system of two interacting electrons in one-dimensional harmonic potential or Hooke's atom is considered, again. On one hand, it appears as a model for quantum dots in a strong confinement regime, and on the other hand, it provides us with a hard test bench for new methods with the "space splitting" arising from the one-dimensional Coulomb potential. Here, we complete the numerous previous studies of the ground state of Hooke's atom by including the excited states and dynamics, not considered earlier. With the perturbation theory, we reach essentially exact eigenstate energies and wave functions for the strong confinement regime as novel results. We also consider external perturbation induced quantum dynamics in a simple separable case. Finally, we test our novel numerical approach based on real-time path integrals (RTPIs) in reproducing the above. The RTPI turns out to be a straightforward approach with exact account of electronic correlations for solving the eigenstates and dynamics without the conventional restrictions of electronic structure methods.

Estimating linear effects in ANOVA designs: the easy way.

PubMed

Pinhas, Michal; Tzelgov, Joseph; Ganor-Stern, Dana

2012-09-01

Research in cognitive science has documented numerous phenomena that are approximated by linear relationships. In the domain of numerical cognition, the use of linear regression for estimating linear effects (e.g., distance and SNARC effects) became common following Fias, Brysbaert, Geypens, and d'Ydewalle's (1996) study on the SNARC effect. While their work has become the model for analyzing linear effects in the field, it requires statistical analysis of individual participants and does not provide measures of the proportions of variability accounted for (cf. Lorch & Myers, 1990). In the present methodological note, using both the distance and SNARC effects as examples, we demonstrate how linear effects can be estimated in a simple way within the framework of repeated measures analysis of variance. This method allows for estimating effect sizes in terms of both slope and proportions of variability accounted for. Finally, we show that our method can easily be extended to estimate linear interaction effects, not just linear effects calculated as main effects.

Investigation of computational and spectral analysis methods for aeroacoustic wave propagation

NASA Technical Reports Server (NTRS)

Vanel, Florence O.

1995-01-01

Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the capabilities of two traditional methods for spectral analysis, namely, the Blackman-Tukey method and periodogram method, are compared in estimating the spectra of a simple-periodic process. The periodogram is then applied to analyze transitory-deterministic processes. Finally, these two methods are compared with a more recent method, referred as the Weighted-Overlapped-Segment-Averaging (WOSA) method, in estimating the spectra of a chaotic (random-like) process. From the demonstrative case for the spectral analyses of data generated by simple-periodic process, the periodogram method is found to give a better estimate of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window is found to perform better with the periodogram method than with the Blackman-Tukey method. Finally, for the spectral analysis of data generated by the chaotic process, the periodogram method does not perform well, whereas, the WOSA and Blackman-Tukey methods give equivalently good results.

OpenMP performance for benchmark 2D shallow water equations using LBM

NASA Astrophysics Data System (ADS)

Sabri, Khairul; Rabbani, Hasbi; Gunawan, Putu Harry

2018-03-01

Shallow water equations or commonly referred as Saint-Venant equations are used to model fluid phenomena. These equations can be solved numerically using several methods, like Lattice Boltzmann method (LBM), SIMPLE-like Method, Finite Difference Method, Godunov-type Method, and Finite Volume Method. In this paper, the shallow water equation will be approximated using LBM or known as LABSWE and will be simulated in performance of parallel programming using OpenMP. To evaluate the performance between 2 and 4 threads parallel algorithm, ten various number of grids Lx and Ly are elaborated. The results show that using OpenMP platform, the computational time for solving LABSWE can be decreased. For instance using grid sizes 1000 × 500, the speedup of 2 and 4 threads is observed 93.54 s and 333.243 s respectively.

Flux control coefficients determined by inhibitor titration: the design and analysis of experiments to minimize errors.

PubMed Central

Small, J R

1993-01-01

This paper is a study into the effects of experimental error on the estimated values of flux control coefficients obtained using specific inhibitors. Two possible techniques for analysing the experimental data are compared: a simple extrapolation method (the so-called graph method) and a non-linear function fitting method. For these techniques, the sources of systematic errors are identified and the effects of systematic and random errors are quantified, using both statistical analysis and numerical computation. It is shown that the graph method is very sensitive to random errors and, under all conditions studied, that the fitting method, even under conditions where the assumptions underlying the fitted function do not hold, outperformed the graph method. Possible ways of designing experiments to minimize the effects of experimental errors are analysed and discussed. PMID:8257434

Numerical Modeling of Sub-Wavelength Anti-Reflective Structures for Solar Module Applications

PubMed Central

Han, Katherine; Chang, Chih-Hung

2014-01-01

This paper reviews the current progress in mathematical modeling of anti-reflective subwavelength structures. Methods covered include effective medium theory (EMT), finite-difference time-domain (FDTD), transfer matrix method (TMM), the Fourier modal method (FMM)/rigorous coupled-wave analysis (RCWA) and the finite element method (FEM). Time-based solutions to Maxwell’s equations, such as FDTD, have the benefits of calculating reflectance for multiple wavelengths of light per simulation, but are computationally intensive. Space-discretized methods such as FDTD and FEM output field strength results over the whole geometry and are capable of modeling arbitrary shapes. Frequency-based solutions such as RCWA/FMM and FEM model one wavelength per simulation and are thus able to handle dispersion for regular geometries. Analytical approaches such as TMM are appropriate for very simple thin films. Initial disadvantages such as neglect of dispersion (FDTD), inaccuracy in TM polarization (RCWA), inability to model aperiodic gratings (RCWA), and inaccuracy with metallic materials (FDTD) have been overcome by most modern software. All rigorous numerical methods have accurately predicted the broadband reflection of ideal, graded-index anti-reflective subwavelength structures; ideal structures are tapered nanostructures with periods smaller than the wavelengths of light of interest and lengths that are at least a large portion of the wavelengths considered. PMID:28348287

Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon min-max optimal control problems with uncertainty

NASA Astrophysics Data System (ADS)

Nikooeinejad, Z.; Delavarkhalafi, A.; Heydari, M.

2018-03-01

The difficulty of solving the min-max optimal control problems (M-MOCPs) with uncertainty using generalised Euler-Lagrange equations is caused by the combination of split boundary conditions, nonlinear differential equations and the manner in which the final time is treated. In this investigation, the shifted Jacobi pseudospectral method (SJPM) as a numerical technique for solving two-point boundary value problems (TPBVPs) in M-MOCPs for several boundary states is proposed. At first, a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented. Then, by applying the generalised Euler-Lagrange equations and expanding the required approximate solutions as elements of shifted Jacobi polynomials, finding a solution of TPBVPs in nonlinear M-MOCPs with uncertainty is reduced to the solution of a system of algebraic equations. Moreover, the Jacobi polynomials are particularly useful for boundary value problems in unbounded domain, which allow us to solve infinite- as well as finite and free final time problems by domain truncation method. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. A comparative study between the proposed method and other existing methods shows that the SJPM is simple and accurate.

Mathematical and computational model for the analysis of micro hybrid rocket motor

NASA Astrophysics Data System (ADS)

Stoia-Djeska, Marius; Mingireanu, Florin

2012-11-01

The hybrid rockets use a two-phase propellant system. In the present work we first develop a simplified model of the coupling of the hybrid combustion process with the complete unsteady flow, starting from the combustion port and ending with the nozzle. The physical and mathematical model are adapted to the simulations of micro hybrid rocket motors. The flow model is based on the one-dimensional Euler equations with source terms. The flow equations and the fuel regression rate law are solved in a coupled manner. The platform of the numerical simulations is an implicit fourth-order Runge-Kutta second order cell-centred finite volume method. The numerical results obtained with this model show a good agreement with published experimental and numerical results. The computational model developed in this work is simple, computationally efficient and offers the advantage of taking into account a large number of functional and constructive parameters that are used by the engineers.

FAST Model Calibration and Validation of the OC5-DeepCwind Floating Offshore Wind System Against Wave Tank Test Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wendt, Fabian F; Robertson, Amy N; Jonkman, Jason

During the course of the Offshore Code Comparison Collaboration, Continued, with Correlation (OC5) project, which focused on the validation of numerical methods through comparison against tank test data, the authors created a numerical FAST model of the 1:50-scale DeepCwind semisubmersible system that was tested at the Maritime Research Institute Netherlands ocean basin in 2013. This paper discusses several model calibration studies that were conducted to identify model adjustments that improve the agreement between the numerical simulations and the experimental test data. These calibration studies cover wind-field-specific parameters (coherence, turbulence), hydrodynamic and aerodynamic modeling approaches, as well as rotor model (blade-pitchmore » and blade-mass imbalances) and tower model (structural tower damping coefficient) adjustments. These calibration studies were conducted based on relatively simple calibration load cases (wave only/wind only). The agreement between the final FAST model and experimental measurements is then assessed based on more-complex combined wind and wave validation cases.« less

Flow of a Casson fluid through a locally-constricted porous channel: a numerical study

NASA Astrophysics Data System (ADS)

Amlimohamadi, Haleh; Akram, Maryammosadat; Sadeghy, Kayvan

2016-05-01

Flow of a Casson fluid through a two-dimensional porous channel containing a local constriction is numerically investigated assuming that the resistance offered by the porous medium obeys the Darcy's law. Treating the constriction as another porous medium which obeys the Darcy-Forcheimer model, the equations governing fluid flow in the main channel and the constriction itself are numerically solved using the finite-volume method (FVM) based on the pseudo-transient SIMPLE algorithm. It is shown that an increase in the porosity of the channel decreases the shear stress exerted on the constriction. On the other hand, an increase in the fluid's yield stress is predicted to increase the maximum shear stress experienced by the constriction near its crest. The porosity of the constriction itself is predicted to have a negligible effect on the plaque's shear stress. But, the momentum of the weak flow passing through the constriction is argued to lower the bulk fluid from separating downstream of the constriction.

The void spectrum in two-dimensional numerical simulations of gravitational clustering

NASA Technical Reports Server (NTRS)

Kauffmann, Guinevere; Melott, Adrian L.

1992-01-01

An algorithm for deriving a spectrum of void sizes from two-dimensional high-resolution numerical simulations of gravitational clustering is tested, and it is verified that it produces the correct results where those results can be anticipated. The method is used to study the growth of voids as clustering proceeds. It is found that the most stable indicator of the characteristic void 'size' in the simulations is the mean fractional area covered by voids of diameter d, in a density field smoothed at its correlation length. Very accurate scaling behavior is found in power-law numerical models as they evolve. Eventually, this scaling breaks down as the nonlinearity reaches larger scales. It is shown that this breakdown is a manifestation of the undesirable effect of boundary conditions on simulations, even with the very large dynamic range possible here. A simple criterion is suggested for deciding when simulations with modest large-scale power may systematically underestimate the frequency of larger voids.

Theoretical and computational analyses of LNG evaporator

NASA Astrophysics Data System (ADS)

Chidambaram, Palani Kumar; Jo, Yang Myung; Kim, Heuy Dong

2017-04-01

Theoretical and numerical analysis on the fluid flow and heat transfer inside a LNG evaporator is conducted in this work. Methane is used instead of LNG as the operating fluid. This is because; methane constitutes over 80% of natural gas. The analytical calculations are performed using simple mass and energy balance equations. The analytical calculations are made to assess the pressure and temperature variations in the steam tube. Multiphase numerical simulations are performed by solving the governing equations (basic flow equations of continuity, momentum and energy equations) in a portion of the evaporator domain consisting of a single steam pipe. The flow equations are solved along with equations of species transport. Multiphase modeling is incorporated using VOF method. Liquid methane is the primary phase. It vaporizes into the secondary phase gaseous methane. Steam is another secondary phase which flows through the heating coils. Turbulence is modeled by a two equation turbulence model. Both the theoretical and numerical predictions are seen to match well with each other. Further parametric studies are planned based on the current research.

Numerical and experimental research on pentagonal cross-section of the averaging Pitot tube

NASA Astrophysics Data System (ADS)

Zhang, Jili; Li, Wei; Liang, Ruobing; Zhao, Tianyi; Liu, Yacheng; Liu, Mingsheng

2017-07-01

Averaging Pitot tubes have been widely used in many fields because of their simple structure and stable performance. This paper introduces a new shape of the cross-section of an averaging Pitot tube. Firstly, the structure of the averaging Pitot tube and the distribution of pressure taps are given. Then, a mathematical model of the airflow around it is formulated. After that, a series of numerical simulations are carried out to optimize the geometry of the tube. The distribution of the streamline and pressures around the tube are given. To test its performance, a test platform was constructed in accordance with the relevant national standards and is described in this paper. Curves are provided, linking the values of flow coefficient with the values of Reynolds number. With a maximum deviation of only  ±3%, the results of the flow coefficient obtained from the numerical simulations were in agreement with those obtained from experimental methods. The proposed tube has a stable flow coefficient and favorable metrological characteristics.

Use of the reciprocity theorem for a closed form solution of scattering of the lowest axially symmetric torsional wave mode by a defect in a pipe.

PubMed

Lee, Jaesun; Achenbach, Jan D; Cho, Younho

2018-03-01

Guided waves can effectively be used for inspection of large scale structures. Surface corrosion is often found as major defect type in large scale structures such as pipelines. Guided wave interaction with surface corrosion can provide useful information for sizing and classification. In this paper, the elastodynamic reciprocity theorem is used to formulate and solve complicated scattering problems in a simple manner. The approach has already been applied to scattering of Rayleigh and Lamb waves by defects to produce closed form solutions of amplitude of scattered waves. In this paper, the scattering of the lowest axially symmetric torsional mode, which is widely used in commercial applications, is analyzed by the reciprocity theorem. In the present paper, the theorem is used to determine the scattering of the lowest torsional mode by a tapered defect that was earlier considered experimentally and numerically by the finite element method. It is shown that by the presented method it is simple to obtain the ratio of amplitudes of scattered torsional modes for a tapered notch. The results show a good agreement with earlier numerical results. The wave field superposition technique in conjunction with the reciprocity theorem simplifies the solution of the scattering problem to yield a closed form solution which can play a significant role in quantitative signal interpretation. Copyright © 2017 Elsevier B.V. All rights reserved.

Preliminary Upper Estimate of Peak Currents in Transcranial Magnetic Stimulation at Distant Locations from a TMS Coil

PubMed Central

Makarov, Sergey N.; Yanamadala, Janakinadh; Piazza, Matthew W.; Helderman, Alex M.; Thang, Niang S.; Burnham, Edward H.; Pascual-Leone, Alvaro

2016-01-01

Goals Transcranial magnetic stimulation (TMS) is increasingly used as a diagnostic and therapeutic tool for numerous neuropsychiatric disorders. The use of TMS might cause whole-body exposure to undesired induced currents in patients and TMS operators. The aim of the present study is to test and justify a simple analytical model known previously, which may be helpful as an upper estimate of eddy current density at a particular distant observation point for any body composition and any coil setup. Methods We compare the analytical solution with comprehensive adaptive mesh refinement-based FEM simulations of a detailed full-body human model, two coil types, five coil positions, about 100,000 observation points, and two distinct pulse rise times, thus providing a representative number of different data sets for comparison, while also using other numerical data. Results Our simulations reveal that, after a certain modification, the analytical model provides an upper estimate for the eddy current density at any location within the body. In particular, it overestimates the peak eddy currents at distant locations from a TMS coil by a factor of 10 on average. Conclusion The simple analytical model tested in the present study may be valuable as a rapid method to safely estimate levels of TMS currents at different locations within a human body. Significance At present, safe limits of general exposure to TMS electric and magnetic fields are an open subject, including fetal exposure for pregnant women. PMID:26685221

Analysis of the role of diffraction in topographic site effects using boundary element techniques

NASA Astrophysics Data System (ADS)

Gomez, Juan; Restrepo, Doriam; Jaramillo, Juan; Valencia, Camilo

2013-10-01

The role played by the diffraction field on the problem of seismic site effects is studied. For that purpose we solve and analyze simple scattering problems under P and SV in-plane wave assumptions, using two well known direct boundary-element-based numerical methods. After establishing the difference between scattered and diffracted motions, and introducing the concept of artificious and physically based incoming fields, we obtain the amplitude of the Fourier spectra for the diffracted part of the response: this is achieved after establishing the connection between the spatial distribution of the transfer function over the studied simple topographies and the diffracted field. From the numerical simulations it is observed that this diffracted part of the response is responsible for the amplification of the surface ground motions due to the geometric effect. Furthermore, it is also found that the diffraction field sets in a fingerprint of the topographic effect in the total ground motions. These conclusions are further supported by observations in the time-domain in terms of snapshots of the propagation patterns over the complete computational model. In this sense the geometric singularities are clearly identified as sources of diffraction and for the considered range of dimensionless frequencies it is evident that larger amplifications are obtained for the geometries containing a larger number of diffraction sources thus resulting in a stronger topographic effect. The need for closed-form solutions of canonical problems to construct a robust analysis method based on the diffraction field is identified.

CAG - computer-aid-georeferencing, or rapid sharing, restructuring and presentation of environmental data using remote-server georeferencing for the GE clients. Educational and scientific implications.

NASA Astrophysics Data System (ADS)

Hronusov, V. V.

2006-12-01

We suggest a method of using external public servers for rearranging, restructuring and rapid sharing of environmental data for the purpose of quick presentations in numerous GE clients. The method allows to add new philosophy for the presentation (publication) of the data (mostly static) stored in the public domain (e.g., Blue Marble, Visible Earth, etc). - The new approach is generated by publishing freely accessible spreadsheets which contain enough information and links to the data. Due to the fact that most of the large depositories of the data on the environmental monitoring have rather simple net address system as well as simple hierarchy mostly based on the date and type of the data, it is possible to develop the http-based link to the file which contains the data. Publication of new data on the server is recorded by a simple entering a new address into a cell in the spreadsheet. At the moment we use the EditGrid (www.editgrid.com) system as a spreadsheet platform. The generation of kml-codes is achieved on the basis of XML data and XSLT procedures. Since the EditGride environment supports "fetch" and similar commands, it is possible to create"smart-adaptive" KML generation on the fly based on the data streams from RSS and XML sources. The previous GIS-based methods could combine hi-definition data combined from various sources, but large- scale comparisons of dynamic processes have been usually out of reach of the technology. The suggested method allows unlimited number of GE clients to view, review and compare dynamic and static process of previously un-combinable sources, and on unprecedent scales. The ease of automated or computer-assisted georeferencing has already led to translation about 3000 raster public domain imagery, point and linear data sources into GE-language. In addition the suggested method allows a user to create rapid animations to demonstrate dynamic processes; roducts of high demand in education, meteorology, volcanology and potentially in a number of industries. In general it is possible to state that the new approach, which we have tested on numerous projects, saves times and energy in creating huge amounts of georeferenced data of various kinds, and thus provided an excellent tools for education and science.

A comparative study of Conroy and Monte Carlo methods applied to multiple quadratures and multiple scattering

NASA Technical Reports Server (NTRS)

Deepak, A.; Fluellen, A.

1978-01-01

An efficient numerical method of multiple quadratures, the Conroy method, is applied to the problem of computing multiple scattering contributions in the radiative transfer through realistic planetary atmospheres. A brief error analysis of the method is given and comparisons are drawn with the more familiar Monte Carlo method. Both methods are stochastic problem-solving models of a physical or mathematical process and utilize the sampling scheme for points distributed over a definite region. In the Monte Carlo scheme the sample points are distributed randomly over the integration region. In the Conroy method, the sample points are distributed systematically, such that the point distribution forms a unique, closed, symmetrical pattern which effectively fills the region of the multidimensional integration. The methods are illustrated by two simple examples: one, of multidimensional integration involving two independent variables, and the other, of computing the second order scattering contribution to the sky radiance.

An efficient shooting algorithm for Evans function calculations in large systems

NASA Astrophysics Data System (ADS)

Humpherys, Jeffrey; Zumbrun, Kevin

2006-08-01

In Evans function computations of the spectra of asymptotically constant-coefficient linear operators, a basic issue is the efficient and numerically stable computation of subspaces evolving according to the associated eigenvalue ODE. For small systems, a fast, shooting algorithm may be obtained by representing subspaces as single exterior products [J.C. Alexander, R. Sachs, Linear instability of solitary waves of a Boussinesq-type equation: A computer assisted computation, Nonlinear World 2 (4) (1995) 471-507; L.Q. Brin, Numerical testing of the stability of viscous shock waves, Ph.D. Thesis, Indiana University, Bloomington, 1998; L.Q. Brin, Numerical testing of the stability of viscous shock waves, Math. Comp. 70 (235) (2001) 1071-1088; L.Q. Brin, K. Zumbrun, Analytically varying eigenvectors and the stability of viscous shock waves, in: Seventh Workshop on Partial Differential Equations, Part I, 2001, Rio de Janeiro, Mat. Contemp. 22 (2002) 19-32; T.J. Bridges, G. Derks, G. Gottwald, Stability and instability of solitary waves of the fifth-order KdV equation: A numerical framework, Physica D 172 (1-4) (2002) 190-216]. For large systems, however, the dimension of the exterior-product space quickly becomes prohibitive, growing as (n/k), where n is the dimension of the system written as a first-order ODE and k (typically ˜n/2) is the dimension of the subspace. We resolve this difficulty by the introduction of a simple polar coordinate algorithm representing “pure” (monomial) products as scalar multiples of orthonormal bases, for which the angular equation is a numerically optimized version of the continuous orthogonalization method of Drury-Davey [A. Davey, An automatic orthonormalization method for solving stiff boundary value problems, J. Comput. Phys. 51 (2) (1983) 343-356; L.O. Drury, Numerical solution of Orr-Sommerfeld-type equations, J. Comput. Phys. 37 (1) (1980) 133-139] and the radial equation is evaluable by quadrature. Notably, the polar-coordinate method preserves the important property of analyticity with respect to parameters.

High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation

NASA Astrophysics Data System (ADS)

Anderson, R.; Dobrev, V.; Kolev, Tz.; Kuzmin, D.; Quezada de Luna, M.; Rieben, R.; Tomov, V.

2017-04-01

In this work we present a FCT-like Maximum-Principle Preserving (MPP) method to solve the transport equation. We use high-order polynomial spaces; in particular, we consider up to 5th order spaces in two and three dimensions and 23rd order spaces in one dimension. The method combines the concepts of positive basis functions for discontinuous Galerkin finite element spatial discretization, locally defined solution bounds, element-based flux correction, and non-linear local mass redistribution. We consider a simple 1D problem with non-smooth initial data to explain and understand the behavior of different parts of the method. Convergence tests in space indicate that high-order accuracy is achieved. Numerical results from several benchmarks in two and three dimensions are also reported.

On the comparison of perturbation-iteration algorithm and residual power series method to solve fractional Zakharov-Kuznetsov equation

NASA Astrophysics Data System (ADS)

Şenol, Mehmet; Alquran, Marwan; Kasmaei, Hamed Daei

2018-06-01

In this paper, we present analytic-approximate solution of time-fractional Zakharov-Kuznetsov equation. This model demonstrates the behavior of weakly nonlinear ion acoustic waves in a plasma bearing cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Basic definitions of fractional derivatives are described in the Caputo sense. Perturbation-iteration algorithm (PIA) and residual power series method (RPSM) are applied to solve this equation with success. The convergence analysis is also presented for both methods. Numerical results are given and then they are compared with the exact solutions. Comparison of the results reveal that both methods are competitive, powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations.

On detection of median filtering in digital images

NASA Astrophysics Data System (ADS)

Kirchner, Matthias; Fridrich, Jessica

2010-01-01

In digital image forensics, it is generally accepted that intentional manipulations of the image content are most critical and hence numerous forensic methods focus on the detection of such 'malicious' post-processing. However, it is also beneficial to know as much as possible about the general processing history of an image, including content-preserving operations, since they can affect the reliability of forensic methods in various ways. In this paper, we present a simple yet effective technique to detect median filtering in digital images-a widely used denoising and smoothing operator. As a great variety of forensic methods relies on some kind of a linearity assumption, a detection of non-linear median filtering is of particular interest. The effectiveness of our method is backed with experimental evidence on a large image database.

Higher-order compositional modeling of three-phase flow in 3D fractured porous media based on cross-flow equilibrium

NASA Astrophysics Data System (ADS)

Moortgat, Joachim; Firoozabadi, Abbas

2013-10-01

Numerical simulation of multiphase compositional flow in fractured porous media, when all the species can transfer between the phases, is a real challenge. Despite the broad applications in hydrocarbon reservoir engineering and hydrology, a compositional numerical simulator for three-phase flow in fractured media has not appeared in the literature, to the best of our knowledge. In this work, we present a three-phase fully compositional simulator for fractured media, based on higher-order finite element methods. To achieve computational efficiency, we invoke the cross-flow equilibrium (CFE) concept between discrete fractures and a small neighborhood in the matrix blocks. We adopt the mixed hybrid finite element (MHFE) method to approximate convective Darcy fluxes and the pressure equation. This approach is the most natural choice for flow in fractured media. The mass balance equations are discretized by the discontinuous Galerkin (DG) method, which is perhaps the most efficient approach to capture physical discontinuities in phase properties at the matrix-fracture interfaces and at phase boundaries. In this work, we account for gravity and Fickian diffusion. The modeling of capillary effects is discussed in a separate paper. We present the mathematical framework, using the implicit-pressure-explicit-composition (IMPEC) scheme, which facilitates rigorous thermodynamic stability analyses and the computation of phase behavior effects to account for transfer of species between the phases. A deceptively simple CFL condition is implemented to improve numerical stability and accuracy. We provide six numerical examples at both small and larger scales and in two and three dimensions, to demonstrate powerful features of the formulation.

Split Node and Stress Glut Methods for Dynamic Rupture Simulations in Finite Elements.

NASA Astrophysics Data System (ADS)

Ramirez-Guzman, L.; Bielak, J.

2008-12-01

I present two numerical techniques to solve the Dynamic problem. I revisit and modify the Split Node approach and introduce a Stress Glut type Method. Both algorithms are implemented using a iso/sub- parametric FEM solver. In the first case, I discuss the formulation and perform an analysis of convergence for different orders of approximation for the acoustic case. I describe the algorithm of the second methodology as well as the assumptions made. The key to the new technique is to have an accurate representation of the traction. Thus, I devote part of the discussion to analyze the tractions for a simple example. The sensitivity of the method is tested by comparing against Split Node solutions.

Hardness of H13 Tool Steel After Non-isothermal Tempering

NASA Astrophysics Data System (ADS)

Nelson, E.; Kohli, A.; Poirier, D. R.

2018-04-01

A direct method to calculate the tempering response of a tool steel (H13) that exhibits secondary hardening is presented. Based on the traditional method of presenting tempering response in terms of isothermal tempering, we show that the tempering response for a steel undergoing a non-isothermal tempering schedule can be predicted. Experiments comprised (1) isothermal tempering, (2) non-isothermal tempering pertaining to a relatively slow heating to process-temperature and (3) fast-heating cycles that are relevant to tempering by induction heating. After establishing the tempering response of the steel under simple isothermal conditions, the tempering response can be applied to non-isothermal tempering by using a numerical method to calculate the tempering parameter. Calculated results are verified by the experiments.

Improvement of Simulation Method in Validation of Software of the Coordinate Measuring Systems

NASA Astrophysics Data System (ADS)

Nieciąg, Halina

2015-10-01

Software is used in order to accomplish various tasks at each stage of the functioning of modern measuring systems. Before metrological confirmation of measuring equipment, the system has to be validated. This paper discusses the method for conducting validation studies of a fragment of software to calculate the values of measurands. Due to the number and nature of the variables affecting the coordinate measurement results and the complex character and multi-dimensionality of measurands, the study used the Monte Carlo method of numerical simulation. The article presents an attempt of possible improvement of results obtained by classic Monte Carlo tools. The algorithm LHS (Latin Hypercube Sampling) was implemented as alternative to the simple sampling schema of classic algorithm.

Investigation of cellular detonation structure formation via linear stability theory and 2D and 3D numerical simulations

NASA Astrophysics Data System (ADS)

Borisov, S. P.; Kudryavtsev, A. N.

2017-10-01

Linear and nonlinear stages of the instability of a plane detonation wave (DW) and the subsequent process of formation of cellular detonation structure are investigated. A simple model with one-step irreversible chemical reaction is used. The linear analysis is employed to predict the DW front structure at the early stages of its formation. An emerging eigenvalue problem is solved with a global method using a Chebyshev pseudospectral method and the LAPACK software library. A local iterative shooting procedure is used for eigenvalue refinement. Numerical simulations of a propagation of a DW in plane and rectangular channels are performed with a shock capturing WENO scheme of 5th order. A special method of a computational domain shift is implemented in order to maintain the DW in the domain. It is shown that the linear analysis gives certain predictions about the DW structure that are in agreement with the numerical simulations of early stages of DW propagation. However, at later stages, a merger of detonation cells occurs so that their number is approximately halved. Computations of DW propagation in a square channel reveal two different types of spatial structure of the DW front, "rectangular" and "diagonal" types. A spontaneous transition from the rectangular to diagonal type of structure is observed during propagation of the DW.

A novel method for the accurate evaluation of Poisson's ratio of soft polymer materials.

PubMed

Lee, Jae-Hoon; Lee, Sang-Soo; Chang, Jun-Dong; Thompson, Mark S; Kang, Dong-Joong; Park, Sungchan; Park, Seonghun

2013-01-01

A new method with a simple algorithm was developed to accurately measure Poisson's ratio of soft materials such as polyvinyl alcohol hydrogel (PVA-H) with a custom experimental apparatus consisting of a tension device, a micro X-Y stage, an optical microscope, and a charge-coupled device camera. In the proposed method, the initial positions of the four vertices of an arbitrarily selected quadrilateral from the sample surface were first measured to generate a 2D 1st-order 4-node quadrilateral element for finite element numerical analysis. Next, minimum and maximum principal strains were calculated from differences between the initial and deformed shapes of the quadrilateral under tension. Finally, Poisson's ratio of PVA-H was determined by the ratio of minimum principal strain to maximum principal strain. This novel method has an advantage in the accurate evaluation of Poisson's ratio despite misalignment between specimens and experimental devices. In this study, Poisson's ratio of PVA-H was 0.44 ± 0.025 (n = 6) for 2.6-47.0% elongations with a tendency to decrease with increasing elongation. The current evaluation method of Poisson's ratio with a simple measurement system can be employed to a real-time automated vision-tracking system which is used to accurately evaluate the material properties of various soft materials.

Simultaneous monitoring of oxidation, deamidation, isomerization, and glycosylation of monoclonal antibodies by liquid chromatography-mass spectrometry method with ultrafast tryptic digestion.

PubMed

Wang, Yi; Li, Xiaojuan; Liu, Yan-Hui; Richardson, Daisy; Li, Huijuan; Shameem, Mohammed; Yang, Xiaoyu

Monoclonal antibodies are subjected to a wide variety of post-translational modifications (PTMs) that cause structural heterogeneity. Characterization and control of these modifications or quality attributes are critical to ensure antibody quality and to define any potential effects on the ultimate safety and potency of antibody therapeutics. The biopharmaceutical industry currently uses numerous tools to analyze these quality attributes individually, which requires substantial time and resources. Here, we report a simple and ultrafast bottom-up liquid chromatography-mass spectrometry (uLC-MS) method with 5 min tryptic digestion to simultaneously analyze multiple modifications, including oxidation, deamidation, isomerization, glycation, glycosylation, and N-terminal pyro-glutamate formation, which can occur during antibody production in mammalian cell culture, during purification and/or on storage. Compared to commonly used preparation procedures, this uLC-MS method eliminates assay artifacts of falsely-increased Met oxidation, Asp isomerization, and Asn deamidation, a problem associated with long digestion times in conventional LC-MS methods. This simple, low artifact multi-attribute uLC-MS method can be used to quickly and accurately analyze samples at any stage of antibody drug development, in particular for clone and media selection during cell culture development.

A moist Boussinesq shallow water equations set for testing atmospheric models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zerroukat, M., E-mail: mohamed.zerroukat@metoffice.gov.uk; Allen, T.

The shallow water equations have long been used as an initial test for numerical methods applied to atmospheric models with the test suite of Williamson et al. being used extensively for validating new schemes and assessing their accuracy. However the lack of physics forcing within this simplified framework often requires numerical techniques to be reworked when applied to fully three dimensional models. In this paper a novel two-dimensional shallow water equations system that retains moist processes is derived. This system is derived from three-dimensional Boussinesq approximation of the hydrostatic Euler equations where, unlike the classical shallow water set, we allowmore » the density to vary slightly with temperature. This results in extra (or buoyancy) terms for the momentum equations, through which a two-way moist-physics dynamics feedback is achieved. The temperature and moisture variables are advected as separate tracers with sources that interact with the mean-flow through a simplified yet realistic bulk moist-thermodynamic phase-change model. This moist shallow water system provides a unique tool to assess the usually complex and highly non-linear dynamics–physics interactions in atmospheric models in a simple yet realistic way. The full non-linear shallow water equations are solved numerically on several case studies and the results suggest quite realistic interaction between the dynamics and physics and in particular the generation of cloud and rain. - Highlights: • Novel shallow water equations which retains moist processes are derived from the three-dimensional hydrostatic Boussinesq equations. • The new shallow water set can be seen as a more general one, where the classical equations are a special case of these equations. • This moist shallow water system naturally allows a feedback mechanism from the moist physics increments to the momentum via buoyancy. • Like full models, temperature and moistures are advected as tracers that interact through a simplified yet realistic phase-change model. • This model is a unique tool to test numerical methods for atmospheric models, and physics–dynamics coupling, in a very realistic and simple way.« less

A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency

NASA Astrophysics Data System (ADS)

Liu, Xiaodong

2017-08-01

A sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very easy and simple to implement. With the help of the factorization of the far field operator, we establish an inf-criterion for characterization of underlying scatterers. This result is then used to give a lower bound of the proposed indicator functional for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functional decays like the bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functional continuously depends on the scattering amplitude, this further implies that the novel sampling method is extremely stable with respect to errors in the data. Different to the classical sampling method such as the linear sampling method or the factorization method, from the numerical point of view, the novel indicator takes its maximum near the boundary of the underlying target and decays like the bessel functions as the sampling points go away from the boundary. The numerical simulations also show that the proposed sampling method can deal with multiple multiscale case, even the different components are close to each other.

Rubber friction and tire dynamics.

PubMed

Persson, B N J

2011-01-12

We propose a simple rubber friction law, which can be used, for example, in models of tire (and vehicle) dynamics. The friction law is tested by comparing numerical results to the full rubber friction theory (Persson 2006 J. Phys.: Condens. Matter 18 7789). Good agreement is found between the two theories. We describe a two-dimensional (2D) tire model which combines the rubber friction model with a simple mass-spring description of the tire body. The tire model is very flexible and can be used to accurately calculate μ-slip curves (and the self-aligning torque) for braking and cornering or combined motion (e.g. braking during cornering). We present numerical results which illustrate the theory. Simulations of anti-blocking system (ABS) braking are performed using two simple control algorithms.

A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.

PubMed

Benhammouda, Brahim; Vazquez-Leal, Hector

2016-01-01

This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.

Waveguide-type optical circuits for recognition of optical 8QAM-coded label

NASA Astrophysics Data System (ADS)

Surenkhorol, Tumendemberel; Kishikawa, Hiroki; Goto, Nobuo; Gonchigsumlaa, Khishigjargal

2017-10-01

Optical signal processing is expected to be applied in network nodes. In photonic routers, label recognition is one of the important functions. We have studied different kinds of label recognition methods so far for on-off keying, binary phase-shift keying, quadrature phase-shift keying, and 16 quadrature amplitude modulation-coded labels. We propose a method based on waveguide circuits to recognize an optical eight quadrature amplitude modulation (8QAM)-coded label by simple passive optical signal processing. The recognition of the proposed method is theoretically analyzed and numerically simulated by the finite difference beam propagation method. The noise tolerance is discussed, and bit-error rate against optical signal-to-noise ratio is evaluated. The scalability of the proposed method is also discussed theoretically for two-symbol length 8QAM-coded labels.

Exceptional points of resonant states on a periodic slab

NASA Astrophysics Data System (ADS)

Abdrabou, Amgad; Lu, Ya Yan

2018-06-01

A special kind of degeneracy, known as exceptional points (EPs), for resonant states on a dielectric periodic slab are investigated. Due to their unique properties, EPs have found important applications in lasing, sensing, unidirectional operations, etc. In general, EPs may appear in non-Hermitian eigenvalue problems, including those related to -parity-time-symmetric systems and those for open dielectric structures (due to the existence of radiation loss). In this paper, we study EPs on a simple periodic structure: a slab with a periodic array of gaps. By using an efficient numerical method, we calculate the EPs and study their dependence on geometric parameters. Analytic results are obtained for the limit as the periodic slab approaches a uniform one. Our work provides a simple platform for further studies concerning EPs on dielectric periodic structures, their unusual properties, and applications.

Deciphering mRNA Sequence Determinants of Protein Production Rate

NASA Astrophysics Data System (ADS)

Szavits-Nossan, Juraj; Ciandrini, Luca; Romano, M. Carmen

2018-03-01

One of the greatest challenges in biophysical models of translation is to identify coding sequence features that affect the rate of translation and therefore the overall protein production in the cell. We propose an analytic method to solve a translation model based on the inhomogeneous totally asymmetric simple exclusion process, which allows us to unveil simple design principles of nucleotide sequences determining protein production rates. Our solution shows an excellent agreement when compared to numerical genome-wide simulations of S. cerevisiae transcript sequences and predicts that the first 10 codons, which is the ribosome footprint length on the mRNA, together with the value of the initiation rate, are the main determinants of protein production rate under physiological conditions. Finally, we interpret the obtained analytic results based on the evolutionary role of the codons' choice for regulating translation rates and ribosome densities.

Numerical modeling of separated flows at moderate Reynolds numbers appropriate for turbine blades and unmanned aero vehicles

NASA Astrophysics Data System (ADS)

Castiglioni, Giacomo

Flows over airfoils and blades in rotating machinery, for unmanned and micro-aerial vehicles, wind turbines, and propellers consist of a laminar boundary layer near the leading edge that is often followed by a laminar separation bubble and transition to turbulence further downstream. Typical Reynolds averaged Navier-Stokes turbulence models are inadequate for such flows. Direct numerical simulation is the most reliable, but is also the most computationally expensive alternative. This work assesses the capability of immersed boundary methods and large eddy simulations to reduce the computational requirements for such flows and still provide high quality results. Two-dimensional and three-dimensional simulations of a laminar separation bubble on a NACA-0012 airfoil at Rec = 5x104 and at 5° of incidence have been performed with an immersed boundary code and a commercial code using body fitted grids. Several sub-grid scale models have been implemented in both codes and their performance evaluated. For the two-dimensional simulations with the immersed boundary method the results show good agreement with the direct numerical simulation benchmark data for the pressure coefficient Cp and the friction coefficient Cf, but only when using dissipative numerical schemes. There is evidence that this behavior can be attributed to the ability of dissipative schemes to damp numerical noise coming from the immersed boundary. For the three-dimensional simulations the results show a good prediction of the separation point, but an inaccurate prediction of the reattachment point unless full direct numerical simulation resolution is used. The commercial code shows good agreement with the direct numerical simulation benchmark data in both two and three-dimensional simulations, but the presence of significant, unquantified numerical dissipation prevents a conclusive assessment of the actual prediction capabilities of very coarse large eddy simulations with low order schemes in general cases. Additionally, a two-dimensional sweep of angles of attack from 0° to 5° is performed showing a qualitative prediction of the jump in lift and drag coefficients due to the appearance of the laminar separation bubble. The numerical dissipation inhibits the predictive capabilities of large eddy simulations whenever it is of the same order of magnitude or larger than the sub-grid scale dissipation. The need to estimate the numerical dissipation is most pressing for low-order methods employed by commercial computational fluid dynamics codes. Following the recent work of Schranner et al., the equations and procedure for estimating the numerical dissipation rate and the numerical viscosity in a commercial code are presented. The method allows for the computation of the numerical dissipation rate and numerical viscosity in the physical space for arbitrary sub-domains in a self-consistent way, using only information provided by the code in question. The method is first tested for a three-dimensional Taylor-Green vortex flow in a simple cubic domain and compared with benchmark results obtained using an accurate, incompressible spectral solver. Afterwards the same procedure is applied for the first time to a realistic flow configuration, specifically to the above discussed laminar separation bubble flow over a NACA 0012 airfoil. The method appears to be quite robust and its application reveals that for the code and the flow in question the numerical dissipation can be significantly larger than the viscous dissipation or the dissipation of the classical Smagorinsky sub-grid scale model, confirming the previously qualitative finding.

Brute force meets Bruno force in parameter optimisation: introduction of novel constraints for parameter accuracy improvement by symbolic computation.

PubMed

Nakatsui, M; Horimoto, K; Lemaire, F; Ürgüplü, A; Sedoglavic, A; Boulier, F

2011-09-01

Recent remarkable advances in computer performance have enabled us to estimate parameter values by the huge power of numerical computation, the so-called 'Brute force', resulting in the high-speed simultaneous estimation of a large number of parameter values. However, these advancements have not been fully utilised to improve the accuracy of parameter estimation. Here the authors review a novel method for parameter estimation using symbolic computation power, 'Bruno force', named after Bruno Buchberger, who found the Gröbner base. In the method, the objective functions combining the symbolic computation techniques are formulated. First, the authors utilise a symbolic computation technique, differential elimination, which symbolically reduces an equivalent system of differential equations to a system in a given model. Second, since its equivalent system is frequently composed of large equations, the system is further simplified by another symbolic computation. The performance of the authors' method for parameter accuracy improvement is illustrated by two representative models in biology, a simple cascade model and a negative feedback model in comparison with the previous numerical methods. Finally, the limits and extensions of the authors' method are discussed, in terms of the possible power of 'Bruno force' for the development of a new horizon in parameter estimation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Quon, Eliot; Platt, Andrew; Yu, Yi-Hsiang

Extreme loads are often a key cost driver for wave energy converters (WECs). As an alternative to exhaustive Monte Carlo or long-term simulations, the most likely extreme response (MLER) method allows mid- and high-fidelity simulations to be used more efficiently in evaluating WEC response to events at the edges of the design envelope, and is therefore applicable to system design analysis. The study discussed in this paper applies the MLER method to investigate the maximum heave, pitch, and surge force of a point absorber WEC. Most likely extreme waves were obtained from a set of wave statistics data based onmore » spectral analysis and the response amplitude operators (RAOs) of the floating body; the RAOs were computed from a simple radiation-and-diffraction-theory-based numerical model. A weakly nonlinear numerical method and a computational fluid dynamics (CFD) method were then applied to compute the short-term response to the MLER wave. Effects of nonlinear wave and floating body interaction on the WEC under the anticipated 100-year waves were examined by comparing the results from the linearly superimposed RAOs, the weakly nonlinear model, and CFD simulations. Overall, the MLER method was successfully applied. In particular, when coupled to a high-fidelity CFD analysis, the nonlinear fluid dynamics can be readily captured.« less

Experiment and numerical simulation for laser ultrasonic measurement of residual stress.

PubMed

Zhan, Yu; Liu, Changsheng; Kong, Xiangwei; Lin, Zhongya

2017-01-01

Laser ultrasonic is a most promising method for non-destructive evaluation of residual stress. The residual stress of thin steel plate is measured by laser ultrasonic technique. The pre-stress loading device is designed which can easily realize the condition of the specimen being laser ultrasonic tested at the same time in the known stress state. By the method of pre-stress loading, the acoustoelastic constants are obtained and the effect of different test directions on the results of surface wave velocity measurement is discussed. On the basis of known acoustoelastic constants, the longitudinal and transverse welding residual stresses are measured by the laser ultrasonic technique. The finite element method is used to simulate the process of surface wave detection of welding residual stress. The pulsed laser is equivalent to the surface load and the relationship between the physical parameters of the laser and the load is established by the correction coefficient. The welding residual stress of the specimen is realized by the ABAQUS function module of predefined field. The results of finite element analysis are in good agreement with the experimental method. The simple and effective numerical and experimental methods for laser ultrasonic measurement of residual stress are demonstrated. Copyright © 2016. Published by Elsevier B.V.

Calculation of water equivalent thickness of materials of arbitrary density, elemental composition and thickness in proton beam irradiation

NASA Astrophysics Data System (ADS)

Zhang, Rui; Newhauser, Wayne D.

2009-03-01

In proton therapy, the radiological thickness of a material is commonly expressed in terms of water equivalent thickness (WET) or water equivalent ratio (WER). However, the WET calculations required either iterative numerical methods or approximate methods of unknown accuracy. The objective of this study was to develop a simple deterministic formula to calculate WET values with an accuracy of 1 mm for materials commonly used in proton radiation therapy. Several alternative formulas were derived in which the energy loss was calculated based on the Bragg-Kleeman rule (BK), the Bethe-Bloch equation (BB) or an empirical version of the Bethe-Bloch equation (EBB). Alternative approaches were developed for targets that were 'radiologically thin' or 'thick'. The accuracy of these methods was assessed by comparison to values from an iterative numerical method that utilized evaluated stopping power tables. In addition, we also tested the approximate formula given in the International Atomic Energy Agency's dosimetry code of practice (Technical Report Series No 398, 2000, IAEA, Vienna) and stopping power ratio approximation. The results of these comparisons revealed that most methods were accurate for cases involving thin or low-Z targets. However, only the thick-target formulas provided accurate WET values for targets that were radiologically thick and contained high-Z material.

Steady flow model user's guide

NASA Astrophysics Data System (ADS)

Doughty, C.; Hellstrom, G.; Tsang, C. F.; Claesson, J.

1984-07-01

Sophisticated numerical models that solve the coupled mass and energy transport equations for nonisothermal fluid flow in a porous medium were used to match analytical results and field data for aquifer thermal energy storage (ATES) systems. As an alternative to the ATES problem the Steady Flow Model (SFM), a simplified but fast numerical model was developed. A steady purely radial flow field is prescribed in the aquifer, and incorporated into the heat transport equation which is then solved numerically. While the radial flow assumption limits the range of ATES systems that can be studied using the SFM, it greatly simplifies use of this code. The preparation of input is quite simple compared to that for a sophisticated coupled mass and energy model, and the cost of running the SFM is far cheaper. The simple flow field allows use of a special calculational mesh that eliminates the numerical dispersion usually associated with the numerical solution of convection problems. The problem is defined, the algorithm used to solve it are outllined, and the input and output for the SFM is described.

Numerical Analyses of Subsoil-structure Interaction in Original Non-commercial Software based on FEM

NASA Astrophysics Data System (ADS)

Cajka, R.; Vaskova, J.; Vasek, J.

2018-04-01

For decades attention has been paid to interaction of foundation structures and subsoil and development of interaction models. Given that analytical solutions of subsoil-structure interaction could be deduced only for some simple shapes of load, analytical solutions are increasingly being replaced by numerical solutions (eg. FEM – Finite element method). Numerical analyses provides greater possibilities for taking into account the real factors involved in the subsoil-structure interaction and was also used in this article. This makes it possible to design the foundation structures more efficiently and still reliably and securely. Currently there are several software that, can deal with the interaction of foundations and subsoil. It has been demonstrated that non-commercial software called MKPINTER (created by Cajka) provides appropriately results close to actual measured values. In MKPINTER software stress-strain analysis of elastic half-space by means of Gauss numerical integration and Jacobean of transformation is done. Input data for numerical analysis were observed by experimental loading test of concrete slab. The loading was performed using unique experimental equipment which was constructed in the area Faculty of Civil Engineering, VŠB-TU Ostrava. The purpose of this paper is to compare resulting deformation of the slab with values observed during experimental loading test.

Generation of anatomically realistic numerical phantoms for photoacoustic and ultrasonic breast imaging

NASA Astrophysics Data System (ADS)

Lou, Yang; Zhou, Weimin; Matthews, Thomas P.; Appleton, Catherine M.; Anastasio, Mark A.

2017-04-01

Photoacoustic computed tomography (PACT) and ultrasound computed tomography (USCT) are emerging modalities for breast imaging. As in all emerging imaging technologies, computer-simulation studies play a critically important role in developing and optimizing the designs of hardware and image reconstruction methods for PACT and USCT. Using computer-simulations, the parameters of an imaging system can be systematically and comprehensively explored in a way that is generally not possible through experimentation. When conducting such studies, numerical phantoms are employed to represent the physical properties of the patient or object to-be-imaged that influence the measured image data. It is highly desirable to utilize numerical phantoms that are realistic, especially when task-based measures of image quality are to be utilized to guide system design. However, most reported computer-simulation studies of PACT and USCT breast imaging employ simple numerical phantoms that oversimplify the complex anatomical structures in the human female breast. We develop and implement a methodology for generating anatomically realistic numerical breast phantoms from clinical contrast-enhanced magnetic resonance imaging data. The phantoms will depict vascular structures and the volumetric distribution of different tissue types in the breast. By assigning optical and acoustic parameters to different tissue structures, both optical and acoustic breast phantoms will be established for use in PACT and USCT studies.

Generation of dark hollow beam by use of phase-only filtering

NASA Astrophysics Data System (ADS)

Liu, Zhengjun; Dai, Jingmin; Zhao, Xiaoyi; Sun, Xiaogang; Liu, Shutian; Ashfaq Ahmad, Muhammad

2009-11-01

A simple but effective scheme to generate dark hollow beams is proposed by use of phase-only filtering and optical Fourier transform. A Gaussian beam of fundamental mode is modulated by a pre-designed phase mask, which is a piecewise modification of an axicon lens, and followed by a Fourier transform to generate an ideal dark hollow beam at the focal plane. This method has an advantage that the total energy of the beam is conserved under paraxial approximation. Numerical calculations are provided to show the validity of the proposed scheme.

Finite-time hybrid projective synchronization of the drive-response complex networks with distributed-delay via adaptive intermittent control

NASA Astrophysics Data System (ADS)

Cheng, Lin; Yang, Yongqing; Li, Li; Sui, Xin

2018-06-01

This paper studies the finite-time hybrid projective synchronization of the drive-response complex networks. In the model, general transmission delays and distributed delays are also considered. By designing the adaptive intermittent controllers, the response network can achieve hybrid projective synchronization with the drive system in finite time. Based on finite-time stability theory and several differential inequalities, some simple finite-time hybrid projective synchronization criteria are derived. Two numerical examples are given to illustrate the effectiveness of the proposed method.

Computer modeling of inversion layer MOS solar cells and arrays

NASA Technical Reports Server (NTRS)

Ho, Fat Duen

1991-01-01

A two dimensional numerical model of the inversion layer metal insulator semiconductor (IL/MIS) solar cell is proposed by using the finite element method. The two-dimensional current flow in the device is taken into account in this model. The electrostatic potential distribution, the electron concentration distribution, and the hole concentration distribution for different terminal voltages are simulated. The results of simple calculation are presented. The existing problems for this model are addressed. Future work is proposed. The MIS structures are studied and some of the results are reported.

Processor design optimization methodology for synthetic vision systems

NASA Astrophysics Data System (ADS)

Wren, Bill; Tarleton, Norman G.; Symosek, Peter F.

1997-06-01

Architecture optimization requires numerous inputs from hardware to software specifications. The task of varying these input parameters to obtain an optimal system architecture with regard to cost, specified performance and method of upgrade considerably increases the development cost due to the infinitude of events, most of which cannot even be defined by any simple enumeration or set of inequalities. We shall address the use of a PC-based tool using genetic algorithms to optimize the architecture for an avionics synthetic vision system, specifically passive millimeter wave system implementation.

A comparative study of scramjet injection strategies for high Mach numbers flows

NASA Technical Reports Server (NTRS)

Riggins, D. W.; Mcclinton, C. R.; Rogers, R. C.; Bittner, R. D.

1992-01-01

A simple method for predicting the axial distribution of supersonic combustor thrust potential is described. A complementary technique for illustrating the spatial evolution and distribution of thrust potential and loss mechanisms in reacting flows is developed. Wall jet cases and swept ramp injector cases for Mach 17 and Mach 13.5 flight enthalpy inflow conditions are numerically modeled and analyzed using these techniques. The visualization of thrust potential in the combustor for the various cases examined provides a unique tool for increasing understanding of supersonic combustor performance potential.

Inverse kinematics of a dual linear actuator pitch/roll heliostat

NASA Astrophysics Data System (ADS)

Freeman, Joshua; Shankar, Balakrishnan; Sundaram, Ganesh

2017-06-01

This work presents a simple, computationally efficient inverse kinematics solution for a pitch/roll heliostat using two linear actuators. The heliostat design and kinematics have been developed, modeled and tested using computer simulation software. A physical heliostat prototype was fabricated to validate the theoretical computations and data. Pitch/roll heliostats have numerous advantages including reduced cost potential and reduced space requirements, with a primary disadvantage being the significantly more complicated kinematics, which are solved here. Novel methods are applied to simplify the inverse kinematics problem which could be applied to other similar problems.