Development and application of a gradient method for solving differential games

NASA Technical Reports Server (NTRS)

Roberts, D. A.; Montgomery, R. C.

1971-01-01

A technique for solving n-dimensional games is developed and applied to two pursuit-evasion games. The first is a two-dimensional game similar to the homicidal chauffeur but modified to resemble an airplane-helicopter engagement. The second is a five-dimensional game of two airplanes at constant altitude and with thrust and turning controls. The performance function to be optimized by the pursuer and evader was the distance between the evader and a given target point in front of the pursuer. The analytic solution to the first game reveals that both unique and nonunique solutions exist. A comparison between the gradient results and the analytic solution shows a dependence on the nominal controls in regions where nonunique solutions exist. In the unique solution region, the results from the two methods agree closely. The results for the five-dimensional two-airplane game are also shown to be dependent on the nominal controls selected and indicate that initial conditions are in a region of nonunique solutions.

A Finite Element Projection Method for the Solution of Particle Transport Problems with Anisotropic Scattering.

DTIC Science & Technology

1984-07-01

piecewise constant energy dependence. This is a seven-dimensional problem with time dependence, three spatial and two angular or directional variables and...in extending the computer implementation of the method to time and energy dependent problems, and to solving and validating this technique on a...problems they have severe limitations. The Monte Carlo method, usually requires the use of many hours of expensive computer time , and for deep

Computation of steady nozzle flow by a time-dependent method

NASA Technical Reports Server (NTRS)

Cline, M. C.

1974-01-01

The equations of motion governing steady, inviscid flow are of a mixed type, that is, hyperbolic in the supersonic region and elliptic in the subsonic region. These mathematical difficulties may be removed by using the so-called time-dependent method, where the governing equations become hyperbolic everywhere. The steady-state solution may be obtained as the asymptotic solution for large time. The object of this research was to develop a production type computer program capable of solving converging, converging-diverging, and plug two-dimensional nozzle flows in computational times of 1 min or less on a CDC 6600 computer.

The Kadomtsev-Petviashvili equation under rapid forcing

NASA Astrophysics Data System (ADS)

Moroz, Irene M.

1997-06-01

We consider the initial value problem for the forced Kadomtsev-Petviashvili equation (KP) when the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced KP are sought by expanding the dependent variable in powers of a small parameter, which is inversely related to the forcing time scale. The unforced system describes weakly nonlinear, weakly dispersive, weakly two-dimensional wave propagation and is studied in two forms, depending upon whether gravity dominates surface tension or vice versa. We focus on the effect that the forcing has on the one-lump solution to the KPI equation (where surface tension dominates) and on the one- and two-line soliton solutions to the KPII equation (when gravity dominates). Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function, which are related to the choice of initial data.

Weakly collisional Landau damping and three-dimensional Bernstein-Greene-Kruskal modes: New results on old problems

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

Ng, C.; Bhattacharjee, A.; Skiff, F.

2006-05-15

Landau damping and Bernstein-Greene-Kruskal (BGK) modes are among the most fundamental concepts in plasma physics. While the former describes the surprising damping of linear plasma waves in a collisionless plasma, the latter describes exact undamped nonlinear solutions of the Vlasov equation. There does exist a relationship between the two: Landau damping can be described as the phase mixing of undamped eigenmodes, the so-called Case-Van Kampen modes, which can be viewed as BGK modes in the linear limit. While these concepts have been around for a long time, unexpected new results are still being discovered. For Landau damping, we show thatmore » the textbook picture of phase mixing is altered profoundly in the presence of collision. In particular, the continuous spectrum of Case-Van Kampen modes is eliminated and replaced by a discrete spectrum, even in the limit of zero collision. Furthermore, we show that these discrete eigenmodes form a complete set of solutions. Landau-damped solutions are then recovered as true eigenmodes (which they are not in the collisionless theory). For BGK modes, our interest is motivated by recent discoveries of electrostatic solitary waves in magnetospheric plasmas. While one-dimensional BGK theory is quite mature, there appear to be no exact three-dimensional solutions in the literature (except for the limiting case when the magnetic field is sufficiently strong so that one can apply the guiding-center approximation). We show, in fact, that two- and three-dimensional solutions that depend only on energy do not exist. However, if solutions depend on both energy and angular momentum, we can construct exact three-dimensional solutions for the unmagnetized case, and two-dimensional solutions for the case with a finite magnetic field. The latter are shown to be exact, fully electromagnetic solutions of the steady-state Vlasov-Poisson-Ampere system.« less

A two-column formalism for time-dependent modelling of stellar convection. I. Description of the method

NASA Astrophysics Data System (ADS)

Stökl, A.

2008-11-01

Context: In spite of all the advances in multi-dimensional hydrodynamics, investigations of stellar evolution and stellar pulsations still depend on one-dimensional computations. This paper devises an alternative to the mixing-length theory or turbulence models usually adopted in modelling convective transport in such studies. Aims: The present work attempts to develop a time-dependent description of convection, which reflects the essential physics of convection and that is only moderately dependent on numerical parameters and far less time consuming than existing multi-dimensional hydrodynamics computations. Methods: Assuming that the most extensive convective patterns generate the majority of convective transport, the convective velocity field is described using two parallel, radial columns to represent up- and downstream flows. Horizontal exchange, in the form of fluid flow and radiation, over their connecting interface couples the two columns and allows a simple circulating motion. The main parameters of this convective description have straightforward geometrical meanings, namely the diameter of the columns (corresponding to the size of the convective cells) and the ratio of the cross-section between up- and downdrafts. For this geometrical setup, the time-dependent solution of the equations of radiation hydrodynamics is computed from an implicit scheme that has the advantage of being unaffected by the Courant-Friedrichs-Lewy time-step limit. This implementation is part of the TAPIR-Code (short for The adaptive, implicit RHD-Code). Results: To demonstrate the approach, results for convection zones in Cepheids are presented. The convective energy transport and convective velocities agree with expectations for Cepheids and the scheme reproduces both the kinetic energy flux and convective overshoot. A study of the parameter influence shows that the type of solution derived for these stars is in fact fairly robust with respect to the constitutive numerical parameters.

Nature of self-diffusion in two-dimensional fluids

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

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Nature of self-diffusion in two-dimensional fluids

DOE PAGES

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; ...

2017-12-18

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Multiple Long-Time Solutions for Intermediate Reynolds Number Flow past a Circular Cylinder with a Nonlinear Inertial and Dissipative Attachment

NASA Astrophysics Data System (ADS)

Blanchard, Antoine B. E.; Bergman, Lawrence A.; Vakakis, Alexander F.; Pearlstein, Arne J.

2016-11-01

We consider two-dimensional flow past a linearly-sprung cylinder allowed to undergo rectilinear motion normal to the mean flow, with an attached "nonlinear energy sink" consisting of a mass allowed to rotate about the cylinder axis, and whose rotational motion is linearly damped by a viscous damper. For Re < 50, where the flow is expected to be two-dimensional, we use different inlet transients to identify multiple long-time solutions, and to study how they depend on Re and a dimensionless spring constant. For fixed values of the ratio of cylinder density to fluid density, dimensionless damping coefficient, and ratio of the rotating mass to the total mass, we find that different inlet transients lead to different long-time solutions, including solutions that are steady and symmetric (with a motionless cylinder), time-periodic, quasi-periodic, and chaotic. The results show that over a wide range of the parameters, the steady symmetric motionless-cylinder solution is locally, but not globally, stable. Supported by NSF Grant CMMI-1363231.

Multigrid for hypersonic viscous two- and three-dimensional flows

NASA Technical Reports Server (NTRS)

Turkel, E.; Swanson, R. C.; Vatsa, V. N.; White, J. A.

1991-01-01

The use of a multigrid method with central differencing to solve the Navier-Stokes equations for hypersonic flows is considered. The time dependent form of the equations is integrated with an explicit Runge-Kutta scheme accelerated by local time stepping and implicit residual smoothing. Variable coefficients are developed for the implicit process that removes the diffusion limit on the time step, producing significant improvement in convergence. A numerical dissipation formulation that provides good shock capturing capability for hypersonic flows is presented. This formulation is shown to be a crucial aspect of the multigrid method. Solutions are given for two-dimensional viscous flow over a NACA 0012 airfoil and three-dimensional flow over a blunt biconic.

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

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

Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra ismore » later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a rotating quadrupole field ion trap are presented. •Exact solutions for magneto-transport in variable electromagnetic fields are shown.« less

Stable exponential cosmological solutions with 3- and l-dimensional factor spaces in the Einstein-Gauss-Bonnet model with a Λ -term

NASA Astrophysics Data System (ADS)

Ivashchuk, V. D.; Kobtsev, A. A.

2018-02-01

A D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term Λ is studied. We assume the metrics to be diagonal cosmological ones. For certain fine-tuned Λ , we find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters H >0 and h, corresponding to factor spaces of dimensions 3 and l > 2, respectively and D = 1 + 3 + l. The fine-tuned Λ = Λ (x, l, α ) depends upon the ratio h/H = x, l and the ratio α = α _2/α _1 of two constants (α _2 and α _1) of the model. For fixed Λ , α and l > 2 the equation Λ (x,l,α ) = Λ is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals (the example l =3 is presented). For certain restrictions on x we prove the stability of the solutions in a class of cosmological solutions with diagonal metrics. A subclass of solutions with small enough variation of the effective gravitational constant G is considered. It is shown that all solutions from this subclass are stable.

Numerical solutions of 3-dimensional Navier-Stokes equations for closed bluff-bodies

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallelepiped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDc VPS 32 computer. The codes are written in 32-bit (half word) FORTRAN, which provides an approximate factor of two decreasing in computational time and doubles the memory size compared to the 54-bit word size.

A time dependent difference theory for sound propagation in ducts with flow. [characteristic of inlet and exhaust ducts of turbofan engines

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1979-01-01

A time dependent numerical solution of the linearized continuity and momentum equation was developed for sound propagation in a two dimensional straight hard or soft wall duct with a sheared mean flow. The time dependent governing acoustic difference equations and boundary conditions were developed along with a numerical determination of the maximum stable time increments. A harmonic noise source radiating into a quiescent duct was analyzed. This explicit iteration method then calculated stepwise in real time to obtain the transient as well as the steady state solution of the acoustic field. Example calculations were presented for sound propagation in hard and soft wall ducts, with no flow and plug flow. Although the problem with sheared flow was formulated and programmed, sample calculations were not examined. The time dependent finite difference analysis was found to be superior to the steady state finite difference and finite element techniques because of shorter solution times and the elimination of large matrix storage requirements.

A computer program for calculating laminar and turbulent boundary layers for two-dimensional time-dependent flows

NASA Technical Reports Server (NTRS)

Cebeci, T.; Carr, L. W.

1978-01-01

A computer program is described which provides solutions of two dimensional equations appropriate to laminar and turbulent boundary layers for boundary conditions with an external flow which fluctuates in magnitude. The program is based on the numerical solution of the governing boundary layer equations by an efficient two point finite difference method. An eddy viscosity formulation was used to model the Reynolds shear stress term. The main features of the method are briefly described and instructions for the computer program with a listing are provided. Sample calculations to demonstrate its usage and capabilities for laminar and turbulent unsteady boundary layers with an external flow which fluctuated in magnitude are presented.

Bäcklund transformation, infinitely-many conservation laws, solitary and periodic waves of an extended (3 + 1)-dimensional Jimbo-Miwa equation with time-dependent coefficients

NASA Astrophysics Data System (ADS)

Deng, Gao-Fu; Gao, Yi-Tian; Gao, Xin-Yi

2018-07-01

In this paper, an extended (3+1)-dimensional Jimbo-Miwa equation with time-dependent coefficients is investigated, which comes from the second member of the Kadomtsev-Petviashvili hierarchy and is shown to be conditionally integrable. Bilinear form, Bäcklund transformation, Lax pair and infinitely-many conservation laws are derived via the binary Bell polynomials and symbolic computation. With the help of the bilinear form, one-, two- and three-soliton solutions are obtained via the Hirota method, one-periodic wave solutions are constructed via the Riemann theta function. Additionally, propagation and interaction of the solitons are investigated analytically and graphically, from which we find that the interaction between the solitons is elastic and the time-dependent coefficients can affect the soliton velocities, but the soliton amplitudes remain unchanged. One-periodic waves approach the one-solitary waves with the amplitudes vanishing and can be viewed as a superposition of the overlapping solitary waves, placed one period apart.

Construction of Three Dimensional Solutions for the Maxwell Equations

NASA Technical Reports Server (NTRS)

Yefet, A.; Turkel, E.

1998-01-01

We consider numerical solutions for the three dimensional time dependent Maxwell equations. We construct a fourth order accurate compact implicit scheme and compare it to the Yee scheme for free space in a box.

Effect of a Starting Model on the Solution of a Travel Time Seismic Tomography Problem

NASA Astrophysics Data System (ADS)

Yanovskaya, T. B.; Medvedev, S. V.; Gobarenko, V. S.

2018-03-01

In the problems of three-dimensional (3D) travel time seismic tomography where the data are travel times of diving waves and the starting model is a system of plane layers where the velocity is a function of depth alone, the solution turns out to strongly depend on the selection of the starting model. This is due to the fact that in the different starting models, the rays between the same points can intersect different layers, which makes the tomography problem fundamentally nonlinear. This effect is demonstrated by the model example. Based on the same example, it is shown how the starting model should be selected to ensure a solution close to the true velocity distribution. The starting model (the average dependence of the seismic velocity on depth) should be determined by the method of successive iterations at each step of which the horizontal velocity variations in the layers are determined by solving the two-dimensional tomography problem. An example illustrating the application of this technique to the P-wave travel time data in the region of the Black Sea basin is presented.

Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

NASA Astrophysics Data System (ADS)

Arendt, V.; Shalchi, A.

2018-06-01

We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker-Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.

An Implicit Characteristic Based Method for Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.; Briley, W. Roger

2001-01-01

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

Solution of the one-dimensional consolidation theory equation with a pseudospectral method

USGS Publications Warehouse

Sepulveda, N.; ,

1991-01-01

The one-dimensional consolidation theory equation is solved for an aquifer system using a pseudospectral method. The spatial derivatives are computed using Fast Fourier Transforms and the time derivative is solved using a fourth-order Runge-Kutta scheme. The computer model calculates compaction based on the void ratio changes accumulated during the simulated periods of time. Compactions and expansions resulting from groundwater withdrawals and recharges are simulated for two observation wells in Santa Clara Valley and two in San Joaquin Valley, California. Field data previously published are used to obtain mean values for the soil grain density and the compression index and to generate depth-dependent profiles for hydraulic conductivity and initial void ratio. The water-level plots for the wells studied were digitized and used to obtain the time dependent profiles of effective stress.

Two-dimensional time-dependent modelling of fume formation in a pulsed gas metal arc welding process

NASA Astrophysics Data System (ADS)

Boselli, M.; Colombo, V.; Ghedini, E.; Gherardi, M.; Sanibondi, P.

2013-06-01

Fume formation in a pulsed gas metal arc welding (GMAW) process is investigated by coupling a time-dependent axi-symmetric two-dimensional model, which takes into account both droplet detachment and production of metal vapour, with a model for fume formation and transport based on the method of moments for the solution of the aerosol general dynamic equation. We report simulative results of a pulsed process (peak current = 350 A, background current 30 A, period = 9 ms) for a 1 mm diameter iron wire, with Ar shielding gas. Results showed that metal vapour production occurs mainly at the wire tip, whereas fume formation is concentrated in the fringes of the arc in the spatial region close to the workpiece, where metal vapours are transported by convection. The proposed modelling approach allows time-dependent tracking of fumes also in plasma processes where temperature-time variations occur faster than nanoparticle transport from the nucleation region to the surrounding atmosphere, as is the case for most pulsed GMAW processes.

Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics

NASA Technical Reports Server (NTRS)

Roe, P. L.

1984-01-01

A possible technique is explored for extending to multidimensional flows some of the upwind-differencing methods that are highly successful in the one-dimensional case. Emphasis is on the two-dimensional case, and the flow domain is assumed to be divided into polygonal computational elements. Inside each element, the flow is represented by a local superposition of elementary solutions consisting of plane waves not necessarily aligned with the element boundaries.

Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator

NASA Astrophysics Data System (ADS)

Vabishchevich, P. N.

2018-03-01

A time-dependent problem in a bounded domain for a fractional diffusion equation is considered. The first-order evolution equation involves a fractional-power second-order elliptic operator with Robin boundary conditions. A finite-element spatial approximation with an additive approximation of the operator of the problem is used. The time approximation is based on a vector scheme. The transition to a new time level is ensured by solving a sequence of standard elliptic boundary value problems. Numerical results obtained for a two-dimensional model problem are presented.

Two-Dimensional Ordering of Solute Nanoclusters at a Close-Packed Stacking Fault: Modeling and Experimental Analysis

PubMed Central

Kimizuka, Hajime; Kurokawa, Shu; Yamaguchi, Akihiro; Sakai, Akira; Ogata, Shigenobu

2014-01-01

Predicting the equilibrium ordered structures at internal interfaces, especially in the case of nanometer-scale chemical heterogeneities, is an ongoing challenge in materials science. In this study, we established an ab-initio coarse-grained modeling technique for describing the phase-like behavior of a close-packed stacking-fault-type interface containing solute nanoclusters, which undergo a two-dimensional disorder-order transition, depending on the temperature and composition. Notably, this approach can predict the two-dimensional medium-range ordering in the nanocluster arrays realized in Mg-based alloys, in a manner consistent with scanning tunneling microscopy-based measurements. We predicted that the repulsively interacting solute-cluster system undergoes a continuous evolution into a highly ordered densely packed morphology while maintaining a high degree of six-fold orientational order, which is attributable mainly to an entropic effect. The uncovered interaction-dependent ordering properties may be useful for the design of nanostructured materials utilizing the self-organization of two-dimensional nanocluster arrays in the close-packed interfaces. PMID:25471232

Navier-Stokes solution on the CYBER-203 by a pseudospectral technique

NASA Technical Reports Server (NTRS)

Lambiotte, J. J.; Hussaini, M. Y.; Bokhari, S.; Orszag, S. A.

1983-01-01

A three-level, time-split, mixed spectral/finite difference method for the numerical solution of the three-dimensional, compressible Navier-Stokes equations has been developed and implemented on the Control Data Corporation (CDC) CYBER-203. This method uses a spectral representation for the flow variables in the streamwise and spanwise coordinates, and central differences in the normal direction. The five dependent variables are interleaved one horizontal plane at a time and the array of their values at the grid points of each horizontal plane is a typical vector in the computation. The code is organized so as to require, per time step, a single forward-backward pass through the entire data base. The one-and two-dimensional Fast Fourier Transforms are performed using software especially developed for the CYBER-203.

Black holes in a cubic Galileon universe

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

Babichev, E.; Charmousis, C.; Lehébel, A.

2016-09-01

We find and study the properties of black hole solutions for a subclass of Horndeski theory including the cubic Galileon term. The theory under study has shift symmetry but not reflection symmetry for the scalar field. The Galileon is assumed to have linear time dependence characterized by a velocity parameter. We give analytic 3-dimensional solutions that are akin to the BTZ solutions but with a non-trivial scalar field that modifies the effective cosmological constant. We then study the 4-dimensional asymptotically flat and de Sitter solutions. The latter present three different branches according to their effective cosmological constant. For two ofmore » these branches, we find families of black hole solutions, parametrized by the velocity of the scalar field. These spherically symmetric solutions, obtained numerically, are different from GR solutions close to the black hole event horizon, while they have the same de-Sitter asymptotic behavior. The velocity parameter represents black hole primary hair.« less

Higher dimensional Taub-NUT spaces and applications

NASA Astrophysics Data System (ADS)

Stelea, Cristian Ionut

In the first part of this thesis we discuss classes of new exact NUT-charged solutions in four dimensions and higher, while in the remainder of the thesis we make a study of their properties and their possible applications. Specifically, in four dimensions we construct new families of axisymmetric vacuum solutions using a solution-generating technique based on the hidden SL(2,R) symmetry of the effective action. In particular, using the Schwarzschild solution as a seed we obtain the Zipoy-Voorhees generalisation of the Taub-NUT solution and of the Eguchi-Hanson soliton. Using the C-metric as a seed, we obtain and study the accelerating versions of all the above solutions. In higher dimensions we present new classes of NUT-charged spaces, generalising the previously known even-dimensional solutions to odd and even dimensions, as well as to spaces with multiple NUT-parameters. We also find the most general form of the odd-dimensional Eguchi-Hanson solitons. We use such solutions to investigate the thermodynamic properties of NUT-charged spaces in (A)dS backgrounds. These have been shown to yield counter-examples to some of the conjectures advanced in the still elusive dS/CFT paradigm (such as the maximal mass conjecture and Bousso's entropic N-bound). One important application of NUT-charged spaces is to construct higher dimensional generalisations of Kaluza-Klein magnetic monopoles, generalising the known 5-dimensional Kaluza-Klein soliton. Another interesting application involves a study of time-dependent higher-dimensional bubbles-of-nothing generated from NUT-charged solutions. We use them to test the AdS/CFT conjecture as well as to generate, by using stringy Hopf-dualities, new interesting time-dependent solutions in string theory. Finally, we construct and study new NUT-charged solutions in higher-dimensional Einstein-Maxwell theories, generalising the known Reissner-Nordstrom solutions.

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

NASA Technical Reports Server (NTRS)

Whitfield, David L.; Taylor, Lafayette K.

1994-01-01

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

A two-dimensional numerical study of the flow inside the combustion chambers of a motored rotary engine

NASA Technical Reports Server (NTRS)

Shih, T. I. P.; Yang, S. L.; Schock, H. J.

1986-01-01

A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

A two-dimensional numerical study of the flow inside the combustion chamber of a motored rotary engine

NASA Technical Reports Server (NTRS)

Shih, T. I-P.; Yang, S. L.; Schock, H. J.

1986-01-01

A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

A two-dimensional transient analytical solution for a ponded ditch drainage system under the influence of source/sink

NASA Astrophysics Data System (ADS)

Sarmah, Ratan; Tiwari, Shubham

2018-03-01

An analytical solution is developed for predicting two-dimensional transient seepage into ditch drainage network receiving water from a non-uniform steady ponding field from the surface of the soil under the influence of source/sink in the flow domain. The flow domain is assumed to be saturated, homogeneous and anisotropic in nature and have finite extends in horizontal and vertical directions. The drains are assumed to be standing vertical and penetrating up to impervious layer. The water levels in the drains are unequal and invariant with time. The flow field is also assumed to be under the continuous influence of time-space dependent arbitrary source/sink term. The correctness of the proposed model is checked by developing a numerical code and also with the existing analytical solution for the simplified case. The study highlights the significance of source/sink influence in the subsurface flow. With the imposition of the source and sink term in the flow domain, the pathline and travel time of water particles started deviating from their original position and above that the side and top discharge to the drains were also observed to have a strong influence of the source/sink terms. The travel time and pathline of water particles are also observed to have a dependency on the height of water in the ditches and on the location of source/sink activation area.

Eroding dipoles and vorticity growth for Euler flows in {{{R}}}^{3}: the hairpin geometry as a model for finite-time blowup

NASA Astrophysics Data System (ADS)

Childress, Stephen; Gilbert, Andrew D.

2018-02-01

A theory of an eroding ‘hairpin’ vortex dipole structure in three-dimensions is developed, extending our previous study of an axisymmetric eroding dipole without swirl. The axisymmetric toroidal dipole was found to lead to maximal growth of vorticity, as {t}4/3. The hairpin is here similarly proposed as a model to produce large ‘self-stretching’ of vorticity, with the possibility of finite-time blow-up. We derive a system of partial differential equations of ‘generalized’ form, involving contour averaging of a locally two-dimensional Euler flow. We do not attempt here to solve the system exactly, but point out that non-existence of physically acceptable solutions would most probably be a result of the axial flow. Because of the axial flow the vorticity distribution within the dipole eddies is no longer of the simple Sadovskii type (vorticity constant over a cross-section) obtained in the axisymmetric problem. Thus the solution of the system depends upon the existence of a larger class of propagating two-dimensional dipoles. The hairpin model is obtained by formal asymptotic analysis. As in the axisymmetric problem a local transformation to ‘shrinking’ coordinates is introduced, but now in a self-similar form appropriate to the study of a possible finite-time singularity. We discuss some properties of the model, including a study of the helicity and a first step in iterating toward a solution from the Sadovskii structure. We also present examples of two-dimensional propagating dipoles not previously studied, which have a vorticity profile consistent with our model. Although no rigorous results can be given, and analysis of the system is only partial, the formal calculations are consistent with the possibility of a finite time blowup of vorticity at a point of vanishing circulation of the dipole eddies, but depending upon the existence of the necessary two-dimensional propagating dipole. Our results also suggest that conservation of kinetic energy as realized in the eroding hairpin excludes a finite time blowup for the corresponding Navier-Stokes model.

Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction

NASA Astrophysics Data System (ADS)

Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh

2016-09-01

A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.

Review of literature on the finite-element solution of the equations of two-dimensional surface-water flow in the horizontal plane

USGS Publications Warehouse

Lee, Jonathan K.; Froehlich, David C.

1987-01-01

Published literature on the application of the finite-element method to solving the equations of two-dimensional surface-water flow in the horizontal plane is reviewed in this report. The finite-element method is ideally suited to modeling two-dimensional flow over complex topography with spatially variable resistance. A two-dimensional finite-element surface-water flow model with depth and vertically averaged velocity components as dependent variables allows the user great flexibility in defining geometric features such as the boundaries of a water body, channels, islands, dikes, and embankments. The following topics are reviewed in this report: alternative formulations of the equations of two-dimensional surface-water flow in the horizontal plane; basic concepts of the finite-element method; discretization of the flow domain and representation of the dependent flow variables; treatment of boundary conditions; discretization of the time domain; methods for modeling bottom, surface, and lateral stresses; approaches to solving systems of nonlinear equations; techniques for solving systems of linear equations; finite-element alternatives to Galerkin's method of weighted residuals; techniques of model validation; and preparation of model input data. References are listed in the final chapter.

Monopole excitations of a harmonically trapped one-dimensional Bose gas from the ideal gas to the Tonks-Girardeau regime.

PubMed

Choi, S; Dunjko, V; Zhang, Z D; Olshanii, M

2015-09-11

Using a time-dependent modified nonlinear Schrödinger equation (MNLSE)-where the conventional chemical potential proportional to the density is replaced by the one inferred from Lieb-Liniger's exact solution-we study frequencies of the collective monopole excitations of a one-dimensional Bose gas. We find that our method accurately reproduces the results of a recent experimental study [E. Haller et al., Science 325, 1224 (2009)] in the full spectrum of interaction regimes from the ideal gas, through the mean-field regime, through the mean-field Thomas-Fermi regime, all the way to the Tonks-Giradeau gas. While the former two are accessible by the standard time-dependent NLSE and inaccessible by the time-dependent local density approximation, the situation reverses in the latter case. However, the MNLSE is shown to treat all these regimes within a single numerical method.

Numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis - Stanford Univ., Mar. 1989

NASA Technical Reports Server (NTRS)

Rogers, Stuart E.

1990-01-01

The current work is initiated in an effort to obtain an efficient, accurate, and robust algorithm for the numerical solution of the incompressible Navier-Stokes equations in two- and three-dimensional generalized curvilinear coordinates for both steady-state and time-dependent flow problems. This is accomplished with the use of the method of artificial compressibility and a high-order flux-difference splitting technique for the differencing of the convective terms. Time accuracy is obtained in the numerical solutions by subiterating the equations in psuedo-time for each physical time step. The system of equations is solved with a line-relaxation scheme which allows the use of very large pseudo-time steps leading to fast convergence for steady-state problems as well as for the subiterations of time-dependent problems. Numerous laminar test flow problems are computed and presented with a comparison against analytically known solutions or experimental results. These include the flow in a driven cavity, the flow over a backward-facing step, the steady and unsteady flow over a circular cylinder, flow over an oscillating plate, flow through a one-dimensional inviscid channel with oscillating back pressure, the steady-state flow through a square duct with a 90 degree bend, and the flow through an artificial heart configuration with moving boundaries. An adequate comparison with the analytical or experimental results is obtained in all cases. Numerical comparisons of the upwind differencing with central differencing plus artificial dissipation indicates that the upwind differencing provides a much more robust algorithm, which requires significantly less computing time. The time-dependent problems require on the order of 10 to 20 subiterations, indicating that the elliptical nature of the problem does require a substantial amount of computing effort.

SUTRA: A model for 2D or 3D saturated-unsaturated, variable-density ground-water flow with solute or energy transport

USGS Publications Warehouse

Voss, Clifford I.; Provost, A.M.

2002-01-01

SUTRA (Saturated-Unsaturated Transport) is a computer program that simulates fluid movement and the transport of either energy or dissolved substances in a subsurface environment. This upgraded version of SUTRA adds the capability for three-dimensional simulation to the former code (Voss, 1984), which allowed only two-dimensional simulation. The code employs a two- or three-dimensional finite-element and finite-difference method to approximate the governing equations that describe the two interdependent processes that are simulated: 1) fluid density-dependent saturated or unsaturated ground-water flow; and 2) either (a) transport of a solute in the ground water, in which the solute may be subject to: equilibrium adsorption on the porous matrix, and both first-order and zero-order production or decay; or (b) transport of thermal energy in the ground water and solid matrix of the aquifer. SUTRA may also be used to simulate simpler subsets of the above processes. A flow-direction-dependent dispersion process for anisotropic media is also provided by the code and is introduced in this report. As the primary calculated result, SUTRA provides fluid pressures and either solute concentrations or temperatures, as they vary with time, everywhere in the simulated subsurface system. SUTRA flow simulation may be employed for two-dimensional (2D) areal, cross sectional and three-dimensional (3D) modeling of saturated ground-water flow systems, and for cross sectional and 3D modeling of unsaturated zone flow. Solute-transport simulation using SUTRA may be employed to model natural or man-induced chemical-species transport including processes of solute sorption, production, and decay. For example, it may be applied to analyze ground-water contaminant transport problems and aquifer restoration designs. In addition, solute-transport simulation with SUTRA may be used for modeling of variable-density leachate movement, and for cross sectional modeling of saltwater intrusion in aquifers at near-well or regional scales, with either dispersed or relatively sharp transition zones between freshwater and saltwater. SUTRA energy-transport simulation may be employed to model thermal regimes in aquifers, subsurface heat conduction, aquifer thermal-energy storage systems, geothermal reservoirs, thermal pollution of aquifers, and natural hydrogeologic convection systems. Mesh construction, which is quite flexible for arbitrary geometries, employs quadrilateral finite elements in 2D Cartesian or radial-cylindrical coordinate systems, and hexahedral finite elements in 3D systems. 3D meshes are currently restricted to be logically rectangular; in other words, they are similar to deformable finite-difference-style grids. Permeabilities may be anisotropic and may vary in both direction and magnitude throughout the system, as may most other aquifer and fluid properties. Boundary conditions, sources and sinks may be time dependent. A number of input data checks are made to verify the input data set. An option is available for storing intermediate results and restarting a simulation at the intermediate time. Output options include fluid velocities, fluid mass and solute mass or energy budgets, and time-varying observations at points in the system. Both the mathematical basis for SUTRA and the program structure are highly general, and are modularized to allow for straightforward addition of new methods or processes to the simulation. The FORTRAN-90 coding stresses clarity and modularity rather than efficiency, providing easy access for later modifications.

Boundary-fitted curvilinear coordinate systems for solution of partial differential equations on fields containing any number of arbitrary two-dimensional bodies

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Thames, F. C.; Mastin, C. W.

1977-01-01

A method is presented for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected two-dimensional region containing any number of arbitrarily shaped bodies. No restrictions are placed on the shape of the boundaries, which may even be time-dependent, and the approach is not restricted in principle to two dimensions. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system in the physical plane. A number of examples of coordinate systems and application thereof to the solution of partial differential equations are given. The FORTRAN computer program and instructions for use are included.

A comparison of two- and three-dimensional stochastic models of regional solute movement

USGS Publications Warehouse

Shapiro, A.M.; Cvetkovic, V.D.

1990-01-01

Recent models of solute movement in porous media that are based on a stochastic description of the porous medium properties have been dedicated primarily to a three-dimensional interpretation of solute movement. In many practical problems, however, it is more convenient and consistent with measuring techniques to consider flow and solute transport as an areal, two-dimensional phenomenon. The physics of solute movement, however, is dependent on the three-dimensional heterogeneity in the formation. A comparison of two- and three-dimensional stochastic interpretations of solute movement in a porous medium having a statistically isotropic hydraulic conductivity field is investigated. To provide an equitable comparison between the two- and three-dimensional analyses, the stochastic properties of the transmissivity are defined in terms of the stochastic properties of the hydraulic conductivity. The variance of the transmissivity is shown to be significantly reduced in comparison to that of the hydraulic conductivity, and the transmissivity is spatially correlated over larger distances. These factors influence the two-dimensional interpretations of solute movement by underestimating the longitudinal and transverse growth of the solute plume in comparison to its description as a three-dimensional phenomenon. Although this analysis is based on small perturbation approximations and the special case of a statistically isotropic hydraulic conductivity field, it casts doubt on the use of a stochastic interpretation of the transmissivity in describing regional scale movement. However, by assuming the transmissivity to be the vertical integration of the hydraulic conductivity field at a given position, the stochastic properties of the hydraulic conductivity can be estimated from the stochastic properties of the transmissivity and applied to obtain a more accurate interpretation of solute movement. ?? 1990 Kluwer Academic Publishers.

An exact solution for the solidification of a liquid slab of binary mixture

NASA Technical Reports Server (NTRS)

Antar, B. N.; Collins, F. G.; Aumalia, A. E.

1986-01-01

The time dependent temperature and concentration profiles of a one dimensional finite slab of a binary liquid alloy is investigated during solidification. The governing equations are reduced to a set of coupled, nonlinear initial value problems using the method outlined by Meyer. Two methods will be used to solve these equations. The first method uses a Runge-Kutta-Fehlberg integrator to solve the equations numerically. The second method comprises of finding closed form solutions of the equations.

Solution of non-continuum flows using BGK-type model with enforced relaxation of moments

NASA Astrophysics Data System (ADS)

Alekseenko, Alexander; Gimelshein, Sergey; Nguyen, Truong; Vedula, Prakash

2016-11-01

A BGK-type model with velocity dependent collision frequency and enforced relaxation rates for selected moments is applied to simulation of one- and two-dimensional super sonic flows. Relaxation rates of the moments are estimated by evaluating the full Boltzmann collision integral several times during the simulation. The solutions show improvements in velocity and temperature profiles as compared to the classical ES-BGK model. However, enforcement of relaxation rates for high order moments increases stiffness of the model.

Global existence and large time asymptotic behavior of strong solutions to the Cauchy problem of 2D density-dependent Navier–Stokes equations with vacuum

NASA Astrophysics Data System (ADS)

Lü, Boqiang; Shi, Xiaoding; Zhong, Xin

2018-06-01

We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier–Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D Cauchy problem of the density-dependent Navier–Stokes equations on the whole space admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Furthermore, we also obtain the large time decay rates of the spatial gradients of the velocity and the pressure, which are the same as those of the homogeneous case.

FRW Solutions and Holography from Uplifted AdS/CFT

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

Dong, Xi; Horn, Bart; /Stanford U., ITP /Stanford U., Phys. Dept. /SLAC

2012-02-15

Starting from concrete AdS/CFT dual pairs, one can introduce ingredients which produce cosmological solutions, including metastable de Sitter and its decay to non-accelerating FRW. We present simple FRW solutions sourced by magnetic flavor branes and analyze correlation functions and particle and brane dynamics. To obtain a holographic description, we exhibit a time-dependent warped metric on the solution and interpret the resulting redshifted region as a Lorentzian low energy effective field theory in one fewer dimension. At finite times, this theory has a finite cutoff, a propagating lower dimensional graviton and a finite covariant entropy bound, but at late times themore » lower dimensional Planck mass and entropy go off to infinity in a way that is dominated by contributions from the low energy effective theory. This opens up the possibility of a precise dual at late times. We reproduce the time-dependent growth of the number of degrees of freedom in the system via a count of available microscopic states in the corresponding magnetic brane construction.« less

FRW solutions and holography from uplifted AdS/CFT systems

NASA Astrophysics Data System (ADS)

Dong, Xi; Horn, Bart; Matsuura, Shunji; Silverstein, Eva; Torroba, Gonzalo

2012-05-01

Starting from concrete AdS/CFT dual pairs, one can introduce ingredients which produce cosmological solutions, including metastable de Sitter and its decay to nonaccelerating Friedmann-Robertson-Walker. We present simple Friedmann-Robertson-Walker solutions sourced by magnetic flavor branes and analyze correlation functions and particle and brane dynamics. To obtain a holographic description, we exhibit a time-dependent warped metric on the solution and interpret the resulting redshifted region as a Lorentzian low energy effective field theory in one fewer dimension. At finite times, this theory has a finite cutoff, a propagating lower-dimensional graviton, and a finite covariant entropy bound, but at late times the lower-dimensional Planck mass and entropy go off to infinity in a way that is dominated by contributions from the low energy effective theory. This opens up the possibility of a precise dual at late times. We reproduce the time-dependent growth of the number of degrees of freedom in the system via a count of available microscopic states in the corresponding magnetic brane construction.

Cosmological rotating black holes in five-dimensional fake supergravity

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

Nozawa, Masato; Maeda, Kei-ichi; Waseda Research Institute for Science and Engineering, Okubo 3-4-1, Shinjuku, Tokyo 169-8555

2011-01-15

In recent series of papers, we found an arbitrary dimensional, time-evolving, and spatially inhomogeneous solution in Einstein-Maxwell-dilaton gravity with particular couplings. Similar to the supersymmetric case, the solution can be arbitrarily superposed in spite of nontrivial time-dependence, since the metric is specified by a set of harmonic functions. When each harmonic has a single point source at the center, the solution describes a spherically symmetric black hole with regular Killing horizons and the spacetime approaches asymptotically to the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology. We discuss in this paper that in 5 dimensions, this equilibrium condition traces back to the first-order 'Killing spinor'more » equation in 'fake supergravity' coupled to arbitrary U(1) gauge fields and scalars. We present a five-dimensional, asymptotically FLRW, rotating black-hole solution admitting a nontrivial 'Killing spinor', which is a spinning generalization of our previous solution. We argue that the solution admits nondegenerate and rotating Killing horizons in contrast with the supersymmetric solutions. It is shown that the present pseudo-supersymmetric solution admits closed timelike curves around the central singularities. When only one harmonic is time-dependent, the solution oxidizes to 11 dimensions and realizes the dynamically intersecting M2/M2/M2-branes in a rotating Kasner universe. The Kaluza-Klein-type black holes are also discussed.« less

Two-dimensional radiative transfer. I - Planar geometry. [in stellar atmospheres

NASA Technical Reports Server (NTRS)

Mihalas, D.; Auer, L. H.; Mihalas, B. R.

1978-01-01

Differential-equation methods for solving the transfer equation in two-dimensional planar geometries are developed. One method, which uses a Hermitian integration formula on ray segments through grid points, proves to be extremely well suited to velocity-dependent problems. An efficient elimination scheme is developed for which the computing time scales linearly with the number of angles and frequencies; problems with large velocity amplitudes can thus be treated accurately. A very accurate and efficient method for performing a formal solution is also presented. A discussion is given of several examples of periodic media and free-standing slabs, both in static cases and with velocity fields. For the free-standing slabs, two-dimensional transport effects are significant near boundaries, but no important effects were found in any of the periodic cases studied.

Using a two-step matrix solution to reduce the run time in KULL's magnetic diffusion package

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

Brunner, T A; Kolev, T V

2010-12-17

Recently a Resistive Magnetohydrodynamics (MHD) package has been added to the KULL code. In order to be compatible with the underlying hydrodynamics algorithm, a new sub-zonal magnetics discretization was developed that supports arbitrary polygonal and polyhedral zones. This flexibility comes at the cost of many more unknowns per zone - approximately ten times more for a hexahedral mesh. We can eliminate some (or all, depending on the dimensionality) of the extra unknowns from the global matrix during assembly by using a Schur complement approach. This trades expensive global work for cache-friendly local work, while still allowing solution for the fullmore » system. Significant improvements in the solution time are observed for several test problems.« less

Meshless Method with Operator Splitting Technique for Transient Nonlinear Bioheat Transfer in Two-Dimensional Skin Tissues

PubMed Central

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-01

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue. PMID:25603180

Meshless method with operator splitting technique for transient nonlinear bioheat transfer in two-dimensional skin tissues.

PubMed

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-16

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue.

Generalized time-dependent Schrödinger equation in two dimensions under constraints

NASA Astrophysics Data System (ADS)

Sandev, Trifce; Petreska, Irina; Lenzi, Ervin K.

2018-01-01

We investigate a generalized two-dimensional time-dependent Schrödinger equation on a comb with a memory kernel. A Dirac delta term is introduced in the Schrödinger equation so that the quantum motion along the x-direction is constrained at y = 0. The wave function is analyzed by using Green's function approach for several forms of the memory kernel, which are of particular interest. Closed form solutions for the cases of Dirac delta and power-law memory kernels in terms of Fox H-function, as well as for a distributed order memory kernel, are obtained. Further, a nonlocal term is also introduced and investigated analytically. It is shown that the solution for such a case can be represented in terms of infinite series in Fox H-functions. Green's functions for each of the considered cases are analyzed and plotted for the most representative ones. Anomalous diffusion signatures are evident from the presence of the power-law tails. The normalized Green's functions obtained in this work are of broader interest, as they are an important ingredient for further calculations and analyses of some interesting effects in the transport properties in low-dimensional heterogeneous media.

Analysis and generation of groundwater concentration time series

NASA Astrophysics Data System (ADS)

Crăciun, Maria; Vamoş, Călin; Suciu, Nicolae

2018-01-01

Concentration time series are provided by simulated concentrations of a nonreactive solute transported in groundwater, integrated over the transverse direction of a two-dimensional computational domain and recorded at the plume center of mass. The analysis of a statistical ensemble of time series reveals subtle features that are not captured by the first two moments which characterize the approximate Gaussian distribution of the two-dimensional concentration fields. The concentration time series exhibit a complex preasymptotic behavior driven by a nonstationary trend and correlated fluctuations with time-variable amplitude. Time series with almost the same statistics are generated by successively adding to a time-dependent trend a sum of linear regression terms, accounting for correlations between fluctuations around the trend and their increments in time, and terms of an amplitude modulated autoregressive noise of order one with time-varying parameter. The algorithm generalizes mixing models used in probability density function approaches. The well-known interaction by exchange with the mean mixing model is a special case consisting of a linear regression with constant coefficients.

The application of Green's theorem to the solution of boundary-value problems in linearized supersonic wing theory

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard

1950-01-01

Following the introduction of the linearized partial differential equation for nonsteady three-dimensional compressible flow, general methods of solution are given for the two and three-dimensional steady-state and two-dimensional unsteady-state equations. It is also pointed out that, in the absence of thickness effects, linear theory yields solutions consistent with the assumptions made when applied to lifting-surface problems for swept-back plan forms at sonic speeds. The solutions of the particular equations are determined in all cases by means of Green's theorem, and thus depend on the use of Green's equivalent layer of sources, sinks, and doublets. Improper integrals in the supersonic theory are treated by means of Hadamard's "finite part" technique.

Analytical solutions for the dynamics of two trapped interacting ultracold atoms

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

Idziaszek, Zbigniew; Calarco, Tommaso; CNR-INFM BEC Center, I-38050 Povo

2006-08-15

We discuss exact solutions of the Schroedinger equation for the system of two ultracold atoms confined in an axially symmetric harmonic potential. We investigate different geometries of the trapping potential, in particular we study the properties of eigenenergies and eigenfunctions for quasi-one-dimensional and quasi-two-dimensional traps. We show that the quasi-one-dimensional and the quasi-two-dimensional regimes for two atoms can be already realized in the traps with moderately large (or small) ratios of the trapping frequencies in the axial and the transverse directions. Finally, we apply our theory to Feshbach resonances for trapped atoms. Introducing in our description an energy-dependent scattering lengthmore » we calculate analytically the eigenenergies for two trapped atoms in the presence of a Feshbach resonance.« less

A numerical model for density-and-viscosity-dependent flows in two-dimensional variably saturated porous media

NASA Astrophysics Data System (ADS)

Boufadel, Michel C.; Suidan, Makram T.; Venosa, Albert D.

1999-04-01

We present a formulation for water flow and solute transport in two-dimensional variably saturated media that accounts for the effects of the solute on water density and viscosity. The governing equations are cast in a dimensionless form that depends on six dimensionless groups of parameters. These equations are discretized in space using the Galerkin finite element formulation and integrated in time using the backward Euler scheme with mass lumping. The modified Picard method is used to linearize the water flow equation. The resulting numerical model, the MARUN model, is verified by comparison to published numerical results. It is then used to investigate beach hydraulics at seawater concentration (about 30 g l -1) in the context of nutrients delivery for bioremediation of oil spills on beaches. Numerical simulations that we conducted in a rectangular section of a hypothetical beach revealed that buoyancy in the unsaturated zone is significant in soils that are fine textured, with low anisotropy ratio, and/or exhibiting low physical dispersion. In such situations, application of dissolved nutrients to a contaminated beach in a freshwater solution is superior to their application in a seawater solution. Concentration-engendered viscosity effects were negligible with respect to concentration-engendered density effects for the cases that we considered.

HST3D; a computer code for simulation of heat and solute transport in three-dimensional ground-water flow systems

USGS Publications Warehouse

Kipp, K.L.

1987-01-01

The Heat- and Soil-Transport Program (HST3D) simulates groundwater flow and associated heat and solute transport in three dimensions. The three governing equations are coupled through the interstitial pore velocity, the dependence of the fluid density on pressure, temperature, the solute-mass fraction , and the dependence of the fluid viscosity on temperature and solute-mass fraction. The solute transport equation is for only a single, solute species with possible linear equilibrium sorption and linear decay. Finite difference techniques are used to discretize the governing equations using a point-distributed grid. The flow-, heat- and solute-transport equations are solved , in turn, after a particle Gauss-reduction scheme is used to modify them. The modified equations are more tightly coupled and have better stability for the numerical solutions. The basic source-sink term represents wells. A complex well flow model may be used to simulate specified flow rate and pressure conditions at the land surface or within the aquifer, with or without pressure and flow rate constraints. Boundary condition types offered include specified value, specified flux, leakage, heat conduction, and approximate free surface, and two types of aquifer influence functions. All boundary conditions can be functions of time. Two techniques are available for solution of the finite difference matrix equations. One technique is a direct-elimination solver, using equations reordered by alternating diagonal planes. The other technique is an iterative solver, using two-line successive over-relaxation. A restart option is available for storing intermediate results and restarting the simulation at an intermediate time with modified boundary conditions. This feature also can be used as protection against computer system failure. Data input and output may be in metric (SI) units or inch-pound units. Output may include tables of dependent variables and parameters, zoned-contour maps, and plots of the dependent variables versus time. (Lantz-PTT)

Dynamical black holes in low-energy string theory

NASA Astrophysics Data System (ADS)

Aniceto, Pedro; Rocha, Jorge V.

2017-05-01

We investigate time-dependent spherically symmetric solutions of the four-dimensional Einstein-Maxwell-axion-dilaton system, with the dilaton coupling that occurs in low-energy effective heterotic string theory. A class of dilaton-electrovacuum radiating solutions with a trivial axion, previously found by Güven and Yörük, is re-derived in a simpler manner and its causal structure is clarified. It is shown that such dynamical spacetimes featuring apparent horizons do not possess a regular light-like past null infinity or future null infinity, depending on whether they are radiating or accreting. These solutions are then extended in two ways. First we consider a Vaidya-like generalisation, which introduces a null dust source. Such spacetimes are used to test the status of cosmic censorship in the context of low-energy string theory. We prove that — within this family of solutions — regular black holes cannot evolve into naked singularities by accreting null dust, unless standard energy conditions are violated. Secondly, we employ S-duality to derive new time-dependent dyon solutions with a nontrivial axion turned on. Although they share the same causal structure as their Einstein-Maxwell-dilaton counterparts, these solutions possess both electric and magnetic charges.

Density functional of a two-dimensional gas of dipolar atoms: Thomas-Fermi-Dirac treatment

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

Fang, Bess; Englert, Berthold-Georg

We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many atoms in a harmonic trap, we give analytical solutions for the single-particle spatial density and the ground-state energy, in dependence on the interaction strength, and we discuss the weak-interaction limit that is relevant for experiments. We then lift the restriction of full spin polarization and account for a time-independent inhomogeneous external magnetic field. The field strength necessary to ensure full spin polarization is derived.

Optimal control of lift/drag ratios on a rotating cylinder

NASA Technical Reports Server (NTRS)

Ou, Yuh-Roung; Burns, John A.

1992-01-01

We present the numerical solution to a problem of maximizing the lift to drag ratio by rotating a circular cylinder in a two-dimensional viscous incompressible flow. This problem is viewed as a test case for the newly developing theoretical and computational methods for control of fluid dynamic systems. We show that the time averaged lift to drag ratio for a fixed finite-time interval achieves its maximum value at an optimal rotation rate that depends on the time interval.

Localized oscillatory states in magnetoconvection.

PubMed

Buckley, Matthew C; Bushby, Paul J

2013-02-01

Localized states are found in many pattern forming systems. The aim of this paper is to investigate the occurrence of oscillatory localized states in two-dimensional Boussinesq magnetoconvection. Initially considering an idealized model, in which the vertical structure of the system has been simplified by a projection onto a small number of Fourier modes, we find that these states are restricted to the low ζ regime (where ζ represents the ratio of the magnetic to thermal diffusivities). These states always exhibit bistability with another nontrivial solution branch; in other words, they show no evidence of subcritical behavior. This is due to the weak flux expulsion that is exhibited by these time-dependent solutions. Using the results of this parameter survey, we locate corresponding states in a fully resolved two-dimensional system, although the mode of oscillation is more complex in this case. This is the first time that a localized oscillatory state, of this kind, has been found in a fully resolved magnetoconvection simulation.

Analytical Solution for Time-drawdown Response to Constant Pumping from a Homogeneous, Confined Horizontal Aquifer with Unidirectional Flow

NASA Astrophysics Data System (ADS)

Parrish, K. E.; Zhang, J.; Teasdale, E.

2007-12-01

An exact analytical solution to the ordinary one-dimensional partial differential equation is derived for transient groundwater flow in a homogeneous, confined, horizontal aquifer using Laplace transformation. The theoretical analysis is based on the assumption that the aquifer is homogeneous and one-dimensional (horizontal); confined between impermeable formations on top and bottom; and of infinite horizontal extent and constant thickness. It is also assumed that there is only a single pumping well penetrating the entire aquifer; flow is everywhere horizontal within the aquifer to the well; the well is pumping with a constant discharge rate; the well diameter is infinitesimally small; and the hydraulic head is uniform throughout the aquifer before pumping. Similar to the Theis solution, this solution is suited to determine transmissivity and storativity for a two- dimensional, vertically confined aquifer, such as a long vertically fractured zone of high permeability within low permeable rocks or a long, high-permeability trench inside a low-permeability porous media. In addition, it can be used to analyze time-drawdown responses to pumping and injection in similar settings. The solution can also be used to approximate the groundwater flow for unconfined conditions if (1) the variation of transmissivity is negligible (groundwater table variation is small in comparison to the saturated thickness); and (2) the unsaturated flow is negligible. The errors associated with the use of the solution to unconfined conditions depend on the accuracies of the above two assumptions. The solution can also be used to assess the impacts of recharge from a seasonal river or irrigation canal on the groundwater system by assuming uniform, time- constant recharge along the river or canal. This paper presents the details for derivation of the analytical solution. The analytical solution is compared to numerical simulation results with example cases. Its accuracy is also assessed and discussed for confined and unconfined conditions.

Time-dependent interaction between a two-level atom and a su(1,1) Lie algebra quantum system

NASA Astrophysics Data System (ADS)

Abdalla, M. Sebaweh; Khalil, E. M.; Obada, A.-S. F.

2017-06-01

The problem of the interaction between a two-level atom and a two-mode field in the parametric amplifier-type is considered. A similar problem appears in an ion trapped in a two-dimensional trap. The problem is transformed into an interaction governed by su(1,1) Lie algebraic operators with phase and coupling parameter depending on time. Under an integrability condition, that relates phase and coupling, a solution to the wavefunction is obtained using the Schrödinger equation. The effects of the functional dependence of the coupling and the initial state of the two-level atom on atomic inversion, the degree of entanglement, the fidelity and the Glauber second-order correlation function are investigated. It is shown that the acceleration term plays an important role in controlling the function behavior of the considered quantities.

ADER schemes for scalar non-linear hyperbolic conservation laws with source terms in three-space dimensions

NASA Astrophysics Data System (ADS)

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

2005-01-01

In this paper we develop non-linear ADER schemes for time-dependent scalar linear and non-linear conservation laws in one-, two- and three-space dimensions. Numerical results of schemes of up to fifth order of accuracy in both time and space illustrate that the designed order of accuracy is achieved in all space dimensions for a fixed Courant number and essentially non-oscillatory results are obtained for solutions with discontinuities. We also present preliminary results for two-dimensional non-linear systems.

The two-dimensional Stefan problem with slightly varying heat flux

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

Gammon, J.; Howarth, J.A.

1995-09-01

The authors solve the two-dimensional stefan problem of solidification in a half-space, where the heat flux at the wall is a slightly varying function of positioning along the wall, by means of a large Stefan number approximation (which turns out to be equivalent to a small time solution), and then by means of the Heat Balance Integral Method, which is valid for all time, and which agrees with the large Stefan number solution for small times. A representative solution is given for a particular form of the heat flux perturbation.

Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two-temperature

NASA Astrophysics Data System (ADS)

Lotfy, K.; Sarkar, N.

2017-11-01

In this work, a novel generalized model of photothermal theory with two-temperature thermoelasticity theory based on memory-dependent derivative (MDD) theory is performed. A one-dimensional problem for an elastic semiconductor material with isotropic and homogeneous properties has been considered. The problem is solved with a new model (MDD) under the influence of a mechanical force with a photothermal excitation. The Laplace transform technique is used to remove the time-dependent terms in the governing equations. Moreover, the general solutions of some physical fields are obtained. The surface taken into consideration is free of traction and subjected to a time-dependent thermal shock. The numerical Laplace inversion is used to obtain the numerical results of the physical quantities of the problem. Finally, the obtained results are presented and discussed graphically.

Hybrid asymptotic-numerical approach for estimating first-passage-time densities of the two-dimensional narrow capture problem.

PubMed

Lindsay, A E; Spoonmore, R T; Tzou, J C

2016-10-01

A hybrid asymptotic-numerical method is presented for obtaining an asymptotic estimate for the full probability distribution of capture times of a random walker by multiple small traps located inside a bounded two-dimensional domain with a reflecting boundary. As motivation for this study, we calculate the variance in the capture time of a random walker by a single interior trap and determine this quantity to be comparable in magnitude to the mean. This implies that the mean is not necessarily reflective of typical capture times and that the full density must be determined. To solve the underlying diffusion equation, the method of Laplace transforms is used to obtain an elliptic problem of modified Helmholtz type. In the limit of vanishing trap sizes, each trap is represented as a Dirac point source that permits the solution of the transform equation to be represented as a superposition of Helmholtz Green's functions. Using this solution, we construct asymptotic short-time solutions of the first-passage-time density, which captures peaks associated with rapid capture by the absorbing traps. When numerical evaluation of the Helmholtz Green's function is employed followed by numerical inversion of the Laplace transform, the method reproduces the density for larger times. We demonstrate the accuracy of our solution technique with a comparison to statistics obtained from a time-dependent solution of the diffusion equation and discrete particle simulations. In particular, we demonstrate that the method is capable of capturing the multimodal behavior in the capture time density that arises when the traps are strategically arranged. The hybrid method presented can be applied to scenarios involving both arbitrary domains and trap shapes.

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

Soliton and periodic solutions for time-dependent coefficient non-linear equation

NASA Astrophysics Data System (ADS)

Guner, Ozkan

2016-01-01

In this article, we establish exact solutions for the generalized (3+1)-dimensional variable coefficient Kadomtsev-Petviashvili (GVCKP) equation. Using solitary wave ansatz in terms of ? functions and the modified sine-cosine method, we find exact analytical bright soliton solutions and exact periodic solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The effectiveness and reliability of the method are shown by its application to the GVCKP equation.

The construction of a two-dimensional reproducing kernel function and its application in a biomedical model.

PubMed

Guo, Qi; Shen, Shu-Ting

2016-04-29

There are two major classes of cardiac tissue models: the ionic model and the FitzHugh-Nagumo model. During computer simulation, each model entails solving a system of complex ordinary differential equations and a partial differential equation with non-flux boundary conditions. The reproducing kernel method possesses significant applications in solving partial differential equations. The derivative of the reproducing kernel function is a wavelet function, which has local properties and sensitivities to singularity. Therefore, study on the application of reproducing kernel would be advantageous. Applying new mathematical theory to the numerical solution of the ventricular muscle model so as to improve its precision in comparison with other methods at present. A two-dimensional reproducing kernel function inspace is constructed and applied in computing the solution of two-dimensional cardiac tissue model by means of the difference method through time and the reproducing kernel method through space. Compared with other methods, this method holds several advantages such as high accuracy in computing solutions, insensitivity to different time steps and a slow propagation speed of error. It is suitable for disorderly scattered node systems without meshing, and can arbitrarily change the location and density of the solution on different time layers. The reproducing kernel method has higher solution accuracy and stability in the solutions of the two-dimensional cardiac tissue model.

A three-dimensional, time-dependent model of Mobile Bay

NASA Technical Reports Server (NTRS)

Pitts, F. H.; Farmer, R. C.

1976-01-01

A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries.

Electromigration of intergranular voids in metal films for microelectronic interconnects

NASA Astrophysics Data System (ADS)

Averbuch, Amir; Israeli, Moshe; Ravve, Igor

2003-04-01

Voids and cracks often occur in the interconnect lines of microelectronic devices. They increase the resistance of the circuits and may even lead to a fatal failure. Voids may occur inside a single grain, but often they appear on the boundary between two grains. In this work, we model and analyze numerically the migration and evolution of an intergranular void subjected to surface diffusion forces and external voltage applied to the interconnect. The grain-void interface is considered one-dimensional, and the physical formulation of the electromigration and diffusion model results in two coupled fourth-order one-dimensional time-dependent PDEs. The boundary conditions are specified at the triple points, which are common to both neighboring grains and the void. The solution of these equations uses a finite difference scheme in space and a Runge-Kutta integration scheme in time, and is also coupled to the solution of a static Laplace equation describing the voltage distribution throughout the grain. Since the voltage distribution is required only along the interface line, the two-dimensional discretization of the grain interior is not needed, and the static problem is solved by the boundary element method at each time step. The motion of the intergranular void was studied for different ratios between the diffusion and the electric field forces, and for different initial configurations of the void.

Analytical solutions of the one-dimensional advection-dispersion solute transport equation subject to time-dependent boundary conditions

USDA-ARS?s Scientific Manuscript database

Analytical solutions of the advection-dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective-dispersive transport subj...

Highly Parallel Alternating Directions Algorithm for Time Dependent Problems

NASA Astrophysics Data System (ADS)

Ganzha, M.; Georgiev, K.; Lirkov, I.; Margenov, S.; Paprzycki, M.

2011-11-01

In our work, we consider the time dependent Stokes equation on a finite time interval and on a uniform rectangular mesh, written in terms of velocity and pressure. For this problem, a parallel algorithm based on a novel direction splitting approach is developed. Here, the pressure equation is derived from a perturbed form of the continuity equation, in which the incompressibility constraint is penalized in a negative norm induced by the direction splitting. The scheme used in the algorithm is composed of two parts: (i) velocity prediction, and (ii) pressure correction. This is a Crank-Nicolson-type two-stage time integration scheme for two and three dimensional parabolic problems in which the second-order derivative, with respect to each space variable, is treated implicitly while the other variable is made explicit at each time sub-step. In order to achieve a good parallel performance the solution of the Poison problem for the pressure correction is replaced by solving a sequence of one-dimensional second order elliptic boundary value problems in each spatial direction. The parallel code is implemented using the standard MPI functions and tested on two modern parallel computer systems. The performed numerical tests demonstrate good level of parallel efficiency and scalability of the studied direction-splitting-based algorithm.

Breathing is different in the quantum world

NASA Astrophysics Data System (ADS)

Bonitz, Michael; Bauch, Sebastian; Balzer, Karsten; Henning, Christian; Hochstuhl, David

2009-11-01

Interacting classicle particles in a harmonic trap are known to possess a radial collective oscillation -- the breathing mode (BM). In case of Coulomb interaction its frequency is universal -- it is independent of the particle number and system dimensionality [1]. Here we study strongly correlated quantum systems. We report a qualitatively different breathing behavior: a quantum system has two BMs one of which is universal whereas the frequency of the other varies with system dimensionality, the particle spin and the strength of the pair interaction. The results are based on exact solutions of the time-dependent Schr"odinger equation for two particles and on time-dependent many-body results for larger particle numbers. Finally, we discuss experimental ways to excite and measure the breathing frequencies which should give direct access to key properties of trapped particles, including their many-body effects [2]. [4pt] [1] C. Henning et al., Phys. Rev. Lett. 101, 045002 (2008) [0pt] [2] S. Bauch, K. Balzer, C. Henning, and M. Bonitz, submitted to Phys. Rev. Lett., arXiv:0903.1993

Solution of 3-dimensional time-dependent viscous flows. Part 2: Development of the computer code

NASA Technical Reports Server (NTRS)

Weinberg, B. C.; Mcdonald, H.

1980-01-01

There is considerable interest in developing a numerical scheme for solving the time dependent viscous compressible three dimensional flow equations to aid in the design of helicopter rotors. The development of a computer code to solve a three dimensional unsteady approximate form of the Navier-Stokes equations employing a linearized block emplicit technique in conjunction with a QR operator scheme is described. Results of calculations of several Cartesian test cases are presented. The computer code can be applied to more complex flow fields such as these encountered on rotating airfoils.

Time dependent shear stress and temperature distribution over an insulated flat plate moving at hypersonic speed.

NASA Technical Reports Server (NTRS)

Rodkiewicz, C. M.; Gupta, R. N.

1971-01-01

The laminar two-dimensional flow over a stepwise accelerated flat plate moving with hypersonic speed at zero angle of attack is analysed. The governing equations in the self-similar form are linearized and solved numerically for small times. The solutions obtained are the deviations of the velocity and the temperature profiles from those of steady state. The presented results may be used to find the first order boundary layer induced pressure on the plate.

Two-dimensional correlation and codistribution spectroscopy (2DCOS and 2DCDS) analyses of time-dependent ATR IR spectra of D-glucose anomers undergoing mutarotation process in water

NASA Astrophysics Data System (ADS)

Noda, Isao

2018-05-01

Two cyclic diastereoisomeric structures, known as α- and β-anomers of D-glucose with different configurations around C1 with OH groups in axial or equitroial positions, undergo the mutarotation conversion to each other in water. Two-dimensional correlation and codistribution spectroscopy (2DCOS and 2DCDS) analyses were applied to the time-dependent ATR IR spectra of aqueous solutions of α- and β-D-glucose undergoing such mutarotation conversion. 2DCOS analysis reveals that the increase and decrease in the IR intensities after the dissolution of α- or β-D-glucose are not fully synchronized, suggesting the mutarotation of D-glucose in water is not a simple binary conversion process but a multi-step reaction involving an intermediate species with a finite and observable concentration level and lifetime. 2DCDS analysis of the time-dependent ATR IR spectra clearly demonstrated the presence of intermediate species contributing to the band positions overlapped close to bands for α- and β-D-glucose. The fact that band positions identified for the intermediate species for α- to β-D-glucose conversion are the same for the reverse reaction suggests that they arise from the same species, most likely the open-ring structure produced by the hydrolysis.

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

Dustin Popp; Zander Mausolff; Sedat Goluoglu

We are proposing to use the code, TDKENO, to model TREAT. TDKENO solves the time dependent, three dimensional Boltzmann transport equation with explicit representation of delayed neutrons. Instead of directly integrating this equation, the neutron flux is factored into two components – a rapidly varying amplitude equation and a slowly varying shape equation and each is solved separately on different time scales. The shape equation is solved using the 3D Monte Carlo transport code KENO, from Oak Ridge National Laboratory’s SCALE code package. Using the Monte Carlo method to solve the shape equation is still computationally intensive, but the operationmore » is only performed when needed. The amplitude equation is solved deterministically and frequently, so the solution gives an accurate time-dependent solution without having to repeatedly We have modified TDKENO to incorporate KENO-VI so that we may accurately represent the geometries within TREAT. This paper explains the motivation behind using generalized geometry, and provides the results of our modifications. TDKENO uses the Improved Quasi-Static method to accomplish this. In this method, the neutron flux is factored into two components. One component is a purely time-dependent and rapidly varying amplitude function, which is solved deterministically and very frequently (small time steps). The other is a slowly varying flux shape function that weakly depends on time and is only solved when needed (significantly larger time steps).« less

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

Bena, Iosif; Bobev, Nikolay; Warner, Nicholas P.

We discuss 'spectral-flow' coordinate transformations that take asymptotically four-dimensional solutions into other asymptotically four-dimensional solutions. We find that spectral flow can relate smooth three-charge solutions with a multicenter Taub-NUT base to solutions where one or several Taub-NUT centers are replaced by two-charge supertubes, and vice versa. We further show that multiparameter spectral flows can map such Taub-NUT centers to more singular centers that are either D2-D0 or pure D0-brane sources. Since supertubes can depend on arbitrary functions, we establish that the moduli space of smooth horizonless black-hole microstate solutions is classically of infinite dimension. We also use the physics ofmore » supertubes to argue that some multicenter solutions that appear to be bound states from a four-dimensional perspective are in fact not bound states when considered from a five- or six-dimensional perspective.« less

Hydrogen Bond Lifetimes and Energetics for Solute-Solvent Complexes Studied with 2D-IR Vibrational Echo Spectroscopy

PubMed Central

Zheng, Junrong; Fayer, Michael D.

2008-01-01

Weak π hydrogen bonded solute-solvent complexes are studied with ultrafast two dimensional infrared (2D-IR) vibrational echo chemical exchange spectroscopy, temperature dependent IR absorption spectroscopy, and density functional theory calculations. Eight solute-solvent complexes composed of a number of phenol derivatives and various benzene derivatives are investigated. The complexes are formed between the phenol derivative (solute) in a mixed solvent of the benzene derivative and CCl4. The time dependence of the 2D-IR vibrational echo spectra of the phenol hydroxyl stretch is used to directly determine the dissociation and formation rates of the hydrogen bonded complexes. The dissociation rates of the weak hydrogen bonds are found to be strongly correlated with their formation enthalpies. The correlation can be described with an equation similar to the Arrhenius equation. The results are discussed in terms of transition state theory. PMID:17373792

An exact solution of the Currie-Hill equations in 1 + 1 dimensional Minkowski space

NASA Astrophysics Data System (ADS)

Balog, János

2014-11-01

We present an exact two-particle solution of the Currie-Hill equations of Predictive Relativistic Mechanics in 1 + 1 dimensional Minkowski space. The instantaneous accelerations are given in terms of elementary functions depending on the relative particle position and velocities. The general solution of the equations of motion is given and by studying the global phase space of this system it is shown that this is a subspace of the full kinematic phase space.

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation.

PubMed

Liu, Wei; Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota's bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides.

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation

PubMed Central

Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota’s bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides. PMID:29432495

Implementation of one and three dimensional models for heat transfer coeffcient identification over the plate cooled by the circular water jets

NASA Astrophysics Data System (ADS)

Malinowski, Zbigniew; Cebo-Rudnicka, Agnieszka; Hadała, Beata; Szajding, Artur; Telejko, Tadeusz

2017-10-01

A cooling rate affects the mechanical properties of steel which strongly depend on microstructure evolution processes. The heat transfer boundary condition for the numerical simulation of steel cooling by water jets can be determined from the local one dimensional or from the three dimensional inverse solutions in space and time. In the present study the inconel plate has been heated to about 900 °C and then cooled by six circular water jets. The plate temperature has been measured by 30 thermocouples. The heat transfer coefficient and the heat flux distributions at the plate surface have been determined in time and space. The one dimensional solutions have given a local error to the heat transfer coefficient of about 35%. The three dimensional inverse solution has allowed reducing the local error to about 20%. The uncertainty test has confirmed that a better approximation of the heat transfer coefficient distribution over the cooled surface can be obtained even for limited number of thermocouples. In such a case it was necessary to constrain the inverse solution with the interpolated temperature sensors.

Fermion localization on a split brane

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

Chumbes, A. E. R.; Vasquez, A. E. O.; Hott, M. B.

2011-05-15

In this work we analyze the localization of fermions on a brane embedded in five-dimensional, warped and nonwarped, space-time. In both cases we use the same nonlinear theoretical model with a nonpolynomial potential featuring a self-interacting scalar field whose minimum energy solution is a soliton (a kink) which can be continuously deformed into a two-kink. Thus a single brane splits into two branes. The behavior of spin 1/2 fermions wave functions on the split brane depends on the coupling of fermions to the scalar field and on the geometry of the space-time.

Dark lump excitations in superfluid Fermi gases

NASA Astrophysics Data System (ADS)

Xu, Yan-Xia; Duan, Wen-Shan

2012-11-01

We study the linear and nonlinear properties of two-dimensional matter-wave pulses in disk-shaped superfluid Fermi gases. A Kadomtsev—Petviashvili I (KPI) solitary wave has been realized for superfluid Fermi gases in the limited cases of Bardeen—Cooper—Schrieffer (BCS) regime, Bose—Einstein condensate (BEC) regime, and unitarity regime. One-lump solution as well as one-line soliton solutions for the KPI equation are obtained, and two-line soliton solutions with the same amplitude are also studied in the limited cases. The dependence of the lump propagating velocity and the sound speed of two-dimensional superfluid Fermi gases on the interaction parameter are investigated for the limited cases of BEC and unitarity.

Bifurcations of solitary wave solutions for (two and three)-dimensional nonlinear partial differential equation in quantum and magnetized plasma by using two different methods

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-06-01

In this research, we study new two techniques that called the extended simple equation method and the novel (G‧/G) -expansion method. The extended simple equation method depend on the auxiliary equation (dϕ/dξ = α + λϕ + μϕ2) which has three ways for solving depends on the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (α = 0) this auxiliary equation reduces to Bernoulli equation and when (α ≠ 0, λ ≠ 0, μ ≠ 0) we the general solutions of this auxiliary equation while the novel (G‧/G) -expansion method depends also on similar auxiliary equation (G‧/G)‧ = μ + λ(G‧/G) + (v - 1)(G‧/G) 2 which depend also on the value of (λ2 - 4 (v - 1) μ) and the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (μ = 0) this auxiliary equation reduces to Bernoulli equation and when (λ2 ≠ 4 (v - 1) μ) we the general solutions of this auxiliary equation. This show how both of these auxiliary equation are special cases of Riccati equation. We apply these methods on two dimensional nonlinear Kadomtsev-Petviashvili Burgers equation in quantum plasma and three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. We obtain the exact traveling wave solutions of these important models and under special condition on the parameters, we get solitary traveling wave solutions. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions.

Stopping dynamics of ions passing through correlated honeycomb clusters

NASA Astrophysics Data System (ADS)

Balzer, Karsten; Schlünzen, Niclas; Bonitz, Michael

2016-12-01

A combined nonequilibrium Green functions-Ehrenfest dynamics approach is developed that allows for a time-dependent study of the energy loss of a charged particle penetrating a strongly correlated system at zero and finite temperatures. Numerical results are presented for finite inhomogeneous two-dimensional Fermi-Hubbard models, where the many-electron dynamics in the target are treated fully quantum mechanically and the motion of the projectile is treated classically. The simulations are based on the solution of the two-time Dyson (Keldysh-Kadanoff-Baym) equations using the second-order Born, third-order, and T -matrix approximations of the self-energy. As application, we consider protons and helium nuclei with a kinetic energy between 1 and 500 keV/u passing through planar fragments of the two-dimensional honeycomb lattice and, in particular, examine the influence of electron-electron correlations on the energy exchange between projectile and electron system. We investigate the time dependence of the projectile's kinetic energy (stopping power), the electron density, the double occupancy, and the photoemission spectrum. Finally, we show that, for a suitable choice of the Hubbard model parameters, the results for the stopping power are in fair agreement with ab initio simulations for particle irradiation of single-layer graphene.

A geometrical multi-scale numerical method for coupled hygro-thermo-mechanical problems in photovoltaic laminates.

PubMed

Lenarda, P; Paggi, M

A comprehensive computational framework based on the finite element method for the simulation of coupled hygro-thermo-mechanical problems in photovoltaic laminates is herein proposed. While the thermo-mechanical problem takes place in the three-dimensional space of the laminate, moisture diffusion occurs in a two-dimensional domain represented by the polymeric layers and by the vertical channel cracks in the solar cells. Therefore, a geometrical multi-scale solution strategy is pursued by solving the partial differential equations governing heat transfer and thermo-elasticity in the three-dimensional space, and the partial differential equation for moisture diffusion in the two dimensional domains. By exploiting a staggered scheme, the thermo-mechanical problem is solved first via a fully implicit solution scheme in space and time, with a specific treatment of the polymeric layers as zero-thickness interfaces whose constitutive response is governed by a novel thermo-visco-elastic cohesive zone model based on fractional calculus. Temperature and relative displacements along the domains where moisture diffusion takes place are then projected to the finite element model of diffusion, coupled with the thermo-mechanical problem by the temperature and crack opening dependent diffusion coefficient. The application of the proposed method to photovoltaic modules pinpoints two important physical aspects: (i) moisture diffusion in humidity freeze tests with a temperature dependent diffusivity is a much slower process than in the case of a constant diffusion coefficient; (ii) channel cracks through Silicon solar cells significantly enhance moisture diffusion and electric degradation, as confirmed by experimental tests.

Gray and multigroup radiation transport models for two-dimensional binary stochastic media using effective opacities

DOE PAGES

Olson, Gordon L.

2015-09-24

One-dimensional models for the transport of radiation through binary stochastic media do not work in multi-dimensions. In addition, authors have attempted to modify or extend the 1D models to work in multidimensions without success. Analytic one-dimensional models are successful in 1D only when assuming greatly simplified physics. State of the art theories for stochastic media radiation transport do not address multi-dimensions and temperature-dependent physics coefficients. Here, the concept of effective opacities and effective heat capacities is found to well represent the ensemble averaged transport solutions in cases with gray or multigroup temperature-dependent opacities and constant or temperature-dependent heat capacities. Inmore » every case analyzed here, effective physics coefficients fit the transport solutions over a useful range of parameter space. The transport equation is solved with the spherical harmonics method with angle orders of n=1 and 5. Although the details depend on what order of solution is used, the general results are similar, independent of angular order.« less

Gray and multigroup radiation transport models for two-dimensional binary stochastic media using effective opacities

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

Olson, Gordon L.

One-dimensional models for the transport of radiation through binary stochastic media do not work in multi-dimensions. In addition, authors have attempted to modify or extend the 1D models to work in multidimensions without success. Analytic one-dimensional models are successful in 1D only when assuming greatly simplified physics. State of the art theories for stochastic media radiation transport do not address multi-dimensions and temperature-dependent physics coefficients. Here, the concept of effective opacities and effective heat capacities is found to well represent the ensemble averaged transport solutions in cases with gray or multigroup temperature-dependent opacities and constant or temperature-dependent heat capacities. Inmore » every case analyzed here, effective physics coefficients fit the transport solutions over a useful range of parameter space. The transport equation is solved with the spherical harmonics method with angle orders of n=1 and 5. Although the details depend on what order of solution is used, the general results are similar, independent of angular order.« less

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Blanchard, D. K.

1975-01-01

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Particle paths and phase plane for time-dependent similarity solutions of the one-dimensional Vlasov-Maxwell equations

NASA Technical Reports Server (NTRS)

Roberts, Dana Aaron; Abraham-Shrauner, Barbara

1987-01-01

The phase trajectories of particles in a plasma described by the one-dimensional Vlasov-Maxwell equations are determined qualitatively, analyzing exact general similarity solutions for the cases of temporally damped and growing (sinusoidal or localized) electric fields. The results of numerical integration in both untransformed and Lie-group point-transformed coordinates are presented in extensive graphs and characterized in detail. The implications of the present analysis for the stability of BGK equilibria are explored, and the existence of nonlinear solutions arbitrarily close to and significantly different from the BGK solutions is demonstrated.

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

Dehghani, M.H.; Research Institute for Astrophysics and Astronomy of Maragha; Khodam-Mohammadi, A.

First, we construct the Taub-NUT/bolt solutions of (2k+2)-dimensional Einstein-Maxwell gravity, when all the factor spaces of 2k-dimensional base space B have positive curvature. These solutions depend on two extra parameters, other than the mass and the NUT charge. These are electric charge q and electric potential at infinity V. We investigate the existence of Taub-NUT solutions and find that in addition to the two conditions of uncharged NUT solutions, there exist two extra conditions. These two extra conditions come from the regularity of vector potential at r=N and the fact that the horizon at r=N should be the outer horizonmore » of the NUT charged black hole. We find that the NUT solutions in 2k+2 dimensions have no curvature singularity at r=N, when the 2k-dimensional base space is chosen to be CP{sup 2k}. For bolt solutions, there exists an upper limit for the NUT parameter which decreases as the potential parameter increases. Second, we study the thermodynamics of these spacetimes. We compute temperature, entropy, charge, electric potential, action and mass of the black hole solutions, and find that these quantities satisfy the first law of thermodynamics. We perform a stability analysis by computing the heat capacity, and show that the NUT solutions are not thermally stable for even k's, while there exists a stable phase for odd k's, which becomes increasingly narrow with increasing dimensionality and wide with increasing V. We also study the phase behavior of the 4 and 6 dimensional bolt solutions in canonical ensemble and find that these solutions have a stable phase, which becomes smaller as V increases.« less

A two-dimensional MHD global coronal model - Steady-state streamers

NASA Technical Reports Server (NTRS)

Wang, A.-H.; Wu, S. T.; Suess, S. T.; Poletto, G.

1992-01-01

A 2D, time-dependent, numerical, MHD model for the simulation of coronal streamers from the solar surface to 15 solar is presented. Three examples are given; for dipole, quadrupole and hexapole (Legendre polynomials P1, P2, and P3) initial field topologies. The computed properties are density, temperature, velocity, and magnetic field. The calculation is set up as an initial-boundary value problem wherein a relaxation in time produces the steady state solution. In addition to the properties of the solutions, their accuracy is discussed. Besides solutions for dipole, quadrupole, and hexapole geometries, the model use of realistic values for the density and Alfven speed while still meeting the requirement that the flow speed be super-Alfvenic at the outer boundary by extending the outer boundary to 15 solar radii.

Progress in the Simulation of Steady and Time-Dependent Flows with 3D Parallel Unstructured Cartesian Methods

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Berger, M. J.; Murman, S. M.; Kwak, Dochan (Technical Monitor)

2002-01-01

The proposed paper will present recent extensions in the development of an efficient Euler solver for adaptively-refined Cartesian meshes with embedded boundaries. The paper will focus on extensions of the basic method to include solution adaptation, time-dependent flow simulation, and arbitrary rigid domain motion. The parallel multilevel method makes use of on-the-fly parallel domain decomposition to achieve extremely good scalability on large numbers of processors, and is coupled with an automatic coarse mesh generation algorithm for efficient processing by a multigrid smoother. Numerical results are presented demonstrating parallel speed-ups of up to 435 on 512 processors. Solution-based adaptation may be keyed off truncation error estimates using tau-extrapolation or a variety of feature detection based refinement parameters. The multigrid method is extended to for time-dependent flows through the use of a dual-time approach. The extension to rigid domain motion uses an Arbitrary Lagrangian-Eulerlarian (ALE) formulation, and results will be presented for a variety of two- and three-dimensional example problems with both simple and complex geometry.

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Yi-Tsann

1993-01-01

A general solution adaptive scheme-based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Yi-Tsann; Usab, William J., Jr.

1993-01-01

A general solution adaptive scheme based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Uncertainty propagation by using spectral methods: A practical application to a two-dimensional turbulence fluid model

NASA Astrophysics Data System (ADS)

Riva, Fabio; Milanese, Lucio; Ricci, Paolo

2017-10-01

To reduce the computational cost of the uncertainty propagation analysis, which is used to study the impact of input parameter variations on the results of a simulation, a general and simple to apply methodology based on decomposing the solution to the model equations in terms of Chebyshev polynomials is discussed. This methodology, based on the work by Scheffel [Am. J. Comput. Math. 2, 173-193 (2012)], approximates the model equation solution with a semi-analytic expression that depends explicitly on time, spatial coordinates, and input parameters. By employing a weighted residual method, a set of nonlinear algebraic equations for the coefficients appearing in the Chebyshev decomposition is then obtained. The methodology is applied to a two-dimensional Braginskii model used to simulate plasma turbulence in basic plasma physics experiments and in the scrape-off layer of tokamaks, in order to study the impact on the simulation results of the input parameter that describes the parallel losses. The uncertainty that characterizes the time-averaged density gradient lengths, time-averaged densities, and fluctuation density level are evaluated. A reasonable estimate of the uncertainty of these distributions can be obtained with a single reduced-cost simulation.

Hydration of an apolar solute in a two-dimensional waterlike lattice fluid

NASA Astrophysics Data System (ADS)

Buzano, C.; de Stefanis, E.; Pretti, M.

2005-05-01

In a previous work, we investigated a two-dimensional lattice-fluid model, displaying some waterlike thermodynamic anomalies. The model, defined on a triangular lattice, is now extended to aqueous solutions with apolar species. Water molecules are of the “Mercedes Benz” type, i.e., they possess a D3 (equilateral triangle) symmetry, with three equivalent bonding arms. Bond formation depends both on orientation and local density. The insertion of inert molecules displays typical signatures of hydrophobic hydration: large positive transfer free energy, large negative transfer entropy (at low temperature), strong temperature dependence of the transfer enthalpy and entropy, i.e., large (positive) transfer heat capacity. Model properties are derived by a generalized first order approximation on a triangle cluster.

Hydration of an apolar solute in a two-dimensional waterlike lattice fluid.

PubMed

Buzano, C; De Stefanis, E; Pretti, M

2005-05-01

In a previous work, we investigated a two-dimensional lattice-fluid model, displaying some waterlike thermodynamic anomalies. The model, defined on a triangular lattice, is now extended to aqueous solutions with apolar species. Water molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three equivalent bonding arms. Bond formation depends both on orientation and local density. The insertion of inert molecules displays typical signatures of hydrophobic hydration: large positive transfer free energy, large negative transfer entropy (at low temperature), strong temperature dependence of the transfer enthalpy and entropy, i.e., large (positive) transfer heat capacity. Model properties are derived by a generalized first order approximation on a triangle cluster.

A cross-diffusion system derived from a Fokker-Planck equation with partial averaging

NASA Astrophysics Data System (ADS)

Jüngel, Ansgar; Zamponi, Nicola

2017-02-01

A cross-diffusion system for two components with a Laplacian structure is analyzed on the multi-dimensional torus. This system, which was recently suggested by P.-L. Lions, is formally derived from a Fokker-Planck equation for the probability density associated with a multi-dimensional Itō process, assuming that the diffusion coefficients depend on partial averages of the probability density with exponential weights. A main feature is that the diffusion matrix of the limiting cross-diffusion system is generally neither symmetric nor positive definite, but its structure allows for the use of entropy methods. The global-in-time existence of positive weak solutions is proved and, under a simplifying assumption, the large-time asymptotics is investigated.

Manipulating matter rogue waves and breathers in Bose-Einstein condensates.

PubMed

Manikandan, K; Muruganandam, P; Senthilvelan, M; Lakshmanan, M

2014-12-01

We construct higher-order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps: (i) the time-independent expulsive trap, (ii) time-dependent monotonous trap, and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second- and third-order rogue waves transform into the first-order-like rogue waves. We also analyze the density profiles of breather solutions. Here we also show that the shapes of the breathers change when we tune the strength of the trap parameter. Our results may help to manage rogue waves experimentally in a BEC system.

Adjoint shape optimization for fluid-structure interaction of ducted flows

NASA Astrophysics Data System (ADS)

Heners, J. P.; Radtke, L.; Hinze, M.; Düster, A.

2018-03-01

Based on the coupled problem of time-dependent fluid-structure interaction, equations for an appropriate adjoint problem are derived by the consequent use of the formal Lagrange calculus. Solutions of both primal and adjoint equations are computed in a partitioned fashion and enable the formulation of a surface sensitivity. This sensitivity is used in the context of a steepest descent algorithm for the computation of the required gradient of an appropriate cost functional. The efficiency of the developed optimization approach is demonstrated by minimization of the pressure drop in a simple two-dimensional channel flow and in a three-dimensional ducted flow surrounded by a thin-walled structure.

Stratified Shear Flows In Pipe Geometries

NASA Astrophysics Data System (ADS)

Harabin, George; Camassa, Roberto; McLaughlin, Richard; UNC Joint Fluids Lab Team Team

2015-11-01

Exact and series solutions to the full Navier-Stokes equations coupled to the advection diffusion equation are investigated in tilted three-dimensional pipe geometries. Analytic techniques for studying the three-dimensional problem provide a means for tackling interesting questions such as the optimal domain for mass transport, and provide new avenues for experimental investigation of diffusion driven flows. Both static and time dependent solutions will be discussed. NSF RTG DMS-0943851, NSF RTG ARC-1025523, NSF DMS-1009750.

Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

NASA Astrophysics Data System (ADS)

Muruganandam, P.; Adhikari, S. K.

2009-10-01

Here we develop simple numerical algorithms for both stationary and non-stationary solutions of the time-dependent Gross-Pitaevskii (GP) equation describing the properties of Bose-Einstein condensates at ultra low temperatures. In particular, we consider algorithms involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method. In a one-space-variable form of the GP equation we consider the one-dimensional, two-dimensional circularly-symmetric, and the three-dimensional spherically-symmetric harmonic-oscillator traps. In the two-space-variable form we consider the GP equation in two-dimensional anisotropic and three-dimensional axially-symmetric traps. The fully-anisotropic three-dimensional GP equation is also considered. Numerical results for the chemical potential and root-mean-square size of stationary states are reported using imaginary-time propagation programs for all the cases and compared with previously obtained results. Also presented are numerical results of non-stationary oscillation for different trap symmetries using real-time propagation programs. A set of convenient working codes developed in Fortran 77 are also provided for all these cases (twelve programs in all). In the case of two or three space variables, Fortran 90/95 versions provide some simplification over the Fortran 77 programs, and these programs are also included (six programs in all). Program summaryProgram title: (i) imagetime1d, (ii) imagetime2d, (iii) imagetime3d, (iv) imagetimecir, (v) imagetimesph, (vi) imagetimeaxial, (vii) realtime1d, (viii) realtime2d, (ix) realtime3d, (x) realtimecir, (xi) realtimesph, (xii) realtimeaxial Catalogue identifier: AEDU_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDU_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 122 907 No. of bytes in distributed program, including test data, etc.: 609 662 Distribution format: tar.gz Programming language: FORTRAN 77 and Fortran 90/95 Computer: PC Operating system: Linux, Unix RAM: 1 GByte (i, iv, v), 2 GByte (ii, vi, vii, x, xi), 4 GByte (iii, viii, xii), 8 GByte (ix) Classification: 2.9, 4.3, 4.12 Nature of problem: These programs are designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-, two- or three-space dimensions with a harmonic, circularly-symmetric, spherically-symmetric, axially-symmetric or anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Solution method: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation, in either imaginary or real time, over small time steps. The method yields the solution of stationary and/or non-stationary problems. Additional comments: This package consists of 12 programs, see "Program title", above. FORTRAN77 versions are provided for each of the 12 and, in addition, Fortran 90/95 versions are included for ii, iii, vi, viii, ix, xii. For the particular purpose of each program please see the below. Running time: Minutes on a medium PC (i, iv, v, vii, x, xi), a few hours on a medium PC (ii, vi, viii, xii), days on a medium PC (iii, ix). Program summary (1)Title of program: imagtime1d.F Title of electronic file: imagtime1d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-space dimension with a harmonic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (2)Title of program: imagtimecir.F Title of electronic file: imagtimecir.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with a circularly-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (3)Title of program: imagtimesph.F Title of electronic file: imagtimesph.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with a spherically-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (4)Title of program: realtime1d.F Title of electronic file: realtime1d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-space dimension with a harmonic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (5)Title of program: realtimecir.F Title of electronic file: realtimecir.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with a circularly-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (6)Title of program: realtimesph.F Title of electronic file: realtimesph.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with a spherically-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (7)Title of programs: imagtimeaxial.F and imagtimeaxial.f90 Title of electronic file: imagtimeaxial.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an axially-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (8)Title of program: imagtime2d.F and imagtime2d.f90 Title of electronic file: imagtime2d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (9)Title of program: realtimeaxial.F and realtimeaxial.f90 Title of electronic file: realtimeaxial.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time Hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an axially-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (10)Title of program: realtime2d.F and realtime2d.f90 Title of electronic file: realtime2d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (11)Title of program: imagtime3d.F and imagtime3d.f90 Title of electronic file: imagtime3d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few days on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (12)Title of program: realtime3d.F and realtime3d.f90 Title of electronic file: realtime3d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum Ram Memory: 8 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Days on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems.

Preliminary Results for the OECD/NEA Time Dependent Benchmark using Rattlesnake, Rattlesnake-IQS and TDKENO

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

DeHart, Mark D.; Mausolff, Zander; Weems, Zach

2016-08-01

One goal of the MAMMOTH M&S project is to validate the analysis capabilities within MAMMOTH. Historical data has shown limited value for validation of full three-dimensional (3D) multi-physics methods. Initial analysis considered the TREAT startup minimum critical core and one of the startup transient tests. At present, validation is focusing on measurements taken during the M8CAL test calibration series. These exercises will valuable in preliminary assessment of the ability of MAMMOTH to perform coupled multi-physics calculations; calculations performed to date are being used to validate the neutron transport solver Rattlesnake\\cite{Rattlesnake} and the fuels performance code BISON. Other validation projects outsidemore » of TREAT are available for single-physics benchmarking. Because the transient solution capability of Rattlesnake is one of the key attributes that makes it unique for TREAT transient simulations, validation of the transient solution of Rattlesnake using other time dependent kinetics benchmarks has considerable value. The Nuclear Energy Agency (NEA) of the Organization for Economic Cooperation and Development (OECD) has recently developed a computational benchmark for transient simulations. This benchmark considered both two-dimensional (2D) and 3D configurations for a total number of 26 different transients. All are negative reactivity insertions, typically returning to the critical state after some time.« less

Type IIB Colliding Plane Waves

NASA Astrophysics Data System (ADS)

Gutperle, M.; Pioline, B.

2003-09-01

Four-dimensional colliding plane wave (CPW) solutions have played an important role in understanding the classical non-linearities of Einstein's equations. In this note, we investigate CPW solutions in 2n+2-dimensional Einstein gravity with a n+1-form flux. By using an isomorphism with the four-dimensional problem, we construct exact solutions analogous to the Szekeres vacuum solution in four dimensions. The higher-dimensional versions of the Khan-Penrose and Bell-Szekeres CPW solutions are studied perturbatively in the vicinity of the light-cone. We find that under small perturbations, a curvature singularity is generically produced, leading to both space-like and time-like singularities. For n = 4, our results pertain to the collision of two ten-dimensional type-IIB Blau-Figueroa o'Farrill-Hull-Papadopoulos plane waves.

An Analytical Solution for Transient Thermal Response of an Insulated Structure

NASA Technical Reports Server (NTRS)

Blosser, Max L.

2012-01-01

An analytical solution was derived for the transient response of an insulated aerospace vehicle structure subjected to a simplified heat pulse. This simplified problem approximates the thermal response of a thermal protection system of an atmospheric entry vehicle. The exact analytical solution is solely a function of two non-dimensional parameters. A simpler function of these two parameters was developed to approximate the maximum structural temperature over a wide range of parameter values. Techniques were developed to choose constant, effective properties to represent the relevant temperature and pressure-dependent properties for the insulator and structure. A technique was also developed to map a time-varying surface temperature history to an equivalent square heat pulse. Using these techniques, the maximum structural temperature rise was calculated using the analytical solutions and shown to typically agree with finite element simulations within 10 to 20 percent over the relevant range of parameters studied.

Two-dimensional correlation and codistribution spectroscopy (2DCOS and 2DCDS) analyses of time-dependent ATR IR spectra of d-glucose anomers undergoing mutarotation process in water.

PubMed

Noda, Isao

2018-05-15

Two cyclic diastereoisomeric structures, known as α- and β-anomers of d-glucose with different configurations around C1 with OH groups in axial or equitroial positions, undergo the mutarotation conversion to each other in water. Two-dimensional correlation and codistribution spectroscopy (2DCOS and 2DCDS) analyses were applied to the time-dependent ATR IR spectra of aqueous solutions of α- and β-d-glucose undergoing such mutarotation conversion. 2DCOS analysis reveals that the increase and decrease in the IR intensities after the dissolution of α- or β-d-glucose are not fully synchronized, suggesting the mutarotation of d-glucose in water is not a simple binary conversion process but a multi-step reaction involving an intermediate species with a finite and observable concentration level and lifetime. 2DCDS analysis of the time-dependent ATR IR spectra clearly demonstrated the presence of intermediate species contributing to the band positions overlapped close to bands for α- and β-d-glucose. The fact that band positions identified for the intermediate species for α- to β-d-glucose conversion are the same for the reverse reaction suggests that they arise from the same species, most likely the open-ring structure produced by the hydrolysis. Copyright © 2017 Elsevier B.V. All rights reserved.

Large-Time Behavior of Solutions to Vlasov-Poisson-Fokker-Planck Equations: From Evanescent Collisions to Diffusive Limit

NASA Astrophysics Data System (ADS)

Herda, Maxime; Rodrigues, L. Miguel

2018-03-01

The present contribution investigates the dynamics generated by the two-dimensional Vlasov-Poisson-Fokker-Planck equation for charged particles in a steady inhomogeneous background of opposite charges. We provide global in time estimates that are uniform with respect to initial data taken in a bounded set of a weighted L^2 space, and where dependencies on the mean-free path τ and the Debye length δ are made explicit. In our analysis the mean free path covers the full range of possible values: from the regime of evanescent collisions τ → ∞ to the strongly collisional regime τ → 0. As a counterpart, the largeness of the Debye length, that enforces a weakly nonlinear regime, is used to close our nonlinear estimates. Accordingly we pay a special attention to relax as much as possible the τ -dependent constraint on δ ensuring exponential decay with explicit τ -dependent rates towards the stationary solution. In the strongly collisional limit τ → 0, we also examine all possible asymptotic regimes selected by a choice of observation time scale. Here also, our emphasis is on strong convergence, uniformity with respect to time and to initial data in bounded sets of a L^2 space. Our proofs rely on a detailed study of the nonlinear elliptic equation defining stationary solutions and a careful tracking and optimization of parameter dependencies of hypocoercive/hypoelliptic estimates.

Aspects of noncommutative (1+1)-dimensional black holes

NASA Astrophysics Data System (ADS)

Mureika, Jonas R.; Nicolini, Piero

2011-08-01

We present a comprehensive analysis of the spacetime structure and thermodynamics of (1+1)-dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length θ cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scales. Depending on the choice of input parameters (black hole mass M, cosmological constant Λ, etc.), black hole solutions with zero, up to six, horizons are possible. The associated thermodynamics allows for the either complete evaporation, or the production of black hole remnants.

What is integrability of discrete variational systems?

PubMed

Boll, Raphael; Petrera, Matteo; Suris, Yuri B

2014-02-08

We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however, having its more remote roots in the theory of pluriharmonic functions, in the Z -invariant models of statistical mechanics and their quasiclassical limit, as well as in the theory of variational symmetries going back to Noether. A d -dimensional pluri-Lagrangian problem can be described as follows: given a d -form [Formula: see text] on an m -dimensional space (called multi-time, m > d ), whose coefficients depend on a sought-after function x of m independent variables (called field), find those fields x which deliver critical points to the action functionals [Formula: see text] for any d -dimensional manifold Σ in the multi-time. We derive the main building blocks of the multi-time Euler-Lagrange equations for a discrete pluri-Lagrangian problem with d =2, the so-called corner equations, and discuss the notion of consistency of the system of corner equations. We analyse the system of corner equations for a special class of three-point two-forms, corresponding to integrable quad-equations of the ABS list. This allows us to close a conceptual gap of the work by Lobb and Nijhoff by showing that the corresponding two-forms are closed not only on solutions of (non-variational) quad-equations, but also on general solutions of the corresponding corner equations. We also find an example of a pluri-Lagrangian system not coming from a multi-dimensionally consistent system of quad-equations.

What is integrability of discrete variational systems?

PubMed Central

Boll, Raphael; Petrera, Matteo; Suris, Yuri B.

2014-01-01

We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however, having its more remote roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics and their quasiclassical limit, as well as in the theory of variational symmetries going back to Noether. A d-dimensional pluri-Lagrangian problem can be described as follows: given a d-form on an m-dimensional space (called multi-time, m>d), whose coefficients depend on a sought-after function x of m independent variables (called field), find those fields x which deliver critical points to the action functionals for any d-dimensional manifold Σ in the multi-time. We derive the main building blocks of the multi-time Euler–Lagrange equations for a discrete pluri-Lagrangian problem with d=2, the so-called corner equations, and discuss the notion of consistency of the system of corner equations. We analyse the system of corner equations for a special class of three-point two-forms, corresponding to integrable quad-equations of the ABS list. This allows us to close a conceptual gap of the work by Lobb and Nijhoff by showing that the corresponding two-forms are closed not only on solutions of (non-variational) quad-equations, but also on general solutions of the corresponding corner equations. We also find an example of a pluri-Lagrangian system not coming from a multi-dimensionally consistent system of quad-equations. PMID:24511254

The effect of disinfectants on dimensional stability of addition and condensation silicone impressions.

PubMed

Sinobad, Tamara; Obradović-Djuricić, Kosovka; Nikolić, Zoran; Dodić, Slobodan; Lazić, Vojkan; Sinobad, Vladimir; Jesenko-Rokvić, Aleksandra

2014-03-01

Dimensional stability and accuracy of an impression after chemical disinfection by immersion in disinfectants are crucial for the accuracy of final prosthetic restorations. The aim of this study was to assess the deformation of addition and condensation silicone impressions after disinfection in antimicrobial solutions. A total of 120 impressions were made on the model of the upper arch representing three full metal-ceramic crown preparations. Four impression materials were used: two condensation silicones (Oranwash L - Zhermack and Xantopren L Blue - Heraeus Kulzer) and two addition silicones (Elite H-D + regular body - Zhermack and Flexitime correct flow - Heraeus Kulzer). After removal from the model the impressions were immediatel immersed in appropriate disinfectant (glutaraldehyde, benzalkonium chloride - Sterigum and 5.25% NaOC1) for a period of 10 min. The control group consisted of samples that were not treated with disinfectant solution. Consecutive measurements of identical impressions were realized with a Canon G9 (12 megapixels, 2 fps, 6x/24x), and automated with a computer Asus Lamborghini VX-2R Intel C2D 2.4 GHz, by using Remote Capture software package, so that time-depending series of images of the same impression were obtained. The dimensional changes of all the samples were significant both as a function of time and the applied disinfectant. The results show significant differences of the obtained dimensional changes between the group of condensation silicones and the group of addition silicones for the same time, and the same applied disinfectant (p = 0.026, F = 3.95). The greatest dimensional changes of addition and condensation silicone impressions appear in the first hour after their separation from the model.

Numerical Simulation of Interaction of Human Vocal Folds and Fluid Flow

NASA Astrophysics Data System (ADS)

Kosík, A.; Feistauer, M.; Horáček, J.; Sváček, P.

Our goal is to simulate airflow in human vocal folds and their flow-induced vibrations. We consider two-dimensional viscous incompressible flow in a time-dependent domain. The fluid flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian formulation. The flow problem is coupled with the elastic behaviour of the solid bodies. The developed solution of the coupled problem based on the finite element method is demonstrated by numerical experiments.

Correlation between discrete probability and reaction front propagation rate in heterogeneous mixtures

NASA Astrophysics Data System (ADS)

Naine, Tarun Bharath; Gundawar, Manoj Kumar

2017-09-01

We demonstrate a very powerful correlation between the discrete probability of distances of neighboring cells and thermal wave propagation rate, for a system of cells spread on a one-dimensional chain. A gamma distribution is employed to model the distances of neighboring cells. In the absence of an analytical solution and the differences in ignition times of adjacent reaction cells following non-Markovian statistics, invariably the solution for thermal wave propagation rate for a one-dimensional system with randomly distributed cells is obtained by numerical simulations. However, such simulations which are based on Monte-Carlo methods require several iterations of calculations for different realizations of distribution of adjacent cells. For several one-dimensional systems, differing in the value of shaping parameter of the gamma distribution, we show that the average reaction front propagation rates obtained by a discrete probability between two limits, shows excellent agreement with those obtained numerically. With the upper limit at 1.3, the lower limit depends on the non-dimensional ignition temperature. Additionally, this approach also facilitates the prediction of burning limits of heterogeneous thermal mixtures. The proposed method completely eliminates the need for laborious, time intensive numerical calculations where the thermal wave propagation rates can now be calculated based only on macroscopic entity of discrete probability.

Symmetry breaking motion of a vortex pair in a driven cavity

NASA Astrophysics Data System (ADS)

McHugh, John; Osman, Kahar; Farias, Jason

2002-11-01

The two-dimensional driven cavity problem with an anti-symmetric sinusoidal forcing has been found to exhibit a subcritical symmetry breaking bifurcation (Farias and McHugh, Phys. Fluids, 2002). Equilibrium solutions are either a symmetric vortex pair or an asymmetric motion. The asymmetric motion is an asymmetric vortex pair at low Reynolds numbers, but merges into a three vortex motion at higher Reynolds numbers. The asymmetric solution is obtained by initiating the flow with a single vortex centered in the domain. Symmetric motion is obtained with no initial vortex, or weak initial vortex. The steady three-vortex motion occurs at a Reynolds number of approximately 3000, where the symmetric vortex pair has already gone through a Hopf bifurcation. Further two-dimensional results show that forcing with two full oscillations across the top of the cavity results in two steady vortex motions, depending on initial conditions. Three-dimensional results have even more steady solutions. The results are computational and theoretical.

SUTRA (Saturated-Unsaturated Transport). A Finite-Element Simulation Model for Saturated-Unsaturated, Fluid-Density-Dependent Ground-Water Flow with Energy Transport or Chemically-Reactive Single-Species Solute Transport.

DTIC Science & Technology

1984-12-30

as three dimensional, when the assumption is made that all SUTRA parameters and coefficients have a constant value in the third space direction. A...finite element. The type of element employed by SUTRA for two-dimensional simulation is a quadrilateral which has a finite thickness in the third ... space dimension. This type of a quad- rilateral element and a typical two-dimensional mesh is shown in Figure 3.1. - All twelve edges of the two

Time-evolving bubbles in two-dimensional stokes flow

NASA Technical Reports Server (NTRS)

Tanveer, Saleh; Vasconcelos, Giovani L.

1994-01-01

A general class of exact solutions is presented for a time evolving bubble in a two-dimensional slow viscous flow in the presence of surface tension. These solutions can describe a bubble in a linear shear flow as well as an expanding or contracting bubble in an otherwise quiescent flow. In the case of expanding bubbles, the solutions have a simple behavior in the sense that for essentially arbitrary initial shapes the bubble will asymptote an expanding circle. Contracting bubbles, on the other hand, can develop narrow structures ('near-cusps') on the interface and may undergo 'break up' before all the bubble-fluid is completely removed. The mathematical structure underlying the existence of these exact solutions is also investigated.

Analytic study of solutions for a (3 + 1) -dimensional generalized KP equation

NASA Astrophysics Data System (ADS)

Gao, Hui; Cheng, Wenguang; Xu, Tianzhou; Wang, Gangwei

2018-03-01

The (3 + 1) -dimensional generalized KP (gKP) equation is an important nonlinear partial differential equation in theoretical and mathematical physics which can be used to describe nonlinear wave motion. Through the Hirota bilinear method, one-solition, two-solition and N-solition solutions are derived via symbolic computation. Two classes of lump solutions, rationally localized in all directions in space, to the dimensionally reduced cases in (2 + 1)-dimensions, are constructed by using a direct method based on the Hirota bilinear form of the equation. It implies that we can derive the lump solutions of the reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Meanwhile, we get interaction solutions between a lump and a kink of the gKP equation. The lump appears from a kink and is swallowed by it with the change of time. This work offers a possibility which can enrich the variety of the dynamical features of solutions for higher-dimensional nonlinear evolution equations.

High performance Solid Rocket Motor (SRM) submerged nozzle/combustion cavity flowfield assessment

NASA Technical Reports Server (NTRS)

Freeman, J. A.; Chan, J. S.; Murph, J. E.; Xiques, K. E.

1987-01-01

Two and three dimensional internal flowfield solutions for critical points in the Space Shuttle solid rocket booster burn time were developed using the Lockheed Huntsville GIM/PAID Navier-Stokes solvers. These perfect gas, viscous solutions for the high performance motor characterize the flow in the aft segment and nozzle of the booster. Two dimensional axisymmetric solutions were developed at t = 20 and t = 85 sec motor burn times. The t = 85 sec solution indicates that the aft segment forward inhibitor stub produces vortices with are shed and convected downwards. A three dimensional 3.5 deg gimbaled nozzle flowfield solution was developed for the aft segment and nozzle at t = 9 sec motor burn time. This perfect gas, viscous analysis, provided a steady state solution for the core region and the flow through the nozzle, but indicated that unsteady flow exists in the region under the nozzle nose and near the flexible boot and nozzle/case joint. The flow in the nozzle/case joint region is characterized by low magnitude pressure waves which travel in the circumferential direction. From the two and three dimensional flowfield calculations presented it can be concluded that there is no evidence from these results that steady state gas dynamics is the primary mechanism resulting in the nozzle pocketing erosion experienced on SRM nozzles 8A or 17B. The steady state flowfield results indicate pocketing erosion is not directly initiated by a steady state gas dynamics phenomenon.

A meshless method using radial basis functions for numerical solution of the two-dimensional KdV-Burgers equation

NASA Astrophysics Data System (ADS)

Zabihi, F.; Saffarian, M.

2016-07-01

The aim of this article is to obtain the numerical solution of the two-dimensional KdV-Burgers equation. We construct the solution by using a different approach, that is based on using collocation points. The solution is based on using the thin plate splines radial basis function, which builds an approximated solution with discretizing the time and the space to small steps. We use a predictor-corrector scheme to avoid solving the nonlinear system. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.

Further investigation of a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

NASA Technical Reports Server (NTRS)

Weatherill, W. H.; Ehlers, F. E.; Yip, E.; Sebastian, J. D.

1980-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.

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.

Overview of the relevant CFD work at Thiokol Corporation

NASA Technical Reports Server (NTRS)

Chwalowski, Pawel; Loh, Hai-Tien

1992-01-01

An in-house developed proprietary advanced computational fluid dynamics code called SHARP (Trademark) is a primary tool for many flow simulations and design analyses. The SHARP code is a time dependent, two dimensional (2-D) axisymmetric numerical solution technique for the compressible Navier-Stokes equations. The solution technique in SHARP uses a vectorizable implicit, second order accurate in time and space, finite volume scheme based on an upwind flux-difference splitting of a Roe-type approximated Riemann solver, Van Leer's flux vector splitting, and a fourth order artificial dissipation scheme with a preconditioning to accelerate the flow solution. Turbulence is simulated by an algebraic model, and ultimately the kappa-epsilon model. Some other capabilities of the code are 2-D two-phase Lagrangian particle tracking and cell blockages. Extensive development and testing has been conducted on the 3-D version of the code with flow, combustion, and turbulence interactions. The emphasis here is on the specific applications of SHARP in Solid Rocket Motor design. Information is given in viewgraph form.

Loss of Energy Concentration in Nonlinear Evolution Beam Equations

NASA Astrophysics Data System (ADS)

Garrione, Maurizio; Gazzola, Filippo

2017-12-01

Motivated by the oscillations that were seen at the Tacoma Narrows Bridge, we introduce the notion of solutions with a prevailing mode for the nonlinear evolution beam equation u_{tt} + u_{xxxx} + f(u)= g(x, t) in bounded space-time intervals. We give a new definition of instability for these particular solutions, based on the loss of energy concentration on their prevailing mode. We distinguish between two different forms of energy transfer, one physiological (unavoidable and depending on the nonlinearity) and one due to the insurgence of instability. We then prove a theoretical result allowing to reduce the study of this kind of infinite-dimensional stability to that of a finite-dimensional approximation. With this background, we study the occurrence of instability for three different kinds of nonlinearities f and for some forcing terms g, highlighting some of their structural properties and performing some numerical simulations.

AdS3 to dS3 transition in the near horizon of asymptotically de Sitter solutions

NASA Astrophysics Data System (ADS)

Sadeghian, S.; Vahidinia, M. H.

2017-08-01

We consider two solutions of Einstein-Λ theory which admit the extremal vanishing horizon (EVH) limit, odd-dimensional multispinning Kerr black hole (in the presence of cosmological constant) and cosmological soliton. We show that the near horizon EVH geometry of Kerr has a three-dimensional maximally symmetric subspace whose curvature depends on rotational parameters and the cosmological constant. In the Kerr-dS case, this subspace interpolates between AdS3 , three-dimensional flat and dS3 by varying rotational parameters, while the near horizon of the EVH cosmological soliton always has a dS3 . The feature of the EVH cosmological soliton is that it is regular everywhere on the horizon. In the near EVH case, these three-dimensional parts turn into the corresponding locally maximally symmetric spacetimes with a horizon: Kerr-dS3 , flat space cosmology or BTZ black hole. We show that their thermodynamics match with the thermodynamics of the original near EVH black holes. We also briefly discuss the holographic two-dimensional CFT dual to the near horizon of EVH solutions.

A study of the effects of macrosegregation and buoyancy-driven flow in binary mixture solidification

NASA Technical Reports Server (NTRS)

Sinha, S. K.; Sundararajan, T.; Garg, V. K.

1993-01-01

A generalized anisotropic porous medium approach is developed for modelling the flow, heat and mass transport processes during binary mixture solidification. Transient predictions are obtained using FEM, coupled with an implicit time-marching scheme, for solidification inside a two-dimensional rectangular enclosure. A parametric study focusing attention on the effects of solutal buoyancy and thermal buoyancy is presented. It is observed that three parameters, namely the thermal Rayleigh number, the solutal Rayleigh number, and the relative density change parameter, significantly alter the flow fields in the liquid and the mushy regions. Depending upon the nature of these flow fields, the solute enrichment caused by macrosegregation may occur in the top or the bottom region of the enclosure.

High-order harmonic generation from a two-dimensional band structure

NASA Astrophysics Data System (ADS)

Jin, Jian-Zhao; Xiao, Xiang-Ru; Liang, Hao; Wang, Mu-Xue; Chen, Si-Ge; Gong, Qihuang; Peng, Liang-You

2018-04-01

In the past few years, harmonic generation in solids has attracted tremendous attention. Recently, some experiments of two-dimensional (2D) monolayer or few-layer materials have been carried out. These studies demonstrated that harmonic generation in the 2D case shows a strong dependence on the laser's orientation and ellipticity, which calls for a quantitative theoretical interpretation. In this work, we carry out a systematic study on the harmonic generation from a 2D band structure based on a numerical solution to the time-dependent Schrödinger equation. By comparing with the 1D case, we find that the generation dynamics can have a significant difference due to the existence of many crossing points in the 2D band structure. In particular, the higher conduction bands can be excited step by step via these crossing points and the total contribution of the harmonic is given by the mixing of transitions between different clusters of conduction bands to the valence band. We also present the orientation dependence of the harmonic yield on the laser polarization direction.

Numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity

NASA Astrophysics Data System (ADS)

Korepanov, V. V.; Matveenko, V. P.; Fedorov, A. Yu.; Shardakov, I. N.

2013-07-01

An algorithm for the numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity is considered. The algorithm is based on separation of a power-law dependence from the finite-element solution in a neighborhood of singular points in the domain under study, where singular solutions are possible. The obtained power-law dependencies allow one to conclude whether the stresses have singularities and what the character of these singularities is. The algorithm was tested for problems of classical elasticity by comparing the stress singularity exponents obtained by the proposed method and from known analytic solutions. Problems with various cases of singular points, namely, body surface points at which either the smoothness of the surface is violated, or the type of boundary conditions is changed, or distinct materials are in contact, are considered as applications. The stress singularity exponents obtained by using the models of classical and asymmetric elasticity are compared. It is shown that, in the case of cracks, the stress singularity exponents are the same for the elasticity models under study, but for other cases of singular points, the stress singularity exponents obtained on the basis of asymmetric elasticity have insignificant quantitative distinctions from the solutions of the classical elasticity.

Aerodynamics of Engine-Airframe Interaction

NASA Technical Reports Server (NTRS)

Caughey, D. A.

1986-01-01

The report describes progress in research directed towards the efficient solution of the inviscid Euler and Reynolds-averaged Navier-Stokes equations for transonic flows through engine inlets, and past complete aircraft configurations, with emphasis on the flowfields in the vicinity of engine inlets. The research focusses upon the development of solution-adaptive grid procedures for these problems, and the development of multi-grid algorithms in conjunction with both, implicit and explicit time-stepping schemes for the solution of three-dimensional problems. The work includes further development of mesh systems suitable for inlet and wing-fuselage-inlet geometries using a variational approach. Work during this reporting period concentrated upon two-dimensional problems, and has been in two general areas: (1) the development of solution-adaptive procedures to cluster the grid cells in regions of high (truncation) error;and (2) the development of a multigrid scheme for solution of the two-dimensional Euler equations using a diagonalized alternating direction implicit (ADI) smoothing algorithm.

From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

NASA Astrophysics Data System (ADS)

Bodin, Jacques

2015-03-01

In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

Common aero vehicle autonomous reentry trajectory optimization satisfying waypoint and no-fly zone constraints

NASA Astrophysics Data System (ADS)

Jorris, Timothy R.

2007-12-01

To support the Air Force's Global Reach concept, a Common Aero Vehicle is being designed to support the Global Strike mission. "Waypoints" are specified for reconnaissance or multiple payload deployments and "no-fly zones" are specified for geopolitical restrictions or threat avoidance. Due to time critical targets and multiple scenario analysis, an autonomous solution is preferred over a time-intensive, manually iterative one. Thus, a real-time or near real-time autonomous trajectory optimization technique is presented to minimize the flight time, satisfy terminal and intermediate constraints, and remain within the specified vehicle heating and control limitations. This research uses the Hypersonic Cruise Vehicle (HCV) as a simplified two-dimensional platform to compare multiple solution techniques. The solution techniques include a unique geometric approach developed herein, a derived analytical dynamic optimization technique, and a rapidly emerging collocation numerical approach. This up-and-coming numerical technique is a direct solution method involving discretization then dualization, with pseudospectral methods and nonlinear programming used to converge to the optimal solution. This numerical approach is applied to the Common Aero Vehicle (CAV) as the test platform for the full three-dimensional reentry trajectory optimization problem. The culmination of this research is the verification of the optimality of this proposed numerical technique, as shown for both the two-dimensional and three-dimensional models. Additionally, user implementation strategies are presented to improve accuracy and enhance solution convergence. Thus, the contributions of this research are the geometric approach, the user implementation strategies, and the determination and verification of a numerical solution technique for the optimal reentry trajectory problem that minimizes time to target while satisfying vehicle dynamics and control limitation, and heating, waypoint, and no-fly zone constraints.

Numerical Studies of Three-dimensional Breakdown in Trailing Vortex Wakes

NASA Technical Reports Server (NTRS)

Evans, P. F.; Hackett, J. E.

1976-01-01

Finite element, three dimensional relaxation methods are used to calculate the development of vortex wakes behind aircraft for a considerable downstream distance. The inclusion of a self-induction term in the solution, dependent upon local curvature and vortex core radius, permits calculation of finite lifetimes for systems for which infinite life would be predicted two dimensionally. The associated computer program is described together with single-pair, twin-pair, and multiple-pair studies carried out using it. It is found, in single-pair studies, that there is a lower limit to the wavelengths at which the Crow-type of instability can occur. Below this limit, self-induction effects cause the plane of the disturbance waves to rotate counter to the vortex direction. Self induction in two dimensionally generated twin spiral waves causes an increase in axial length which becomes more marked with decreasing initial wavelength. The time taken for vortex convergence toward the center plane is correspondingly increased. The limited parametric twin-pair study performed suggests that time-to-converge increases with increasing flap span. Limited studies of Boeing 747 configurations show correct qualitative response to removal of the outer flap and to gear deployment, as compared with wind tunnel and flight test experience.

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems, task 1: Ducted propfan analysis

NASA Technical Reports Server (NTRS)

Hall, Edward J.; Delaney, Robert A.; Bettner, James L.

1990-01-01

The time-dependent three-dimensional Euler equations of gas dynamics were solved numerically to study the steady compressible transonic flow about ducted propfan propulsion systems. Aerodynamic calculations were based on a four-stage Runge-Kutta time-marching finite volume solution technique with added numerical dissipation. An implicit residual smoothing operator was used to aid convergence. Two calculation grids were employed in this study. The first grid utilized an H-type mesh network with a branch cut opening to represent the axisymmetric cowl. The second grid utilized a multiple-block mesh system with a C-type grid about the cowl. The individual blocks were numerically coupled in the Euler solver. Grid systems were generated by a combined algebraic/elliptic algortihm developed specifically for ducted propfans. Numerical calculations were initially performed for unducted propfans to verify the accuracy of the three-dimensional Euler formulation. The Euler analyses were then applied for the calculation of ducted propfan flows, and predicted results were compared with experimental data for two cases. The three-dimensional Euler analyses displayed exceptional accuracy, although certain parameters were observed to be very sensitive to geometric deflections. Both solution schemes were found to be very robust and demonstrated nearly equal efficiency and accuracy, although it was observed that the multi-block C-grid formulation provided somewhat better resolution of the cowl leading edge region.

Nonautonomous dark soliton solutions in two-component Bose—Einstein condensates with a linear time-dependent potential

NASA Astrophysics Data System (ADS)

Li, Qiu-Yan; Wang, Shuang-Jin; Li, Zai-Dong

2014-06-01

We report the analytical nonautonomous soliton solutions (NSSs) for two-component Bose—Einstein condensates with the presence of a time-dependent potential. These solutions show that the time-dependent potential can affect the velocity of NSS. The velocity shows the characteristic of both increasing and oscillation with time. A detailed analysis for the asymptotic behavior of NSSs demonstrates that the collision of two NSSs of each component is elastic.

Unsteady flows in rotor-stator cascades

NASA Astrophysics Data System (ADS)

Lee, Yu-Tai; Bein, Thomas W.; Feng, Jin Z.; Merkle, Charles L.

1991-03-01

A time-accurate potential-flow calculation method has been developed for unsteady incompressible flows through two-dimensional multi-blade-row linear cascades. The method represents the boundary surfaces by distributing piecewise linear-vortex and constant-source singularities on discrete panels. A local coordinate is assigned to each independently moving object. Blade-shed vorticity is traced at each time step. The unsteady Kutta condition applied is nonlinear and requires zero blade trailing-edge loading at each time. Its influence on the solutions depends on the blade trailing-edge shapes. Steady biplane and cascade solutions are presented and compared to exact solutions and experimental data. Unsteady solutions are validated with the Wagner function for an airfoil moving impulsively from rest and the Theodorsen function for an oscillating airfoil. The shed vortex motion and its interaction with blades are calculated and compared to an analytic solution. For multi-blade-row cascade, the potential effect between blade rows is predicted using steady and quasi unsteady calculations. The accuracy of the predictions is demonstrated using experimental results for a one-stage turbine stator-rotor.

NLSEmagic: Nonlinear Schrödinger equation multi-dimensional Matlab-based GPU-accelerated integrators using compact high-order schemes

NASA Astrophysics Data System (ADS)

Caplan, R. M.

2013-04-01

We present a simple to use, yet powerful code package called NLSEmagic to numerically integrate the nonlinear Schrödinger equation in one, two, and three dimensions. NLSEmagic is a high-order finite-difference code package which utilizes graphic processing unit (GPU) parallel architectures. The codes running on the GPU are many times faster than their serial counterparts, and are much cheaper to run than on standard parallel clusters. The codes are developed with usability and portability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with the MEX-compiler interface. The packages are freely distributed, including user manuals and set-up files. Catalogue identifier: AEOJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOJ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 124453 No. of bytes in distributed program, including test data, etc.: 4728604 Distribution format: tar.gz Programming language: C, CUDA, MATLAB. Computer: PC, MAC. Operating system: Windows, MacOS, Linux. Has the code been vectorized or parallelized?: Yes. Number of processors used: Single CPU, number of GPU processors dependent on chosen GPU card (max is currently 3072 cores on GeForce GTX 690). Supplementary material: Setup guide, Installation guide. RAM: Highly dependent on dimensionality and grid size. For typical medium-large problem size in three dimensions, 4GB is sufficient. Keywords: Nonlinear Schröodinger Equation, GPU, high-order finite difference, Bose-Einstien condensates. Classification: 4.3, 7.7. Nature of problem: Integrate solutions of the time-dependent one-, two-, and three-dimensional cubic nonlinear Schrödinger equation. Solution method: The integrators utilize a fully-explicit fourth-order Runge-Kutta scheme in time and both second- and fourth-order differencing in space. The integrators are written to run on NVIDIA GPUs and are interfaced with MATLAB including built-in visualization and analysis tools. Restrictions: The main restriction for the GPU integrators is the amount of RAM on the GPU as the code is currently only designed for running on a single GPU. Unusual features: Ability to visualize real-time simulations through the interaction of MATLAB and the compiled GPU integrators. Additional comments: Setup guide and Installation guide provided. Program has a dedicated web site at www.nlsemagic.com. Running time: A three-dimensional run with a grid dimension of 87×87×203 for 3360 time steps (100 non-dimensional time units) takes about one and a half minutes on a GeForce GTX 580 GPU card.

Heat pipe dynamic behavior

NASA Technical Reports Server (NTRS)

Issacci, F.; Roche, G. L.; Klein, D. B.; Catton, I.

1988-01-01

The vapor flow in a heat pipe was mathematically modeled and the equations governing the transient behavior of the core were solved numerically. The modeled vapor flow is transient, axisymmetric (or two-dimensional) compressible viscous flow in a closed chamber. The two methods of solution are described. The more promising method failed (a mixed Galerkin finite difference method) whereas a more common finite difference method was successful. Preliminary results are presented showing that multi-dimensional flows need to be treated. A model of the liquid phase of a high temperature heat pipe was developed. The model is intended to be coupled to a vapor phase model for the complete solution of the heat pipe problem. The mathematical equations are formulated consistent with physical processes while allowing a computationally efficient solution. The model simulates time dependent characteristics of concern to the liquid phase including input phase change, output heat fluxes, liquid temperatures, container temperatures, liquid velocities, and liquid pressure. Preliminary results were obtained for two heat pipe startup cases. The heat pipe studied used lithium as the working fluid and an annular wick configuration. Recommendations for implementation based on the results obtained are presented. Experimental studies were initiated using a rectangular heat pipe. Both twin beam laser holography and laser Doppler anemometry were investigated. Preliminary experiments were completed and results are reported.

Evolution of magnetic field and atmospheric response. I - Three-dimensional formulation by the method of projected characteristics. II - Formulation of proper boundary equations. [stellar magnetohydrodynamics

NASA Technical Reports Server (NTRS)

Nakagawa, Y.

1981-01-01

The method described as the method of nearcharacteristics by Nakagawa (1980) is renamed the method of projected characteristics. Making full use of properties of the projected characteristics, a new and simpler formulation is developed. As a result, the formulation for the examination of the general three-dimensional problems is presented. It is noted that since in practice numerical solutions must be obtained, the final formulation is given in the form of difference equations. The possibility of including effects of viscous and ohmic dissipations in the formulation is considered, and the physical interpretation is discussed. A systematic manner is then presented for deriving physically self-consistent, time-dependent boundary equations for MHD initial boundary problems. It is demonstrated that the full use of the compatibility equations (differential equations relating variations at two spatial locations and times) is required in determining the time-dependent boundary conditions. In order to provide a clear physical picture as an example, the evolution of axisymmetric global magnetic field by photospheric differential rotation is considered.

Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe; Kwak, Dochan; Vinokur, Marcel

1992-01-01

A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the velocity. This choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

Category 3: Sound Generation by Interacting with a Gust

NASA Technical Reports Server (NTRS)

Scott, James R.

2004-01-01

The cascade-gust interaction problem is solved employing a time-domain approach. The purpose of this problem is to test the ability of a CFD/CAA code to accurately predict the unsteady aerodynamic and aeroacoustic response of a single airfoil to a two-dimensional, periodic vortical gust.Nonlinear time dependent Euler equations are solved using higher order spatial differencing and time marching techniques. The solutions indicate the generation and propagation of expected mode orders for the given configuration and flow conditions. The blade passing frequency (BPF) is cut off for this cascade while higher harmonic, 2BPF and 3BPF, modes are cut on.

Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma

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

Ghosh, Samiran, E-mail: sran_g@yahoo.com; Chakrabarti, Nikhil, E-mail: nikhil.chakrabarti@saha.ac.in

2016-08-15

The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev–Petviashvili solitons.

General solution of the Dirac equation for quasi-two-dimensional electrons

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

Eremko, Alexander, E-mail: eremko@bitp.kiev.ua; Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua; Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua

2016-06-15

The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that themore » general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.« less

Thermosolutal convection during directional solidification. II - Flow transitions

NASA Technical Reports Server (NTRS)

Mcfadden, G. B.; Coriell, S. R.

1987-01-01

The influence of thermosolutal convection on solute segregation in crystals grown by vertical directional solidification of binary metallic alloys or semiconductors is studied. Finite differences are used in a two-dimensional time-dependent model which assumes a planar crystal-melt interface to obtain numerical results. It is assumed that the configuration is periodic in the horizontal direction. Consideration is given to the possibility of multiple flow states sharing the same period. The results are represented in bifurcation diagrams of the nonlinear states associated with the critical points of linear theory. Variations of the solutal Rayleigh number can lead to the occurrence of multiple steady states, time-periodic states, and quasi-periodic states. This case is compared to that of thermosolutal convection with linear vertical gradients and stress-free boundaries.

Black holes and stars in Horndeski theory

NASA Astrophysics Data System (ADS)

Babichev, Eugeny; Charmousis, Christos; Lehébel, Antoine

2016-08-01

We review black hole and star solutions for Horndeski theory. For non-shift symmetric theories, black holes involve a Kaluza-Klein reduction of higher dimensional Lovelock solutions. On the other hand, for shift symmetric theories of Horndeski and beyond Horndeski, black holes involve two classes of solutions: those that include, at the level of the action, a linear coupling to the Gauss-Bonnet term and those that involve time dependence in the galileon field. We analyze the latter class in detail for a specific subclass of Horndeski theory, discussing the general solution of a static and spherically symmetric spacetime. We then discuss stability issues, slowly rotating solutions as well as black holes coupled to matter. The latter case involves a conformally coupled scalar field as well as an electromagnetic field and the (primary) hair black holes thus obtained. We review and discuss the recent results on neutron stars in Horndeski theories.

Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations.

PubMed

Martirosyan, A; Saakian, David B

2011-08-01

We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the chemical master equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs.

Time-Dependent Parabolic Finite Difference Formulation for Harmonic Sound Propagation in a Two-Dimensional Duct with Flow

NASA Technical Reports Server (NTRS)

Kreider, Kevin L.; Baumeister, Kenneth J.

1996-01-01

An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

On the construction of a direct numerical simulation of a breaking inertia-gravity wave in the upper mesosphere

NASA Astrophysics Data System (ADS)

Fruman, Mark D.; Remmler, Sebastian; Achatz, Ulrich; Hickel, Stefan

2014-10-01

A systematic approach to the direct numerical simulation (DNS) of breaking upper mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is presented. Normal mode or singular vector analysis applied in a frame of reference moving with the phase velocity of the wave (in which the wave is a steady solution) is used to determine the most likely scale and structure of the primary instability and to initialize nonlinear "2.5-D" simulations (with three-dimensional velocity and vorticity fields but depending only on two spatial coordinates). Singular vector analysis is then applied to the time-dependent 2.5-D solution to predict the transition of the breaking event to three-dimensional turbulence and to initialize three-dimensional DNS. The careful choice of the computational domain and the relatively low Reynolds numbers, on the order of 25,000, relevant to breaking waves in the upper mesosphere, makes the three-dimensional DNS tractable with present-day computing clusters. Three test cases are presented: a statically unstable low-frequency inertia-gravity wave, a statically and dynamically stable inertia-gravity wave, and a statically unstable high-frequency gravity wave. The three-dimensional DNS are compared to ensembles of 2.5-D simulations. In general, the decay of the wave and generation of turbulence is faster in three dimensions, but the results are otherwise qualitatively and quantitatively similar, suggesting that results of 2.5-D simulations are meaningful if the domain and initial condition are chosen properly.

Cross Validation Through Two-Dimensional Solution Surface for Cost-Sensitive SVM.

PubMed

Gu, Bin; Sheng, Victor S; Tay, Keng Yeow; Romano, Walter; Li, Shuo

2017-06-01

Model selection plays an important role in cost-sensitive SVM (CS-SVM). It has been proven that the global minimum cross validation (CV) error can be efficiently computed based on the solution path for one parameter learning problems. However, it is a challenge to obtain the global minimum CV error for CS-SVM based on one-dimensional solution path and traditional grid search, because CS-SVM is with two regularization parameters. In this paper, we propose a solution and error surfaces based CV approach (CV-SES). More specifically, we first compute a two-dimensional solution surface for CS-SVM based on a bi-parameter space partition algorithm, which can fit solutions of CS-SVM for all values of both regularization parameters. Then, we compute a two-dimensional validation error surface for each CV fold, which can fit validation errors of CS-SVM for all values of both regularization parameters. Finally, we obtain the CV error surface by superposing K validation error surfaces, which can find the global minimum CV error of CS-SVM. Experiments are conducted on seven datasets for cost sensitive learning and on four datasets for imbalanced learning. Experimental results not only show that our proposed CV-SES has a better generalization ability than CS-SVM with various hybrids between grid search and solution path methods, and than recent proposed cost-sensitive hinge loss SVM with three-dimensional grid search, but also show that CV-SES uses less running time.

Nonlinear zero-sum differential game analysis by singular perturbation methods

NASA Technical Reports Server (NTRS)

Sinar, J.; Farber, N.

1982-01-01

A class of nonlinear, zero-sum differential games, exhibiting time-scale separation properties, can be analyzed by singular-perturbation techniques. The merits of such an analysis, leading to an approximate game solution, as well as the 'well-posedness' of the formulation, are discussed. This approach is shown to be attractive for investigating pursuit-evasion problems; the original multidimensional differential game is decomposed to a 'simple pursuit' (free-stream) game and two independent (boundary-layer) optimal-control problems. Using multiple time-scale boundary-layer models results in a pair of uniformly valid zero-order composite feedback strategies. The dependence of suboptimal strategies on relative geometry and own-state measurements is demonstrated by a three dimensional, constant-speed example. For game analysis with realistic vehicle dynamics, the technique of forced singular perturbations and a variable modeling approach is proposed. Accuracy of the analysis is evaluated by comparison with the numerical solution of a time-optimal, variable-speed 'game of two cars' in the horizontal plane.

Avalanches and plasticity for colloids in a time dependent optical trap

DOE PAGES

Olson Reichhardt, Cynthia Jane; McDermott, Danielle Marie; Reichhardt, Charles

2015-08-25

Here, with the use of optical traps it is possible to confine assemblies of colloidal particles in two-dimensional and quasi-one-dimensional arrays. Here we examine how colloidal particles rearrange in a quasi-one-dimensional trap with a time dependent confining potential. The particle motion occurs both through slow elastic uniaxial distortions as well as through abrupt large-scale two-dimensional avalanches associated with plastic rearrangements. During the avalanches the particle velocity distributions extend over a broad range and can be fit to a power law consistent with other studies of plastic events mediated by dislocations.

Thermoelectric transport in two-dimensional giant Rashba systems

NASA Astrophysics Data System (ADS)

Xiao, Cong; Li, Dingping; Ma, Zhongshui; Niu, Qian

Thermoelectric transport in strongly spin-orbit coupled two-dimensional Rashba systems is studied using the analytical solution of the linearized Boltzmann equation. To highlight the effects of inter-band scattering, we assume point-like potential impurities, and obtain the band-and energy-dependent transport relaxation times. Unconventional transport behaviors arise when the Fermi level lies near or below the band crossing point (BCP), such as the non-Drude electrical conducivity below the BCP, the failure of the standard Mott relation linking the Peltier coefficient to the electrical conductivity near the BCP, the enhancement of diffusion thermopower and figure of merit below the BCP, the zero-field Hall coefficient which is not inversely proportional to and not a monotonic function of the carrier density, the enhanced Nernst coefficient below the BCP, and the enhanced current-induced spin-polarization efficiency.

Two-boundary grid generation for the solution of the three dimensional compressible Navier-Stokes equations. Ph.D. Thesis - Old Dominion Univ.

NASA Technical Reports Server (NTRS)

Smith, R. E.

1981-01-01

A grid generation technique called the two boundary technique is developed and applied for the solution of the three dimensional Navier-Stokes equations. The Navier-Stokes equations are transformed from a cartesian coordinate system to a computational coordinate system, and the grid generation technique provides the Jacobian matrix describing the transformation. The two boundary technique is based on algebraically defining two distinct boundaries of a flow domain and the distribution of the grid is achieved by applying functions to the uniform computational grid which redistribute the computational independent variables and consequently concentrate or disperse the grid points in the physical domain. The Navier-Stokes equations are solved using a MacCormack time-split technique. Grids and supersonic laminar flow solutions are obtained for a family of three dimensional corners and two spike-nosed bodies.

Development of a solution adaptive unstructured scheme for quasi-3D inviscid flows through advanced turbomachinery cascades

NASA Technical Reports Server (NTRS)

Usab, William J., Jr.; Jiang, Yi-Tsann

1991-01-01

The objective of the present research is to develop a general solution adaptive scheme for the accurate prediction of inviscid quasi-three-dimensional flow in advanced compressor and turbine designs. The adaptive solution scheme combines an explicit finite-volume time-marching scheme for unstructured triangular meshes and an advancing front triangular mesh scheme with a remeshing procedure for adapting the mesh as the solution evolves. The unstructured flow solver has been tested on a series of two-dimensional airfoil configurations including a three-element analytic test case presented here. Mesh adapted quasi-three-dimensional Euler solutions are presented for three spanwise stations of the NASA rotor 67 transonic fan. Computed solutions are compared with available experimental data.

Stationary Solutions of A One-dimensional Thermodynamic Radiative Sea Ice Model

NASA Astrophysics Data System (ADS)

Taylor, P. D.; Feltham, D. L.

A one-dimensional thermodynamic model of sea ice is coupled to a two-stream radi- ation model and the stationary (time-independent) solutions analysed. The stationary model represents the state of the sea ice subjected to persistent or slowly varying forc- ing. Two physically realisable stationary solutions (real and positive ice thickness) occur for a large range of positive oceanic heat flux ( 20,Wm-2). The two station- ary solutions are due to the two-stream radiation model, which allows radiation to be reflected at the ice-ocean interface. Thick ice ( 1,m) only absorbs radiation near its surface, whereas thin ice ( 0.1,m) absorbs radiation across its entire depth. The two stationary solutions are caused by these two different radiative regimes. The results of this analysis have relevance to the interpretation and implementation of thermody- namic models of sea ice and the interpretation of thickness data.

Unsteady three-dimensional marginal separation caused by surface-mounted obstacles and/or local suction

NASA Astrophysics Data System (ADS)

Braun, Stefan; Kluwick, Alfred

2004-09-01

Earlier investigations of steady two-dimensional marginally separated laminar boundary layers have shown that the non-dimensional wall shear (or equivalently the negative non-dimensional perturbation displacement thickness) is governed by a nonlinear integro-differential equation. This equation contains a single controlling parameter Gamma characterizing, for example, the angle of attack of a slender airfoil and has the important property that (real) solutions exist up to a critical value Gamma_c of Gamma only. Here we investigate three-dimensional unsteady perturbations of an incompressible steady two-dimensional marginally separated laminar boundary layer with special emphasis on the flow behaviour near Gamma_c. Specifically, it is shown that the integro differential equation which governs these disturbances if Gamma_c {-} Gamma {=} O(1) reduces to a nonlinear partial differential equation known as the Fisher equation as Gamma approaches the critical value Gamma_c. This in turn leads to a significant simplification of the problem allowing, among other things, a systematic study of devices used in boundary-layer control and an analytical investigation of the conditions leading to the formation of finite-time singularities which have been observed in earlier numerical studies of unsteady two-dimensional and three-dimensional flows in the vicinity of a line of symmetry. Also, it is found that it is possible to construct exact solutions which describe waves of constant form travelling in the spanwise direction. These waves may contain singularities which can be interpreted as vortex sheets. The existence of these solutions strongly suggests that solutions of the Fisher equation which lead to finite-time blow-up may be extended beyond the blow-up time, thereby generating moving singularities which can be interpreted as vortical structures qualitatively similar to those emerging in direct numerical simulations of near critical (i.e. transitional) laminar separation bubbles. This is supported by asymptotic analysis.

Modeling Three-Dimensional Flow in Confined Aquifers by Superposition of Both Two- and Three-Dimensional Analytic Functions

NASA Astrophysics Data System (ADS)

Haitjema, Henk M.

1985-10-01

A technique is presented to incorporate three-dimensional flow in a Dupuit-Forchheimer model. The method is based on superposition of approximate analytic solutions to both two- and three-dimensional flow features in a confined aquifer of infinite extent. Three-dimensional solutions are used in the domain of interest, while farfield conditions are represented by two-dimensional solutions. Approximate three- dimensional solutions have been derived for a partially penetrating well and a shallow creek. Each of these solutions satisfies the condition that no flow occurs across the confining layers of the aquifer. Because of this condition, the flow at some distance of a three-dimensional feature becomes nearly horizontal. Consequently, remotely from a three-dimensional feature, its three-dimensional solution is replaced by a corresponding two-dimensional one. The latter solution is trivial as compared to its three-dimensional counterpart, and its use greatly enhances the computational efficiency of the model. As an example, the flow is modeled between a partially penetrating well and a shallow creek that occur in a regional aquifer system.

Stochastic solution to quantum dynamics

NASA Technical Reports Server (NTRS)

John, Sarah; Wilson, John W.

1994-01-01

The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.

On local strong solutions to the three-dimensional nonhomogeneous incompressible magnetohydrodynamic equations with density-dependent viscosity and vacuum

NASA Astrophysics Data System (ADS)

Song, Sisi

2018-04-01

This paper concerns the three-dimensional nonhomogeneous incompressible magnetohydrodynamic equations with density-dependent viscosity and vacuum on Ω \\subset R^3. The domain Ω \\subset R^3 is a general connected smooth one, either bounded or unbounded. In particular, the initial density can have compact support when Ω is unbounded. First, we obtain the local existence and uniqueness of strong solution to the three-dimensional nonhomogeneous incompressible magnetohydrodynamic equations without any compatibility condition assumed on the initial data. Then, we also prove the continuous dependence of strong solution on the initial data under an additional compatibility condition.

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

2017-08-01

In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

A finite difference solution for the propagation of sound in near sonic flows

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Lester, H. C.

1983-01-01

An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.

Solvent viscosity mismatch between the solute plug and the mobile phase: Considerations in the applications of two-dimensional HPLC

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

Shalliker, R. Andrew; Guiochon, Georges A

Understanding the nature of viscosity contrast induced flow instabilities is an important aspect in the design of two-dimensional HPLC separations. When the viscosity contrast between the sample plug and the mobile phase is sufficiently large, the phenomenon known as viscous fingering can be induced. Viscous fingering is a flow instability phenomenon that occurs at the interface between two fluids with different viscosities. In liquid chromatography, viscous fingering results in the solute band undergoing a change in form as it enters into the chromatography column. Moreover, even in the absence of viscous fingering, band shapes change shape at low viscosity contrasts.more » These changes can result in a noticeable change in separation performance, with the result depending on whether the solvent pushing the solute plug has a higher or lower viscosity than the solute plug. These viscosity induced changes become more important as the solute injection volume increases and hence understanding the process becomes critical in the implementation of multidimensional HPLC techniques, since in these techniques the sample injection plug into the second dimension is an order of magnitude greater than in one-dimensional HPLC. This review article assesses the current understanding of the viscosity contrast induced processes as they relate to liquid chromatographic separation behaviour.« less

An implicit higher-order spatially accurate scheme for solving time dependent flows on unstructured meshes

NASA Astrophysics Data System (ADS)

Tomaro, Robert F.

1998-07-01

The present research is aimed at developing a higher-order, spatially accurate scheme for both steady and unsteady flow simulations using unstructured meshes. The resulting scheme must work on a variety of general problems to ensure the creation of a flexible, reliable and accurate aerodynamic analysis tool. To calculate the flow around complex configurations, unstructured grids and the associated flow solvers have been developed. Efficient simulations require the minimum use of computer memory and computational times. Unstructured flow solvers typically require more computer memory than a structured flow solver due to the indirect addressing of the cells. The approach taken in the present research was to modify an existing three-dimensional unstructured flow solver to first decrease the computational time required for a solution and then to increase the spatial accuracy. The terms required to simulate flow involving non-stationary grids were also implemented. First, an implicit solution algorithm was implemented to replace the existing explicit procedure. Several test cases, including internal and external, inviscid and viscous, two-dimensional, three-dimensional and axi-symmetric problems, were simulated for comparison between the explicit and implicit solution procedures. The increased efficiency and robustness of modified code due to the implicit algorithm was demonstrated. Two unsteady test cases, a plunging airfoil and a wing undergoing bending and torsion, were simulated using the implicit algorithm modified to include the terms required for a moving and/or deforming grid. Secondly, a higher than second-order spatially accurate scheme was developed and implemented into the baseline code. Third- and fourth-order spatially accurate schemes were implemented and tested. The original dissipation was modified to include higher-order terms and modified near shock waves to limit pre- and post-shock oscillations. The unsteady cases were repeated using the higher-order spatially accurate code. The new solutions were compared with those obtained using the second-order spatially accurate scheme. Finally, the increased efficiency of using an implicit solution algorithm in a production Computational Fluid Dynamics flow solver was demonstrated for steady and unsteady flows. A third- and fourth-order spatially accurate scheme has been implemented creating a basis for a state-of-the-art aerodynamic analysis tool.

A Semi-Analytical Solution to Time Dependent Groundwater Flow Equation Incorporating Stream-Wetland-Aquifer Interactions

NASA Astrophysics Data System (ADS)

Boyraz, Uǧur; Melek Kazezyılmaz-Alhan, Cevza

2017-04-01

Groundwater is a vital element of hydrologic cycle and the analytical & numerical solutions of different forms of groundwater flow equations play an important role in understanding the hydrological behavior of subsurface water. The interaction between groundwater and surface water bodies can be determined using these solutions. In this study, new hypothetical approaches are implemented to groundwater flow system in order to contribute to the studies on surface water/groundwater interactions. A time dependent problem is considered in a 2-dimensional stream-wetland-aquifer system. The sloped stream boundary is used to represent the interaction between stream and aquifer. The rest of the aquifer boundaries are assumed as no-flux boundary. In addition, a wetland is considered as a surface water body which lies over the whole aquifer. The effect of the interaction between the wetland and the aquifer is taken into account with a source/sink term in the groundwater flow equation and the interaction flow is calculated by using Darcy's approach. A semi-analytical solution is developed for the 2-dimensional groundwater flow equation in 5 steps. First, Laplace and Fourier cosine transforms are employed to obtain the general solution in Fourier and Laplace domain. Then, the initial and boundary conditions are applied to obtain the particular solution. Finally, inverse Fourier transform is carried out analytically and inverse Laplace transform is carried out numerically to obtain the final solution in space and time domain, respectively. In order to verify the semi-analytical solution, an explicit finite difference algorithm is developed and analytical and numerical solutions are compared for synthetic examples. The comparison of the analytical and numerical solutions shows that the analytical solution gives accurate results.

TEMPEST: A computer code for three-dimensional analysis of transient fluid dynamics

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

Fort, J.A.

TEMPEST (Transient Energy Momentum and Pressure Equations Solutions in Three dimensions) is a powerful tool for solving engineering problems in nuclear energy, waste processing, chemical processing, and environmental restoration because it analyzes and illustrates 3-D time-dependent computational fluid dynamics and heat transfer analysis. It is a family of codes with two primary versions, a N- Version (available to public) and a T-Version (not currently available to public). This handout discusses its capabilities, applications, numerical algorithms, development status, and availability and assistance.

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.

Electrokinetically driven microfluidic mixing with patchwise surface heterogeneity and AC applied electric field

NASA Astrophysics Data System (ADS)

Luo, Win-Jet; Yue, Cheng-Feng

2004-12-01

This paper investigates two-dimensional, time-dependent electroosmotic flows driven by an AC electric field via patchwise surface heterogeneities distributed along the microchannel walls. The time-dependent flow fields through the microchannel are simulated for various patchwise heterogeneous surface patterns using the backwards-Euler time stepping numerical method. Different heterogeneous surface patterns are found to create significantly different electrokinetic transport phenomena. It is shown that the presence of oppositely charged surface heterogeneities on the microchannel walls results in the formation of localized flow circulations within the bulk flow. These circulation regions grow and decay periodically in accordance with the applied periodic AC electric field intensity. The circulations provide an effective means of enhancing species mixing in the microchannel. A suitable design of the patchwise heterogeneous surface pattern permits the mixing channel length and the retention time required to attain a homogeneous solution to be reduced significantly.

An implicit solution of the three-dimensional Navier-Stokes equations for an airfoil spanning a wind tunnel. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Moitra, A.

1982-01-01

An implicit finite-difference algorithm is developed for the numerical solution of the incompressible three dimensional Navier-Stokes equations in the non-conservative primitive-variable formulation. The flow field about an airfoil spanning a wind-tunnel is computed. The coordinate system is generated by an extension of the two dimensional body-fitted coordinate generation techniques of Thompson, as well as that of Sorenson, into three dimensions. Two dimensional grids are stacked along a spanwise coordinate defined by a simple analytical function. A Poisson pressure equation for advancing the pressure in time is arrived at by performing a divergence operation on the momentum equations. The pressure at each time-step is calculated on the assumption that continuity be unconditionally satisfied. An eddy viscosity coefficient, computed according to the algebraic turbulence formulation of Baldwin and Lomax, simulates the effects of turbulence.

Existence of global weak solution for a reduced gravity two and a half layer model

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

Guo, Zhenhua, E-mail: zhenhua.guo.math@gmail.com; Li, Zilai, E-mail: lizilai0917@163.com; Yao, Lei, E-mail: yaolei1056@hotmail.com

2013-12-15

We investigate the existence of global weak solution to a reduced gravity two and a half layer model in one-dimensional bounded spatial domain or periodic domain. Also, we show that any possible vacuum state has to vanish within finite time, then the weak solution becomes a unique strong one.

Detecting Moving Targets by Use of Soliton Resonances

NASA Technical Reports Server (NTRS)

Zak, Michael; Kulikov, Igor

2003-01-01

A proposed method of detecting moving targets in scenes that include cluttered or noisy backgrounds is based on a soliton-resonance mathematical model. The model is derived from asymptotic solutions of the cubic Schroedinger equation for a one-dimensional system excited by a position-and-time-dependent externally applied potential. The cubic Schroedinger equation has general significance for time-dependent dispersive waves. It has been used to approximate several phenomena in classical as well as quantum physics, including modulated beams in nonlinear optics, and superfluids (in particular, Bose-Einstein condensates). In the proposed method, one would take advantage of resonant interactions between (1) a soliton excited by the position-and-time-dependent potential associated with a moving target and (2) eigen-solitons, which represent dispersive waves and are solutions of the cubic Schroedinger equation for a time-independent potential.

Radially Symmetric Motions of Nonlinearly Viscoelastic Bodies Under Live Loads

NASA Astrophysics Data System (ADS)

Stepanov, Alexey B.; Antman, Stuart S.

2017-12-01

This paper treats radially symmetric motions of nonlinearly viscoelastic circular-cylindrical and spherical shells subjected to the live loads of centrifugal force and (time-dependent) hydrostatic pressures. The governing equations are exact versions of those for 3-dimensional continuum mechanics (so shell does not connote an approximate via some shell theory). These motions are governed by quasilinear third-order parabolic-hyperbolic equations having but one independent spatial variable. The principal part of such a partial differential equation is determined by a general family of nonlinear constitutive equations. The presence of strains in two orthogonal directions requires a careful treatment of constitutive restrictions that are physically natural and support the analysis. The interaction of geometrically exact formulations, the compatible use of general constitutive equations for material response, and the presence of live loads show how these factors play crucial roles in the behavior of solutions. In particular, for different kinds of live loads there are thresholds separating materials that produce qualitatively different dynamical behavior. The analysis (using classical methods) covers infinite-time blowup for cylindrical shells subject to centrifugal forces, infinite-time blowup for cylindrical shells subject to steady and time-dependent hydrostatic pressures, finite-time blowup for spherical shells subject to steady and time-dependent hydrostatic pressures, and the preclusion of total compression. This paper concludes with a sketch (using some modern methods) of the existence of regular solutions until the time of blowup.

Effects of ethanol addition on micellar solubilization and plume migration during surfactant enhanced recovery of tetrachloroethene.

PubMed

Taylor, Tammy P; Rathfelder, Klaus M; Pennell, Kurt D; Abriola, Linda M

2004-03-01

Alcohol addition has been suggested for use in combination with surfactant flushing to enhance solubilization kinetics and permit density control of dense non-aqueous phase liquid (DNAPL)-laden surfactant plumes. This study examined the effects of adding ethanol (EtOH) to a 4% Tween 80 (polyoxyethylene (20) sorbitan monooleate) solution used to flush tetrachloroethene (PCE)-contaminated porous media. The influence of EtOH concentration, subsurface layering and scale on flushing solution delivery and PCE recovery was investigated through a combination of experimental and mathematical modeling studies. Results of batch experiments demonstrated that the addition of 2.5%, 5% and 10% (wt.) EtOH incrementally increased the PCE solubilization capacity and viscosity of the surfactant solution, while reducing solution density from 1.002 to 0.986 g/cm3. Effluent concentration data obtained from one-dimensional (1-D) column experiments were used to characterize rate-limited micellar solubilization of residual PCE, which was strongly dependent upon flow velocity and weakly dependent upon EtOH concentration. Two-dimensional (2-D) box studies illustrated that minor differences (0.008 g/cm3) between flushing and resident solution density can strongly influence surfactant front propagation. A two-dimensional multiphase simulator, MISER, was used to model the influence of EtOH composition on the aqueous flow field and PCE mass recovery. The ability of the numerical simulator to predict effluent concentrations and front propagation was demonstrated for both 1-D columns and 2-D boxes flushed with EtOH-amended Tween 80 solutions. Results of this study quantify the potential influence of alcohol addition on surfactant solution properties and solubilization capacity, and demonstrate the importance of considering small density variations in remedial design.

High-Fidelity Real-Time Simulation on Deployed Platforms

DTIC Science & Technology

2010-08-26

three–dimensional transient heat conduction “ Swiss Cheese ” problem; and a three–dimensional unsteady incompressible Navier- Stokes low–Reynolds–number...our approach with three examples: a two?dimensional Helmholtz acoustics ?horn? problem; a three?dimensional transient heat conduction ? Swiss Cheese ...solutions; a transient lin- ear heat conduction problem in a three–dimensional “ Swiss Cheese ” configuration Ω — to illustrate treat- ment of many

Computer simulation of two-dimensional unsteady flows in estuaries and embayments by the method of characteristics : basic theory and the formulation of the numerical method

USGS Publications Warehouse

Lai, Chintu

1977-01-01

Two-dimensional unsteady flows of homogeneous density in estuaries and embayments can be described by hyperbolic, quasi-linear partial differential equations involving three dependent and three independent variables. A linear combination of these equations leads to a parametric equation of characteristic form, which consists of two parts: total differentiation along the bicharacteristics and partial differentiation in space. For its numerical solution, the specified-time-interval scheme has been used. The unknown, partial space-derivative terms can be eliminated first by suitable combinations of difference equations, converted from the corresponding differential forms and written along four selected bicharacteristics and a streamline. Other unknowns are thus made solvable from the known variables on the current time plane. The computation is carried to the second-order accuracy by using trapezoidal rule of integration. Means to handle complex boundary conditions are developed for practical application. Computer programs have been written and a mathematical model has been constructed for flow simulation. The favorable computer outputs suggest further exploration and development of model worthwhile. (Woodard-USGS)

CALIBRATING NON-CONVEX PENALIZED REGRESSION IN ULTRA-HIGH DIMENSION.

PubMed

Wang, Lan; Kim, Yongdai; Li, Runze

2013-10-01

We investigate high-dimensional non-convex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is nonunique and is not guaranteed to contain the oracle estimator; (2) even if a solution path is known to contain the oracle estimator, the optimal tuning parameter depends on many unknown factors and is hard to estimate. To address these two challenging issues, we first prove that an easy-to-calculate calibrated CCCP algorithm produces a consistent solution path which contains the oracle estimator with probability approaching one. Furthermore, we propose a high-dimensional BIC criterion and show that it can be applied to the solution path to select the optimal tuning parameter which asymptotically identifies the oracle estimator. The theory for a general class of non-convex penalties in the ultra-high dimensional setup is established when the random errors follow the sub-Gaussian distribution. Monte Carlo studies confirm that the calibrated CCCP algorithm combined with the proposed high-dimensional BIC has desirable performance in identifying the underlying sparsity pattern for high-dimensional data analysis.

CALIBRATING NON-CONVEX PENALIZED REGRESSION IN ULTRA-HIGH DIMENSION

PubMed Central

Wang, Lan; Kim, Yongdai; Li, Runze

2014-01-01

We investigate high-dimensional non-convex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is nonunique and is not guaranteed to contain the oracle estimator; (2) even if a solution path is known to contain the oracle estimator, the optimal tuning parameter depends on many unknown factors and is hard to estimate. To address these two challenging issues, we first prove that an easy-to-calculate calibrated CCCP algorithm produces a consistent solution path which contains the oracle estimator with probability approaching one. Furthermore, we propose a high-dimensional BIC criterion and show that it can be applied to the solution path to select the optimal tuning parameter which asymptotically identifies the oracle estimator. The theory for a general class of non-convex penalties in the ultra-high dimensional setup is established when the random errors follow the sub-Gaussian distribution. Monte Carlo studies confirm that the calibrated CCCP algorithm combined with the proposed high-dimensional BIC has desirable performance in identifying the underlying sparsity pattern for high-dimensional data analysis. PMID:24948843

The modified semi-discrete two-dimensional Toda lattice with self-consistent sources

NASA Astrophysics Data System (ADS)

Gegenhasi

2017-07-01

In this paper, we derive the Grammian determinant solutions to the modified semi-discrete two-dimensional Toda lattice equation, and then construct the semi-discrete two-dimensional Toda lattice equation with self-consistent sources via source generation procedure. The algebraic structure of the resulting coupled modified differential-difference equation is clarified by presenting its Grammian determinant solutions and Casorati determinant solutions. As an application of the Grammian determinant and Casorati determinant solution, the explicit one-soliton and two-soliton solution of the modified semi-discrete two-dimensional Toda lattice equation with self-consistent sources are given. We also construct another form of the modified semi-discrete two-dimensional Toda lattice equation with self-consistent sources which is the Bäcklund transformation for the semi-discrete two-dimensional Toda lattice equation with self-consistent sources.

Theory of ion-matrix-sheath dynamics

NASA Astrophysics Data System (ADS)

Kos, L.; Tskhakaya, D. D.

2018-01-01

The time evolution of a one-dimensional, uni-polar ion sheath (an "ion matrix sheath") is investigated. The analytical solutions for the ion-fluid and Poisson's equations are found for an arbitrary time dependence of the wall-applied negative potential. In the case that the wall potential is large and remains constant after its ramp-up application, the explicit time dependencies of the sheath's parameters during the initial stage of the process are given. The characteristic rate of approaching the stationary state, satisfying the Child-Langmuir law, is determined.

An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows

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

Snider, D.M.; O`Rourke, P.J.; Andrews, M.J.

1997-06-01

A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles,more » with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.« less

Vectorization of a particle simulation method for hypersonic rarefied flow

NASA Technical Reports Server (NTRS)

Mcdonald, Jeffrey D.; Baganoff, Donald

1988-01-01

An efficient particle simulation technique for hypersonic rarefied flows is presented at an algorithmic and implementation level. The implementation is for a vector computer architecture, specifically the Cray-2. The method models an ideal diatomic Maxwell molecule with three translational and two rotational degrees of freedom. Algorithms are designed specifically for compatibility with fine grain parallelism by reducing the number of data dependencies in the computation. By insisting on this compatibility, the method is capable of performing simulation on a much larger scale than previously possible. A two-dimensional simulation of supersonic flow over a wedge is carried out for the near-continuum limit where the gas is in equilibrium and the ideal solution can be used as a check on the accuracy of the gas model employed in the method. Also, a three-dimensional, Mach 8, rarefied flow about a finite-span flat plate at a 45 degree angle of attack was simulated. It utilized over 10 to the 7th particles carried through 400 discrete time steps in less than one hour of Cray-2 CPU time. This problem was chosen to exhibit the capability of the method in handling a large number of particles and a true three-dimensional geometry.

New families of interpolating type IIB backgrounds

NASA Astrophysics Data System (ADS)

Minasian, Ruben; Petrini, Michela; Zaffaroni, Alberto

2010-04-01

We construct new families of interpolating two-parameter solutions of type IIB supergravity. These correspond to D3-D5 systems on non-compact six-dimensional manifolds which are mathbb{T}2 fibrations over Eguchi-Hanson and multi-center Taub-NUT spaces, respectively. One end of the interpolation corresponds to a solution with only D5 branes and vanishing NS three-form flux. A topology changing transition occurs at the other end, where the internal space becomes a direct product of the four-dimensional surface and the two-torus and the complexified NS-RR three-form flux becomes imaginary self-dual. Depending on the choice of the connections on the torus fibre, the interpolating family has either mathcal{N}=2 or mathcal{N}=1 supersymmetry. In the mathcal{N}=2 case it can be shown that the solutions are regular.

Phase-field simulations of velocity selection in rapidly solidified binary alloys

NASA Astrophysics Data System (ADS)

Fan, Jun; Greenwood, Michael; Haataja, Mikko; Provatas, Nikolas

2006-09-01

Time-dependent simulations of two-dimensional isothermal Ni-Cu dendrites are simulated using a phase-field model solved with a finite-difference adaptive mesh refinement technique. Dendrite tip velocity selection is examined and found to exhibit a transition between two markedly different regimes as undercooling is increased. At low undercooling, the dendrite tip growth rate is consistent with the kinetics of the classical Stefan problem, where the interface is assume to be in local equilibrium. At high undercooling, the growth velocity selected approaches a linear dependence on melt undercooling, consistent with the continuous growth kinetics of Aziz and with a one-dimensional steady-state phase-field asymptotic analysis of Ahmad [Phys. Rev. E 58, 3436 (1998)]. Our simulations are also consistent with other previously observed behaviors of dendritic growth as undercooling is increased. These include the transition of dendritic morphology to absolute stability and nonequilibrium solute partitioning. Our results show that phase-field models of solidification, which inherently contain a nonzero interface width, can be used to study the dynamics of complex solidification phenomena involving both equilibrium and nonequilibrium interface growth kinetics.

Bernstein-Greene-Kruskal Modes in a Three-Dimensional Plasma

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

Ng, C.S.; Bhattacharjee, A.

2005-12-09

Bernstein-Greene-Kruskal modes in a three-dimensional (3D) unmagnetized plasma are constructed. It is shown that 3D solutions that depend only on energy do not exist. However, 3D solutions that depend on energy and additional constants of motion (such as angular momentum) do exist. Exact analytical as well as numerical solutions are constructed assuming spherical symmetry, and their properties are contrasted with those of 1D solutions. Possible extensions to solutions with cylindrical symmetry with or without a finite magnetic guide field are discussed.

Bifurcations and chaos in convection taking non-Fourier heat-flux

NASA Astrophysics Data System (ADS)

Layek, G. C.; Pati, N. C.

2017-11-01

In this Letter, we report the influences of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo-Christov hyperbolic model for heat propagation. A five-dimensional nonlinear system is obtained for a low-order Galerkin expansion, and it reduces to Lorenz system for Cattaneo number tending to zero. The linear stability agreed with existing results that depend on Cattaneo number C. It also gives a threshold Cattaneo number, CT, above which only oscillatory solutions can persist. The oscillatory solutions branch terminates at the subcritical steady branch with a heteroclinic loop connecting a pair of saddle points for subcritical steady-state solutions. For subcritical onset of convection two stable solutions coexist, that is, hysteresis phenomenon occurs at this stage. The steady solution undergoes a Hopf bifurcation and is of subcritical type for small value of C, while it becomes supercritical for moderate Cattaneo number. The system goes through period-doubling/noisy period-doubling transition to chaos depending on the control parameters. There after the system exhibits Shil'nikov chaos via homoclinic explosion. The complexity of spiral strange attractor is analyzed using fractal dimension and return map.

Rayleigh-Taylor mixing with time-dependent acceleration

NASA Astrophysics Data System (ADS)

Abarzhi, Snezhana

2016-10-01

We extend the momentum model to describe Rayleigh-Taylor (RT) mixing driven by a time-dependent acceleration. The acceleration is a power-law function of time, similarly to astrophysical and plasma fusion applications. In RT flow the dynamics of a fluid parcel is driven by a balance per unit mass of the rates of momentum gain and loss. We find analytical solutions in the cases of balanced and imbalanced gains and losses, and identify their dependence on the acceleration exponent. The existence is shown of two typical regimes of self-similar RT mixing-acceleration-driven Rayleigh-Taylor-type and dissipation-driven Richtymer-Meshkov-type with the latter being in general non-universal. Possible scenarios are proposed for transitions from the balanced dynamics to the imbalanced self-similar dynamics. Scaling and correlations properties of RT mixing are studied on the basis of dimensional analysis. Departures are outlined of RT dynamics with time-dependent acceleration from canonical cases of homogeneous turbulence as well as blast waves with first and second kind self-similarity. The work is supported by the US National Science Foundation.

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

NASA Astrophysics Data System (ADS)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

Action-minimizing solutions of the one-dimensional N-body problem

NASA Astrophysics Data System (ADS)

Yu, Xiang; Zhang, Shiqing

2018-05-01

We supplement the following result of C. Marchal on the Newtonian N-body problem: A path minimizing the Lagrangian action functional between two given configurations is always a true (collision-free) solution when the dimension d of the physical space R^d satisfies d≥2. The focus of this paper is on the fixed-ends problem for the one-dimensional Newtonian N-body problem. We prove that a path minimizing the action functional in the set of paths joining two given configurations and having all the time the same order is always a true (collision-free) solution. Considering the one-dimensional N-body problem with equal masses, we prove that (i) collision instants are isolated for a path minimizing the action functional between two given configurations, (ii) if the particles at two endpoints have the same order, then the path minimizing the action functional is always a true (collision-free) solution and (iii) when the particles at two endpoints have different order, although there must be collisions for any path, we can prove that there are at most N! - 1 collisions for any action-minimizing path.

Curl forces and the nonlinear Fokker-Planck equation.

PubMed

Wedemann, R S; Plastino, A R; Tsallis, C

2016-12-01

Nonlinear Fokker-Planck equations endowed with curl drift forces are investigated. The conditions under which these evolution equations admit stationary solutions, which are q exponentials of an appropriate potential function, are determined. It is proved that when these stationary solutions exist, the nonlinear Fokker-Planck equations satisfy an H theorem in terms of a free-energy-like quantity involving the S_{q} entropy. A particular two-dimensional model admitting analytical, time-dependent q-Gaussian solutions is discussed in detail. This model describes a system of particles with short-range interactions, performing overdamped motion under drag effects due to a rotating resisting medium. It is related to models that have been recently applied to the study of type-II superconductors. The relevance of the present developments to the study of complex systems in physics, astronomy, and biology is discussed.

Iterative spectral methods and spectral solutions to compressible flows

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Zang, T. A.

1982-01-01

A spectral multigrid scheme is described which can solve pseudospectral discretizations of self-adjoint elliptic problems in O(N log N) operations. An iterative technique for efficiently implementing semi-implicit time-stepping for pseudospectral discretizations of Navier-Stokes equations is discussed. This approach can handle variable coefficient terms in an effective manner. Pseudospectral solutions of compressible flow problems are presented. These include one dimensional problems and two dimensional Euler solutions. Results are given both for shock-capturing approaches and for shock-fitting ones.

Analytical solutions for solute transport in groundwater and riverine flow using Green's Function Method and pertinent coordinate transformation method

NASA Astrophysics Data System (ADS)

Sanskrityayn, Abhishek; Suk, Heejun; Kumar, Naveen

2017-04-01

In this study, analytical solutions of one-dimensional pollutant transport originating from instantaneous and continuous point sources were developed in groundwater and riverine flow using both Green's Function Method (GFM) and pertinent coordinate transformation method. Dispersion coefficient and flow velocity are considered spatially and temporally dependent. The spatial dependence of the velocity is linear, non-homogeneous and that of dispersion coefficient is square of that of velocity, while the temporal dependence is considered linear, exponentially and asymptotically decelerating and accelerating. Our proposed analytical solutions are derived for three different situations depending on variations of dispersion coefficient and velocity, respectively which can represent real physical processes occurring in groundwater and riverine systems. First case refers to steady solute transport situation in steady flow in which dispersion coefficient and velocity are only spatially dependent. The second case represents transient solute transport in steady flow in which dispersion coefficient is spatially and temporally dependent while the velocity is spatially dependent. Finally, the third case indicates transient solute transport in unsteady flow in which both dispersion coefficient and velocity are spatially and temporally dependent. The present paper demonstrates the concentration distribution behavior from a point source in realistically occurring flow domains of hydrological systems including groundwater and riverine water in which the dispersivity of pollutant's mass is affected by heterogeneity of the medium as well as by other factors like velocity fluctuations, while velocity is influenced by water table slope and recharge rate. Such capabilities give the proposed method's superiority about application of various hydrological problems to be solved over other previously existing analytical solutions. Especially, to author's knowledge, any other solution doesn't exist for both spatially and temporally variations of dispersion coefficient and velocity. In this study, the existing analytical solutions from previous widely known studies are used for comparison as validation tools to verify the proposed analytical solution as well as the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) code and the developed 1D finite difference code (FDM). All such solutions show perfect match with the respective proposed solutions.

A vortex wake capturing method for potential flow calculations

NASA Technical Reports Server (NTRS)

Murman, E. M.; Stremel, P. M.

1982-01-01

A method is presented for modifying finite difference solutions of the potential equation to include the calculation of non-planar vortex wake features. The approach is an adaptation of Baker's 'cloud in cell' algorithm developed for the stream function-vorticity equations. The vortex wake is tracked in a Lagrangian frame of reference as a group of discrete vortex filaments. These are distributed to the Eulerian mesh system on which the velocity is calculated by a finite difference solution of the potential equation. An artificial viscosity introduced by the finite difference equations removes the singular nature of the vortex filaments. Computed examples are given for the two-dimensional time dependent roll-up of vortex wakes generated by wings with different spanwise loading distributions.

Optimal Electrodynamic Tether Phasing Maneuvers

NASA Technical Reports Server (NTRS)

Bitzer, Matthew S.; Hall, Christopher D.

2007-01-01

We study the minimum-time orbit phasing maneuver problem for a constant-current electrodynamic tether (EDT). The EDT is assumed to be a point mass and the electromagnetic forces acting on the tether are always perpendicular to the local magnetic field. After deriving and non-dimensionalizing the equations of motion, the only input parameters become current and the phase angle. Solution examples, including initial Lagrange costates, time of flight, thrust plots, and thrust angle profiles, are given for a wide range of current magnitudes and phase angles. The two-dimensional cases presented use a non-tilted magnetic dipole model, and the solutions are compared to existing literature. We are able to compare similar trajectories for a constant thrust phasing maneuver and we find that the time of flight is longer for the constant thrust case with similar initial thrust values and phase angles. Full three-dimensional solutions, which use a titled magnetic dipole model, are also analyzed for orbits with small inclinations.

Deterministic Stress Modeling of Hot Gas Segregation in a Turbine

NASA Technical Reports Server (NTRS)

Busby, Judy; Sondak, Doug; Staubach, Brent; Davis, Roger

1998-01-01

Simulation of unsteady viscous turbomachinery flowfields is presently impractical as a design tool due to the long run times required. Designers rely predominantly on steady-state simulations, but these simulations do not account for some of the important unsteady flow physics. Unsteady flow effects can be modeled as source terms in the steady flow equations. These source terms, referred to as Lumped Deterministic Stresses (LDS), can be used to drive steady flow solution procedures to reproduce the time-average of an unsteady flow solution. The goal of this work is to investigate the feasibility of using inviscid lumped deterministic stresses to model unsteady combustion hot streak migration effects on the turbine blade tip and outer air seal heat loads using a steady computational approach. The LDS model is obtained from an unsteady inviscid calculation. The LDS model is then used with a steady viscous computation to simulate the time-averaged viscous solution. Both two-dimensional and three-dimensional applications are examined. The inviscid LDS model produces good results for the two-dimensional case and requires less than 10% of the CPU time of the unsteady viscous run. For the three-dimensional case, the LDS model does a good job of reproducing the time-averaged viscous temperature migration and separation as well as heat load on the outer air seal at a CPU cost that is 25% of that of an unsteady viscous computation.

An efficient and robust algorithm for two dimensional time dependent incompressible Navier-Stokes equations: High Reynolds number flows

NASA Technical Reports Server (NTRS)

Goodrich, John W.

1991-01-01

An algorithm is presented for unsteady two-dimensional incompressible Navier-Stokes calculations. This algorithm is based on the fourth order partial differential equation for incompressible fluid flow which uses the streamfunction as the only dependent variable. The algorithm is second order accurate in both time and space. It uses a multigrid solver at each time step. It is extremely efficient with respect to the use of both CPU time and physical memory. It is extremely robust with respect to Reynolds number.

Observation of quantum interferences via light-induced conical intersections in diatomic molecules

DOE PAGES

Natan, Adi; Ware, Matthew R.; Prabhudesai, Vaibhav S.; ...

2016-04-07

We observe energy-dependent angle-resolved diffraction patterns in protons from strong-field dissociation of the molecular hydrogen ion H + 2. The interference is a characteristic of dissociation around a laser-induced conical intersection (LICI), which is a point of contact between two surfaces in the dressed 2-dimensional Born-Oppenheimer potential energy landscape of a diatomic molecule in a strong laser field. The interference magnitude and angular period depend strongly on the energy difference between the initial state and the LICI, consistent with coherent diffraction around a cone-shaped potential barrier whose width and thickness depend on the relative energy of the initial state andmore » the cone apex. As a result, these findings are supported by numerical solutions of the time-dependent Schrodinger equation for similar experimental conditions.« less

Observation of quantum interferences via light-induced conical intersections in diatomic molecules

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

Natan, Adi; Ware, Matthew R.; Prabhudesai, Vaibhav S.

We observe energy-dependent angle-resolved diffraction patterns in protons from strong-field dissociation of the molecular hydrogen ion H + 2. The interference is a characteristic of dissociation around a laser-induced conical intersection (LICI), which is a point of contact between two surfaces in the dressed 2-dimensional Born-Oppenheimer potential energy landscape of a diatomic molecule in a strong laser field. The interference magnitude and angular period depend strongly on the energy difference between the initial state and the LICI, consistent with coherent diffraction around a cone-shaped potential barrier whose width and thickness depend on the relative energy of the initial state andmore » the cone apex. As a result, these findings are supported by numerical solutions of the time-dependent Schrodinger equation for similar experimental conditions.« less

Modeling of a piezoelectric/piezomagnetic nano energy harvester based on two dimensional theory

NASA Astrophysics Data System (ADS)

Yan, Zhi

2018-01-01

This work presents a two dimensional theory for a piezoelectric/piezomagnetic bilayer nanoplate in coupled extensional and flexural vibrations with both flexoelectric and surface effects. The magneto-electro-elastic (MEE) coupling equations are derived from three-dimensional equations and Kirchhoff plate theory. Based on the developed theory, a piezoelectric/piezomagnetic nano energy harvester is proposed, which can generate electricity under time-harmonic applied magnetic field. The approximate solutions for the mechanical responses and voltage of the energy harvester are obtained using the weighted residual method. Results show that the properties of the proposed energy harvester are size-dependent due to the flexoelectric and surface effects, and such effects are more pronounced when the bilayer thickness is reduced to dozens of nanometers. It is also found that the magnetoelectric coupling coefficient and power density of the energy harvester are sensitive to the load resistance, the thickness fraction of the piezoelectric or the piezomagnetic layer and damping ratios. Moreover, results indicate that the flexoelectric effect could be made use to build a dielectric/piezomagnetic nano energy harvester. This work provides modeling techniques and numerical methods for investigating the size-dependent properties of MEE nanoplate-based energy harvester and could be helpful for designing nano energy harvesters using the principle of flexoelectricity.

Design of two-dimensional channels with prescribed velocity distributions along the channel walls

NASA Technical Reports Server (NTRS)

Stanitz, John D

1953-01-01

A general method of design is developed for two-dimensional unbranched channels with prescribed velocities as a function of arc length along the channel walls. The method is developed for both compressible and incompressible, irrotational, nonviscous flow and applies to the design of elbows, diffusers, nozzles, and so forth. In part I solutions are obtained by relaxation methods; in part II solutions are obtained by a Green's function. Five numerical examples are given in part I including three elbow designs with the same prescribed velocity as a function of arc length along the channel walls but with incompressible, linearized compressible, and compressible flow. One numerical example is presented in part II for an accelerating elbow with linearized compressible flow, and the time required for the solution by a Green's function in part II was considerably less than the time required for the same solution by relaxation methods in part I.

Analytically-derived sensitivities in one-dimensional models of solute transport in porous media

USGS Publications Warehouse

Knopman, D.S.

1987-01-01

Analytically-derived sensitivities are presented for parameters in one-dimensional models of solute transport in porous media. Sensitivities were derived by direct differentiation of closed form solutions for each of the odel, and by a time integral method for two of the models. Models are based on the advection-dispersion equation and include adsorption and first-order chemical decay. Boundary conditions considered are: a constant step input of solute, constant flux input of solute, and exponentially decaying input of solute at the upstream boundary. A zero flux is assumed at the downstream boundary. Initial conditions include a constant and spatially varying distribution of solute. One model simulates the mixing of solute in an observation well from individual layers in a multilayer aquifer system. Computer programs produce output files compatible with graphics software in which sensitivities are plotted as a function of either time or space. (USGS)

Response solutions and quasi-periodic degenerate bifurcations for quasi-periodically forced systems

NASA Astrophysics Data System (ADS)

Si, Wen; Si, Jianguo

2018-06-01

This paper includes two parts. In the first part, we first focus on quasi-periodic time dependent perturbations of one-dimensional quasi-periodically forced systems with degenerate equilibrium. We study the system in two cases, for one of which system admits a response solution under a non-resonant condition on the frequency vector weaker than Brjuno–Rüssmann’s and for another of which system also admits a response solution without any non-resonant conditions. Next, we investigate the existence of response solutions of a quasi-periodic perturbed system with degenerate (including completely degenerate) equilibrium under Brjuno–Rüssmann’s non-resonant condition by using the Herman method. In the second part, we consider, firstly, the quasi-periodic perturbation of a universal unfolding of one-dimensional degenerate vector field . Secondly, we consider the perturbation of a universal unfolding of normal two-dimensional Hamiltonian system with completely degenerate equilibrium. With KAM theory and singularity theory, we show that these two classes of universal unfolding can persist on large Cantor sets under Brjuno–Rüssmann’s non-resonant condition, which implies all the invariant tori in the integrable part and all the bifurcation scenario can survive on large Cantor sets. The result for Hamiltonian system can apply directly to the response context for quasi-periodically forced systems. Our results in this paper can be regarded as an improvement with respect to several results in various literature (Broer et al 2005 Nonlinearity 18 1735–69 Broer et al 2006 J. Differ. Equ. 222 233–62 Wagener 2005 J. Differ. Equ. 216 216–81 Xu 2010 J. Differ. Equ. 250 551–71 Xu and Jiang 2010 Ergod. Theor. Dynam. Syst. 31 599–611 Lu and Xu 2014 Nonlinear Differ. Equ. Appl. 21 361–70). This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11171185, 11571201).

Nonalgebraic integrability of one reversible dynamical system of the Cremona type

NASA Astrophysics Data System (ADS)

Rerikh, K. V.

1998-05-01

A reversible dynamical system (RDS) and a system of nonlinear functional equations, defined by a certain rational quadratic Cremona mapping and arising from the static model of the dispersion approach in the theory of strong interactions [the Chew-Low-type equations with crossing-symmetry matrix A(l,1)], are considered. This RDS is split into one- and two-dimensional ones. An explicit Cremona transformation that completely determines the exact solution of the two-dimensional system is found. This solution depends on an odd function satisfying a nonlinear autonomous three-point functional equation. Nonalgebraic integrability of RDS under consideration is proved using the method of Poincaré normal forms and the Siegel theorem on biholomorphic linearization of a mapping at a nonresonant fixed point.

Robust Multigrid Smoothers for Three Dimensional Elliptic Equations with Strong Anisotropies

NASA Technical Reports Server (NTRS)

Llorente, Ignacio M.; Melson, N. Duane

1998-01-01

We discuss the behavior of several plane relaxation methods as multigrid smoothers for the solution of a discrete anisotropic elliptic model problem on cell-centered grids. The methods compared are plane Jacobi with damping, plane Jacobi with partial damping, plane Gauss-Seidel, plane zebra Gauss-Seidel, and line Gauss-Seidel. Based on numerical experiments and local mode analysis, we compare the smoothing factor of the different methods in the presence of strong anisotropies. A four-color Gauss-Seidel method is found to have the best numerical and architectural properties of the methods considered in the present work. Although alternating direction plane relaxation schemes are simpler and more robust than other approaches, they are not currently used in industrial and production codes because they require the solution of a two-dimensional problem for each plane in each direction. We verify the theoretical predictions of Thole and Trottenberg that an exact solution of each plane is not necessary and that a single two-dimensional multigrid cycle gives the same result as an exact solution, in much less execution time. Parallelization of the two-dimensional multigrid cycles, the kernel of the three-dimensional implicit solver, is also discussed. Alternating-plane smoothers are found to be highly efficient multigrid smoothers for anisotropic elliptic problems.

Measured Electron Spin Relaxation Rates in Frozen Solutions of Azurin, VITAMIN-B12R, and Nitrosyl Ferrous Myoglobin.

NASA Astrophysics Data System (ADS)

Muench, Philip James

Rates in frozen glycerin/water solutions at temperatures between 1.4 K and 20 K are reported for a copper-containing protein, azurin, and a cobalt-containing biomolecular complex, vitamin B_{rm 12r}, the paramagnetic product of the photolysis of coenzyme B_{12}. Results are interpreted in terms of a spectral dimensionality. Rates are also reported for nitrosyl ferrous myoglobin in frozen water solution, which exhibits a dominant one-phonon relaxation process up to 20 K and thus does not reveal spectral dimensionality. The anomalous variation of rate with temperature observed in several iron-containing proteins is not conspicuous here. In a model two-phonon mechanism of relaxation, temperature dependence is fixed by a spectral dimensionality, m, which specifies the variation of vibrational density of states with frequency rho(nu ) ~ nu ^{rm m-1} and is named in analogy with the Debye density of states in 1-, 2-, and 3-dimensional crystals. At sufficiently high temperatures, a non-resonant two-phonon process (Raman) should dominate the relaxation of a paramagnetic ion unless low-lying (under ^{~}70 cm^ {-1}) electronic states are present, as in many rare earths and in high spin ferric complexes, including many ferric proteins. The temperature dependence of the Raman rate for a Kramers ion (odd number of electrons) is T^{rm 3+2m} if temperature is sufficiently lower than Theta = hnu_{rm max} /k, the Debye temperature. The values of m from relaxation data on frozen solutions of a protein have sometimes been dependent upon solvent conditions. The maximum values of m for heme proteins, iron-sulfur proteins, and one copper -and-iron-containing protein, have ranged from about 1.3 to 1.8. Pulse saturation/recovery was used. The recoveries were not exponential, but rates were estimated from semilogarithmic displays of signals or from numerical fitting. The temperature dependence of the rates for azurin between 1.5 K and 22 K can be fit with a spectral dimensionality of 3 and a rather low Debye temperature near 69 K, in contrast to iron proteins. Relaxation of vitamin B_{ rm 12r} differed between samples, indicating varied photolysis or freezing. The Raman relaxation was well fit by a simple power law in temperature, but the values of m varied from 1.14 to 1.48 between samples.

A finite-volume ELLAM for three-dimensional solute-transport modeling

USGS Publications Warehouse

Russell, T.F.; Heberton, C.I.; Konikow, Leonard F.; Hornberger, G.Z.

2003-01-01

A three-dimensional finite-volume ELLAM method has been developed, tested, and successfully implemented as part of the U.S. Geological Survey (USGS) MODFLOW-2000 ground water modeling package. It is included as a solver option for the Ground Water Transport process. The FVELLAM uses space-time finite volumes oriented along the streamlines of the flow field to solve an integral form of the solute-transport equation, thus combining local and global mass conservation with the advantages of Eulerian-Lagrangian characteristic methods. The USGS FVELLAM code simulates solute transport in flowing ground water for a single dissolved solute constituent and represents the processes of advective transport, hydrodynamic dispersion, mixing from fluid sources, retardation, and decay. Implicit time discretization of the dispersive and source/sink terms is combined with a Lagrangian treatment of advection, in which forward tracking moves mass to the new time level, distributing mass among destination cells using approximate indicator functions. This allows the use of large transport time increments (large Courant numbers) with accurate results, even for advection-dominated systems (large Peclet numbers). Four test cases, including comparisons with analytical solutions and benchmarking against other numerical codes, are presented that indicate that the FVELLAM can usually yield excellent results, even if relatively few transport time steps are used, although the quality of the results is problem-dependent.

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

Bena, Iosif; Kraus, Per; Warner, Nicholas P.

We construct the most generic three-charge, three-dipole-charge, BPS black-ring solutions in a Taub-NUT background. These solutions depend on seven charges and six moduli, and interpolate between a four-dimensional black hole and a five-dimensional black ring. They are also instrumental in determining the correct microscopic description of the five-dimensional BPS black rings.

On the localisation of four-dimensional brane-world black holes: II. The general case

NASA Astrophysics Data System (ADS)

Kanti, P.; Pappas, N.; Pappas, T.

2016-01-01

We perform a comprehensive analysis of a number of scalar field theories in an attempt to find analytically five-dimensional, localised-on-the-brane, black-hole solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz for the five-dimensional metric tensor that allows for a time-dependent, non-trivial profile of the mass function in terms of the bulk coordinate and a deviation from the over-restricting Schwarzschild-type solution on the brane. In order to support such a solution, we study a variety of theories including single or multiple scalar fields, with canonical or non-canonical kinetic terms, minimally or non-minimally coupled to gravity. We demonstrate that for such a metric ansatz and for a carefully chosen energy-momentum tensor which is non-isotropic in five dimensions, solutions that have the form of a Schwarzschild-(anti)de Sitter or Reissner-Nordstrom type of solution do emerge. However, the resulting profile of the mass function along the bulk coordinate, when allowed, is not the correct one for eliminating bulk singularities.

Spectral-based propagation schemes for time-dependent quantum systems with application to carbon nanotubes

NASA Astrophysics Data System (ADS)

Chen, Zuojing; Polizzi, Eric

2010-11-01

Effective modeling and numerical spectral-based propagation schemes are proposed for addressing the challenges in time-dependent quantum simulations of systems ranging from atoms, molecules, and nanostructures to emerging nanoelectronic devices. While time-dependent Hamiltonian problems can be formally solved by propagating the solutions along tiny simulation time steps, a direct numerical treatment is often considered too computationally demanding. In this paper, however, we propose to go beyond these limitations by introducing high-performance numerical propagation schemes to compute the solution of the time-ordered evolution operator. In addition to the direct Hamiltonian diagonalizations that can be efficiently performed using the new eigenvalue solver FEAST, we have designed a Gaussian propagation scheme and a basis-transformed propagation scheme (BTPS) which allow to reduce considerably the simulation times needed by time intervals. It is outlined that BTPS offers the best computational efficiency allowing new perspectives in time-dependent simulations. Finally, these numerical schemes are applied to study the ac response of a (5,5) carbon nanotube within a three-dimensional real-space mesh framework.

A versatile approach to the study of the transient response of a submerged thin shell

NASA Astrophysics Data System (ADS)

Leblond, C.; Sigrist, J.-F.

2010-01-01

The transient response of submerged two-dimensional thin shell subjected to weak acoustical or mechanical excitations is addressed in this paper. The proposed approach is first exposed in a detailed manner: it is based on Laplace transform in time, in vacuo eigenvector expansion with time-dependent coefficients for the structural dynamics and boundary-integral formulation for the fluid. The projection of the fluid pressure on the in vacuo eigenvectors leads to a fully coupled system involving the modal time-dependent displacement coefficients, which are the problem unknowns. They are simply determined by matrix inversion in the Laplace domain. Application of the method to the response of a two-dimensional immersed shell to a weak acoustical excitation is then exposed: the proposed test-case corresponds to the design of immersed structures subjected to underwater explosions, which is of paramount importance in naval shipbuilding. Comparison of a numerical calculation based on the proposed approach with an analytical solution is exposed; versatility of the method is also highlighted by referring to "classical" FEM/FEM or FEM/BEM simulations. As a conspicuous feature of the method, calculation of the fluid response functions corresponding to a given geometry has to be performed once, allowing various simulations for different material properties of the structure, as well as for various excitations on the structure. This versatile approach can therefore be efficiently and extensively used for design purposes.

Analysis of Electrokinetic Mixing Using AC Electric Field and Patchwise Surface Heterogeneities

NASA Astrophysics Data System (ADS)

Luo, Win-Jet; Yarn, Kao-Feng; Hsu, Shou-Ping

2007-04-01

In this paper, the authors investigate the use of an applied AC electric field and microchannel surface heterogeneities to carry out the microfluidic mixing of two-dimensional, time-dependent electroosmotic flows. The time-dependent flow fields within the microchannel are simulated using the backwards-Euler time-stepping numerical method. The mixing efficiencies obtained in microchannels with two different patchwise surface heterogeneity patterns are investigated. In general, the results show that the application of an AC electric field significantly reduces the required mixing length compared with the use of a DC electric field. Furthermore, the presence of oppositely charged surface heterogeneities on the microchannel walls results in the formation of localized flow circulation regions within the bulk flow. These circulation regions grow and decay periodically in accordance with the periodic variation of the AC electric field intensity and provide an effective means of enhancing species mixing in the microchannel. Consequently, the use of an AC electric field together with patchwise surface heterogeneities permits a significant reduction in both the mixing channel length and the retention time required to attain a homogeneous solution.

Magnetoconvection dynamics in a stratified layer. 1: Two-dimensional simulations and visualization

NASA Astrophysics Data System (ADS)

Lantz, Steven R.; Sudan, R. N.

1995-03-01

To gain insight in the problem of fluid convection below solar photosphere, time-dependent magnetohydrodynamic convection is studied by numerical simulation to the magneto-anelastic equations, a model appropiate for low Mach numbers. Numerical solutions to the equations are generated on a two-dimensional Cartesian mesh by a finite-difference, predictor-corrector algorithm. The thermodynamic properties of the fluid are held constant at the rigid, stress-free top and bottom boundaries of the computational box, while lateral boundaries are treated as periodic. In most runs the background polytropic fluid configuration is held fixed at Rayleigh number R = 5.44 times the critical value, Prandtl number P = 1.8, and aspect ratio a = 1, while the magnetic parameters are allowed to vary. The resulting dynamical behavior is shown to be strongly influenced by a horizontal magnetic field which is imposed at the bottom boundary. As the field strength increases from zero, an initially unsteady 'single-roll' state, featuring complex time dependence is replaced by a steady 'traveling-wave tilted state; then, an oscillatory or 'sloshing' state; then, a steady two-poll state with no tilting; and finally, a stationary state. Because the magnetic field is matched onto a potential field at the top boundary, it can penetrate into the nonconducting region above. By varying a magnetic diffusivity, the concentrations of weak magnetic fields at the top of these flows can be shown to be explainable in terms of an advection-diffusion balance.

Thermodynamics of charged dilatonic BTZ black holes in rainbow gravity

NASA Astrophysics Data System (ADS)

Dehghani, M.

2018-02-01

In this paper, the charged three-dimensional Einstein's theory coupled to a dilatonic field has been considered in the rainbow gravity. The dilatonic potential has been written as the linear combination of two Liouville-type potentials. Four new classes of charged dilatonic rainbow black hole solutions, as the exact solution to the coupled field equations of the energy dependent space time, have been obtained. Two of them are correspond to the Coulomb's electric field and the others are consequences of a modified Coulomb's law. Total charge and mass as well as the entropy, temperature and electric potential of the new charged black holes have been calculated in the presence of rainbow functions. Although the thermodynamic quantities are affected by the rainbow functions, it has been found that the first law of black hole thermodynamics is still valid for all of the new black hole solutions. At the final stage, making use of the canonical ensemble method and regarding the black hole heat capacity, the thermal stability or phase transition of the new rainbow black hole solutions have been analyzed.

Moiré patterns in doubly differential electron-momentum distributions in atomic ionization by mid-infrared lasers

NASA Astrophysics Data System (ADS)

Dran, Martín; Arbó, Diego G.

2018-05-01

We analyze the doubly differential electron momentum distribution in above-threshold ionization of atomic hydrogen by a linearly polarized mid-infrared laser pulse. We reproduce side rings in the momentum distribution with forward-backward symmetry previously observed by Lemell et al. [Phys. Rev. A 87, 013421 (2013), 10.1103/PhysRevA.87.013421], whose origin, as far as we know, has not been explained so far. By developing a Fourier theory of moiré patterns, we demonstrate that such structures stem from the interplay between intra- and intercycle interference patterns which work as two separate grids in the two-dimensional momentum domain. We use a three-dimensional (3D) description based on the saddle-point approximation (SPA) to unravel the nature of these structures. When the periods of the two grids (intra- and intercycle) are similar, principal moiré patterns arise symmetrically as concentric rings in the forward and backward directions at high electron kinetic energy. Higher order moiré patterns are observed and characterized when the period of one grid is multiple of the other. We find a scale law for the position (in momentum space) of the center of the moiré rings in the tunneling regime. We verify the SPA predictions by comparison with time-dependent distorted-wave strong-field approximation calculations and the solutions of the full 3D time-dependent Schrödinger equation.

Three-dimensional thermocapillary flow regimes with evaporation

NASA Astrophysics Data System (ADS)

Bekezhanova, V. B.; Goncharova, O. N.

2017-10-01

A three-dimensional problem of evaporative convection in a system of the immiscible media with a common thermocapillary interface is studied. New exact solution, which is a generalization of the Ostroumov - Birikh solution of the Navier - Stokes equations in the Oberbeck - Boussinesq approximation, is presented in order to describe the joint flows of the liquid and gas - vapor mixture in an infinite channel with a rectangular cross-section. The motion occurs in the bulk force field under action of a constant longitudinal temperature gradient. The velocity components depend only on the transverse coordinates. The functions of pressure, temperature and concentration of vapor in the gas are characterized by the linear dependence on the longitudinal coordinate. In the framework of the problem statement, which takes into account diffusive mass flux through the interface and zero vapor flux at the upper boundary of the channel, the influence of the gravity and intensity of the thermal action on flow structure is studied. The original three-dimensional problem is reduced to a chain of two-dimensional problems which are solved numerically with help of modification of the method of alternating directions. Arising flows can be characterized as a translational-rotational motion, under that the symmetrical double, quadruple or sextuple vortex structures are formed. Quantity, shape and structure of the vortexes also depend on properties of the working media.

A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation

USGS Publications Warehouse

Smith, Peter E.

2006-01-01

A semi-implicit, finite-difference method for the numerical solution of the three-dimensional equations for circulation in estuaries is presented and tested. The method uses a three-time-level, leapfrog-trapezoidal scheme that is essentially second-order accurate in the spatial and temporal numerical approximations. The three-time-level scheme is shown to be preferred over a two-time-level scheme, especially for problems with strong nonlinearities. The stability of the semi-implicit scheme is free from any time-step limitation related to the terms describing vertical diffusion and the propagation of the surface gravity waves. The scheme does not rely on any form of vertical/horizontal mode-splitting to treat the vertical diffusion implicitly. At each time step, the numerical method uses a double-sweep method to transform a large number of small tridiagonal equation systems and then uses the preconditioned conjugate-gradient method to solve a single, large, five-diagonal equation system for the water surface elevation. The governing equations for the multi-level scheme are prepared in a conservative form by integrating them over the height of each horizontal layer. The layer-integrated volumetric transports replace velocities as the dependent variables so that the depth-integrated continuity equation that is used in the solution for the water surface elevation is linear. Volumetric transports are computed explicitly from the momentum equations. The resulting method is mass conservative, efficient, and numerically accurate.

Wake-shock interaction at a Mach number of 6

NASA Technical Reports Server (NTRS)

Walsh, M. J.

1978-01-01

Measurements of mean pitot pressure, static pressure, and total temperature were made in the two dimensional turbulent mixing region of a wake downstream of an interaction with a shock-expansion wave system. The results indicated that: (1) the shock increased the mixing, and (2) the expansion field that followed the shock decreased the turbulent mixing. The overall effect of the shock-expansion wave interaction was dependent on the orientation of the expansion wave with respect to the intersecting shock wave. These data could be used to validate nonequilibrium turbulence modeling and numerical solution of the time averaged Navier-Stokes equations.

The One-Dimensional Damped Forced Harmonic Oscillator Revisited

ERIC Educational Resources Information Center

Flores-Hidalgo, G.; Barone, F. A.

2011-01-01

In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.

Semi-implicit finite difference methods for three-dimensional shallow water flow

USGS Publications Warehouse

Casulli, Vincenzo; Cheng, Ralph T.

1992-01-01

A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.

Three-dimensional fracture instability of a displacement-weakening planar interface under locally peaked nonuniform loading

NASA Astrophysics Data System (ADS)

Uenishi, Koji

2018-06-01

We consider stability of fracture on a three-dimensional planar interface subjected to a loading stress that is locally peaked spatially, the level of which increases quasi-statically in time. Similar to the earlier study on the two-dimensional case (Uenishi and Rice, 2003; Rice and Uenishi, 2010), as the loading stress increases, a crack, or a region of displacement discontinuity (opening gap in tension or slip for shear fracture), develops on the interface where the stress is presumed to decrease according to a displacement-weakening constitutive relation. Upon reaching the instability point at which no further quasi-static solution for the extension of the crack on the interface exists, dynamic fracture follows. For the investigation of this instability point, we employ a dimensional analysis as well as an energy approach that gives a Rayleigh-Ritz approximation for the dependence of crack size and maximum displacement discontinuity on the level and quadratic shape of the loading stress distribution. We show that, if the linear displacement-weakening law is applied and the crack may be assumed of an elliptical form, the critical crack size at instability is independent of the curvature of the loading stress distribution and it is of the same order for all two- and three-dimensional cases.

Imaging bolometer

DOEpatents

Wurden, G.A.

1999-01-19

Radiation-hard, steady-state imaging bolometer is disclosed. A bolometer employing infrared (IR) imaging of a segmented-matrix absorber of plasma radiation in a cooled-pinhole camera geometry is described. The bolometer design parameters are determined by modeling the temperature of the foils from which the absorbing matrix is fabricated by using a two-dimensional time-dependent solution of the heat conduction equation. The resulting design will give a steady-state bolometry capability, with approximately 100 Hz time resolution, while simultaneously providing hundreds of channels of spatial information. No wiring harnesses will be required, as the temperature-rise data will be measured via an IR camera. The resulting spatial data may be used to tomographically investigate the profile of plasmas. 2 figs.

Imaging bolometer

DOEpatents

Wurden, Glen A.

1999-01-01

Radiation-hard, steady-state imaging bolometer. A bolometer employing infrared (IR) imaging of a segmented-matrix absorber of plasma radiation in a cooled-pinhole camera geometry is described. The bolometer design parameters are determined by modeling the temperature of the foils from which the absorbing matrix is fabricated by using a two-dimensional time-dependent solution of the heat conduction equation. The resulting design will give a steady-state bolometry capability, with approximately 100 Hz time resolution, while simultaneously providing hundreds of channels of spatial information. No wiring harnesses will be required, as the temperature-rise data will be measured via an IR camera. The resulting spatial data may be used to tomographically investigate the profile of plasmas.

Photon-momentum transfer in molecular photoionization

NASA Astrophysics Data System (ADS)

Chelkowski, Szczepan; Bandrauk, André D.

2018-05-01

In most models and theoretical calculations describing multiphoton ionization by infrared light, the dipole approximation is used. This is equivalent to setting the very small photon momentum to zero. Using numerical solutions of the (nondipole) three-dimensional time-dependent Schrödinger equation for one electron in a H2+ molecular ion we investigate the effect the photon-momentum transfer to the photoelectron in an H2+ ion in various regimes. We find that the photon-momentum transfer in a molecule is very different from the transfer in atoms due to two-center interference effects. The photon-momentum transfer is very sensitive to the symmetry of the initial electronic state and is strongly dependent on the internuclear distance and on the ellipticity of the laser.

Heating 7.2 user`s manual

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

Childs, K.W.

1993-02-01

HEATING is a general-purpose conduction heat transfer program written in Fortran 77. HEATING can solve steady-state and/or transient heat conduction problems in one-, two-, or three-dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may also be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heat-generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- andmore » position-dependent. The boundary conditions, which may be surface-to-environment or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General gray-body radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING uses a runtime memory allocation scheme to avoid having to recompile to match memory requirements for each specific problem. HEATING utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution, and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method. The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

Heating 7. 2 user's manual

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

Childs, K.W.

1993-02-01

HEATING is a general-purpose conduction heat transfer program written in Fortran 77. HEATING can solve steady-state and/or transient heat conduction problems in one-, two-, or three-dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may also be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heat-generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- andmore » position-dependent. The boundary conditions, which may be surface-to-environment or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General gray-body radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING uses a runtime memory allocation scheme to avoid having to recompile to match memory requirements for each specific problem. HEATING utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution, and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method. The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

Scale size-dependent characteristics of the nightside aurora

NASA Astrophysics Data System (ADS)

Humberset, B. K.; Gjerloev, J. W.; Samara, M.; Michell, R. G.

2017-02-01

We have determined the spatiotemporal characteristics of the magnetosphere-ionosphere (M-I) coupling using auroral imaging. Observations at fixed positions for an extended period of time are provided by a ground-based all-sky imager measuring the 557.7 nm auroral emissions. We report on a single event of nightside aurora (˜22 magnetic local time) preceding a substorm onset. To determine the spatiotemporal characteristics, we perform an innovative analysis of an all-sky imager movie (19 min duration, images at 3.31 Hz) that combines a two-dimensional spatial fast Fourier transform with a temporal correlation. We find a scale size-dependent variability where the largest scale sizes are stable on timescales of minutes while the small scale sizes are more variable. When comparing two smaller time intervals of different types of auroral displays, we find a variation in their characteristics. The characteristics averaged over the event are in remarkable agreement with the spatiotemporal characteristics of the nightside field-aligned currents during moderately disturbed times. Thus, two different electrodynamical parameters of the M-I coupling show similar behavior. This gives independent support to the claim of a system behavior that uses repeatable solutions to transfer energy and momentum from the magnetosphere to the ionosphere.

Documentation of the Surface-Water Routing (SWR1) Process for modeling surface-water flow with the U.S. Geological Survey Modular Ground-Water Model (MODFLOW-2005)

USGS Publications Warehouse

Hughes, Joseph D.; Langevin, Christian D.; Chartier, Kevin L.; White, Jeremy T.

2012-01-01

A flexible Surface-Water Routing (SWR1) Process that solves the continuity equation for one-dimensional and two-dimensional surface-water flow routing has been developed for the U.S. Geological Survey three-dimensional groundwater model, MODFLOW-2005. Simple level- and tilted-pool reservoir routing and a diffusive-wave approximation of the Saint-Venant equations have been implemented. Both methods can be implemented in the same model and the solution method can be simplified to represent constant-stage elements that are functionally equivalent to the standard MODFLOW River or Drain Package boundary conditions. A generic approach has been used to represent surface-water features (reaches) and allows implementation of a variety of geometric forms. One-dimensional geometric forms include rectangular, trapezoidal, and irregular cross section reaches to simulate one-dimensional surface-water features, such as canals and streams. Two-dimensional geometric forms include reaches defined using specified stage-volume-area-perimeter (SVAP) tables and reaches covering entire finite-difference grid cells to simulate two-dimensional surface-water features, such as wetlands and lakes. Specified SVAP tables can be used to represent reaches that are smaller than the finite-difference grid cell (for example, isolated lakes), or reaches that cannot be represented accurately using the defined top of the model. Specified lateral flows (which can represent point and distributed flows) and stage-dependent rainfall and evaporation can be applied to each reach. The SWR1 Process can be used with the MODFLOW Unsaturated Zone Flow (UZF1) Package to permit dynamic simulation of runoff from the land surface to specified reaches. Surface-water/groundwater interactions in the SWR1 Process are mathematically defined to be a function of the difference between simulated stages and groundwater levels, and the specific form of the reach conductance equation used in each reach. Conductance can be specified directly or calculated as a function of the simulated wetted perimeter and defined reach bed hydraulic properties, or as a weighted combination of both reach bed hydraulic properties and horizontal hydraulic conductivity. Each reach can be explicitly coupled to a single specific groundwater-model layer or coupled to multiple groundwater-model layers based on the reach geometry and groundwater-model layer elevations in the row and column containing the reach. Surface-water flow between reservoirs is simulated using control structures. Surface-water flow between reaches, simulated by the diffusive-wave approximation, can also be simulated using control structures. A variety of control structures have been included in the SWR1 Process and include (1) excess-volume structures, (2) uncontrolled-discharge structures, (3) pumps, (4) defined stage-discharge relations, (5) culverts, (6) fixed- or movable-crest weirs, and (7) fixed or operable gated spillways. Multiple control structures can be implemented in individual reaches and are treated as composite flow structures. Solution of the continuity equation at the reach-group scale (a single reach or a user-defined collection of individual reaches) is achieved using exact Newton methods with direct solution methods or exact and inexact Newton methods with Krylov sub-space methods. Newton methods have been used in the SWR1 Process because of their ability to solve nonlinear problems. Multiple SWR1 time steps can be simulated for each MODFLOW time step, and a simple adaptive time-step algorithm, based on user-specified rainfall, stage, flow, or convergence constraints, has been implemented to better resolve surface-water response. A simple linear- or sigmoid-depth scaling approach also has been implemented to account for increased bed roughness at small surface-water depths and to increase numerical stability. A line-search algorithm also has been included to improve the quality of the Newton-step upgrade vector, if possible. The SWR1 Process has been benchmarked against one- and two-dimensional numerical solutions from existing one- and two-dimensional numerical codes that solve the dynamic-wave approximation of the Saint-Venant equations. Two-dimensional solutions test the ability of the SWR1 Process to simulate the response of a surface-water system to (1) steady flow conditions for an inclined surface (solution of Manning's equation), and (2) transient inflow and rainfall for an inclined surface. The one-dimensional solution tests the ability of the SWR1 Process to simulate a looped network with multiple upstream inflows and several control structures. The SWR1 Process also has been compared to a level-pool reservoir solution. A synthetic test problem was developed to evaluate a number of different SWR1 solution options and simulate surface-water/groundwater interaction. The solution approach used in the SWR1 Process may not be applicable for all surface-water/groundwater problems. The SWR1 Process is best suited for modeling long-term changes (days to years) in surface-water and groundwater flow. Use of the SWR1 Process is not recommended for modeling the transient exchange of water between streams and aquifers when local and convective acceleration and other secondary effects (for example, wind and Coriolis forces) are substantial. Dam break evaluations and two-dimensional evaluations of spatially extensive domains are examples where acceleration terms and secondary effects would be significant, respectively.

An analytical solution for transient flow of Bingham viscoplastic materials in rock fractures

USGS Publications Warehouse

Amadei, B.; Savage, W.Z.

2001-01-01

We present below an analytical solution to model the one-dimensional transient flow of a Bingham viscoplastic material in a fracture with parallel walls (smooth or rough) that is subjected to an applied pressure gradient. The solution models the acceleration and the deceleration of the material as the pressure gradient changes with time. Two cases are considered: A pressure gradient applied over a finite time interval and an applied pressure gradient that is constant over time. The solution is expressed in dimensionless form and can therefore be used for a wide range of Bingham viscoplastic materials. The solution is also capable of capturing the transition that takes place in a fracture between viscoplastic flow and rigid plug flow. Also, it shows the development of a rigid central layer in fractures, the extent of which depends on the fluid properties (viscosity and yield stress), the magnitude of the pressure gradient, and the fracture aperture and surface roughness. Finally, it is shown that when a pressure gradient is applied and kept constant, the solution for the fracture flow rate converges over time to a steady-state solution that can be defined as a modified cubic law. In this case, the fracture transmissivity is found to be a non-linear function of the head gradient. This solution provides a tool for a better understanding of the flow of Bingham materials in rock fractures, interfaces, and cracks. ?? 2001 Elsevier Science Ltd. All rights reserved.

An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations

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

Sun, Wenjun, E-mail: sun_wenjun@iapcm.ac.cn; Jiang, Song, E-mail: jiang@iapcm.ac.cn; Xu, Kun, E-mail: makxu@ust.hk

The solutions of radiative transport equations can cover both optical thin and optical thick regimes due to the large variation of photon's mean-free path and its interaction with the material. In the small mean free path limit, the nonlinear time-dependent radiative transfer equations can converge to an equilibrium diffusion equation due to the intensive interaction between radiation and material. In the optical thin limit, the photon free transport mechanism will emerge. In this paper, we are going to develop an accurate and robust asymptotic preserving unified gas kinetic scheme (AP-UGKS) for the gray radiative transfer equations, where the radiation transportmore » equation is coupled with the material thermal energy equation. The current work is based on the UGKS framework for the rarefied gas dynamics [14], and is an extension of a recent work [12] from a one-dimensional linear radiation transport equation to a nonlinear two-dimensional gray radiative system. The newly developed scheme has the asymptotic preserving (AP) property in the optically thick regime in the capturing of diffusive solution without using a cell size being smaller than the photon's mean free path and time step being less than the photon collision time. Besides the diffusion limit, the scheme can capture the exact solution in the optical thin regime as well. The current scheme is a finite volume method. Due to the direct modeling for the time evolution solution of the interface radiative intensity, a smooth transition of the transport physics from optical thin to optical thick can be accurately recovered. Many numerical examples are included to validate the current approach.« less

Implicit solution of three-dimensional internal turbulent flows

NASA Technical Reports Server (NTRS)

Michelassi, V.; Liou, M.-S.; Povinelli, Louis A.; Martelli, F.

1991-01-01

The scalar form of the approximate factorization method was used to develop a new code for the solution of three dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form were iterated in time until a steady solution was reached. Evidence was given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at the domain boundaries was proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects were accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. The flow in a developing S-duct was then solved in the laminar regime in a Reynolds number (Re) of 790 and in the turbulent regime at Re equals 40,000 by using the Baldwin-Lomax model. The Stanitz elbow was then solved by using an invicid version of the same code at M sub inlet equals 0.4. Grid dependence and convergence rate were investigated, showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re equals 2.5 times 10(exp 6) was solved with the Baldwin-Lomax and the q-omega models. Both approaches show satisfactory agreement with experiments, although the q-omega model was slightly more accurate.

Time dependent wave envelope finite difference analysis of sound propagation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1984-01-01

A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.

Hybrid Fourier pseudospectral/discontinuous Galerkin time-domain method for wave propagation

NASA Astrophysics Data System (ADS)

Pagán Muñoz, Raúl; Hornikx, Maarten

2017-11-01

The Fourier Pseudospectral time-domain (Fourier PSTD) method was shown to be an efficient way of modelling acoustic propagation problems as described by the linearized Euler equations (LEE), but is limited to real-valued frequency independent boundary conditions and predominantly staircase-like boundary shapes. This paper presents a hybrid approach to solve the LEE, coupling Fourier PSTD with a nodal Discontinuous Galerkin (DG) method. DG exhibits almost no restrictions with respect to geometrical complexity or boundary conditions. The aim of this novel method is to allow the computation of complex geometries and to be a step towards the implementation of frequency dependent boundary conditions by using the benefits of DG at the boundaries, while keeping the efficient Fourier PSTD in the bulk of the domain. The hybridization approach is based on conformal meshes to avoid spatial interpolation of the DG solutions when transferring values from DG to Fourier PSTD, while the data transfer from Fourier PSTD to DG is done utilizing spectral interpolation of the Fourier PSTD solutions. The accuracy of the hybrid approach is presented for one- and two-dimensional acoustic problems and the main sources of error are investigated. It is concluded that the hybrid methodology does not introduce significant errors compared to the Fourier PSTD stand-alone solver. An example of a cylinder scattering problem is presented and accurate results have been obtained when using the proposed approach. Finally, no instabilities were found during long-time calculation using the current hybrid methodology on a two-dimensional domain.

A GPU-accelerated implicit meshless method for compressible flows

NASA Astrophysics Data System (ADS)

Zhang, Jia-Le; Ma, Zhi-Hua; Chen, Hong-Quan; Cao, Cheng

2018-05-01

This paper develops a recently proposed GPU based two-dimensional explicit meshless method (Ma et al., 2014) by devising and implementing an efficient parallel LU-SGS implicit algorithm to further improve the computational efficiency. The capability of the original 2D meshless code is extended to deal with 3D complex compressible flow problems. To resolve the inherent data dependency of the standard LU-SGS method, which causes thread-racing conditions destabilizing numerical computation, a generic rainbow coloring method is presented and applied to organize the computational points into different groups by painting neighboring points with different colors. The original LU-SGS method is modified and parallelized accordingly to perform calculations in a color-by-color manner. The CUDA Fortran programming model is employed to develop the key kernel functions to apply boundary conditions, calculate time steps, evaluate residuals as well as advance and update the solution in the temporal space. A series of two- and three-dimensional test cases including compressible flows over single- and multi-element airfoils and a M6 wing are carried out to verify the developed code. The obtained solutions agree well with experimental data and other computational results reported in the literature. Detailed analysis on the performance of the developed code reveals that the developed CPU based implicit meshless method is at least four to eight times faster than its explicit counterpart. The computational efficiency of the implicit method could be further improved by ten to fifteen times on the GPU.

Electrical level of defects in single-layer two-dimensional TiO2

NASA Astrophysics Data System (ADS)

Song, X. F.; Hu, L. F.; Li, D. H.; Chen, L.; Sun, Q. Q.; Zhou, P.; Zhang, D. W.

2015-11-01

The remarkable properties of graphene and transition metal dichalcogenides (TMDCs) have attracted increasing attention on two-dimensional materials, but the gate oxide, one of the key components of two-dimensional electronic devices, has rarely reported. We found the single-layer oxide can be used as the two dimensional gate oxide in 2D electronic structure, such as TiO2. However, the electrical performance is seriously influenced by the defects existing in the single-layer oxide. In this paper, a nondestructive and noncontact solution based on spectroscopic ellipsometry has been used to detect the defect states and energy level of single-layer TiO2 films. By fitting the Lorentz oscillator model, the results indicate the exact position of defect energy levels depends on the estimated band gap and the charge state of the point defects of TiO2.

Solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili dynamic equation in dust-acoustic plasmas

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-09-01

Nonlinear two-dimensional Kadomtsev-Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the two-dimensional nonlinear KP equation by implementing sech-tanh, sinh-cosh, extended direct algebraic and fraction direct algebraic methods. We found the electrostatic field potential and electric field in the form travelling wave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of Mathematica program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.

A model for near-wall dynamics in turbulent Rayleigh Bénard convection

NASA Astrophysics Data System (ADS)

Theerthan, S. Ananda; Arakeri, Jaywant H.

1998-10-01

Experiments indicate that turbulent free convection over a horizontal surface (e.g. Rayleigh Bénard convection) consists of essentially line plumes near the walls, at least for moderately high Rayleigh numbers. Based on this evidence, we propose here a two-dimensional model for near-wall dynamics in Rayleigh Bénard convection and in general for convection over heated horizontal surfaces. The model proposes a periodic array of steady laminar two-dimensional plumes. A plume is fed on either side by boundary layers on the wall. The results from the model are obtained in two ways. One of the methods uses the similarity solution of Rotem & Classen (1969) for the boundary layer and the similarity solution of Fuji (1963) for the plume. We have derived expressions for mean temperature and temperature and velocity fluctuations near the wall. In the second approach, we compute the two-dimensional flow field in a two-dimensional rectangular open cavity. The number of plumes in the cavity depends on the length of the cavity. The plume spacing is determined from the critical length at which the number of plumes increases by one. The results for average plume spacing and the distribution of r.m.s. temperature and velocity fluctuations are shown to be in acceptable agreement with experimental results.

Communication: On the calculation of time-dependent electron flux within the Born-Oppenheimer approximation: A flux-flux reflection principle

NASA Astrophysics Data System (ADS)

Albert, Julian; Hader, Kilian; Engel, Volker

2017-12-01

It is commonly assumed that the time-dependent electron flux calculated within the Born-Oppenheimer (BO) approximation vanishes. This is not necessarily true if the flux is directly determined from the continuity equation obeyed by the electron density. This finding is illustrated for a one-dimensional model of coupled electronic-nuclear dynamics. There, the BO flux is in perfect agreement with the one calculated from a solution of the time-dependent Schrödinger equation for the coupled motion. A reflection principle is derived where the nuclear BO flux is mapped onto the electronic flux.

Polymer diffusion in the interphase between surface and solution.

PubMed

Weger, Lukas; Weidmann, Monika; Ali, Wael; Hildebrandt, Marcus; Gutmann, Jochen Stefan; Hoffmann-Jacobsen, Kerstin

2018-05-22

Total internal reflection fluorescence correlation spectroscopy (TIR-FCS) is applied to study the self-diffusion of polyethylene glycol solutions in the presence of weakly attractive interfaces. Glass coverslips modified with aminopropyl- and propyl-terminated silanes are used to study the influence of solid surfaces on polymer diffusion. A model of three phases of polymer diffusion allows to describe the experimental fluorescence autocorrelation functions. Besides the two-dimensional diffusion of adsorbed polymer on the substrate and three-dimensional free diffusion in bulk solution, a third diffusion time scale is observed with intermediate diffusion times. This retarded three-dimensional diffusion in solution is assigned to long range effects of solid surfaces on diffusional dynamics of polymers. The respective diffusion constants show Rouse scaling (D~N -1 ) indicating a screening of hydrodynamic interactions by the presence of the surface. Hence, the presented TIR-FCS method proves to be a valuable tool to investigate the effect of surfaces on polymer diffusion beyond the first adsorbed polymer layer on the 100 nm length scale.

Vortex methods for separated flows

NASA Technical Reports Server (NTRS)

Spalart, Philippe R.

1988-01-01

The numerical solution of the Euler or Navier-Stokes equations by Lagrangian vortex methods is discussed. The mathematical background is presented and includes the relationship with traditional point-vortex studies, convergence to smooth solutions of the Euler equations, and the essential differences between two and three-dimensional cases. The difficulties in extending the method to viscous or compressible flows are explained. Two-dimensional flows around bluff bodies are emphasized. Robustness of the method and the assessment of accuracy, vortex-core profiles, time-marching schemes, numerical dissipation, and efficient programming are treated. Operation counts for unbounded and periodic flows are given, and two algorithms designed to speed up the calculations are described.

Similarity solutions of some two-space-dimensional nonlinear wave evolution equations

NASA Technical Reports Server (NTRS)

Redekopp, L. G.

1980-01-01

Similarity reductions of the two-space-dimensional versions of the Korteweg-de Vries, modified Korteweg-de Vries, Benjamin-Davis-Ono, and nonlinear Schroedinger equations are presented, and some solutions of the reduced equations are discussed. Exact dispersive solutions of the two-dimensional Korteweg-de Vries equation are obtained, and the similarity solution of this equation is shown to be reducible to the second Painleve transcendent.

A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials

NASA Astrophysics Data System (ADS)

Sun, Zheng; Carrillo, José A.; Shu, Chi-Wang

2018-01-01

We consider a class of time-dependent second order partial differential equations governed by a decaying entropy. The solution usually corresponds to a density distribution, hence positivity (non-negativity) is expected. This class of problems covers important cases such as Fokker-Planck type equations and aggregation models, which have been studied intensively in the past decades. In this paper, we design a high order discontinuous Galerkin method for such problems. If the interaction potential is not involved, or the interaction is defined by a smooth kernel, our semi-discrete scheme admits an entropy inequality on the discrete level. Furthermore, by applying the positivity-preserving limiter, our fully discretized scheme produces non-negative solutions for all cases under a time step constraint. Our method also applies to two dimensional problems on Cartesian meshes. Numerical examples are given to confirm the high order accuracy for smooth test cases and to demonstrate the effectiveness for preserving long time asymptotics.

On Takens’ last problem: tangencies and time averages near heteroclinic networks

NASA Astrophysics Data System (ADS)

Labouriau, Isabel S.; Rodrigues, Alexandre A. P.

2017-05-01

We obtain a structurally stable family of smooth ordinary differential equations exhibiting heteroclinic tangencies for a dense subset of parameters. We use this to find vector fields C 2-close to an element of the family exhibiting a tangency, for which the set of solutions with historic behaviour contains an open set. This provides an affirmative answer to Takens’ last problem (Takens 2008 Nonlinearity 21 T33-6). A limited solution with historic behaviour is one for which the time averages do not converge as time goes to infinity. Takens’ problem asks for dynamical systems where historic behaviour occurs persistently for initial conditions in a set with positive Lebesgue measure. The family appears in the unfolding of a degenerate differential equation whose flow has an asymptotically stable heteroclinic cycle involving two-dimensional connections of non-trivial periodic solutions. We show that the degenerate problem also has historic behaviour, since for an open set of initial conditions starting near the cycle, the time averages approach the boundary of a polygon whose vertices depend on the centres of gravity of the periodic solutions and their Floquet multipliers. We illustrate our results with an explicit example where historic behaviour arises C 2-close of a \\mathbf{SO}(2) -equivariant vector field.

Blading Design for Axial Turbomachines

DTIC Science & Technology

1989-05-01

three- dimensional, viscous computation systems appear to have a long development period ahead, in which fluid shear stress modeling and computation time ...and n directions and T is the shear stress , As a consequence the solution time is longer than for integral methods, dependent largely on thc accuracy of...distributions over airfoils is an adaptation of thin plate deflection theory from stress analysis. At the same time , it minimizes designer effort

Glass transition and relaxation dynamics of propylene glycol-water solutions confined in clay

NASA Astrophysics Data System (ADS)

Elamin, Khalid; Björklund, Jimmy; Nyhlén, Fredrik; Yttergren, Madeleine; Mârtensson, Lena; Swenson, Jan

2014-07-01

The molecular dynamics of aqueous solutions of propylene glycol (PG) and propylene glycol methylether (PGME) confined in a two-dimensional layer-structured Na-vermiculite clay has been studied by broadband dielectric spectroscopy and differential scanning calorimetry. As typical for liquids in confined geometries the intensity of the cooperative α-relaxation becomes considerably more suppressed than the more local β-like relaxation processes. In fact, at high water contents the calorimetric glass transition and related structural α-relaxation cannot even be observed, due to the confinement. Thus, the intensity of the viscosity related α-relaxation is dramatically reduced, but its time scale as well as the related glass transition temperature Tg are for both systems only weakly influenced by the confinement. In the case of the PGME-water solutions it is an important finding since in the corresponding bulk system a pronounced non-monotonic concentration dependence of the glass transition related dynamics has been observed due to the growth of hydrogen bonded relaxing entities of water bridging between PGME molecules [J. Sjöström, J. Mattsson, R. Bergman, and J. Swenson, Phys. Chem. B 115, 10013 (2011)]. The present results suggest that the same type of structural entities are formed in the quasi-two-dimensional space between the clay platelets. It is also observed that the main water relaxation cannot be distinguished from the β-relaxation of PG or PGME in the concentration range up to intermediate water contents. This suggests that these two processes are coupled and that the water molecules affect the time scale of the β-relaxation. However, this is most likely true also for the corresponding bulk solutions, which exhibit similar time scales of this combined relaxation process below Tg. Finally, it is found that at higher water contents the water relaxation does not merge with, or follow, the α-relaxation above Tg, but instead crosses the α-relaxation, indicating that the two relaxation processes are independent of each other. This can only occur if the two processes do not occur in the same parts of the confined solutions. Most likely the hydration shell of the interlayer Na+ ions is causing this water relaxation, which does not participate in the α-relaxation at any temperature.

Glass transition and relaxation dynamics of propylene glycol-water solutions confined in clay.

PubMed

Elamin, Khalid; Björklund, Jimmy; Nyhlén, Fredrik; Yttergren, Madeleine; Mårtensson, Lena; Swenson, Jan

2014-07-21

The molecular dynamics of aqueous solutions of propylene glycol (PG) and propylene glycol methylether (PGME) confined in a two-dimensional layer-structured Na-vermiculite clay has been studied by broadband dielectric spectroscopy and differential scanning calorimetry. As typical for liquids in confined geometries the intensity of the cooperative α-relaxation becomes considerably more suppressed than the more local β-like relaxation processes. In fact, at high water contents the calorimetric glass transition and related structural α-relaxation cannot even be observed, due to the confinement. Thus, the intensity of the viscosity related α-relaxation is dramatically reduced, but its time scale as well as the related glass transition temperature Tg are for both systems only weakly influenced by the confinement. In the case of the PGME-water solutions it is an important finding since in the corresponding bulk system a pronounced non-monotonic concentration dependence of the glass transition related dynamics has been observed due to the growth of hydrogen bonded relaxing entities of water bridging between PGME molecules [J. Sjöström, J. Mattsson, R. Bergman, and J. Swenson, Phys. Chem. B 115, 10013 (2011)]. The present results suggest that the same type of structural entities are formed in the quasi-two-dimensional space between the clay platelets. It is also observed that the main water relaxation cannot be distinguished from the β-relaxation of PG or PGME in the concentration range up to intermediate water contents. This suggests that these two processes are coupled and that the water molecules affect the time scale of the β-relaxation. However, this is most likely true also for the corresponding bulk solutions, which exhibit similar time scales of this combined relaxation process below Tg. Finally, it is found that at higher water contents the water relaxation does not merge with, or follow, the α-relaxation above Tg, but instead crosses the α-relaxation, indicating that the two relaxation processes are independent of each other. This can only occur if the two processes do not occur in the same parts of the confined solutions. Most likely the hydration shell of the interlayer Na(+) ions is causing this water relaxation, which does not participate in the α-relaxation at any temperature.

Nonlocal birth-death competitive dynamics with volume exclusion

NASA Astrophysics Data System (ADS)

Khalil, Nagi; López, Cristóbal; Hernández-García, Emilio

2017-06-01

A stochastic birth-death competition model for particles with excluded volume is proposed. The particles move, reproduce, and die on a regular lattice. While the death rate is constant, the birth rate is spatially nonlocal and implements inter-particle competition by a dependence on the number of particles within a finite distance. The finite volume of particles is accounted for by fixing an upper value to the number of particles that can occupy a lattice node, compromising births and movements. We derive closed macroscopic equations for the density of particles and spatial correlation at two adjacent sites. Under different conditions, the description is further reduced to a single equation for the particle density that contains three terms: diffusion, a linear death, and a highly nonlinear and nonlocal birth term. Steady-state homogeneous solutions, their stability which reveals spatial pattern formation, and the dynamics of time-dependent homogeneous solutions are discussed and compared, in the one-dimensional case, with numerical simulations of the particle system.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Sampling design for groundwater solute transport: Tests of methods and analysis of Cape Cod tracer test data

USGS Publications Warehouse

Knopman, Debra S.; Voss, Clifford I.; Garabedian, Stephen P.

1991-01-01

Tests of a one-dimensional sampling design methodology on measurements of bromide concentration collected during the natural gradient tracer test conducted by the U.S. Geological Survey on Cape Cod, Massachusetts, demonstrate its efficacy for field studies of solute transport in groundwater and the utility of one-dimensional analysis. The methodology was applied to design of sparse two-dimensional networks of fully screened wells typical of those often used in engineering practice. In one-dimensional analysis, designs consist of the downstream distances to rows of wells oriented perpendicular to the groundwater flow direction and the timing of sampling to be carried out on each row. The power of a sampling design is measured by its effectiveness in simultaneously meeting objectives of model discrimination, parameter estimation, and cost minimization. One-dimensional models of solute transport, differing in processes affecting the solute and assumptions about the structure of the flow field, were considered for description of tracer cloud migration. When fitting each model using nonlinear regression, additive and multiplicative error forms were allowed for the residuals which consist of both random and model errors. The one-dimensional single-layer model of a nonreactive solute with multiplicative error was judged to be the best of those tested. Results show the efficacy of the methodology in designing sparse but powerful sampling networks. Designs that sample five rows of wells at five or fewer times in any given row performed as well for model discrimination as the full set of samples taken up to eight times in a given row from as many as 89 rows. Also, designs for parameter estimation judged to be good by the methodology were as effective in reducing the variance of parameter estimates as arbitrary designs with many more samples. Results further showed that estimates of velocity and longitudinal dispersivity in one-dimensional models based on data from only five rows of fully screened wells each sampled five or fewer times were practically equivalent to values determined from moments analysis of the complete three-dimensional set of 29,285 samples taken during 16 sampling times.

PACE-90 water and solute transport calculations for 0.01, 0.1, and 0. 5 mm/yr infiltration into Yucca Mountain; Yucca Mountain Site Characterization Project

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

Dykhuizen, R.C.; Eaton, R.R.; Hopkins, P.L.

1991-12-01

Numerical results are presented for the Performance Assessment Calculational Exercise (PACE-90). One- and two-dimensional water and solute transport are presented for steady infiltration into Yucca Mountain. Evenly distributed infiltration rates of 0.01, 0.1, and 0.5 mm/yr were considered. The calculations of solute transport show that significant amounts of radionuclides can reach the water table over 100,000 yr at the 0.5 mm/yr rate. For time periods less than 10,000 yr or infiltrations less than 0.1 mm/yr very little solute reaches the water table. The numerical simulations clearly demonstrate that multi-dimensional effects can result in significant decreases in the travel time ofmore » solute through the modeled domain. Dual continuum effects are shown to be negligible for the low steady state fluxes considered. However, material heterogeneities may cause local amplification of the flux level in multi-dimensional flows. These higher flux levels may then require modeling of a dual continuum porous medium.« less

Reaction mechanisms of methylene-blue degradation in three-dimensionally integrated micro-solution plasma

NASA Astrophysics Data System (ADS)

Shirafuji, Tatsuru; Ishida, Yodai; Nomura, Ayano; Hayashi, Yui; Goto, Motonobu

2017-06-01

We have performed matrix-assisted laser desorption ionization time-of-flight (MALDI-TOF) mass spectrometry (MS) on methylene-blue aqueous solutions treated with three-dimensionally integrated micro-solution plasma, in which we have acquired the time evolution of mass spectra as a function of treatment time. The time evolution of mass spectral peak intensities for major detected species has clearly indicated that the parent methylene-blue molecules are degraded through consecutive reactions. The primary reaction is the oxidation of the parent molecules. The oxidized species still have two benzene rings in the parent molecules. The secondary reactions are the separation of the oxidized species and the formation of compounds with one benzene ring. We have also performed the numerical fitting of the time evolution of the mass spectral peak intensities, the results of which have indicated that we must assume additional primary reactions before the primary oxidation for better agreement with experimental results.

Parallel computation in a three-dimensional elastic-plastic finite-element analysis

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Bigelow, C. A.; Newman, J. C., Jr.

1992-01-01

A CRAY parallel processing technique called autotasking was implemented in a three-dimensional elasto-plastic finite-element code. The technique was evaluated on two CRAY supercomputers, a CRAY 2 and a CRAY Y-MP. Autotasking was implemented in all major portions of the code, except the matrix equations solver. Compiler directives alone were not able to properly multitask the code; user-inserted directives were required to achieve better performance. It was noted that the connect time, rather than wall-clock time, was more appropriate to determine speedup in multiuser environments. For a typical example problem, a speedup of 2.1 (1.8 when the solution time was included) was achieved in a dedicated environment and 1.7 (1.6 with solution time) in a multiuser environment on a four-processor CRAY 2 supercomputer. The speedup on a three-processor CRAY Y-MP was about 2.4 (2.0 with solution time) in a multiuser environment.

Effect of nose shape on three-dimensional stagnation region streamlines and heating rates

NASA Technical Reports Server (NTRS)

Hassan, Basil; Dejarnette, Fred R.; Zoby, E. V.

1991-01-01

A new method for calculating the three-dimensional inviscid surface streamlines and streamline metrics using Cartesian coordinates and time as the independent variable of integration has been developed. The technique calculates the streamline from a specified point on the body to a point near the stagnation point by using a prescribed pressure distribution in the Euler equations. The differential equations, which are singular at the stagnation point, are of the two point boundary value problem type. Laminar heating rates are calculated using the axisymmetric analog concept for three-dimensional boundary layers and approximate solutions to the axisymmetric boundary layer equations. Results for elliptic conic forebody geometries show that location of the point of maximum heating depends on the type of conic in the plane of symmetry and the angle of attack, and that this location is in general different from the stagnation point. The new method was found to give smooth predictions of heat transfer in the nose region where previous methods gave oscillatory results.

Dynamics and Stability of Rolling Viscoelastic Tires

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

Potter, Trevor

2013-04-30

Current steady state rolling tire calculations often do not include treads because treads destroy the rotational symmetry of the tire. We describe two methodologies to compute time periodic solutions of a two-dimensional viscoelastic tire with treads: solving a minimization problem and solving a system of equations. We also expand on work by Oden and Lin on free spinning rolling elastic tires in which they disovered a hierachy of N-peak steady state standing wave solutions. In addition to discovering a two-dimensional hierarchy of standing wave solutions that includes their N-peak hiearchy, we consider the eects of viscoelasticity on the standing wavemore » solutions. Finally, a commonplace model of viscoelasticity used in our numerical experiments led to non-physical elastic energy growth for large tire speeds. We show that a viscoelastic model of Govindjee and Reese remedies the problem.« less

Resonance phenomena in a time-dependent, three-dimensional model of an idealized eddy

NASA Astrophysics Data System (ADS)

Rypina, I. I.; Pratt, L. J.; Wang, P.; Äe; -zgökmen, T. M.; Mezic, I.

2015-08-01

We analyze the geometry of Lagrangian motion and material barriers in a time-dependent, three-dimensional, Ekman-driven, rotating cylinder flow, which serves as an idealization for an isolated oceanic eddy and other overturning cells with cylindrical geometry in the ocean and atmosphere. The flow is forced at the top through an oscillating upper lid, and the response depends on the frequency and amplitude of lid oscillations. In particular, the Lagrangian geometry changes near the resonant tori of the unforced flow, whose frequencies are rationally related to the forcing frequencies. Multi-scale analytical expansions are used to simplify the flow in the vicinity of resonant trajectories and to investigate the resonant flow geometries. The resonance condition and scaling can be motivated by simple physical argument. The theoretically predicted flow geometries near resonant trajectories have then been confirmed through numerical simulations in a phenomenological model and in a full solution of the Navier-Stokes equations.

Compositions comprising free-standing two-dimensional nanocrystals

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

Barsoum, Michel W.; Gogotsi, Yury; Abdelmalak, Michael Naguib

2017-12-05

The present invention is directed to methods of transferring urea from an aqueous solution comprising urea to a MXene composition, the method comprising contacting the aqueous solution comprising urea with the MXene composition for a time sufficient to form an intercalated MXene composition comprising urea.

A grid generation and flow solution method for the Euler equations on unstructured grids

NASA Astrophysics Data System (ADS)

Anderson, W. Kyle

1994-01-01

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

NASA Technical Reports Server (NTRS)

Tseng, K.

1984-01-01

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

3D visualization of unsteady 2D airplane wake vortices

NASA Technical Reports Server (NTRS)

Ma, Kwan-Liu; Zheng, Z. C.

1994-01-01

Air flowing around the wing tips of an airplane forms horizontal tornado-like vortices that can be dangerous to following aircraft. The dynamics of such vortices, including ground and atmospheric effects, can be predicted by numerical simulation, allowing the safety and capacity of airports to be improved. In this paper, we introduce three-dimensional techniques for visualizing time-dependent, two-dimensional wake vortex computations, and the hazard strength of such vortices near the ground. We describe a vortex core tracing algorithm and a local tiling method to visualize the vortex evolution. The tiling method converts time-dependent, two-dimensional vortex cores into three-dimensional vortex tubes. Finally, a novel approach calculates the induced rolling moment on the following airplane at each grid point within a region near the vortex tubes and thus allows three-dimensional visualization of the hazard strength of the vortices. We also suggest ways of combining multiple visualization methods to present more information simultaneously.

One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

Asymptotic solution of the turbulent mixing layer for velocity ratio close to unity

NASA Technical Reports Server (NTRS)

Higuera, F. J.; Jimenez, J.; Linan, A.

1996-01-01

The equations describing the first two terms of an asymptotic expansion of the solution of the planar turbulent mixing layer for values of the velocity ratio close to one are obtained. The first term of this expansion is the solution of the well-known time-evolving problem and the second, which includes the effects of the increase of the turbulence scales in the stream-wise direction, obeys a linear system of equations. Numerical solutions of these equations for a two-dimensional reacting mixing layer show that the correction to the time-evolving solution may explain the asymmetry of the entrainment and the differences in product generation observed in flip experiments.

Comparison of two- and three-dimensional flow computations with laser anemometer measurements in a transonic compressor rotor

NASA Technical Reports Server (NTRS)

Chima, R. V.; Strazisar, A. J.

1982-01-01

Two and three dimensional inviscid solutions for the flow in a transonic axial compressor rotor at design speed are compared with probe and laser anemometers measurements at near-stall and maximum-flow operating points. Experimental details of the laser anemometer system and computational details of the two dimensional axisymmetric code and three dimensional Euler code are described. Comparisons are made between relative Mach number and flow angle contours, shock location, and shock strength. A procedure for using an efficient axisymmetric code to generate downstream pressure input for computationally expensive Euler codes is discussed. A film supplement shows the calculations of the two operating points with the time-marching Euler code.

Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel.

PubMed

Marcos; Yang, C; Ooi, K T; Wong, T N; Masliyah, J H

2004-07-15

This article presents an analysis of the frequency- and time-dependent electroosmotic flow in a closed-end rectangular microchannel. An exact solution to the modified Navier-Stokes equation governing the ac electroosmotic flow field is obtained by using the Green's function formulation in combination with a complex variable approach. An analytical expression for the induced backpressure gradient is derived. With the Debye-Hückel approximation, the electrical double-layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Since the counterparts of the flow rate and the electrical current are shown to be linearly proportional to the applied electric field and the pressure gradient, Onsager's principle of reciprocity is demonstrated for transient and ac electroosmotic flows. The time evolution of the electroosmotic flow and the effect of a frequency-dependent ac electric field on the oscillating electroosmotic flow in a closed-end rectangular microchannel are examined. Specifically, the induced pressure gradient is analyzed under effects of the channel dimension and the frequency of electric field. In addition, based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical scheme developed in this study. Copyright 2004 Elsevier Inc.

Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Luo, Li-Shi

2007-01-01

In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method.

PubMed

Reck, Kasper; Thomsen, Erik V; Hansen, Ole

2011-01-31

The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.

Causal Structure around Spinning 5-DIMENSIONAL Cosmic Strings

NASA Astrophysics Data System (ADS)

Slagter, Reinoud Jan

2008-09-01

We present a numerical solution of a stationary 5-dimensional spinning cosmic string in the Einstein-Yang-Mills (EYM) model, where the extra bulk coordinate ψ is periodic. It turns out that when gψψ approaches zero, i.e., a closed time-like curve (CTC) would appear, the solution becomes singular. We also investigated the geometrical structure of the static 5D cosmic string. Two opposite moving 5D strings could, in contrast with the 4D case, fulfil the Gott condition for CTC formation.

Nonequilibrium segregation and phase instability in alloy films during elevated-temperature irradiation in a high-voltage electron microscope

NASA Astrophysics Data System (ADS)

Lam, N. Q.; Okamoto, P. R.

1984-05-01

The effects of defect-production rate gradients, caused by the radial nonuniformity in the electron flux distribution, on solute segregation and phase stability in alloy films undergoing high-voltage electron-microscope (HVEM) irradiation at high temperatures are assessed. Two-dimensional (axially symmetric) compositional redistributions were calculated, taking into account both axial and transverse radial defect fluxes. It was found that when highly focused beams were employed radiation-induced segregation consisted of two stages: dominant axial segregation at the film surfaces at short irradiation times and competitive radial segregation at longer times. The average alloy composition within the irradiated region could differ greatly from that irradiated with a uniform beam, because of the additional atom transport from or to the region surrounding the irradiated zone under the influence of radial fluxes. Damage-rate gradient effects must be taken into account when interpreting in-situ HVEM observations of segregation-induced phase instabilities. The theoretical predictions are compared with experimental observations of the temporal and spatial dependence of segregation-induced precipitation in thin films of Ni-Al, Ni-Ge and Ni-Si solid solutions.

Stabilization and control of distributed systems with time-dependent spatial domains

NASA Technical Reports Server (NTRS)

Wang, P. K. C.

1990-01-01

This paper considers the problem of the stabilization and control of distributed systems with time-dependent spatial domains. The evolution of the spatial domains with time is described by a finite-dimensional system of ordinary differential equations, while the distributed systems are described by first-order or second-order linear evolution equations defined on appropriate Hilbert spaces. First, results pertaining to the existence and uniqueness of solutions of the system equations are presented. Then, various optimal control and stabilization problems are considered. The paper concludes with some examples which illustrate the application of the main results.

Gravity-Driven Thin Film Flow of an Ellis Fluid.

PubMed

Kheyfets, Vitaly O; Kieweg, Sarah L

2013-12-01

The thin film lubrication approximation has been studied extensively for moving contact lines of Newtonian fluids. However, many industrial and biological applications of the thin film equation involve shear-thinning fluids, which often also exhibit a Newtonian plateau at low shear. This study presents new numerical simulations of the three-dimensional (i.e. two-dimensional spreading), constant-volume, gravity-driven, free surface flow of an Ellis fluid. The numerical solution was validated with a new similarity solution, compared to previous experiments, and then used in a parametric study. The parametric study centered around rheological data for an example biological application of thin film flow: topical drug delivery of anti-HIV microbicide formulations, e.g. hydroxyethylcellulose (HEC) polymer solutions. The parametric study evaluated how spreading length and front velocity saturation depend on Ellis parameters. A lower concentration polymer solution with smaller zero shear viscosity ( η 0 ), τ 1/2 , and λ values spread further. However, when comparing any two fluids with any possible combinations of Ellis parameters, the impact of changing one parameter on spreading length depends on the direction and magnitude of changes in the other two parameters. In addition, the isolated effect of the shear-thinning parameter, λ , on the front velocity saturation depended on τ 1/2 . This study highlighted the relative effects of the individual Ellis parameters, and showed that the shear rates in this flow were in both the shear-thinning and plateau regions of rheological behavior, emphasizing the importance of characterizing the full range of shear-rates in rheological measurements. The validated numerical model and parametric study provides a useful tool for future steps to optimize flow of a fluid with rheological behavior well-described by the Ellis constitutive model, in a range of industrial and biological applications.

A One Dimensional, Time Dependent Inlet/Engine Numerical Simulation for Aircraft Propulsion Systems

NASA Technical Reports Server (NTRS)

Garrard, Doug; Davis, Milt, Jr.; Cole, Gary

1999-01-01

The NASA Lewis Research Center (LeRC) and the Arnold Engineering Development Center (AEDC) have developed a closely coupled computer simulation system that provides a one dimensional, high frequency inlet/engine numerical simulation for aircraft propulsion systems. The simulation system, operating under the LeRC-developed Application Portable Parallel Library (APPL), closely coupled a supersonic inlet with a gas turbine engine. The supersonic inlet was modeled using the Large Perturbation Inlet (LAPIN) computer code, and the gas turbine engine was modeled using the Aerodynamic Turbine Engine Code (ATEC). Both LAPIN and ATEC provide a one dimensional, compressible, time dependent flow solution by solving the one dimensional Euler equations for the conservation of mass, momentum, and energy. Source terms are used to model features such as bleed flows, turbomachinery component characteristics, and inlet subsonic spillage while unstarted. High frequency events, such as compressor surge and inlet unstart, can be simulated with a high degree of fidelity. The simulation system was exercised using a supersonic inlet with sixty percent of the supersonic area contraction occurring internally, and a GE J85-13 turbojet engine.

Gapped fermionic spectrum from a domain wall in seven dimension

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Subir; Rai, Nishal

2018-05-01

We obtain a domain wall solution in maximally gauged seven dimensional supergravity, which interpolates between two AdS spaces and spontaneously breaks a U (1) symmetry. We analyse frequency dependence of conductivity and find power law behaviour at low frequency. We consider certain fermions of supergravity in the background of this domain wall and compute holographic spectral function of the operators in the dual six dimensional theory. We find fermionic operators involving bosons with non-zero expectation value lead to gapped spectrum.

Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management

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

D'Ambroise, J.; Salerno, M.; Kevrekidis, P. G.

The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds. We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined.more » We also found that other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. Finally, the possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.« less

Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management

DOE PAGES

D'Ambroise, J.; Salerno, M.; Kevrekidis, P. G.; ...

2015-11-19

The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds. We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined.more » We also found that other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. Finally, the possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.« less

The simulation of a two-dimensional (2D) transport problem in a rectangular region with Lattice Boltzmann method with two-relaxation-time

NASA Astrophysics Data System (ADS)

Sugiyanto, S.; Hardyanto, W.; Marwoto, P.

2018-03-01

Transport phenomena are found in many problems in many engineering and industrial sectors. We analyzed a Lattice Boltzmann method with Two-Relaxation Time (LTRT) collision operators for simulation of pollutant moving through the medium as a two-dimensional (2D) transport problem in a rectangular region model. This model consists of a 2D rectangular region with 54 length (x), 27 width (y), and it has isotropic homogeneous medium. Initially, the concentration is zero and is distributed evenly throughout the region of interest. A concentration of 1 is maintained at 9 < y < 18, whereas the concentration of zero is maintained at 0 < y < 9 and 18 < y < 27. A specific discharge (Darcy velocity) of 1.006 is assumed. A diffusion coefficient of 0.8333 is distributed uniformly with a uniform porosity of 0.35. A computer program is written in MATLAB to compute the concentration of pollutant at any specified place and time. The program shows that LTRT solution with quadratic equilibrium distribution functions (EDFs) and relaxation time τa=1.0 are in good agreement result with other numerical solutions methods such as 3DLEWASTE (Hybrid Three-dimensional Lagrangian-Eulerian Finite Element Model of Waste Transport Through Saturated-Unsaturated Media) obtained by Yeh and 3DFEMWATER-LHS (Three-dimensional Finite Element Model of Water Flow Through Saturated-Unsaturated Media with Latin Hypercube Sampling) obtained by Hardyanto.

Siegert-state expansion for nonstationary systems. IV. Three-dimensional case

NASA Astrophysics Data System (ADS)

Tolstikhin, Oleg I.

2008-03-01

The Siegert-state expansion approach [O. I. Tolstikhin, Phys. Rev. A 73, 062705 (2006)] is extended to the three-dimensional case. Coupled equations defining the time evolution of coefficients in the expansion of the solution to the time-dependent Schrödinger equation in terms of partial-wave Siegert states are derived, and physical observables (probabilities of transitions to discrete states and the momentum distribution of ejected particles) are expressed in terms of these coefficients. The approach is implemented in terms of Siegert pseudostates and illustrated by calculations of the photodetachment of H- by strong high-frequency laser pulses. The present calculations demonstrate that the interference effect in the laser-atom interaction dynamics found recently in the one-dimensional case [K. Toyota , Phys. Rev. A 76, 043418 (2007)] reveals itself in the three-dimensional case as well.

Space-time adaptive solution of inverse problems with the discrete adjoint method

NASA Astrophysics Data System (ADS)

Alexe, Mihai; Sandu, Adrian

2014-08-01

This paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent, adaptive grid, adaptive step models. Discrete adjoints are attractive in practice since they can be generated with low effort using automatic differentiation. However, this approach brings several important challenges. The space-time adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations. A reduction in accuracy of the discrete adjoint sensitivities may appear due to the inter-grid transfer operators. Moreover, the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations. This work shows that several of these potential issues can be avoided through a multi-level optimization strategy using discontinuous Galerkin (DG) hp-adaptive discretizations paired with Runge-Kutta (RK) time integration. We extend the concept of dual (adjoint) consistency to space-time RK-DG discretizations, which are then shown to be well suited for the adaptive solution of time-dependent inverse problems. Furthermore, we prove that DG mesh transfer operators on general meshes are also dual consistent. This allows the simultaneous derivation of the discrete adjoint for both the numerical solver and the mesh transfer logic with an automatic code generation mechanism such as algorithmic differentiation (AD), potentially speeding up development of large-scale simulation codes. The theoretical analysis is supported by numerical results reported for a two-dimensional non-stationary inverse problem.

Intrinsic coherence time of trions in monolayer MoSe2 measured via two-dimensional coherent spectroscopy

NASA Astrophysics Data System (ADS)

Titze, Michael; Li, Bo; Zhang, Xiang; Ajayan, Pulickel M.; Li, Hebin

2018-05-01

Quantum coherence and its dynamics in monolayer transition metal dichalcogenides (TMDs) are essential information to fully control valley pseudospin for valleytronics applications. Experimental understanding of coherence dephasing dynamics has been limited for excitons and largely unexplored for trions in monolayer TMDs. Here we use optical two-dimensional coherent spectroscopy to measure the trion coherence dephasing time in monolayer MoSe2 by analyzing the homogeneous linewidth. An intrinsic coherence time of 182 fs is extrapolated from the excitation density and temperature dependence measurement. The results show that trion-trion and trion-phonon interactions strongly affect the coherence dephasing time, while the intrinsic coherence time at zero excitation and zero temperature is primarily limited by the pure dephasing due to defect states. Our experiment also confirms optical two-dimensional coherent spectroscopy as a reliable technique for studying valley quantum dynamics in two-dimensional layered materials.

Conjugate-gradient optimization method for orbital-free density functional calculations.

PubMed

Jiang, Hong; Yang, Weitao

2004-08-01

Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient numerical methodology. In this paper, we developed a conjugate-gradient method for the numerical solution of spin-dependent extended Thomas-Fermi equation by incorporating techniques previously used in Kohn-Sham calculations. The key ingredient of the method is an approximate line-search scheme and a collective treatment of two spin densities in the case of spin-dependent extended Thomas-Fermi problem. Test calculations for a quartic two-dimensional quantum dot system and a three-dimensional sodium cluster Na216 with a local pseudopotential demonstrate that the method is accurate and efficient. (c) 2004 American Institute of Physics.

Flux-vector splitting algorithm for chain-rule conservation-law form

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Nguyen, H. L.; Willis, E. A.; Steinthorsson, E.; Li, Z.

1991-01-01

A flux-vector splitting algorithm with Newton-Raphson iteration was developed for the 'full compressible' Navier-Stokes equations cast in chain-rule conservation-law form. The algorithm is intended for problems with deforming spatial domains and for problems whose governing equations cannot be cast in strong conservation-law form. The usefulness of the algorithm for such problems was demonstrated by applying it to analyze the unsteady, two- and three-dimensional flows inside one combustion chamber of a Wankel engine under nonfiring conditions. Solutions were obtained to examine the algorithm in terms of conservation error, robustness, and ability to handle complex flows on time-dependent grid systems.

The Effect of Three-Dimensional Freestream Disturbances on the Supersonic Flow Past a Wedge

NASA Technical Reports Server (NTRS)

Duck, Peter W.; Lasseigne, D. Glenn; Hussaini, M. Y.

1997-01-01

The interaction between a shock wave (attached to a wedge) and small amplitude, three-dimensional disturbances of a uniform, supersonic, freestream flow are investigated. The paper extends the two-dimensional study of Duck et al, through the use of vector potentials, which render the problem tractable by the same techniques as in the two-dimensional case, in particular by expansion of the solution by means of a Fourier-Bessel series, in appropriately chosen coordinates. Results are presented for specific classes of freestream disturbances, and the study shows conclusively that the shock is stable to all classes of disturbances (i.e. time periodic perturbations to the shock do not grow downstream), provided the flow downstream of the shock is supersonic (loosely corresponding to the weak shock solution). This is shown from our numerical results and also by asymptotic analysis of the Fourier-Bessel series, valid far downstream of the shock.

Fractional calculus phenomenology in two-dimensional plasma models

NASA Astrophysics Data System (ADS)

Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

2006-10-01

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

Mixing Regimes in a Spatially Confined, Two-Dimensional, Supersonic Shear Layer

DTIC Science & Technology

1992-07-31

MODEL ................................... 3 THE MODEL PROBLEMS .............................................. 6 THE ONE-DIMENSIONAL PROBLEM...the effects of the numerical diffusion on the spectrum. Guirguis et al.ś and Farouk et al."’ have studied spatially evolving mixing layers for equal...approximations. Physical and Numerical Model General Formulation We solve the time-dependent, two-dimensional, compressible, Navier-Stokes equations for a

Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping

2016-10-01

Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such DSWs in two space one time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to the cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with very good agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations.

A SERS characterization of the stability of polythionates at the gold-electrolyte interface

NASA Astrophysics Data System (ADS)

Mirza, Jeff; Smith, Scott R.; Baron, Janet Y.; Choi, Yeonuk; Lipkowski, Jacek

2015-01-01

A gold nanorod (AuNR) array electrode was employed to record SERS spectra as a function of immersion time in electrolyte solutions of tetrathionate, trithionate, the [Au(S2O3)2]3- complex, sulfide and thiosulfate. The generalized two-dimensional correlation spectroscopy was employed to deconvolute broad bands in the SERS spectra. The results show that the polythionates, tetrathionate and trithionate, sulfide, and the [Au(S2O3)2]3- complex decompose to form cyclo-S8, polymeric and monoatomic sulfur at the gold surface. The relative amount of these different forms of sulfur in the film formed at the surface depends on the nature of the electrolyte species. The decomposition of tetrathionate leads predominantly to the formation of cyclo-S8. Comparable amounts of all three forms of sulfur are formed in the solution of the [Au(S2O3)2]3- complex. Monoatomic sulfur is formed predominantly at the gold surface in solutions of trithionate and thiosulfate. In contrast to the previous suggestions, the results of this study demonstrate that polythionates are not present in the passive layer during gold leaching from thiosulfate solutions at a prolonged leaching times.

Chronoamperometric study of the films formed by 4,4'-bipyridyl cation radical salts on mercury in the presence of iodide ions: consecutive two-dimensional phase transitions.

PubMed

Gómez, L; Ruiz, J J; Camacho, L; Rodríguez-Amaro, R

2005-01-04

This paper reports a new mathematical model for consecutive two-dimensional phase transitions that accounts for the chronoamperometric behavior observed in the formation of electrochemical phases by 4,4'-bipyridyl cation radical (BpyH(2)(*)(+)) on mercury in aqueous iodide solutions. Also, a new interpretation for the induction time is proposed.

Tensor of effective susceptibility in random magnetic composites: Application to two-dimensional and three-dimensional cases

NASA Astrophysics Data System (ADS)

Posnansky, Oleg P.

2018-05-01

The measuring of dynamic magnetic susceptibility by nuclear magnetic resonance is used for revealing information about the internal structure of various magnetoactive composites. The response of such material on the applied external static and time-varying magnetic fields encodes intrinsic dynamic correlations and depends on links between macroscopic effective susceptibility and structure on the microscopic scale. In the current work we carried out computational analysis of the frequency dependent dynamic magnetic susceptibility and demonstrated its dependence on the microscopic architectural elements while also considering Euclidean dimensionality. The proposed numerical method is efficient in the simulation of nuclear magnetic resonance experiments in two- and three-dimensional random magnetic media by choosing and modeling the influence of the concentration of components and internal hierarchical characteristics of physical parameters.

Generalization of one-dimensional solute transport: A stochastic-convective flow conceptualization

NASA Astrophysics Data System (ADS)

Simmons, C. S.

1986-04-01

A stochastic-convective representation of one-dimensional solute transport is derived. It is shown to conceptually encompass solutions of the conventional convection-dispersion equation. This stochastic approach, however, does not rely on the assumption that dispersive flux satisfies Fick's diffusion law. Observable values of solute concentration and flux, which together satisfy a conservation equation, are expressed as expectations over a flow velocity ensemble, representing the inherent random processess that govern dispersion. Solute concentration is determined by a Lagrangian pdf for random spatial displacements, while flux is determined by an equivalent Eulerian pdf for random travel times. A condition for such equivalence is derived for steady nonuniform flow, and it is proven that both Lagrangian and Eulerian pdfs are required to account for specified initial and boundary conditions on a global scale. Furthermore, simplified modeling of transport is justified by proving that an ensemble of effectively constant velocities always exists that constitutes an equivalent representation. An example of how a two-dimensional transport problem can be reduced to a single-dimensional stochastic viewpoint is also presented to further clarify concepts.

A finite-element method for large-amplitude, two-dimensional panel flutter at hypersonic speeds

NASA Technical Reports Server (NTRS)

Mei, Chuh; Gray, Carl E.

1989-01-01

The nonlinear flutter behavior of a two-dimensional panel in hypersonic flow is investigated analytically. An FEM formulation based unsteady third-order piston theory (Ashley and Zartarian, 1956; McIntosh, 1970) and taking nonlinear structural and aerodynamic phenomena into account is derived; the solution procedure is outlined; and typical results are presented in extensive tables and graphs. A 12-element finite-element solution obtained using an alternative method for linearizing the assumed limit-cycle time function is shown to give predictions in good agreement with classical analytical results for large-amplitude vibration in a vacuum and large-amplitude panel flutter, using linear aerodynamics.

Phase slips in superconducting weak links

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

Kimmel, Gregory; Glatz, Andreas; Aranson, Igor S.

2017-01-01

Superconducting vortices and phase slips are primary mechanisms of dissipation in superconducting, superfluid, and cold-atom systems. While the dynamics of vortices is fairly well described, phase slips occurring in quasi-one- dimensional superconducting wires still elude understanding. The main reason is that phase slips are strongly nonlinear time-dependent phenomena that cannot be cast in terms of small perturbations of the superconducting state. Here we study phase slips occurring in superconducting weak links. Thanks to partial suppression of superconductivity in weak links, we employ a weakly nonlinear approximation for dynamic phase slips. This approximation is not valid for homogeneous superconducting wires andmore » slabs. Using the numerical solution of the time-dependent Ginzburg-Landau equation and bifurcation analysis of stationary solutions, we show that the onset of phase slips occurs via an infinite period bifurcation, which is manifested in a specific voltage-current dependence. Our analytical results are in good agreement with simulations.« less

Kinetics of Surface-Mediated Fibrillization of Amyloid-β (12-28) Peptides.

PubMed

Lin, Yi-Chih; Li, Chen; Fakhraai, Zahra

2018-04-17

Surfaces or interfaces are considered to be key factors in facilitating the formation of amyloid fibrils under physiological conditions. In this report, we study the kinetics of the surface-mediated fibrillization (SMF) of an amyloid-β fragment (Aβ 12-28 ) on mica. We employ a spin-coating-based drying procedure to control the exposure time of the substrate to a low-concentration peptide solution and then monitor the fibril growth as a function of time via atomic force microscopy (AFM). The evolution of surface-mediated fibril growth is quantitatively characterized in terms of the length histogram of imaged fibrils and their surface concentration. A two-dimensional (2D) kinetic model is proposed to numerically simulate the length evolution of surface-mediated fibrils by assuming a diffusion-limited aggregation (DLA) process along with size-dependent rate constants. We find that both monomer and fibril diffusion on the surface are required to obtain length histograms as a function of time that resemble those observed in experiments. The best-fit simulated data can accurately describe the key features of experimental length histograms and suggests that the mobility of loosely bound amyloid species is crucial in regulating the kinetics of SMF. We determine that the mobility exponent for the size dependence of the DLA rate constants is α = 0.55 ± 0.05, which suggests that the diffusion of loosely bound surface fibrils roughly depends on the inverse of the square root of their size. These studies elucidate the influence of deposition rate and surface diffusion on the formation of amyloid fibrils through SMF. The method used here can be broadly adopted to study the diffusion and aggregation of peptides or proteins on various surfaces to investigate the role of chemical interactions in two-dimensional fibril formation and diffusion.

Investigating the time-dependent zeta potential of wood surfaces.

PubMed

Muff, Livius F; Luxbacher, Thomas; Burgert, Ingo; Michen, Benjamin

2018-05-15

This work reports on streaming potential measurements through natural capillaries in wood and investigates the cause of a time-dependent zeta potential measured during the equilibration of wood cell-walls with an electrolyte solution. For the biomaterial, this equilibration phase takes several hours, which is much longer than for many other materials that have been characterized by electrokinetic measurements. During this equilibration phase the zeta potential magnitude is decaying due to two parallel mechanisms: (i) the swelling of the cell-wall which causes a dimensional change reducing the charge density at the capillary interface; (ii) the transport of ions from the electrolyte solution into the permeable cell-wall which alters the electrical potential at the interface by internal charge compensation. The obtained results demonstrate the importance of equilibration kinetics for an accurate determination of the zeta potential, especially for materials that interact strongly with the measurement electrolyte. Moreover, the change in zeta potential with time can be correlated with the bulk swelling of wood if the effect of electrolyte ion diffusion is excluded. This study shows the potential of streaming potential measurements of wood, and possibly of other hygroscopic and nanoporous materials, to reveal kinetic information about their interaction with liquids, such as swelling and ion uptake. Copyright © 2018 Elsevier Inc. All rights reserved.

Lump and lump-soliton solutions to the (2+1) -dimensional Ito equation

NASA Astrophysics Data System (ADS)

Yang, Jin-Yun; Ma, Wen-Xiu; Qin, Zhenyun

2017-06-01

Based on the Hirota bilinear form of the (2+1) -dimensional Ito equation, one class of lump solutions and two classes of interaction solutions between lumps and line solitons are generated through analysis and symbolic computations with Maple. Analyticity is naturally guaranteed for the presented lump and interaction solutions, and the interaction solutions reduce to lumps (or line solitons) while the hyperbolic-cosine (or the quadratic function) disappears. Three-dimensional plots and contour plots are made for two specific examples of the resulting interaction solutions.

The wide-angle equation and its solution through the short-time iterative Lanczos method.

PubMed

Campos-Martínez, José; Coalson, Rob D

2003-03-20

Properties of the wide-angle equation (WAEQ), a nonparaxial scalar wave equation used to propagate light through media characterized by inhomogeneous refractive-index profiles, are studied. In particular, it is shown that the WAEQ is not equivalent to the more complicated but more fundamental Helmholtz equation (HEQ) when the index of refraction profile depends on the position along the propagation axis. This includes all nonstraight waveguides. To study the quality of the WAEQ approximation, we present a novel method for computing solutions to the WAEQ. This method, based on a short-time iterative Lanczos (SIL) algorithm, can be applied directly to the full three-dimensional case, i.e., systems consisting of the propagation axis coordinate and two transverse coordinates. Furthermore, the SIL method avoids series-expansion procedures (e.g., Padé approximants) and thus convergence problems associated with such procedures. Detailed comparisons of solutions to the HEQ, WAEQ, and the paraxial equation (PEQ) are presented for two cases in which numerically exact solutions to the HEQ can be obtained by independent analysis, namely, (i) propagation in a uniform dielectric medium and (ii) propagation along a straight waveguide that has been tilted at an angle to the propagation axis. The quality of WAEQ and PEQ, compared with exact HEQ results, is investigated. Cases are found for which the WAEQ actually performs worse than the PEQ.

Computations of Axisymmetric Flows in Hypersonic Shock Tubes

NASA Technical Reports Server (NTRS)

Sharma, Surendra P.; Wilson, Gregory J.

1995-01-01

A time-accurate two-dimensional fluid code is used to compute test times in shock tubes operated at supersonic speeds. Unlike previous studies, this investigation resolves the finer temporal details of the shock-tube flow by making use of modern supercomputers and state-of-the-art computational fluid dynamic solution techniques. The code, besides solving the time-dependent fluid equations, also accounts for the finite rate chemistry in the hypersonic environment. The flowfield solutions are used to estimate relevant shock-tube parameters for laminar flow, such as test times, and to predict density and velocity profiles. Boundary-layer parameters such as bar-delta(sub u), bar-delta(sup *), and bar-tau(sub w), and test time parameters such as bar-tau and particle time of flight t(sub f), are computed and compared with those evaluated by using Mirels' correlations. This article then discusses in detail the effects of flow nonuniformities on particle time-of-flight behind the normal shock and, consequently, on the interpretation of shock-tube data. This article concludes that for accurate interpretation of shock-tube data, a detailed analysis of flowfield parameters, using a computer code such as used in this study, must be performed.

Three-Dimensional Navier-Stokes Calculations Using the Modified Space-Time CESE Method

NASA Technical Reports Server (NTRS)

Chang, Chau-lyan

2007-01-01

The space-time conservation element solution element (CESE) method is modified to address the robustness issues of high-aspect-ratio, viscous, near-wall meshes. In this new approach, the dependent variable gradients are evaluated using element edges and the corresponding neighboring solution elements while keeping the original flux integration procedure intact. As such, the excellent flux conservation property is retained and the new edge-based gradients evaluation significantly improves the robustness for high-aspect ratio meshes frequently encountered in three-dimensional, Navier-Stokes calculations. The order of accuracy of the proposed method is demonstrated for oblique acoustic wave propagation, shock-wave interaction, and hypersonic flows over a blunt body. The confirmed second-order convergence along with the enhanced robustness in handling hypersonic blunt body flow calculations makes the proposed approach a very competitive CFD framework for 3D Navier-Stokes simulations.

An Assessment of Artificial Compressibility and Pressure Projection Methods for Incompressible Flow Simulations

NASA Technical Reports Server (NTRS)

Kwak, Dochan; Kiris, C.; Smith, Charles A. (Technical Monitor)

1998-01-01

Performance of the two commonly used numerical procedures, one based on artificial compressibility method and the other pressure projection method, are compared. These formulations are selected primarily because they are designed for three-dimensional applications. The computational procedures are compared by obtaining steady state solutions of a wake vortex and unsteady solutions of a curved duct flow. For steady computations, artificial compressibility was very efficient in terms of computing time and robustness. For an unsteady flow which requires small physical time step, pressure projection method was found to be computationally more efficient than an artificial compressibility method. This comparison is intended to give some basis for selecting a method or a flow solution code for large three-dimensional applications where computing resources become a critical issue.

Numerical simulation of the hydrodynamical combustion to strange quark matter

NASA Astrophysics Data System (ADS)

Niebergal, Brian; Ouyed, Rachid; Jaikumar, Prashanth

2010-12-01

We present results from a numerical solution to the burning of neutron matter inside a cold neutron star into stable u,d,s quark matter. Our method solves hydrodynamical flow equations in one dimension with neutrino emission from weak equilibrating reactions, and strange quark diffusion across the burning front. We also include entropy change from heat released in forming the stable quark phase. Our numerical results suggest burning front laminar speeds of 0.002-0.04 times the speed of light, much faster than previous estimates derived using only a reactive-diffusive description. Analytic solutions to hydrodynamical jump conditions with a temperature-dependent equation of state agree very well with our numerical findings for fluid velocities. The most important effect of neutrino cooling is that the conversion front stalls at lower density (below ≈2 times saturation density). In a two-dimensional setting, such rapid speeds and neutrino cooling may allow for a flame wrinkle instability to develop, possibly leading to detonation.

Non steady-state descriptions of drug permeation through stratum corneum. I. The biphasic brick-and-mortar model.

PubMed

Heisig, M; Lieckfeldt, R; Wittum, G; Mazurkevich, G; Lee, G

1996-03-01

The diffusion equation should be solved for the non-steady-state problem of drug diffusion within a two-dimensional, biphasic stratum corneum membrane having homogeneous lipid and corneocyte phases. A numerical method was developed for a brick-and-mortar SC-geometry, enabling an explicit solution for time-dependent drug concentration within both phases. The lag time and permeability were calculated. It is shown how the barrier property of this model membrane depends on relative phase permeability, corneocyte alignment, and corneocyte-lipid partition coefficient. Additionally, the time-dependent drug concentration profiles within the membrane can be observed during the lag and steady-state phases. The model SC-membrane predicts, from purely morphological principles, lag times and permeabilities that are in good agreement with experimental values. The long lag times and very small permeabilities reported for human SC can only be predicted for a highly-staggered corneocyte geometry and corneocytes that are 1000 times less permeable than the lipid phase. Although the former conclusion is reasonable, the latter is questionable. The elongated, flattened corneocyte shape renders lag time and permeability insensitive to large changes in their alignment within the SC. Corneocyte/lipid partitioning is found to be fundamentally different to SC/donor partitioning, since increasing drug lipophilicity always reduces both lag time and permeability.

Vorticity vector-potential method based on time-dependent curvilinear coordinates for two-dimensional rotating flows in closed configurations

NASA Astrophysics Data System (ADS)

Fu, Yuan; Zhang, Da-peng; Xie, Xi-lin

2018-04-01

In this study, a vorticity vector-potential method for two-dimensional viscous incompressible rotating driven flows is developed in the time-dependent curvilinear coordinates. The method is applicable in both inertial and non-inertial frames of reference with the advantage of a fixed and regular calculation domain. The numerical method is applied to triangle and curved triangle configurations in constant and varying rotational angular velocity cases respectively. The evolutions of flow field are studied. The geostrophic effect, unsteady effect and curvature effect on the evolutions are discussed.

Vorticity vector-potential method based on time-dependent curvilinear coordinates for two-dimensional rotating flows in closed configurations

NASA Astrophysics Data System (ADS)

Fu, Yuan; Zhang, Da-peng; Xie, Xi-lin

2018-03-01

In this study, a vorticity vector-potential method for two-dimensional viscous incompressible rotating driven flows is developed in the time-dependent curvilinear coordinates. The method is applicable in both inertial and non-inertial frames of reference with the advantage of a fixed and regular calculation domain. The numerical method is applied to triangle and curved triangle configurations in constant and varying rotational angular velocity cases respectively. The evolutions of flow field are studied. The geostrophic effect, unsteady effect and curvature effect on the evolutions are discussed.

CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

Testing density-dependent groundwater models: Two-dimensional steady state unstable convection in infinite, finite and inclined porous layers

USGS Publications Warehouse

Weatherill, D.; Simmons, C.T.; Voss, C.I.; Robinson, N.I.

2004-01-01

This study proposes the use of several problems of unstable steady state convection with variable fluid density in a porous layer of infinite horizontal extent as two-dimensional (2-D) test cases for density-dependent groundwater flow and solute transport simulators. Unlike existing density-dependent model benchmarks, these problems have well-defined stability criteria that are determined analytically. These analytical stability indicators can be compared with numerical model results to test the ability of a code to accurately simulate buoyancy driven flow and diffusion. The basic analytical solution is for a horizontally infinite fluid-filled porous layer in which fluid density decreases with depth. The proposed test problems include unstable convection in an infinite horizontal box, in a finite horizontal box, and in an infinite inclined box. A dimensionless Rayleigh number incorporating properties of the fluid and the porous media determines the stability of the layer in each case. Testing the ability of numerical codes to match both the critical Rayleigh number at which convection occurs and the wavelength of convection cells is an addition to the benchmark problems currently in use. The proposed test problems are modelled in 2-D using the SUTRA [SUTRA-A model for saturated-unsaturated variable-density ground-water flow with solute or energy transport. US Geological Survey Water-Resources Investigations Report, 02-4231, 2002. 250 p] density-dependent groundwater flow and solute transport code. For the case of an infinite horizontal box, SUTRA results show a distinct change from stable to unstable behaviour around the theoretical critical Rayleigh number of 4??2 and the simulated wavelength of unstable convection agrees with that predicted by the analytical solution. The effects of finite layer aspect ratio and inclination on stability indicators are also tested and numerical results are in excellent agreement with theoretical stability criteria and with numerical results previously reported in traditional fluid mechanics literature. ?? 2004 Elsevier Ltd. All rights reserved.

DENSITY-DEPENDENT FLOW IN ONE-DIMENSIONAL VARIABLY-SATURATED MEDIA

EPA Science Inventory

A one-dimensional finite element is developed to simulate density-dependent flow of saltwater in variably saturated media. The flow and solute equations were solved in a coupled mode (iterative), in a partially coupled mode (non-iterative), and in a completely decoupled mode. P...

Differential invariants and exact solutions of the Einstein equations

NASA Astrophysics Data System (ADS)

Lychagin, Valentin; Yumaguzhin, Valeriy

2017-06-01

In this paper (cf. Lychagin and Yumaguzhin, in Anal Math Phys, 2016) a class of totally geodesics solutions for the vacuum Einstein equations is introduced. It consists of Einstein metrics of signature (1,3) such that 2-dimensional distributions, defined by the Weyl tensor, are completely integrable and totally geodesic. The complete and explicit description of metrics from these class is given. It is shown that these metrics depend on two functions in one variable and one harmonic function.

Numerical applications of the advective-diffusive codes for the inner magnetosphere

NASA Astrophysics Data System (ADS)

Aseev, N. A.; Shprits, Y. Y.; Drozdov, A. Y.; Kellerman, A. C.

2016-11-01

In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.

Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations

NASA Astrophysics Data System (ADS)

Abdulwahhab, Muhammad Alim

2016-10-01

Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.

Information entropy to measure the spatial and temporal complexity of solute transport in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Li, Weiyao; Huang, Guanhua; Xiong, Yunwu

2016-04-01

The complexity of the spatial structure of porous media, randomness of groundwater recharge and discharge (rainfall, runoff, etc.) has led to groundwater movement complexity, physical and chemical interaction between groundwater and porous media cause solute transport in the medium more complicated. An appropriate method to describe the complexity of features is essential when study on solute transport and conversion in porous media. Information entropy could measure uncertainty and disorder, therefore we attempted to investigate complexity, explore the contact between the information entropy and complexity of solute transport in heterogeneous porous media using information entropy theory. Based on Markov theory, two-dimensional stochastic field of hydraulic conductivity (K) was generated by transition probability. Flow and solute transport model were established under four conditions (instantaneous point source, continuous point source, instantaneous line source and continuous line source). The spatial and temporal complexity of solute transport process was characterized and evaluated using spatial moment and information entropy. Results indicated that the entropy increased as the increase of complexity of solute transport process. For the point source, the one-dimensional entropy of solute concentration increased at first and then decreased along X and Y directions. As time increased, entropy peak value basically unchanged, peak position migrated along the flow direction (X direction) and approximately coincided with the centroid position. With the increase of time, spatial variability and complexity of solute concentration increase, which result in the increases of the second-order spatial moment and the two-dimensional entropy. Information entropy of line source was higher than point source. Solute entropy obtained from continuous input was higher than instantaneous input. Due to the increase of average length of lithoface, media continuity increased, flow and solute transport complexity weakened, and the corresponding information entropy also decreased. Longitudinal macro dispersivity declined slightly at early time then rose. Solute spatial and temporal distribution had significant impacts on the information entropy. Information entropy could reflect the change of solute distribution. Information entropy appears a tool to characterize the spatial and temporal complexity of solute migration and provides a reference for future research.

Steady state magnetic field configurations for the earth's magnetotail

NASA Technical Reports Server (NTRS)

Hau, L.-N.; Wolf, R. A.; Voigt, G.-H.; Wu, C. C.

1989-01-01

A two-dimensional, force-balance magnetic field model is presented. The theoretical existence of a steady state magnetic field configuration that is force-balanced and consistent with slow, lossless, adiabatic, earthward convection within the limit of the ideal MHD is demonstrated. A numerical solution is obtained for a two-dimensional magnetosphere with a rectangular magnetopause and nonflaring tail. The results are consistent with the convection time sequences reported by Erickson (1985).

Three dimensional thermal pollution models. Volume 1: Review of mathematical formulations. [waste heat discharge from power plants and effects on ecosystems

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.

1978-01-01

A mathematical model package for thermal pollution analyses and prediction is presented. These models, intended as user's manuals, are three dimensional and time dependent using the primitive equation approach. Although they have sufficient generality for application at sites with diverse topographical features; they also present specific instructions regarding data preparation for program execution and sample problems. The mathematical formulation of these models is presented including assumptions, approximations, governing equations, boundary and initial conditions, numerical method of solution, and same results.

Lax pair, conservation laws and solitons for a (2 + 1)-dimensional fourth-order nonlinear Schrödinger equation governing an α-helical protein

NASA Astrophysics Data System (ADS)

Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong

2015-11-01

Energy transfer through a (2+1)-dimensional α-helical protein can be described by a (2+1)-dimensional fourth-order nonlinear Schrödinger equation. For such an equation, a Lax pair and the infinitely-many conservation laws are derived. Using an auxiliary function and a bilinear formulation, we get the one-, two-, three- and N-soliton solutions via the Hirota method. The soliton velocity is linearly related to the lattice parameter γ, while the soliton' direction and amplitude do not depend on γ. Interactions between the two solitons are elastic, while those among the three solitons are pairwise elastic. Oblique, head-on and overtaking interactions between the two solitons are displayed. Oblique interaction among the three solitons and interactions among the two parallel solitons and a single one are presented as well.

A two-dimensional kinematic dynamo model of the ionospheric magnetic field at Venus

NASA Technical Reports Server (NTRS)

Cravens, T. E.; Wu, D.; Shinagawa, H.

1990-01-01

The results of a high-resolution, two-dimensional, time dependent, kinematic dynamo model of the ionospheric magnetic field of Venus are presented. Various one-dimensional models are considered and the two-dimensional model is then detailed. In this model, the two-dimensional magnetic induction equation, the magnetic diffusion-convection equation, is numerically solved using specified plasma velocities. Origins of the vertical velocity profile and of the horizontal velocities are discussed. It is argued that the basic features of the vertical magnetic field profile remain unaltered by horizontal flow effects and also that horizontal plasma flow can strongly affect the magnetic field for altitudes above 300 km.

Poly[2,5-bis(3-dodecylthiophen-2-yl)thieno[3,2-b]thiophene] Oligomer Single-Crystal Nanowires from Supercritical Solution and Their Anisotropic Exciton Dynamics.

PubMed

Colella, Nicholas S; Labastide, Joelle A; Cherniawski, Benjamin P; Thompson, Hilary B; Marques, Sarah R; Zhang, Lei; Usluer, Özlem; Watkins, James J; Briseno, Alejandro L; Barnes, Michael D

2017-07-06

Supercritical fluids, exhibiting a combination of liquid-like solvation power and gas-like diffusivity, are a relatively unexplored medium for processing and crystallization of oligomer and polymeric semiconductors whose optoelectronic properties critically depend on the microstructure. Here we report oligomer crystallization from the polymer organic semiconductor, poly[2,5-bis(3-dodecylthiophen-2-yl)thieno[3,2-b]thiophene] (PBTTT) in supercritical hexane, yielding needle-like single crystals up to several microns in length. We characterize the crystals' photophysical properties by time- and polarization-resolved photoluminescence (TPRPL) spectroscopy. These techniques reveal two-dimensional interchromophore coupling facilitated by the high degree of π-stacking order within the crystal. Furthermore, the crystals obtained from supercritical fluid were found to be similar photophysically as the crystallites found in solution-cast thin films and distinct from solution-grown crystals that exhibited spectroscopic signatures indicative of different packing geometries.

Approximate furrow infiltration model for time-variable ponding depth

USDA-ARS?s Scientific Manuscript database

A methodology is proposed for estimating furrow infiltration under time-variable ponding depth conditions. The methodology approximates the solution to the two-dimensional Richards equation, and is a modification of a procedure that was originally proposed for computing infiltration under constant ...

Efficient Fourier-based algorithms for time-periodic unsteady problems

NASA Astrophysics Data System (ADS)

Gopinath, Arathi Kamath

2007-12-01

This dissertation work proposes two algorithms for the simulation of time-periodic unsteady problems via the solution of Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations. These algorithms use a Fourier representation in time and hence solve for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). In contrast to conventional Fourier-based techniques which solve the governing equations in frequency space, the new algorithms perform all the calculations in the time domain, and hence require minimal modifications to an existing solver. The complete space-time solution is obtained by iterating in a fifth pseudo-time dimension. Various time-periodic problems such as helicopter rotors, wind turbines, turbomachinery and flapping-wings can be simulated using the Time Spectral method. The algorithm is first validated using pitching airfoil/wing test cases. The method is further extended to turbomachinery problems, and computational results verified by comparison with a time-accurate calculation. The technique can be very memory intensive for large problems, since the solution is computed (and hence stored) simultaneously at all time levels. Often, the blade counts of a turbomachine are rescaled such that a periodic fraction of the annulus can be solved. This approximation enables the solution to be obtained at a fraction of the cost of a full-scale time-accurate solution. For a viscous computation over a three-dimensional single-stage rescaled compressor, an order of magnitude savings is achieved. The second algorithm, the reduced-order Harmonic Balance method is applicable only to turbomachinery flows, and offers even larger computational savings than the Time Spectral method. It simulates the true geometry of the turbomachine using only one blade passage per blade row as the computational domain. In each blade row of the turbomachine, only the dominant frequencies are resolved, namely, combinations of neighbor's blade passing. An appropriate set of frequencies can be chosen by the analyst/designer based on a trade-off between accuracy and computational resources available. A cost comparison with a time-accurate computation for an Euler calculation on a two-dimensional multi-stage compressor obtained an order of magnitude savings, and a RANS calculation on a three-dimensional single-stage compressor achieved two orders of magnitude savings, with comparable accuracy.

New exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in multi-temperature electron plasmas

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Tian, Yu; Zeng, Zhi-Fang

2017-10-01

In this paper, we aim to introduce a new form of the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation for the long waves of small amplitude with slow dependence on the transverse coordinate. By using the Hirota's bilinear form and the extended homoclinic test approach, new exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation are presented. Moreover, the properties and characteristics for these new exact periodic solitary-wave solutions are discussed with some figures.

On applications of chimera grid schemes to store separation

NASA Technical Reports Server (NTRS)

Cougherty, F. C.; Benek, J. A.; Steger, J. L.

1985-01-01

A finite difference scheme which uses multiple overset meshes to simulate the aerodynamics of aircraft/store interaction and store separation is described. In this chimera, or multiple mesh, scheme, a complex configuration is mapped using a major grid about the main component of the configuration, and minor overset meshes are used to map each additional component such as a store. As a first step in modeling the aerodynamics of store separation, two dimensional inviscid flow calculations were carried out in which one of the minor meshes is allowed to move with respect to the major grid. Solutions of calibrated two dimensional problems indicate that allowing one mesh to move with respect to another does not adversely affect the time accuracy of an unsteady solution. Steady, inviscid three dimensional computations demonstrate the capability to simulate complex configurations, including closely packed multiple bodies.

On the relationship between kinetic and fluid formalisms for convection in the inner magnetosphere

NASA Astrophysics Data System (ADS)

Song, Yang; Sazykin, Stanislav; Wolf, Richard A.

2008-08-01

In the inner magnetosphere, the plasma flows are mostly slow compared to thermal or Alfvén speeds, but the convection is far away from the ideal magnetohydrodynamic regime since the gradient/curvature drifts become significant. Both kinetic (Wolf, 1983) and two-fluid (Peymirat and Fontaine, 1994; Heinemann, 1999) formalisms have been used to describe plasma dynamics, but it is not fully understood how they relate to each other. We explore the relations among kinetic, fluid, and recently developed "average" (Liu, 2006) models in an attempt to find the simplest yet realistic way to describe the convection. First, we prove analytically that the model of (Liu, 2006), when closed with the assumption of a Maxwellian distribution, is equivalent to the fluid model of (Heinemann, 1999). Second, we analyze the transport of both one-dimensional and two-dimensional Gaussian-shaped blob of hot plasma. For the kinetic case, it is known that the time evolution of such a blob is gradual spreading in time. For the fluid case, Heinemann and Wolf (2001a, 2001b) showed that in a one-dimensional idealized case, the blob separates into two drifting at different speeds. We present a fully nonlinear solution of this case, confirming this behavior but demonstrating what appears to be a shocklike steepening of the faster drifting secondary blob. A new, more realistic two-dimensional example using the dipole geometry with a uniform electric field confirms the one-dimensional solutions. Implications for the numerical simulations of magnetospheric dynamics are discussed.

Fundamental differences between glassy dynamics in two and three dimensions.

PubMed

Flenner, Elijah; Szamel, Grzegorz

2015-06-12

The two-dimensional freezing transition is very different from its three-dimensional counterpart. In contrast, the glass transition is usually assumed to have similar characteristics in two and three dimensions. Using computer simulations, here we show that glassy dynamics in supercooled two- and three-dimensional fluids are fundamentally different. Specifically, transient localization of particles on approaching the glass transition is absent in two dimensions, whereas it is very pronounced in three dimensions. Moreover, the temperature dependence of the relaxation time of orientational correlations is decoupled from that of the translational relaxation time in two dimensions but not in three dimensions. Last, the relationships between the characteristic size of dynamically heterogeneous regions and the relaxation time are very different in two and three dimensions. These results strongly suggest that the glass transition in two dimensions is different than in three dimensions.

Analytical solutions of Landau (1+1)-dimensional hydrodynamics

DOE PAGES

Wong, Cheuk-Yin; Sen, Abhisek; Gerhard, Jochen; ...

2014-12-17

To help guide our intuition, summarize important features, and point out essential elements, we review the analytical solutions of Landau (1+1)-dimensional hydrodynamics and exhibit the full evolution of the dynamics from the very beginning to subsequent times. Special emphasis is placed on the matching and the interplay between the Khalatnikov solution and the Riemann simple wave solution at the earliest times and in the edge regions at later times.

Stochastic modeling of experimental chaotic time series.

PubMed

Stemler, Thomas; Werner, Johannes P; Benner, Hartmut; Just, Wolfram

2007-01-26

Methods developed recently to obtain stochastic models of low-dimensional chaotic systems are tested in electronic circuit experiments. We demonstrate that reliable drift and diffusion coefficients can be obtained even when no excessive time scale separation occurs. Crisis induced intermittent motion can be described in terms of a stochastic model showing tunneling which is dominated by state space dependent diffusion. Analytical solutions of the corresponding Fokker-Planck equation are in excellent agreement with experimental data.

Spectroscopic properties of a two-dimensional time-dependent Cepheid model. I. Description and validation of the model

NASA Astrophysics Data System (ADS)

Vasilyev, V.; Ludwig, H.-G.; Freytag, B.; Lemasle, B.; Marconi, M.

2017-10-01

Context. Standard spectroscopic analyses of Cepheid variables are based on hydrostatic one-dimensional model atmospheres, with convection treated using various formulations of mixing-length theory. Aims: This paper aims to carry out an investigation of the validity of the quasi-static approximation in the context of pulsating stars. We check the adequacy of a two-dimensional time-dependent model of a Cepheid-like variable with focus on its spectroscopic properties. Methods: With the radiation-hydrodynamics code CO5BOLD, we construct a two-dimensional time-dependent envelope model of a Cepheid with Teff = 5600 K, log g = 2.0, solar metallicity, and a 2.8-day pulsation period. Subsequently, we perform extensive spectral syntheses of a set of artificial iron lines in local thermodynamic equilibrium. The set of lines allows us to systematically study effects of line strength, ionization stage, and excitation potential. Results: We evaluate the microturbulent velocity, line asymmetry, projection factor, and Doppler shifts. The microturbulent velocity, averaged over all lines, depends on the pulsational phase and varies between 1.5 and 2.7 km s-1. The derived projection factor lies between 1.23 and 1.27, which agrees with observational results. The mean Doppler shift is non-zero and negative, -1 km s-1, after averaging over several full periods and lines. This residual line-of-sight velocity (related to the "K-term") is primarily caused by horizontal inhomogeneities, and consequently we interpret it as the familiar convective blueshift ubiquitously present in non-pulsating late-type stars. Limited statistics prevent firm conclusions on the line asymmetries. Conclusions: Our two-dimensional model provides a reasonably accurate representation of the spectroscopic properties of a short-period Cepheid-like variable star. Some properties are primarily controlled by convective inhomogeneities rather than by the Cepheid-defining pulsations. Extended multi-dimensional modelling offers new insight into the nature of pulsating stars.

Numerical prediction of fire resistance of RC beams

NASA Astrophysics Data System (ADS)

Serega, Szymon; Wosatko, Adam

2018-01-01

Fire resistance of different structural members is an important issue of their strength and durability. A simple but effective tool to investigate multi-span reinforced concrete beams exposed to fire is discussed in the paper. Assumptions and simplifications of the theory as well as numerical aspects are briefly reviewed. Two steps of nonlinear finite element analysis and two levels of observation are distinguished. The first step is the solution of transient heat transfer problem in representative two-dimensional reinforced concrete cross-section of a beam. The second part is a nonlinear mechanical analysis of the whole beam. All spans are uniformly loaded, but an additional time-dependent thermal load due to fire acts on selected ones. Global changes of curvature and bending moment functions induce deterioration of the stiffness. Benchmarks are shown to confirm the correctness of the model.

Comparison between two meshless methods based on collocation technique for the numerical solution of four-species tumor growth model

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Mohammadi, Vahid

2017-03-01

As is said in [27], the tumor-growth model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models [27]. Simulations of this practical model using numerical methods can be applied for evaluating it. The present paper investigates the solution of the tumor growth model with meshless techniques. Meshless methods are applied based on the collocation technique which employ multiquadrics (MQ) radial basis function (RBFs) and generalized moving least squares (GMLS) procedures. The main advantages of these choices come back to the natural behavior of meshless approaches. As well as, a method based on meshless approach can be applied easily for finding the solution of partial differential equations in high-dimension using any distributions of points on regular and irregular domains. The present paper involves a time-dependent system of partial differential equations that describes four-species tumor growth model. To overcome the time variable, two procedures will be used. One of them is a semi-implicit finite difference method based on Crank-Nicolson scheme and another one is based on explicit Runge-Kutta time integration. The first case gives a linear system of algebraic equations which will be solved at each time-step. The second case will be efficient but conditionally stable. The obtained numerical results are reported to confirm the ability of these techniques for solving the two and three-dimensional tumor-growth equations.

Efficient variable time-stepping scheme for intense field-atom interactions

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

Cerjan, C.; Kosloff, R.

1993-03-01

The recently developed Residuum method [Tal-Ezer, Kosloff, and Cerjan, J. Comput. Phys. 100, 179 (1992)], a Krylov subspace technique with variable time-step integration for the solution of the time-dependent Schroedinger equation, is applied to the frequently used soft Coulomb potential in an intense laser field. This one-dimensional potential has asymptotic Coulomb dependence with a softened'' singularity at the origin; thus it models more realistic phenomena. Two of the more important quantities usually calculated in this idealized system are the photoelectron and harmonic photon generation spectra. These quantities are shown to be sensitive to the choice of a numerical integration scheme:more » some spectral features are incorrectly calculated or missing altogether. Furthermore, the Residuum method allows much larger grid spacings for equivalent or higher accuracy in addition to the advantages of variable time stepping. Finally, it is demonstrated that enhanced high-order harmonic generation accompanies intense field stabilization and that preparation of the atom in an intermediate Rydberg state leads to stabilization at much lower laser intensity.« less

An efficient method for solving the steady Euler equations

NASA Technical Reports Server (NTRS)

Liou, M.-S.

1986-01-01

An efficient numerical procedure for solving a set of nonlinear partial differential equations, the steady Euler equations, using Newton's linearization procedure is presented. A theorem indicating quadratic convergence for the case of differential equations is demonstrated. A condition for the domain of quadratic convergence Omega(2) is obtained which indicates that whether an approximation lies in Omega(2) depends on the rate of change and the smoothness of the flow vectors, and hence is problem-dependent. The choice of spatial differencing, of particular importance for the present method, is discussed. The treatment of boundary conditions is addressed, and the system of equations resulting from the foregoing analysis is summarized and solution strategies are discussed. The convergence of calculated solutions is demonstrated by comparing them with exact solutions to one and two-dimensional problems.

Asymptotic study of pulsating evolution of overdriven and CJ detonation with a chain-branching kinetics model

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

Short, Mark; Chliquete, Carlos

2011-01-20

The pulsating dynamics of gaseous detonations with a model two-step chain-branching kinetic mechanism are studied both numerically and asymptotically. The model studied here was also used in [4], [3] and [2] and mimics the attributes of some chain-branching reaction mechanisms. Specifically, the model comprises a chain-initiationlbranching zone with an Arrhenius temperature-sensitive rate behind the detonation shock where fuel is converted into chain-radical with no heat release. This is followed by a chain-termination zone having a temperature insensitive rate where the exothermic heat of reaction is released. The lengths of these two zones depend on the relative rates of each stage.more » It was determined in [4] and [3] via asymptotic and numerical analysis that the ratio of the length of the chain-branching zone to that of the chain-initation zone relative to the size of the von Neumann state scaled activation energy in the chain initiation/branching zone has a primary influence of the stability of one-dimensional pulsating instability behavior for this model. In [2], the notion of a specific stability parameter related to this ratio was proposed that determines the boundary between stable and unstable waves. In [4], a slow-time varying asymptotic study was conducted of pulsating instability of Chapman-Jouguet (CJ) detonations with the above two-step rate model, assuming a large activation energy for the chain-initiation zone and a chain-termination zone longer than the chain-initiation zone. Deviations D{sub n}{sup (1)} ({tau}) of the detonation velocity from Chapman-Jouguet were of the order of the non-dimensional activation energy. Solutions were sought for a pulsation timescale of the order of the non-dimensional activation energy times the particle transit time through the induction zone. On this time-scale, the evolution of the chain-initation zone is quasi-steady. In [4], a time-dependent non-linear evolution equation for D{sub n}{sup (1)} ({tau}) was then constructed via a perturbation procedure for cases where the ratio of the length of the chain-termination zone to chain-initiation zone was less than the non-dimensional activation energy. To leading order, the steady CJ detonation was found to be unstable; higher-order corrections lead to the construction of a stability limit between stable and unsteady pulsating solutions. One conclusion from this study is that for a stability limit to occur at leading order, the period of pulsation of the detonation must occur on the time scale of particle passage through the longer chain-termination zone, while the length of the chain-termination zone must be of order of the non-dimensional activation energy longer than the chain-initiation zone. The relevance of these suggested scalings was verified via numerical solutions of the full Euler system in [3], and formed the basis of the stability parameter criteria suggested in [2]. In the following, we formulate an asymptotic study based on these new suggested scales, studying the implications for describing pulsating behavior in gaseous chain-branching detonations. Specifically, we find that the chain-induction zone structure is the same as that studied in [4]. However, the study of unsteady evolution in the chain-termination region is now governed by a set of asymptotically derived nonlinear POEs. Equations for the linear stablity behavior of this set of POE's is obtained, while the nonlinear POEs are solved numerically using a shock-attached, shock-fitting method developed by Henrick et aJ. [1]. The results thus far show that the stability threshold calculated using the new ratio of the chain-termination zone length to that of the chain-initiation zone yields a marked improvement over [2]. Additionally, solutions will be compared with predictions obtained from the solution of the full Euler system. Finally, the evolution equation previously derived in [4] has been generalized to consider both arbitrary reaction orders and any degree of overdrive.« less

A multiple-block multigrid method for the solution of the three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Atkins, Harold

1991-01-01

A multiple block multigrid method for the solution of the three dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell vertex method which employs central difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques and variable coefficient numerical dissipation results in an efficient and robust scheme is discussed. The multiblock strategy places the block loop within the Runge-Kutta Loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one and two block calculations in which the two block grid is generated by splitting the one block grid. Results are presented for both Euler and Navier-Stokes computations of wing/fuselage combinations.

Stabilizing the long-time behavior of the forced Navier-Stokes and damped Euler systems by large mean flow

NASA Astrophysics Data System (ADS)

Cyranka, Jacek; Mucha, Piotr B.; Titi, Edriss S.; Zgliczyński, Piotr

2018-04-01

The paper studies the issue of stability of solutions to the forced Navier-Stokes and damped Euler systems in periodic boxes. It is shown that for large, but fixed, Grashoff (Reynolds) number the turbulent behavior of all Leray-Hopf weak solutions of the three-dimensional Navier-Stokes equations, in periodic box, is suppressed, when viewed in the right frame of reference, by large enough average flow of the initial data; a phenomenon that is similar in spirit to the Landau damping. Specifically, we consider an initial data which have large enough spatial average, then by means of the Galilean transformation, and thanks to the periodic boundary conditions, the large time independent forcing term changes into a highly oscillatory force; which then allows us to employ some averaging principles to establish our result. Moreover, we also show that under the action of fast oscillatory-in-time external forces all two-dimensional regular solutions of the Navier-Stokes and the damped Euler equations converge to a unique time-periodic solution.

Dynamic growth of mixed-mode shear cracks

USGS Publications Warehouse

Andrews, D.J.

1994-01-01

A pure mode II (in-plane) shear crack cannot propagate spontaneously at a speed between the Rayleigh and S-wave speeds, but a three-dimensional (3D) or two-dimensional (2D) mixed-mode shear crack can propagate in this range, being driven by the mode III (antiplane) component. Two different analytic solutions have been proposed for the mode II component in this case. The first is the solution valid for crack speed less than the Rayleigh speed. When applied above the Rayleigh speed, it predicts a negative stress intensity factor, which implies that energy is generated at the crack tip. Burridge proposed a second solution, which is continuous at the crack tip, but has a singularity in slip velocity at the Rayleigh wave. Spontaneous propagation of a mixed-mode rupture has been calculated with a slip-weakening friction law, in which the slip velocity vector is colinear with the total traction vector. Spontaneous trans-Rayleigh rupture speed has been found. The solution depends on the absolute stress level. The solution for the in-plane component appears to be a superposition of smeared-out versions of the two analytic solutions. The proportion of the first solution increases with increasing absolute stress. The amplitude of the negative in-plane traction pulse is less than the absolute final sliding traction, so that total in-plane traction does not reverse. The azimuth of the slip velocity vector varies rapidly between the onset of slip and the arrival of the Rayleigh wave. The variation is larger at smaller absolute stress.

a Bounded Finite-Difference Discretization of a Two-Dimensional Diffusion Equation with Logistic Nonlinear Reaction

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

In the present manuscript, we introduce a finite-difference scheme to approximate solutions of the two-dimensional version of Fisher's equation from population dynamics, which is a model for which the existence of traveling-wave fronts bounded within (0,1) is a well-known fact. The method presented here is a nonstandard technique which, in the linear regime, approximates the solutions of the original model with a consistency of second order in space and first order in time. The theory of M-matrices is employed here in order to elucidate conditions under which the method is able to preserve the positivity and the boundedness of solutions. In fact, our main result establishes relatively flexible conditions under which the preservation of the positivity and the boundedness of new approximations is guaranteed. Some simulations of the propagation of a traveling-wave solution confirm the analytical results derived in this work; moreover, the experiments evince a good agreement between the numerical result and the analytical solutions.

The Prediction of Scattered Broadband Shock-Associated Noise

NASA Technical Reports Server (NTRS)

Miller, Steven A. E.

2015-01-01

A mathematical model is developed for the prediction of scattered broadband shock-associated noise. Model arguments are dependent on the vector Green's function of the linearized Euler equations, steady Reynolds-averaged Navier-Stokes solutions, and the two-point cross-correlation of the equivalent source. The equivalent source is dependent on steady Reynolds-averaged Navier-Stokes solutions of the jet flow, that capture the nozzle geometry and airframe surface. Contours of the time-averaged streamwise velocity component and turbulent kinetic energy are examined with varying airframe position relative to the nozzle exit. Propagation effects are incorporated by approximating the vector Green's function of the linearized Euler equations. This approximation involves the use of ray theory and an assumption that broadband shock-associated noise is relatively unaffected by the refraction of the jet shear layer. A non-dimensional parameter is proposed that quantifies the changes of the broadband shock-associated noise source with varying jet operating condition and airframe position. Scattered broadband shock-associated noise possesses a second set of broadband lobes that are due to the effect of scattering. Presented predictions demonstrate relatively good agreement compared to a wide variety of measurements.

Numerical solution of the Navier-Stokes equations for blunt nosed bodies in supersonic flows

NASA Technical Reports Server (NTRS)

Warsi, Z. U. A.; Devarayalu, K.; Thompson, J. F.

1978-01-01

A time dependent, two dimensional Navier-Stokes code employing the method of body fitted coordinate technique was developed for supersonic flows past blunt bodies of arbitrary shapes. The bow shock ahead of the body is obtained as part of the solution, viz., by shock capturing. A first attempt at mesh refinement in the shock region was made by using the forcing function in the coordinate generating equations as a linear function of the density gradients. The technique displaces a few lines from the neighboring region into the shock region. Numerical calculations for Mach numbers 2 and 4.6 and Reynolds numbers from 320 to 10,000 were performed for a circular cylinder with and without a fairing. Results of Mach number 4.6 and Reynolds number 10,000 for an isothermal wall temperature of 556 K are presented in detail.

Diffraction of a shock wave by a compression corner; regular and single Mach reflection

NASA Technical Reports Server (NTRS)

Vijayashankar, V. S.; Kutler, P.; Anderson, D.

1976-01-01

The two dimensional, time dependent Euler equations which govern the flow field resulting from the injection of a planar shock with a compression corner are solved with initial conditions that result in either regular reflection or single Mach reflection of the incident planar shock. The Euler equations which are hyperbolic are transformed to include the self similarity of the problem. A normalization procedure is employed to align the reflected shock and the Mach stem as computational boundaries to implement the shock fitting procedure. A special floating fitting scheme is developed in conjunction with the method of characteristics to fit the slip surface. The reflected shock, the Mach stem, and the slip surface are all treated as harp discontinuities, thus, resulting in a more accurate description of the inviscid flow field. The resulting numerical solutions are compared with available experimental data and existing first-order, shock-capturing numerical solutions.

On the equivalence of dynamically orthogonal and bi-orthogonal methods: Theory and numerical simulations

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

Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em, E-mail: george_karniadakis@brown.edu

2014-08-01

The Karhunen–Lòeve (KL) decomposition provides a low-dimensional representation for random fields as it is optimal in the mean square sense. Although for many stochastic systems of practical interest, described by stochastic partial differential equations (SPDEs), solutions possess this low-dimensional character, they also have a strongly time-dependent form and to this end a fixed-in-time basis may not describe the solution in an efficient way. Motivated by this limitation of standard KL expansion, Sapsis and Lermusiaux (2009) [26] developed the dynamically orthogonal (DO) field equations which allow for the simultaneous evolution of both the spatial basis where uncertainty ‘lives’ but also themore » stochastic characteristics of uncertainty. Recently, Cheng et al. (2013) [28] introduced an alternative approach, the bi-orthogonal (BO) method, which performs the exact same tasks, i.e. it evolves the spatial basis and the stochastic characteristics of uncertainty. In the current work we examine the relation of the two approaches and we prove theoretically and illustrate numerically their equivalence, in the sense that one method is an exact reformulation of the other. We show this by deriving a linear and invertible transformation matrix described by a matrix differential equation that connects the BO and the DO solutions. We also examine a pathology of the BO equations that occurs when two eigenvalues of the solution cross, resulting in an instantaneous, infinite-speed, internal rotation of the computed spatial basis. We demonstrate that despite the instantaneous duration of the singularity this has important implications on the numerical performance of the BO approach. On the other hand, it is observed that the BO is more stable in nonlinear problems involving a relatively large number of modes. Several examples, linear and nonlinear, are presented to illustrate the DO and BO methods as well as their equivalence.« less

Comparison of two- and three-dimensional Navier-Stokes solutions with NASA experimental data for CAST-10 airfoil

NASA Technical Reports Server (NTRS)

Swanson, R. Charles; Radespiel, Rolf; Mccormick, V. Edward

1989-01-01

The two-dimensional (2-D) and three-dimensional Navier-Stokes equations are solved for flow over a NAE CAST-10 airfoil model. Recently developed finite-volume codes that apply a multistage time stepping scheme in conjunction with steady state acceleration techniques are used to solve the equations. Two-dimensional results are shown for flow conditions uncorrected and corrected for wind tunnel wall interference effects. Predicted surface pressures from 3-D simulations are compared with those from 2-D calculations. The focus of the 3-D computations is the influence of the sidewall boundary layers. Topological features of the 3-D flow fields are indicated. Lift and drag results are compared with experimental measurements.

Electroosmotic flow hysteresis for dissimilar ionic solutions

PubMed Central

Lim, An Eng; Lam, Yee Cheong

2015-01-01

Electroosmotic flow (EOF) with two or more fluids is commonly encountered in various microfluidics applications. However, no investigation has hitherto been conducted to investigate the hysteretic or flow direction-dependent behavior during the displacement flow of solutions with dissimilar ionic species. In this investigation, electroosmotic displacement flow involving dissimilar ionic solutions was studied experimentally through a current monitoring method and numerically through finite element simulations. The flow hysteresis can be characterized by the turning and displacement times; turning time refers to the abrupt gradient change of current-time curve while displacement time is the time for one solution to completely displace the other solution. Both experimental and simulation results illustrate that the turning and displacement times for a particular solution pair can be directional-dependent, indicating that the flow conditions in the microchannel are not the same in the two different flow directions. The mechanics of EOF hysteresis was elucidated through the theoretical model which includes the ionic mobility of each species, a major governing parameter. Two distinct mechanics have been identified as the causes for the EOF hysteresis involving dissimilar ionic solutions: the widening/sharpening effect of interfacial region between the two solutions and the difference in ion concentration distributions (and thus average zeta potentials) in different flow directions. The outcome of this investigation contributes to the fundamental understanding of flow behavior in microfluidic systems involving solution pair with dissimilar ionic species. PMID:25945139

Time-dependent density functional theory for open systems with a positivity-preserving decomposition scheme for environment spectral functions

NASA Astrophysics Data System (ADS)

Wang, RuLin; Zheng, Xiao; Kwok, YanHo; Xie, Hang; Chen, GuanHua; Yam, ChiYung

2015-04-01

Understanding electronic dynamics on material surfaces is fundamentally important for applications including nanoelectronics, inhomogeneous catalysis, and photovoltaics. Practical approaches based on time-dependent density functional theory for open systems have been developed to characterize the dissipative dynamics of electrons in bulk materials. The accuracy and reliability of such approaches depend critically on how the electronic structure and memory effects of surrounding material environment are accounted for. In this work, we develop a novel squared-Lorentzian decomposition scheme, which preserves the positive semi-definiteness of the environment spectral matrix. The resulting electronic dynamics is guaranteed to be both accurate and convergent even in the long-time limit. The long-time stability of electronic dynamics simulation is thus greatly improved within the current decomposition scheme. The validity and usefulness of our new approach are exemplified via two prototypical model systems: quasi-one-dimensional atomic chains and two-dimensional bilayer graphene.

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C.

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

Gap heating with pressure gradients. [for Shuttle Orbiter thermal protection system tiles

NASA Technical Reports Server (NTRS)

Scott, C. D.; Maraia, R. J.

1979-01-01

The heating rate distribution and temperature response on the gap walls of insulating tiles is analyzed to determine significant phenomena and parameters in flows where there is an external surface pressure gradient. Convective heating due to gap flow, modeled as fully developed pipe flow, is coupled with a two-dimensional thermal model of the tiles that includes conduction and radiative heat transfer. To account for geometry and important environmental parameters, scale factors are obtained by curve-fitting measured temperatures to analytical solutions. These scale factors are then used to predict the time-dependent gap heat flux and temperature response of tile gaps on the Space Shuttle Orbiter during entry.

Contaminant transport in soil with depth-dependent reaction coefficients and time-dependent boundary conditions.

PubMed

Gao, Guangyao; Fu, Bojie; Zhan, Hongbin; Ma, Ying

2013-05-01

Predicting the fate and movement of contaminant in soils and groundwater is essential to assess and reduce the risk of soil contamination and groundwater pollution. Reaction processes of contaminant often decreased monotonously with depth. Time-dependent input sources usually occurred at the inlet of natural or human-made system such as radioactive waste disposal site. This study presented a one-dimensional convection-dispersion equation (CDE) for contaminant transport in soils with depth-dependent reaction coefficients and time-dependent inlet boundary conditions, and derived its analytical solution. The adsorption coefficient and degradation rate were represented as sigmoidal functions of soil depth. Solute breakthrough curves (BTCs) and concentration profiles obtained from CDE with depth-dependent and constant reaction coefficients were compared, and a constant effective reaction coefficient, which was calculated by arithmetically averaging the depth-dependent reaction coefficient, was proposed to reflect the lumped depth-dependent reaction effect. With the effective adsorption coefficient and degradation rate, CDE could produce similar BTCs and concentration profiles as those from CDE with depth-dependent reactions in soils with moderate chemical heterogeneity. In contrast, the predicted concentrations of CDE with fitted reaction coefficients at a certain depth departed significantly from those of CDE with depth-dependent reactions. Parametric analysis was performed to illustrate the effects of sinusoidally and exponentially decaying input functions on solute BTCs. The BTCs and concentration profiles obtained from the solutions for finite and semi-infinite domain were compared to investigate the effects of effluent boundary condition. The finite solution produced higher concentrations at the increasing limb of the BTCs and possessed a higher peak concentration than the semi-infinite solution which had a slightly long tail. Furthermore, the finite solution gave a higher concentration in the immediate vicinity of the exit boundary than the semi-infinite solution. The applicability of the proposed model was tested with a field herbicide and tracer leaching experiment in an agricultural area of northeastern Greece. The simulation results indicated that the proposed CDE with depth-dependent reaction coefficients was able to capture the evolution of metolachlor concentration at the upper soil depths. However, the simulation results at deep depths were not satisfactory as the proposed model did not account for preferential flow observed in the field. Copyright © 2013 Elsevier Ltd. All rights reserved.

Holographic cosmology and phase transitions of SYM theory

NASA Astrophysics Data System (ADS)

Ghoroku, Kazuo; Meyer, René; Toyoda, Fumihiko

2017-10-01

We study the time development of strongly coupled N =4 supersymmetric Yang Mills (SYM) theory on cosmological Friedmann-Robertson-Walker (FRW) backgrounds via the AdS/CFT correspondence. We implement the cosmological background as a boundary metric fulfilling the Friedmann equation with a four-dimensional cosmological constant and a dark radiation term. We analyze the dual bulk solution of the type IIB supergravity and find that the time dependence of the FRW background strongly influences the dynamical properties of the SYM theory. We in particular find a phase transition between a confined and a deconfined phase. We also argue that some cosmological solutions could be related to the inflationary scenario.

Excitation of low-frequency residual currents at combination frequencies of an ionising two-colour laser pulse

NASA Astrophysics Data System (ADS)

Vvedenskii, N. V.; Kostin, V. A.; Laryushin, I. D.; Silaev, A. A.

2016-05-01

We have studied the processes of excitation of low-frequency residual currents in a plasma produced through ionisation of gases by two-colour laser pulses in laser-plasma schemes for THz generation. We have developed an analytical approach that allows one to find residual currents in the case when one of the components of a two-colour pulse is weak enough. The derived analytical expressions show that the effective generation of the residual current (and hence the effective THz generation) is possible if the ratio of the frequencies in the two-colour laser pulse is close to a rational fraction with a not very big odd sum of the numerator and denominator. The results of numerical calculations (including those based on the solution of the three-dimensional time-dependent Schrödinger equation) agree well with the analytical results.

The possible equilibrium shapes of static pendant drops

NASA Astrophysics Data System (ADS)

Sumesh, P. T.; Govindarajan, Rama

2010-10-01

Analytical and numerical studies are carried out on the shapes of two-dimensional and axisymmetric pendant drops hanging under gravity from a solid surface. Drop shapes with both pinned and equilibrium contact angles are obtained naturally from a single boundary condition in the analytical energy optimization procedure. The numerical procedure also yields optimum energy shapes, satisfying Young's equation without the explicit imposition of a boundary condition at the plate. It is shown analytically that a static pendant two-dimensional drop can never be longer than 3.42 times the capillary length. A related finding is that a range of existing solutions for long two-dimensional drops correspond to unphysical drop shapes. Therefore, two-dimensional drops of small volume display only one static solution. In contrast, it is known that axisymmetric drops can display multiple solutions for a given volume. We demonstrate numerically that there is no limit to the height of multiple-lobed Kelvin drops, but the total volume is finite, with the volume of successive lobes forming a convergent series. The stability of such drops is in question, though. Drops of small volume can attain large heights. A bifurcation is found within the one-parameter space of Laplacian shapes, with a range of longer drops displaying a minimum in energy in the investigated space. Axisymmetric Kelvin drops exhibit an infinite number of bifurcations.

A one-dimensional sectional model to simulate multicomponent aerosol dynamics in the marine boundary layer 3. Numerical methods and comparisons with exact solutions

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

Gelbard, F.; Fitzgerald, J.W.; Hoppel, W.A.

1998-07-01

We present the theoretical framework and computational methods that were used by {ital Fitzgerald} {ital et al.} [this issue (a), (b)] describing a one-dimensional sectional model to simulate multicomponent aerosol dynamics in the marine boundary layer. The concepts and limitations of modeling spatially varying multicomponent aerosols are elucidated. New numerical sectional techniques are presented for simulating multicomponent aerosol growth, settling, and eddy transport, coupled to time-dependent and spatially varying condensing vapor concentrations. Comparisons are presented with new exact solutions for settling and particle growth by simultaneous dynamic condensation of one vapor and by instantaneous equilibration with a spatially varying secondmore » vapor. {copyright} 1998 American Geophysical Union« less

Numerical modeling of simultaneous tracer release and piscicide treatment for invasive species control in the Chicago Sanitary and Ship Canal, Chicago, Illinois

USGS Publications Warehouse

Zhu, Zhenduo; Motta, Davide; Jackson, P. Ryan; Garcia, Marcelo H.

2017-01-01

In December 2009, during a piscicide treatment targeting the invasive Asian carp in the Chicago Sanitary and Ship Canal, Rhodamine WT dye was released to track and document the transport and dispersion of the piscicide. In this study, two modeling approaches are presented to reproduce the advection and dispersion of the dye tracer (and piscicide), a one-dimensional analytical solution and a three-dimensional numerical model. The two approaches were compared with field measurements of concentration and their applicability is discussed. Acoustic Doppler current profiler measurements were used to estimate the longitudinal dispersion coefficients at ten cross sections, which were taken as reference for calibrating the longitudinal dispersion coefficient in the one-dimensional analytical solution. While the analytical solution is fast, relatively simple, and can fairly accurately predict the core of the observed concentration time series at points downstream, it does not capture the tail of the breakthrough curves. These tails are well reproduced by the three-dimensional model, because it accounts for the effects of dead zones and a power plant which withdraws nearly 80 % of the water from the canal for cooling purposes before returning it back to the canal.

Self-dual Skyrmions on the spheres S2 N +1

NASA Astrophysics Data System (ADS)

Amari, Y.; Ferreira, L. A.

2018-04-01

We construct self-dual sectors for scalar field theories on a (2 N +2 )-dimensional Minkowski space-time with the target space being the 2 N +1 -dimensional sphere S2 N +1. The construction of such self-dual sectors is made possible by the introduction of an extra functional in the action that renders the static energy and the self-duality equations conformally invariant on the (2 N +1 )-dimensional spatial submanifold. The conformal and target-space symmetries are used to build an ansatz that leads to an infinite number of exact self-dual solutions with arbitrary values of the topological charge. The five-dimensional case is discussed in detail, where it is shown that two types of theories admit self-dual sectors. Our work generalizes the known results in the three-dimensional case that lead to an infinite set of self-dual Skyrmion solutions.

The 2.5-dimensional equivalent sources method for directly exposed and shielded urban canyons.

PubMed

Hornikx, Maarten; Forssén, Jens

2007-11-01

When a domain in outdoor acoustics is invariant in one direction, an inverse Fourier transform can be used to transform solutions of the two-dimensional Helmholtz equation to a solution of the three-dimensional Helmholtz equation for arbitrary source and observer positions, thereby reducing the computational costs. This previously published approach [D. Duhamel, J. Sound Vib. 197, 547-571 (1996)] is called a 2.5-dimensional method and has here been extended to the urban geometry of parallel canyons, thereby using the equivalent sources method to generate the two-dimensional solutions. No atmospheric effects are considered. To keep the error arising from the transform small, two-dimensional solutions with a very fine frequency resolution are necessary due to the multiple reflections in the canyons. Using the transform, the solution for an incoherent line source can be obtained much more efficiently than by using the three-dimensional solution. It is shown that the use of a coherent line source for shielded urban canyon observer positions leads mostly to an overprediction of levels and can yield erroneous results for noise abatement schemes. Moreover, the importance of multiple facade reflections in shielded urban areas is emphasized by vehicle pass-by calculations, where cases with absorptive and diffusive surfaces have been modeled.

Approximation and Numerical Analysis of Nonlinear Equations of Evolution.

DTIC Science & Technology

1980-01-31

dominant convective terms, or Stefan type problems such as the flow of fluids through porous media or the melting and freezing of ice. Such problems...means of formulating time-dependent Stefan problems was initiated. Classes of problems considered here include the one-phase and two-phase Stefan ...some new numerical methods were 2 developed for two dimensional, two-phase Stefan problems with time dependent boundary conditions. A variety of example

Time dependent deformation and stress in the lithosphere. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Yang, M.

1980-01-01

Efficient computer programs incorporating frontal solution and time stepping procedure were developed for the modelling of geodynamic problems. This scheme allows for investigating the quasi static phenomena including the effects of the rheological structure of a tectonically active region. From three dimensional models of strike slip earthquakes, it was found that lateral variation of viscosity affects the characteristics of surface deformations. The vertical deformation is especially informative about the viscosity structure in a strike slip fault zone. A three dimensional viscoelastic model of a thrust earthquake indicated that the transient disturbance on plate velocity due to a great plate boundary earthquake is significant at intermediate distances, but becomes barely measurable 1000 km away from the source.

Ion-pairing dynamics of Li{sup +} and SCN{sup -} in dimethylformamide solution: Chemical exchange two-dimensional infrared spectroscopy

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

Lee, Kyung-Koo; Park, Kwang-Hee; Kwon, Donghyun

2011-02-14

Ultrafast two-dimensional infrared (2DIR) spectroscopy has been proven to be an exceptionally useful method to study chemical exchange processes between different vibrational chromophores under thermal equilibria. Here, we present experimental results on the thermal equilibrium ion pairing dynamics of Li{sup +} and SCN{sup -} ions in N,N-dimethylformamide. Li{sup +} and SCN{sup -} ions can form a contact ion pair (CIP). Varying the relative concentration of Li{sup +} in solution, we could control the equilibrium CIP and free SCN{sup -} concentrations. Since the CN stretch frequency of Li-SCN CIP is blue-shifted by about 16 cm{sup -1} from that of free SCN{supmore » -} ion, the CN stretch IR spectrum is a doublet. The temperature-dependent IR absorption spectra reveal that the CIP formation is an endothermic (0.57 kJ/mol) process and the CIP state has larger entropy by 3.12 J/(K mol) than the free ion states. Since the two ionic configurations are spectrally distinguishable, this salt solution is ideally suited for nonlinear IR spectroscopic investigations to study ion pair association and dissociation dynamics. Using polarization-controlled IR pump-probe methods, we first measured the lifetimes and orientational relaxation times of these two forms of ionic configurations. The vibrational population relaxation times of both the free ion and CIP are about 32 ps. However, the orientational relaxation time of the CIP, which is {approx}47 ps, is significantly longer than that of the free SCN{sup -}, which is {approx}7.7 ps. This clearly indicates that the effective moment of inertia of the CIP is much larger than that of the free SCN{sup -}. Then, using chemical exchange 2DIR spectroscopy and analyzing the diagonal peak and cross-peak amplitude changes with increasing the waiting time, we determined the contact ion pair association and dissociation time constants that are found to be 165 and 190 ps, respectively. The results presented and discussed in this paper are believed to be important, not only because the ion-pairing dynamics is one of the most fundamental physical chemistry problems but also because such molecular ion-ion interactions are of critical importance in understanding Hofmeister effects on protein stability.« less

Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid

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

Starodumov, Ilya; Kropotin, Nikolai

2016-08-10

We investigate the three-dimensional mathematical model of crystal growth called PFC (Phase Field Crystal) in a hyperbolic modification. This model is also called the modified model PFC (originally PFC model is formulated in parabolic form) and allows to describe both slow and rapid crystallization processes on atomic length scales and on diffusive time scales. Modified PFC model is described by the differential equation in partial derivatives of the sixth order in space and second order in time. The solution of this equation is possible only by numerical methods. Previously, authors created the software package for the solution of the Phasemore » Field Crystal problem, based on the method of isogeometric analysis (IGA) and PetIGA program library. During further investigation it was found that the quality of the solution can strongly depends on the discretization parameters of a numerical method. In this report, we show the features that should be taken into account during constructing the computational grid for the numerical simulation.« less

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

Vacuum solutions of five dimensional Einstein equations generated by inverse scattering method. II. Production of the black ring solution

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

Tomizawa, Shinya; Nozawa, Masato

2006-06-15

We study vacuum solutions of five-dimensional Einstein equations generated by the inverse scattering method. We reproduce the black ring solution which was found by Emparan and Reall by taking the Euclidean Levi-Civita metric plus one-dimensional flat space as a seed. This transformation consists of two successive processes; the first step is to perform the three-solitonic transformation of the Euclidean Levi-Civita metric with one-dimensional flat space as a seed. The resulting metric is the Euclidean C-metric with extra one-dimensional flat space. The second is to perform the two-solitonic transformation by taking it as a new seed. Our result may serve asmore » a stepping stone to find new exact solutions in higher dimensions.« less

Solving time-dependent two-dimensional eddy current problems

NASA Technical Reports Server (NTRS)

Lee, Min Eig; Hariharan, S. I.; Ida, Nathan

1990-01-01

Transient eddy current calculations are presented for an EM wave-scattering and field-penetrating case in which a two-dimensional transverse magnetic field is incident on a good (i.e., not perfect) and infinitely long conductor. The problem thus posed is of initial boundary-value interface type, where the boundary of the conductor constitutes the interface. A potential function is used for time-domain modeling of the situation, and finite difference-time domain techniques are used to march the potential function explicitly in time. Attention is given to the case of LF radiation conditions.

Dynamics of Robertson–Walker spacetimes with diffusion

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

Alho, A., E-mail: aalho@math.ist.utl.pt; Calogero, S., E-mail: calogero@chalmers.se; Machado Ramos, M.P., E-mail: mpr@mct.uminho.pt

2015-03-15

We study the dynamics of spatially homogeneous and isotropic spacetimes containing a fluid undergoing microscopic velocity diffusion in a cosmological scalar field. After deriving a few exact solutions of the equations, we continue by analyzing the qualitative behavior of general solutions. To this purpose we recast the equations in the form of a two dimensional dynamical system and perform a global analysis of the flow. Among the admissible behaviors, we find solutions that are asymptotically de-Sitter both in the past and future time directions and which undergo accelerated expansion at all times.

Full evaporation dynamic headspace in combination with selectable one-dimensional/two-dimensional gas chromatography-mass spectrometry for the determination of suspected fragrance allergens in cosmetic products.

PubMed

Devos, Christophe; Ochiai, Nobuo; Sasamoto, Kikuo; Sandra, Pat; David, Frank

2012-09-14

Suspected fragrance allergens were determined in cosmetic products using a combination of full evaporation-dynamic headspace (FEDHS) with selectable one-dimensional/two-dimensional GC-MS. The full evaporation dynamic headspace approach allows the non-discriminating extraction and injection of both apolar and polar fragrance compounds, without contamination of the analytical system by high molecular weight non-volatile matrix compounds. The method can be applied to all classes of cosmetic samples, including water containing matrices such as shower gels or body creams. In combination with selectable (1)D/(2)D GC-MS, consisting of a dedicated heart-cutting GC-MS configuration using capillary flow technology (CFT) and low thermal mass GC (LTM-GC), a highly flexible and easy-to-use analytical solution is offered. Depending on the complexity of the perfume fraction, analyses can be performed in one-dimensional GC-MS mode or in heart-cutting two-dimensional GC-MS mode, without the need of hardware reconfiguration. The two-dimensional mode with independent temperature control of the first and second dimension column is especially useful to confirm the presence of detected allergen compounds when mass spectral deconvolution is not possible. Copyright © 2012 Elsevier B.V. All rights reserved.

Numerical solutions of several reflected shock-wave flow fields with nonequilibrium chemical reactions

NASA Technical Reports Server (NTRS)

Hanson, R. K.; Presley, L. L.; Williams, E. V.

1972-01-01

The method of characteristics for a chemically reacting gas is used in the construction of the time-dependent, one-dimensional flow field resulting from the normal reflection of an incident shock wave at the end wall of a shock tube. Nonequilibrium chemical reactions are allowed behind both the incident and reflected shock waves. All the solutions are evaluated for oxygen, but the results are generally representative of any inviscid, nonconducting, and nonradiating diatomic gas. The solutions clearly show that: (1) both the incident- and reflected-shock chemical relaxation times are important in governing the time to attain steady state thermodynamic properties; and (2) adjacent to the end wall, an excess-entropy layer develops wherein the steady state values of all the thermodynamic variables except pressure differ significantly from their corresponding Rankine-Hugoniot equilibrium values.

1-Propanol probing methodology: two-dimensional characterization of the effect of solute on H2O.

PubMed

Koga, Yoshikata

2013-09-21

The wording "hydrophobicity/hydrophilicity" has been used in a loose manner based on human experiences. We have devised a more quantitative way to redefine "hydrophobes" and "hydrophiles" in terms of the mole fraction dependence pattern of one of the third derivative quantities, the enthalpic interaction between solute molecules. We then devised a thermodynamic methodology to characterize the effect of a solute on H2O in terms of its hydrophobicity and/or hydrophilicity. We use a thermodynamic signature, the enthalpic interaction of 1-propanol, H, to monitor how the test solute modifies H2O. By this method, characterization is facilitated by two indices; one pertaining to its hydrophobicity and the other its hydrophilicity. Hence differences among amphiphiles are quantified in a two-dimensional manner. Furthermore, an individual ion can be characterized independent of a counter ion. By using this methodology, we have studied the effects on H2O of a number of solutes, and gained some important new insights. For example, such commonly used examples of hydrophobes in the literature as tetramethyl urea, trimethylamine-N-oxide, and tetramethylammonium salts are in fact surprisingly hydrophilic. Hence the conclusions about "hydrophobes" using these samples ought to be interpreted with caution. The effects of anions on H2O found by this methodology are in the same sequence of the Hofmeister ranking, which will no doubt aid a further investigation into this enigma in biochemistry. Thus, it is likely that this methodology could play an important role in the characterization of the effects of solutes in H2O, and a perspective view may be useful. Here, we describe the basis on which the methodology is developed and the methodology itself in m.ore detail than given in individual papers. We then summarize the results in two dimensional hydrophobicity/hydrophilicity maps.

Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two Dimensional Scalar Equation

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2002-01-01

The framework for constructing a high-order, conservative Spectral (Finite) Volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner. The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and non-linear model problems with and without discontinuities.

Fundamental differences between glassy dynamics in two and three dimensions

PubMed Central

Flenner, Elijah; Szamel, Grzegorz

2015-01-01

The two-dimensional freezing transition is very different from its three-dimensional counterpart. In contrast, the glass transition is usually assumed to have similar characteristics in two and three dimensions. Using computer simulations, here we show that glassy dynamics in supercooled two- and three-dimensional fluids are fundamentally different. Specifically, transient localization of particles on approaching the glass transition is absent in two dimensions, whereas it is very pronounced in three dimensions. Moreover, the temperature dependence of the relaxation time of orientational correlations is decoupled from that of the translational relaxation time in two dimensions but not in three dimensions. Last, the relationships between the characteristic size of dynamically heterogeneous regions and the relaxation time are very different in two and three dimensions. These results strongly suggest that the glass transition in two dimensions is different than in three dimensions. PMID:26067877

Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem.

PubMed

Schilde, M; Doerner, K F; Hartl, R F

2014-10-01

In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches.

Computational and experimental aftbody flow fields for hypersonic, airbreathing configurations with scramjet exhaust flow simulation

NASA Technical Reports Server (NTRS)

Huebner, Lawrence D.; Tatum, Kenneth E.

1991-01-01

Computational results are presented for three issues pertinent to hypersonic, airbreathing vehicles employing scramjet exhaust flow simulation. The first issue consists of a comparison of schlieren photographs obtained on the aftbody of a cruise missile configuration under powered conditions with two-dimensional computational solutions. The second issue presents the powered aftbody effects of modeling the inlet with a fairing to divert the external flow as compared to an operating flow-through inlet on a generic hypersonic vehicle. Finally, a comparison of solutions examining the potential of testing powered configurations in a wind-off, instead of a wind-on, environment, indicate that, depending on the extent of the three-dimensional plume, it may be possible to test aftbody powered hypersonic, airbreathing configurations in a wind-off environment.

Holocinematographic velocimeter for measuring time-dependent, three-dimensional flows

NASA Technical Reports Server (NTRS)

Beeler, George B.; Weinstein, Leonard M.

1987-01-01

Two simulatneous, orthogonal-axis holographic movies are made of tracer particles in a low-speed water tunnel to determine the time-dependent, three-dimensional velocity field. This instrument is called a Holocinematographic Velocimeter (HCV). The holographic movies are reduced to the velocity field with an automatic data reduction system. This permits the reduction of large numbers of holograms (time steps) in a reasonable amount of time. The current version of the HCV, built for proof-of-concept tests, uses low-frame rate holographic cameras and a prototype of a new type of water tunnel. This water tunnel is a unique low-disturbance facility which has minimal wall effects on the flow. This paper presents the first flow field examined by the HCV, the two-dimensional von Karman vortex street downstream of an unswept circular cylinder. Key factors in the HCV are flow speed, spatial and temporal resolution required, measurement volume, film transport speed, and laser pulse length. The interactions between these factors are discussed.

Structural, thermodynamic, and electrical properties of polar fluids and ionic solutions on a hypersphere: Results of simulations

NASA Astrophysics Data System (ADS)

Caillol, J. M.; Levesque, D.

1992-01-01

The reliability and the efficiency of a new method suitable for the simulations of dielectric fluids and ionic solutions is established by numerical computations. The efficiency depends on the use of a simulation cell which is the surface of a four-dimensional sphere. The reliability originates from a charge-charge potential solution of the Poisson equation in this confining volume. The computation time, for systems of a few hundred molecules, is reduced by a factor of 2 or 3 compared to this of a simulation performed in a cubic volume with periodic boundary conditions and the Ewald charge-charge potential.

Vector matter waves in two-component Bose-Einstein condensates with spatially modulated nonlinearities

NASA Astrophysics Data System (ADS)

Xu, Si-Liu; He, Jun-Rong; Xue, Li; Belić, Milivoj R.

2018-02-01

We demonstrate three-dimensional (3D) vector solitary waves in the coupled (3 + 1)-D nonlinear Gross-Pitaevskii equations with variable nonlinearity coefficients. The analysis is carried out in spherical coordinates, providing novel localized solutions that depend on three modal numbers, l, m, and n. Using the similarity transformation (ST) method in 3D, vector solitary waves are built with the help of a combination of harmonic and trapping potentials, including multipole solutions and necklace rings. In general, the solutions found are stable for low values of the modal numbers; for values larger than 2, the solutions are found to be unstable. Variable nonlinearity allows the utilization of soliton management methods.

A lattice Boltzmann model for the Burgers-Fisher equation.

PubMed

Zhang, Jianying; Yan, Guangwu

2010-06-01

A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption. (c) 2010 American Institute of Physics.

Direct computation of stochastic flow in reservoirs with uncertain parameters

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

Dainton, M.P.; Nichols, N.K.; Goldwater, M.H.

1997-01-15

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point andmore » to the field convariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data. 14 refs., 14 figs., 3 tabs.« less

Computational simulation of laser heat processing of materials

NASA Astrophysics Data System (ADS)

Shankar, Vijaya; Gnanamuthu, Daniel

1987-04-01

A computational model simulating the laser heat treatment of AISI 4140 steel plates with a CW CO2 laser beam has been developed on the basis of the three-dimensional, time-dependent heat equation (subject to the appropriate boundary conditions). The solution method is based on Newton iteration applied to a triple-approximate factorized form of the equation. The method is implicit and time-accurate; the maintenance of time-accuracy in the numerical formulation is noted to be critical for the simulation of finite length workpieces with a finite laser beam dwell time.

Critical Intermediate Structure That Directs the Crystalline Texture and Surface Morphology of Organo-Lead Trihalide Perovskite.

PubMed

Chia, Hao-Chung; Sheu, Hwo-Shuenn; Hsiao, Yu-Yun; Li, Shao-Sian; Lan, Yi-Kang; Lin, Chung-Yao; Chang, Je-Wei; Kuo, Yen-Chien; Chen, Chia-Hao; Weng, Shih-Chang; Su, Chun-Jen; Su, An-Chung; Chen, Chun-Wei; Jeng, U-Ser

2017-10-25

We have identified an often observed yet unresolved intermediate structure in a popular processing with dimethylformamide solutions of lead chloride and methylammonium iodide for perovskite solar cells. With subsecond time-resolved grazing-incidence X-ray scattering and X-ray photoemission spectroscopy, supplemental with ab initio calculation, the resolved intermediate structure (CH 3 NH 3 ) 2 PbI 2 Cl 2 ·CH 3 NH 3 I features two-dimensional (2D) perovskite bilayers of zigzagged lead-halide octahedra and sandwiched CH 3 NH 3 I layers. Such intermediate structure reveals a hidden correlation between the intermediate phase and the composition of the processing solution. Most importantly, the 2D perovskite lattice of the intermediate phase is largely crystallographically aligned with the [110] planes of the three-dimensional perovskite cubic phase; consequently, with sublimation of Cl ions from the organo-lead octahedral terminal corners in prolonged annealing, the zigzagged octahedral layers of the intermediate phase can merge with the intercalated methylammonium iodide layers for templated growth of perovskite crystals. Regulated by annealing temperature and the activation energies of the intermediate and perovskite, deduced from analysis of temperature-dependent structural kinetics, the intermediate phase is found to selectively mature first and then melt along the layering direction for epitaxial conversion into perovskite crystals. The unveiled epitaxial conversion under growth kinetics controls might be general for solution-processed and intermediate-templated perovskite formation.

Generalizations of the Toda molecule

NASA Astrophysics Data System (ADS)

Van Velthoven, W. P. G.; Bais, F. A.

1986-12-01

Finite-energy monopole solutions are constructed for the self-dual equations with spherical symmetry in an arbitrary integer graded Lie algebra. The constraint of spherical symmetry in a complex noncoordinate basis leads to a dimensional reduction. The resulting two-dimensional ( r, t) equations are of second order and furnish new generalizations of the Toda molecule equations. These are then solved by a technique which is due to Leznov and Saveliev. For time-independent solutions a further reduction is made, leading to an ansatz for all SU(2) embeddings of the Lie algebra. The regularity condition at the origin for the solutions, needed to ensure finite energy, is also solved for a special class of nonmaximal embeddings. Explicit solutions are given for the groups SU(2), SO(4), Sp(4) and SU(4).

A numerical solution for two-dimensional Fredholm integral equations of the second kind with kernels of the logarithmic potential form

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Uenal, A.

1981-01-01

Two dimensional Fredholm integral equations with logarithmic potential kernels are numerically solved. The explicit consequence of these solutions to their true solutions is demonstrated. The results are based on a previous work in which numerical solutions were obtained for Fredholm integral equations of the second kind with continuous kernels.

An efficient semi-implicit method for three-dimensional non-hydrostatic flows in compliant arterial vessels.

PubMed

Fambri, Francesco; Dumbser, Michael; Casulli, Vincenzo

2014-11-01

Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article, blood is treated as an incompressible Newtonian fluid that flows through compliant vessels of general cross section. A three-dimensional semi-implicit finite difference and finite volume model is derived so that numerical stability is obtained at a low computational cost on a staggered grid. The key idea of the method consists in a splitting of the pressure into a hydrostatic and a non-hydrostatic part, where first a small quasi-one-dimensional nonlinear system is solved for the hydrostatic pressure and only in a second step the fully three-dimensional non-hydrostatic pressure is computed from a three-dimensional nonlinear system as a correction to the hydrostatic one. The resulting algorithm is robust, efficient, locally and globally mass conservative, and applies to hydrostatic and non-hydrostatic flows in one, two and three space dimensions. These features are illustrated on nontrivial test cases for flows in tubes with circular or elliptical cross section where the exact analytical solution is known. Test cases of steady and pulsatile flows in uniformly curved rigid and elastic tubes are presented. Wherever possible, axial velocity development and secondary flows are shown and compared with previously published results. Copyright © 2014 John Wiley & Sons, Ltd.

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

Giunta, G.; Belouettar, S.

In this paper, the static response of three-dimensional beams made of functionally graded materials is investigated through a family of hierarchical one-dimensional finite elements. A wide variety of elements is proposed differing by the kinematic formulation and the number of nodes per elements along the beam axis. Elements’ stiffness matrix and load vector are derived in a unified nuclear form that does not depend upon the a priori expansion order over the cross-section nor the finite element approximation along the beam axis. Results are validated towards three-dimensional finite element models as well as equivalent Navier-type analytical solutions. The numerical investigationsmore » show that accurate and efficient solutions (when compared with full three-dimensional FEM solutions) can be obtained by the proposed family of hierarchical one-dimensional elements’ family.« less

Noniterative three-dimensional grid generation using parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Edwards, T. A.

1985-01-01

A new algorithm for generating three-dimensional grids has been developed and implemented which numerically solves a parabolic partial differential equation (PDE). The solution procedure marches outward in two coordinate directions, and requires inversion of a scalar tridiagonal system in the third. Source terms have been introduced to control the spacing and angle of grid lines near the grid boundaries, and to control the outer boundary point distribution. The method has been found to generate grids about 100 times faster than comparable grids generated via solution of elliptic PDEs, and produces smooth grids for finite-difference flow calculations.

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.

Numerical modeling of the early interaction of a planar shock with a dense particle field

NASA Astrophysics Data System (ADS)

Regele, Jonathan; Blanquart, Guillaume

2011-11-01

Dense compressible multiphase flows are of interest for multiphase turbomachinary and energetic material detonations. Still, there is little understanding of the detailed interaction mechanisms between shock waves and dense (particle volume fraction αd > 0 . 001) particle fields. A recent experimental study [Wagner et al, AIAA Aero. Sci., Orlando, 2011-188] has focused on the impingement of a planar shock wave on a dense particle curtain. In the present work, numerical solutions of the Euler equations in one and two dimensions are performed for a planar shock wave impinging on a fixed particle curtain and are compared to the experimental data for early times. Comparison of the one- and two-dimensional results demonstrate that the one-dimensional description captures the large scale flow behavior, but is inadequate to capture all the details observed in the experiments. The two-dimensional solutions are shown to reproduce the experimentally observed flow structures and provide insight into how these details originate.

Huygens' inspired multi-pendulum setups: Experiments and stability analysis

NASA Astrophysics Data System (ADS)

Hoogeboom, F. N.; Pogromsky, A. Y.; Nijmeijer, H.

2016-11-01

This paper examines synchronization of a set of metronomes placed on a lightweight foam platform. Two configurations of the set of metronomes are considered: a row setup containing one-dimensional coupling and a cross setup containing two-dimensional coupling. Depending on the configuration and coupling between the metronomes, i.e., the platform parameters, in- and/or anti-phase synchronized behavior is observed in the experiments. To explain this behavior, mathematical models of a metronome and experimental setups have been derived and used in a local stability analysis. It is numerically and experimentally demonstrated that varying the coupling parameters for both configurations has a significant influence on the stability of the synchronized solutions.

Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction

NASA Astrophysics Data System (ADS)

Cui, Tiangang; Marzouk, Youssef; Willcox, Karen

2016-06-01

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting-both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a heterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters.

Three-dimensional multigrid Navier-Stokes computations for turbomachinery applications

NASA Astrophysics Data System (ADS)

Subramanian, S. V.

1989-07-01

The fully three-dimensional, time-dependent compressible Navier-Stokes equations in cylindrical coordinates are presently used, in conjunction with the multistage Runge-Kutta numerical integration scheme for solution of the governing flow equations, to simulate complex flowfields within turbomechanical components whose pertinent effects encompass those of viscosity, compressibility, blade rotation, and tip clearance. Computed results are presented for selected cascades, emphasizing the code's capabilities in the accurate prediction of such features as airfoil loadings, exit flow angles, shocks, and secondary flows. Computations for several test cases have been performed on a Cray-YMP, using nearly 90,000 grid points.

Exact three-dimensional spectral solution to surface-groundwater interactions with arbitrary surface topography

USGS Publications Warehouse

Worman, A.; Packman, A.I.; Marklund, L.; Harvey, J.W.; Stone, S.H.

2006-01-01

It has been long known that land surface topography governs both groundwater flow patterns at the regional-to-continental scale and on smaller scales such as in the hyporheic zone of streams. Here we show that the surface topography can be separated in a Fourier-series spectrum that provides an exact solution of the underlying three-dimensional groundwater flows. The new spectral solution offers a practical tool for fast calculation of subsurface flows in different hydrological applications and provides a theoretical platform for advancing conceptual understanding of the effect of landscape topography on subsurface flows. We also show how the spectrum of surface topography influences the residence time distribution for subsurface flows. The study indicates that the subsurface head variation decays exponentially with depth faster than it would with equivalent two-dimensional features, resulting in a shallower flow interaction. Copyright 2006 by the American Geophysical Union.

Couplings between hierarchical conformational dynamics from multi-time correlation functions and two-dimensional lifetime spectra: Application to adenylate kinase

NASA Astrophysics Data System (ADS)

Ono, Junichi; Takada, Shoji; Saito, Shinji

2015-06-01

An analytical method based on a three-time correlation function and the corresponding two-dimensional (2D) lifetime spectrum is developed to elucidate the time-dependent couplings between the multi-timescale (i.e., hierarchical) conformational dynamics in heterogeneous systems such as proteins. In analogy with 2D NMR, IR, electronic, and fluorescence spectroscopies, the waiting-time dependence of the off-diagonal peaks in the 2D lifetime spectra can provide a quantitative description of the dynamical correlations between the conformational motions with different lifetimes. The present method is applied to intrinsic conformational changes of substrate-free adenylate kinase (AKE) using long-time coarse-grained molecular dynamics simulations. It is found that the hierarchical conformational dynamics arise from the intra-domain structural transitions among conformational substates of AKE by analyzing the one-time correlation functions and one-dimensional lifetime spectra for the donor-acceptor distances corresponding to single-molecule Förster resonance energy transfer experiments with the use of the principal component analysis. In addition, the complicated waiting-time dependence of the off-diagonal peaks in the 2D lifetime spectra for the donor-acceptor distances is attributed to the fact that the time evolution of the couplings between the conformational dynamics depends upon both the spatial and temporal characters of the system. The present method is expected to shed light on the biological relationship among the structure, dynamics, and function.

Couplings between hierarchical conformational dynamics from multi-time correlation functions and two-dimensional lifetime spectra: Application to adenylate kinase

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

Ono, Junichi; Takada, Shoji; Department of Biophysics, Graduate School of Science, Kyoto University, Kyoto 606-8502

2015-06-07

An analytical method based on a three-time correlation function and the corresponding two-dimensional (2D) lifetime spectrum is developed to elucidate the time-dependent couplings between the multi-timescale (i.e., hierarchical) conformational dynamics in heterogeneous systems such as proteins. In analogy with 2D NMR, IR, electronic, and fluorescence spectroscopies, the waiting-time dependence of the off-diagonal peaks in the 2D lifetime spectra can provide a quantitative description of the dynamical correlations between the conformational motions with different lifetimes. The present method is applied to intrinsic conformational changes of substrate-free adenylate kinase (AKE) using long-time coarse-grained molecular dynamics simulations. It is found that the hierarchicalmore » conformational dynamics arise from the intra-domain structural transitions among conformational substates of AKE by analyzing the one-time correlation functions and one-dimensional lifetime spectra for the donor-acceptor distances corresponding to single-molecule Förster resonance energy transfer experiments with the use of the principal component analysis. In addition, the complicated waiting-time dependence of the off-diagonal peaks in the 2D lifetime spectra for the donor-acceptor distances is attributed to the fact that the time evolution of the couplings between the conformational dynamics depends upon both the spatial and temporal characters of the system. The present method is expected to shed light on the biological relationship among the structure, dynamics, and function.« less

Early stage aggregation of a coarse-grained model of polyglutamine

NASA Astrophysics Data System (ADS)

Haaga, Jason; Gunton, J. D.; Buckles, C. Nadia; Rickman, J. M.

2018-01-01

In this paper, we study the early stages of aggregation of a model of polyglutamine (polyQ) for different repeat lengths (number of glutamine amino acid groups in the chain). In particular, we use the Large-scale Atomic/Molecular Massively Parallel Simulator to study a generic coarse-grained model proposed by Bereau and Deserno. We focus on the primary nucleation mechanism involved and find that our results for the initial self-assembly process are consistent with the two-dimensional classical nucleation theory of Kashchiev and Auer. More specifically, we find that with decreasing supersaturation, the oligomer fibril (protofibril) transforms from a one-dimensional β sheet to two-, three-, and higher layer β sheets as the critical nucleus size increases. We also show that the results are consistent with several predictions of their theory, including the dependence of the critical nucleus size on the supersaturation. Our results for the time dependence of the mass aggregation are in reasonable agreement with an approximate analytical solution of the filament theory by Knowles and collaborators that corresponds to an additional secondary nucleation arising from filament fragmentation. Finally, we study the dependence of the critical nucleus size on the repeat length of polyQ. We find that for the larger length polyglutamine chain that we study, the critical nucleus is a monomer, in agreement with experiment and in contrast to the case for the smaller chain, for which the smallest critical nucleus size is four.

Numerical Solutions for Supersonic Flow of an Ideal Gas Around Blunt Two-Dimensional Bodies

NASA Technical Reports Server (NTRS)

Fuller, Franklyn B.

1961-01-01

The method described is an inverse one; the shock shape is chosen and the solution proceeds downstream to a body. Bodies blunter than circular cylinders are readily accessible, and any adiabatic index can be chosen. The lower limit to the free-stream Mach number available in any case is determined by the extent of the subsonic field, which in turn depends upon the body shape. Some discussion of the stability of the numerical processes is given. A set of solutions for flows about circular cylinders at several Mach numbers and several values of the adiabatic index is included.

Real-time monitoring of the solution concentration variation during the crystallization process of protein-lysozyme by using digital holographic interferometry.

PubMed

Zhang, Yanyan; Zhao, Jianlin; Di, Jianglei; Jiang, Hongzhen; Wang, Qian; Wang, Jun; Guo, Yunzhu; Yin, Dachuan

2012-07-30

We report a real-time measurement method of the solution concentration variation during the growth of protein-lysozyme crystals based on digital holographic interferometry. A series of holograms containing the information of the solution concentration variation in the whole crystallization process is recorded by CCD. Based on the principle of double-exposure holographic interferometry and the relationship between the phase difference of the reconstructed object wave and the solution concentration, the solution concentration variation with time for arbitrary point in the solution can be obtained, and then the two-dimensional concentration distribution of the solution during crystallization process can also be figured out under the precondition which the refractive index is constant through the light propagation direction. The experimental results turns out that it is feasible to in situ, full-field and real-time monitor the crystal growth process by using this method.

The time course of explicit and implicit categorization.

PubMed

Smith, J David; Zakrzewski, Alexandria C; Herberger, Eric R; Boomer, Joseph; Roeder, Jessica L; Ashby, F Gregory; Church, Barbara A

2015-10-01

Contemporary theory in cognitive neuroscience distinguishes, among the processes and utilities that serve categorization, explicit and implicit systems of category learning that learn, respectively, category rules by active hypothesis testing or adaptive behaviors by association and reinforcement. Little is known about the time course of categorization within these systems. Accordingly, the present experiments contrasted tasks that fostered explicit categorization (because they had a one-dimensional, rule-based solution) or implicit categorization (because they had a two-dimensional, information-integration solution). In Experiment 1, participants learned categories under unspeeded or speeded conditions. In Experiment 2, they applied previously trained category knowledge under unspeeded or speeded conditions. Speeded conditions selectively impaired implicit category learning and implicit mature categorization. These results illuminate the processing dynamics of explicit/implicit categorization.

Multi-dimensional multi-species modeling of transient electrodeposition in LIGA microfabrication.

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

Evans, Gregory Herbert; Chen, Ken Shuang

2004-06-01

This report documents the efforts and accomplishments of the LIGA electrodeposition modeling project which was headed by the ASCI Materials and Physics Modeling Program. A multi-dimensional framework based on GOMA was developed for modeling time-dependent diffusion and migration of multiple charged species in a dilute electrolyte solution with reduction electro-chemical reactions on moving deposition surfaces. By combining the species mass conservation equations with the electroneutrality constraint, a Poisson equation that explicitly describes the electrolyte potential was derived. The set of coupled, nonlinear equations governing species transport, electric potential, velocity, hydrodynamic pressure, and mesh motion were solved in GOMA, using themore » finite-element method and a fully-coupled implicit solution scheme via Newton's method. By treating the finite-element mesh as a pseudo solid with an arbitrary Lagrangian-Eulerian formulation and by repeatedly performing re-meshing with CUBIT and re-mapping with MAPVAR, the moving deposition surfaces were tracked explicitly from start of deposition until the trenches were filled with metal, thus enabling the computation of local current densities that potentially influence the microstructure and frictional/mechanical properties of the deposit. The multi-dimensional, multi-species, transient computational framework was demonstrated in case studies of two-dimensional nickel electrodeposition in single and multiple trenches, without and with bath stirring or forced flow. Effects of buoyancy-induced convection on deposition were also investigated. To further illustrate its utility, the framework was employed to simulate deposition in microscreen-based LIGA molds. Lastly, future needs for modeling LIGA electrodeposition are discussed.« less

High-Resolution Genuinely Multidimensional Solution of Conservation Laws by the Space-Time Conservation Element and Solution Element Method

NASA Technical Reports Server (NTRS)

Himansu, Ananda; Chang, Sin-Chung; Yu, Sheng-Tao; Wang, Xiao-Yen; Loh, Ching-Yuen; Jorgenson, Philip C. E.

1999-01-01

In this overview paper, we review the basic principles of the method of space-time conservation element and solution element for solving the conservation laws in one and two spatial dimensions. The present method is developed on the basis of local and global flux conservation in a space-time domain, in which space and time are treated in a unified manner. In contrast to the modern upwind schemes, the approach here does not use the Riemann solver and the reconstruction procedure as the building blocks. The drawbacks of the upwind approach, such as the difficulty of rationally extending the 1D scalar approach to systems of equations and particularly to multiple dimensions is here contrasted with the uniformity and ease of generalization of the Conservation Element and Solution Element (CE/SE) 1D scalar schemes to systems of equations and to multiple spatial dimensions. The assured compatibility with the simplest type of unstructured meshes, and the uniquely simple nonreflecting boundary conditions of the present method are also discussed. The present approach has yielded high-resolution shocks, rarefaction waves, acoustic waves, vortices, ZND detonation waves, and shock/acoustic waves/vortices interactions. Moreover, since no directional splitting is employed, numerical resolution of two-dimensional calculations is comparable to that of the one-dimensional calculations. Some sample applications displaying the strengths and broad applicability of the CE/SE method are reviewed.

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.

A novel approach to interpretation of the time-dependent self-diffusion coefficient as a probe of porous media geometry.

PubMed

Loskutov, V V; Sevriugin, V A

2013-05-01

This article presents a new approximation describing fluid diffusion in porous media. Time dependence of the self-diffusion coefficient D(t) in the permeable porous medium is studied based on the assumption that diffusant molecules move randomly. An analytical expression for time dependence of the self-diffusion coefficient was obtained in the following form: D(t)=(D0-D∞)exp(-D0t/λ)+D∞, where D0 is the self-diffusion coefficient of bulk fluid, D∞ is the asymptotic value of the self-diffusion coefficient in the limit of long time values (t→∞), λ is the characteristic parameter of this porous medium with dimensionality of length. Applicability of the solution obtained to the analysis of experimental data is shown. The possibility of passing to short-time and long-time regimes is discussed. Copyright © 2013 Elsevier Inc. All rights reserved.

Closure to new results for an approximate method for calculating two-dimensional furrow infiltration

USDA-ARS?s Scientific Manuscript database

In a discussion paper, Ebrahimian and Noury (2015) raised several concerns about an approximate solution to the two-dimensional Richards equation presented by Bautista et al (2014). The solution is based on a procedure originally proposed by Warrick et al. (2007). Such a solution is of practical i...

Homotopy decomposition method for solving one-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Abuasad, Salah; Hashim, Ishak

2018-04-01

In this paper, we present the homotopy decomposition method with a modified definition of beta fractional derivative for the first time to find exact solution of one-dimensional time-fractional diffusion equation. In this method, the solution takes the form of a convergent series with easily computable terms. The exact solution obtained by the proposed method is compared with the exact solution obtained by using fractional variational homotopy perturbation iteration method via a modified Riemann-Liouville derivative.

An interaction algorithm for prediction of mean and fluctuating velocities in two-dimensional aerodynamic wake flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Orzechowski, J. A.

1980-01-01

A theoretical analysis is presented yielding sets of partial differential equations for determination of turbulent aerodynamic flowfields in the vicinity of an airfoil trailing edge. A four phase interaction algorithm is derived to complete the analysis. Following input, the first computational phase is an elementary viscous corrected two dimensional potential flow solution yielding an estimate of the inviscid-flow induced pressure distribution. Phase C involves solution of the turbulent two dimensional boundary layer equations over the trailing edge, with transition to a two dimensional parabolic Navier-Stokes equation system describing the near-wake merging of the upper and lower surface boundary layers. An iteration provides refinement of the potential flow induced pressure coupling to the viscous flow solutions. The final phase is a complete two dimensional Navier-Stokes analysis of the wake flow in the vicinity of a blunt-bases airfoil. A finite element numerical algorithm is presented which is applicable to solution of all partial differential equation sets of inviscid-viscous aerodynamic interaction algorithm. Numerical results are discussed.

Information transport in classical statistical systems

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-02-01

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.

Plasmon mass scale in two-dimensional classical nonequilibrium gauge theory

NASA Astrophysics Data System (ADS)

Lappi, T.; Peuron, J.

2018-02-01

We study the plasmon mass scale in classical gluodynamics in a two-dimensional configuration that mimics the boost-invariant initial color fields in a heavy-ion collision. We numerically measure the plasmon mass scale using three different methods: a hard thermal loop (HTL) expression involving the quasiparticle spectrum constructed from Coulomb gauge field correlators, an effective dispersion relation, and the measurement of oscillations between electric and magnetic energies after introducing a spatially uniform perturbation to the electric field. We find that the HTL expression and the uniform electric field measurement are in rough agreement. The effective dispersion relation agrees with other methods within a factor of 2. We also study the dependence on time and occupation number, observing similar trends as in three spatial dimensions, where a power-law dependence sets in after an occupation-number-dependent transient time. We observe a decrease of the plasmon mass squared as t-1 / 3 at late times.

On the generation of cnoidal waves in ion beam-dusty plasma containing superthermal electrons and ions

NASA Astrophysics Data System (ADS)

El-Bedwehy, N. A.

2016-07-01

The reductive perturbation technique is used for investigating an ion beam-dusty plasma system consisting of two opposite polarity dusty grains, and superthermal electrons and ions in addition to ion beam. A two-dimensional Kadomtsev-Petviashvili equation is derived. The solution of this equation, employing Painlevé analysis, leads to cnoidal waves. The dependence of the structural features of these waves on the physical plasma parameters is investigated.

On the generation of cnoidal waves in ion beam-dusty plasma containing superthermal electrons and ions

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

El-Bedwehy, N. A., E-mail: nab-elbedwehy@yahoo.com

2016-07-15

The reductive perturbation technique is used for investigating an ion beam-dusty plasma system consisting of two opposite polarity dusty grains, and superthermal electrons and ions in addition to ion beam. A two-dimensional Kadomtsev–Petviashvili equation is derived. The solution of this equation, employing Painlevé analysis, leads to cnoidal waves. The dependence of the structural features of these waves on the physical plasma parameters is investigated.

A Two-Dimensional Helmholtz Equation Solution for the Multiple Cavity Scattering Problem

DTIC Science & Technology

2013-02-01

obtained by using the block Gauss – Seidel iterative meth- od. To show the convergence of the iterative method, we define the error between two...models to the general multiple cavity setting. Numerical examples indicate that the convergence of the Gauss – Seidel iterative method depends on the...variational approach. A block Gauss – Seidel iterative method is introduced to solve the cou- pled system of the multiple cavity scattering problem, where

An iterative bidirectional heuristic placement algorithm for solving the two-dimensional knapsack packing problem

NASA Astrophysics Data System (ADS)

Shiangjen, Kanokwatt; Chaijaruwanich, Jeerayut; Srisujjalertwaja, Wijak; Unachak, Prakarn; Somhom, Samerkae

2018-02-01

This article presents an efficient heuristic placement algorithm, namely, a bidirectional heuristic placement, for solving the two-dimensional rectangular knapsack packing problem. The heuristic demonstrates ways to maximize space utilization by fitting the appropriate rectangle from both sides of the wall of the current residual space layer by layer. The iterative local search along with a shift strategy is developed and applied to the heuristic to balance the exploitation and exploration tasks in the solution space without the tuning of any parameters. The experimental results on many scales of packing problems show that this approach can produce high-quality solutions for most of the benchmark datasets, especially for large-scale problems, within a reasonable duration of computational time.

Extensive packet excitations in FPU and Toda lattices

NASA Astrophysics Data System (ADS)

Christodoulidi, H.

2017-08-01

At low energies, the excitation of low-frequency packets of normal modes in the Fermi-Pasta-Ulam (FPU) and in the Toda model leads to exponentially localized energy profiles which resemble staircases and are identified by a slope σ that depends logarithmically on the specific energy \\varepsilon=E/N . Such solutions are found to lie on stable lower-dimensional tori, named q-tori. At higher energies there is a sharp transition of the system's localization profile to a straight-line one, determined by an N-dependent slope of the form σ ∼ (\\varepsilon N)-d , d > 0. We find that the energy crossover \\varepsilon c between the two energy regimes decays as 1/N , which indicates that q-tori disappear in the thermodynamic limit. Furthermore, we focus on the times that such localization profiles are practically frozen and we find that these “stickiness times” can rapidly and accurately distinguish between a power-law and a stretched exponential dependence in 1/\\varepsilon .

Localization of toroidal motion and shear heating in 3-D high Rayleigh number convection with temperature-dependent viscosity

NASA Technical Reports Server (NTRS)

Balachandar, S.; Yuen, D. A.; Reuteler, D. M.

1995-01-01

We have applied spectral-transform methods to study three-dimensional thermal convection with temperature-dependent viscosity. The viscosity varies exponentially with the form exp(-BT), where B controls the viscosity contrast and T is temperature. Solutions for high Rayleigh numbers, up to an effective Ra of 6.25 x 10(exp 6), have been obtained for an aspect-ratio of 5x5x1 and a viscosity contrast of 25. Solutions show the localization of toroidal velocity fields with increasing vigor of convection to a coherent network of shear-zones. Viscous dissipation increases with Rayleigh number and is particularly strong in regions of convergent flows and shear deformation. A time-varying depth-dependent mean-flow is generated because of the correlation between laterally varying viscosity and velocity gradients.

Relationship Between Integro-Differential Schrodinger Equation with a Symmetric Kernel and Position-Dependent Effective Mass

NASA Astrophysics Data System (ADS)

Khosropour, B.; Moayedi, S. K.; Sabzali, R.

2018-07-01

The solution of integro-differential Schrodinger equation (IDSE) which was introduced by physicists has a great role in the fields of science. The purpose of this paper comes in two parts. First, studying the relationship between integro-differential Schrodinger equation with a symmetric non-local potential and one-dimensional Schrodinger equation with a position-dependent effective mass. Second, we show that the quantum Hamiltonian for a particle with position-dependent mass after applying Liouville-Green transformations will be converted to a quantum Hamiltonian for a particle with constant mass.

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

Gauge/Gravity correspondence and black hole attractors in various dimensions

NASA Astrophysics Data System (ADS)

Li, Wei

This thesis investigates several topics on Gauge/Gravity correspondence and black hole attractors in various dimensions. The first chapter contains a brief review and summary of main results. Chapters 2 and 3 aim at a microscopic description of black objects in five dimensions. Chapter 2 studies higher-derivative corrections for 5D black rings and spinning black holes. It shows that certain R 2 terms found in Calabi-Yau compactifications of M-theory yield macroscopic corrections to the entropies that match the microscopic corrections. Chapter 3 constructs probe brane configurations that preserve half of the enhanced near-horizon supersymmetry of 5D spinning black holes, whose near-horizon geometry is squashed AdS2 x S 3. There are supersymmetric zero-brane probes stabilized by orbital angular momentum on S3 and one-brane probes with momentum and winding around a U(1)L x U(1)R torus in S3. Chapter 4 constructs and analyzes generic single-centered and multi-centered black hole attractor solutions in various four-dimensional models which, after Kaluza-Klein reduction, admit a description in terms of 3D gravity coupled to a sigma model whose target space is symmetric coset space. The solutions correspond to certain nilpotent generators of the coset algebra. The non-BPS black hole attractors are found to be drastically different from their BPS counterparts. Chapter 5 examines three-dimensional topologically massive gravity with negative cosmological constant in asymptotically AdS 3 spacetimes. It proves that the theory is unitary and stable only at a special value of Chern-Simons coupling, where the theory becomes chiral. This suggests the existence of a stable, consistent quantum gravity theory at the chiral point which is dual to a holomorphic boundary CFT 2. Finally, Chapter 6 studies the two-dimensional N = 1 critical string theory with a linear dilaton background. It constructs time-dependent boundary state solutions that correspond to D0-branes falling toward the Liouville wall. It also shows that there exist four types of stable, falling D0-branes (two branes and two anti-branes) in Type 0A projection and two unstable ones in Type 0B projection.

On the motion of viscous fluids in the presence of diffusion

NASA Astrophysics Data System (ADS)

Secchi, Paolo

1988-01-01

The flow of a viscous incompressible two-component fluid with Fick's-law diffusion is investigated analytically. The existence of a unique global solution for small values of the diffusion coefficient (lambda) is proved for two-dimensional flow. The two- and three-dimensional solutions are also shown to converge toward the solutions of the Navier-Stokes equations for inhomogeneous fluids as lambda approaches zero.

Three- and two-dimensional simulations of counter-propagating shear experiments at high energy densities at the National Ignition Facility

DOE PAGES

Wang, Ping; Zhou, Ye; MacLaren, Stephan A.; ...

2015-11-06

Three- and two-dimensional numerical studies have been carried out to simulate recent counter-propagating shear flow experiments on the National Ignition Facility. A multi-physics three-dimensional, time-dependent radiation hydrodynamics simulation code is used. Using a Reynolds Averaging Navier-Stokes model, we show that the evolution of the mixing layer width obtained from the simulations agrees well with that measured from the experiments. A sensitivity study is conducted to illustrate a 3D geometrical effect that could confuse the measurement at late times, if the energy drives from the two ends of the shock tube are asymmetric. Implications for future experiments are discussed.

Anisotropic dielectric properties of two-dimensional matrix in pseudo-spin ferroelectric system

NASA Astrophysics Data System (ADS)

Kim, Se-Hun

2016-10-01

The anisotropic dielectric properties of a two-dimensional (2D) ferroelectric system were studied using the statistical calculation of the pseudo-spin Ising Hamiltonian model. It is necessary to delay the time for measurements of the observable and the independence of the new spin configuration under Monte Carlo sampling, in which the thermal equilibrium state depends on the temperature and size of the system. The autocorrelation time constants of the normalized relaxation function were determined by taking temperature and 2D lattice size into account. We discuss the dielectric constants of a two-dimensional ferroelectric system by using the Metropolis method in view of the Slater-Takagi defect energies.

Influence of the extrinsic curvature on two-dimensional nematic films.

PubMed

Napoli, Gaetano; Vergori, Luigi

2018-05-01

Nematic films are thin fluid structures, ideally two dimensional, endowed with an in-plane degenerate nematic order. In this paper we examine a generalization of the classical Plateau problem to an axisymmetric nematic film bounded by two coaxial parallel rings. At equilibrium, the shape of the nematic film results from the competition between surface tension, which favors the minimization of the area, and the nematic elasticity, which instead promotes the alignment of the molecules along a common direction. We find two classes of equilibrium solutions in which the molecules are uniformly aligned along the meridians or parallels. Depending on two dimensionless parameters, one related to the geometry of the film and the other to the constitutive moduli, the Gaussian curvature of the equilibrium shape may be everywhere negative, vanishing, or positive. The stability of these equilibrium configurations is investigated.

Influence of the extrinsic curvature on two-dimensional nematic films

NASA Astrophysics Data System (ADS)

Napoli, Gaetano; Vergori, Luigi

2018-05-01

Nematic films are thin fluid structures, ideally two dimensional, endowed with an in-plane degenerate nematic order. In this paper we examine a generalization of the classical Plateau problem to an axisymmetric nematic film bounded by two coaxial parallel rings. At equilibrium, the shape of the nematic film results from the competition between surface tension, which favors the minimization of the area, and the nematic elasticity, which instead promotes the alignment of the molecules along a common direction. We find two classes of equilibrium solutions in which the molecules are uniformly aligned along the meridians or parallels. Depending on two dimensionless parameters, one related to the geometry of the film and the other to the constitutive moduli, the Gaussian curvature of the equilibrium shape may be everywhere negative, vanishing, or positive. The stability of these equilibrium configurations is investigated.

Anisotropic Defect-Mediated Melting of Two-Dimensional Colloidal Crystals

NASA Astrophysics Data System (ADS)

Eisenmann, C.; Gasser, U.; Keim, P.; Maret, G.

2004-09-01

The melting transition of anisotropic two-dimensional (2D) crystals is studied in a model system of superparamagnetic colloids. The anisotropy of the induced dipole-dipole interaction is varied by tilting the external magnetic field off the normal to the particle plane. By analyzing the time-dependent Lindemann parameter as well as translational and orientational order we observe a 2D smecticlike phase. The Kosterlitz-Thouless-Halperin-Nelson-Young scenario of isotropic melting is modified: dislocation pairs and dislocations appear with different probabilities depending on their orientation with respect to the in-plane field.

Distance measurements across randomly distributed nitroxide probes from the temperature dependence of the electron spin phase memory time at 240 GHz

NASA Astrophysics Data System (ADS)

Edwards, Devin T.; Takahashi, Susumu; Sherwin, Mark S.; Han, Songi

2012-10-01

At 8.5 T, the polarization of an ensemble of electron spins is essentially 100% at 2 K, and decreases to 30% at 20 K. The strong temperature dependence of the electron spin polarization between 2 and 20 K leads to the phenomenon of spin bath quenching: temporal fluctuations of the dipolar magnetic fields associated with the energy-conserving spin "flip-flop" process are quenched as the temperature of the spin bath is lowered to the point of nearly complete spin polarization. This work uses pulsed electron paramagnetic resonance (EPR) at 240 GHz to investigate the effects of spin bath quenching on the phase memory times (TM) of randomly-distributed ensembles of nitroxide molecules below 20 K at 8.5 T. For a given electron spin concentration, a characteristic, dipolar flip-flop rate (W) is extracted by fitting the temperature dependence of TM to a simple model of decoherence driven by the spin flip-flop process. In frozen solutions of 4-Amino-TEMPO, a stable nitroxide radical in a deuterated water-glass, a calibration is used to quantify average spin-spin distances as large as r¯=6.6 nm from the dipolar flip-flop rate. For longer distances, nuclear spin fluctuations, which are not frozen out, begin to dominate over the electron spin flip-flop processes, placing an effective ceiling on this method for nitroxide molecules. For a bulk solution with a three-dimensional distribution of nitroxide molecules at concentration n, we find W∝n∝1/r, which is consistent with magnetic dipolar spin interactions. Alternatively, we observe W∝n for nitroxides tethered to a quasi two-dimensional surface of large (Ø ˜ 200 nm), unilamellar, lipid vesicles, demonstrating that the quantification of spin bath quenching can also be used to discern the geometry of molecular assembly or organization.

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

Tipireddy, R.; Stinis, P.; Tartakovsky, A. M.

In this paper, we present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support ourmore » construction with numerical experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Lastly, our results show that highly accurate global solutions can be obtained with significantly reduced computational costs.« less

Efficient self-consistent viscous-inviscid solutions for unsteady transonic flow

NASA Technical Reports Server (NTRS)

Howlett, J. T.

1985-01-01

An improved method is presented for coupling a boundary layer code with an unsteady inviscid transonic computer code in a quasi-steady fashion. At each fixed time step, the boundary layer and inviscid equations are successively solved until the process converges. An explicit coupling of the equations is described which greatly accelerates the convergence process. Computer times for converged viscous-inviscid solutions are about 1.8 times the comparable inviscid values. Comparison of the results obtained with experimental data on three airfoils are presented. These comparisons demonstrate that the explicitly coupled viscous-inviscid solutions can provide efficient predictions of pressure distributions and lift for unsteady two-dimensional transonic flows.

Efficient self-consistent viscous-inviscid solutions for unsteady transonic flow

NASA Technical Reports Server (NTRS)

Howlett, J. T.

1985-01-01

An improved method is presented for coupling a boundary layer code with an unsteady inviscid transonic computer code in a quasi-steady fashion. At each fixed time step, the boundary layer and inviscid equations are successively solved until the process converges. An explicit coupling of the equations is described which greatly accelerates the convergence process. Computer times for converged viscous-inviscid solutions are about 1.8 times the comparable inviscid values. Comparison of the results obtained with experimental data on three airfoils are presented. These comparisons demonstrate that the explicitly coupled viscous-inviscid solutions can provide efficient predictions of pressure distributions and lift for unsteady two-dimensional transonic flow.

3DFEMWATER: A three-dimensional finite element model of water flow through saturated-unsaturated media

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

Yeh, G.T.

1987-08-01

The 3DFEMWATER model is designed to treat heterogeneous and anisotropic media consisting of as many geologic formations as desired, consider both distributed and point sources/sinks that are spatially and temporally dependent, accept the prescribed initial conditions or obtain them by simulating a steady state version of the system under consideration, deal with a transient head distributed over the Dirichlet boundary, handle time-dependent fluxes due to pressure gradient varying along the Neumann boundary, treat time-dependent total fluxes distributed over the Cauchy boundary, automatically determine variable boundary conditions of evaporation, infiltration, or seepage on the soil-air interface, include the off-diagonal hydraulic conductivitymore » components in the modified Richards equation for dealing with cases when the coordinate system does not coincide with the principal directions of the hydraulic conductivity tensor, give three options for estimating the nonlinear matrix, include two options (successive subregion block iterations and successive point interactions) for solving the linearized matrix equations, automatically reset time step size when boundary conditions or source/sinks change abruptly, and check the mass balance computation over the entire region for every time step. The model is verified with analytical solutions or other numerical models for three examples.« less

Upscaling heterogeneity in aquifer reactivity via exposure-time concept: forward model.

PubMed

Seeboonruang, Uma; Ginn, Timothy R

2006-03-20

Reactive properties of aquifer solid phase materials play an important role in solute fate and transport in the natural subsurface on time scales ranging from years in contaminant remediation to millennia in dynamics of aqueous geochemistry. Quantitative tools for dealing with the impact of natural heterogeneity in solid phase reactivity on solute fate and transport are limited. Here we describe the use of a structural variable to keep track of solute flux exposure to reactive surfaces. With this approach, we develop a non-reactive tracer model that is useful for determining the signature of multi-scale reactive solid heterogeneity in terms of solute flux distributions at the field scale, given realizations of three-dimensional reactive site density fields. First, a governing Eulerian equation for the non-reactive tracer model is determined by an upscaling technique in which it is found that the exposure time of solution to reactive surface areas evolves via both a macroscopic velocity and a macroscopic dispersion in the artificial dimension of exposure time. Second, we focus on the Lagrangian approach in the context of a streamtube ensemble and demonstrate the use of the distribution of solute flux over the exposure time dimension in modeling two-dimensional transport of a solute undergoing simplified linear reversible reactions, in hypothetical conditions following prior laboratory experiments. The distribution of solute flux over exposure time in a given case is a signature of the impact of heterogeneous aquifer reactivity coupled with a particular physical heterogeneity, boundary conditions, and hydraulic gradient. Rigorous application of this approach in a simulation sense is limited here to linear kinetically controlled reactions.

A mechanism for hot-spot generation in a reactive two-dimensional sheared viscous layer

NASA Astrophysics Data System (ADS)

Timms, Robert; Purvis, Richard; Curtis, John P.

2018-05-01

A two-dimensional model for the non-uniform melting of a thin sheared viscous layer is developed. An asymptotic solution is presented for both a non-reactive and a reactive material. It is shown that the melt front is linearly stable to small perturbations in the non-reactive case, but becomes linearly unstable upon introduction of an Arrhenius source term to model the chemical reaction. Results demonstrate that non-uniform melting acts as a mechanism to generate hot spots that are found to be sufficient to reduce the time to ignition when compared with the corresponding one-dimensional model of melting.

Computation of the radiation amplitude of oscillons

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

Fodor, Gyula; Forgacs, Peter; LMPT, CNRS-UMR 6083, Universite de Tours, Parc de Grandmont, 37200 Tours

2009-03-15

The radiation loss of small-amplitude oscillons (very long-living, spatially localized, time-dependent solutions) in one-dimensional scalar field theories is computed in the small-amplitude expansion analytically using matched asymptotic series expansions and Borel summation. The amplitude of the radiation is beyond all orders in perturbation theory and the method used has been developed by Segur and Kruskal in Phys. Rev. Lett. 58, 747 (1987). Our results are in good agreement with those of long-time numerical simulations of oscillons.

Humidity-insensitive water evaporation from molecular complex fluids.

PubMed

Salmon, Jean-Baptiste; Doumenc, Frédéric; Guerrier, Béatrice

2017-09-01

We investigated theoretically water evaporation from concentrated supramolecular mixtures, such as solutions of polymers or amphiphilic molecules, using numerical resolutions of a one-dimensional model based on mass transport equations. Solvent evaporation leads to the formation of a concentrated solute layer at the drying interface, which slows down evaporation in a long-time-scale regime. In this regime, often referred to as the falling rate period, evaporation is dominated by diffusive mass transport within the solution, as already known. However, we demonstrate that, in this regime, the rate of evaporation does not also depend on the ambient humidity for many molecular complex fluids. Using analytical solutions in some limiting cases, we first demonstrate that a sharp decrease of the water chemical activity at high solute concentration leads to evaporation rates which depend weakly on the humidity, as the solute concentration at the drying interface slightly depends on the humidity. However, we also show that a strong decrease of the mutual diffusion coefficient of the solution enhances considerably this effect, leading to nearly independent evaporation rates over a wide range of humidity. The decrease of the mutual diffusion coefficient indeed induces strong concentration gradients at the drying interface, which shield the concentration profiles from humidity variations, except in a very thin region close to the drying interface.

Direct numerical simulations of three-dimensional electrokinetic flows

NASA Astrophysics Data System (ADS)

Chiam, Keng-Hwee

2006-11-01

We discuss direct numerical simulations of three-dimensional electrokinetic flows in microfluidic devices. In particular, we focus on the study of the electrokinetic instability that develops when two solutions with different electrical conductivities are coupled to an external electric field. We characterize this ``mixing'' instability as a function of the parameters of the model, namely the Reynolds number of the flow, the electric Peclet number of the electrolyte solution, and the ratio of the electroosmotic to the electroviscous time scales. Finally, we describe how this model breaks down when the length scale of the device approaches the nanoscale, where the width of the electric Debye layer is comparable to the width of the channel, and discuss solutions to overcome this.

One shot methods for optimal control of distributed parameter systems 1: Finite dimensional control

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1991-01-01

The efficient numerical treatment of optimal control problems governed by elliptic partial differential equations (PDEs) and systems of elliptic PDEs, where the control is finite dimensional is discussed. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problems.

Thermo-viscoelastic analysis of composite materials, volume 1

NASA Technical Reports Server (NTRS)

Lin, K. Y.; Hwang, I. H.

1988-01-01

Advanced composite materials, especially graphite/epoxy, are being applied to aircraft structures in order to improve performance and save weight. An important consideration in composite design is the residual strength of a structure containing holes, delaminations, or interlaminar damage when subjected to compressive loads. Recent studies have revealed the importance of viscoelastic effects in polymer-based composites. The viscoelastic effect is particularly significant at elevated temperature/moisture conditions since the matrix material is strongly affected by the environment. The solution of viscoelastic problems in composites was limited to special cases which can be solved by classical lamination theory. A finite element procedure is presented for calculating time-dependent stresses and strains in composite structures with general configurations and complicated boundary conditions. Using this procedure the in-plane and interlaminar stress distributions and histories in notched and unnotched composites were obtained for mechanical and thermal loads. Both two-dimensional and three-dimensional viscoelastic problems are analyzed. The effects of layup orientation and load spectrum on creep response and stress relaxation were also studied.

Multiple periodic-soliton solutions of the (3+1)-dimensional generalised shallow water equation

NASA Astrophysics Data System (ADS)

Li, Ye-Zhou; Liu, Jian-Guo

2018-06-01

Based on the extended variable-coefficient homogeneous balance method and two new ansätz functions, we construct auto-Bäcklund transformation and multiple periodic-soliton solutions of (3 {+} 1)-dimensional generalised shallow water equations. Completely new periodic-soliton solutions including periodic cross-kink wave, periodic two-solitary wave and breather type of two-solitary wave are obtained. In addition, cross-kink three-soliton and cross-kink four-soliton solutions are derived. Furthermore, propagation characteristics and interactions of the obtained solutions are discussed and illustrated in figures.

Active ideal sedimentation: exact two-dimensional steady states.

PubMed

Hermann, Sophie; Schmidt, Matthias

2018-02-28

We consider an ideal gas of active Brownian particles that undergo self-propelled motion and both translational and rotational diffusion under the influence of gravity. We solve analytically the corresponding Smoluchowski equation in two space dimensions for steady states. The resulting one-body density is given as a series, where each term is a product of an orientation-dependent Mathieu function and a height-dependent exponential. A lower hard wall is implemented as a no-flux boundary condition. Numerical evaluation of the suitably truncated analytical solution shows the formation of two different spatial regimes upon increasing Peclet number. These regimes differ in their mean particle orientation and in their variation of the orientation-averaged density with height.

Time-discretized steady compressible Navier-Stokes equations with inflow and outflow boundaries

NASA Astrophysics Data System (ADS)

Yoon, Gangjoon; Yang, Sung-Dae; Song, Minsu; Gunzburger, Max

2013-12-01

The time-discretized steady compressible Navier-Stokes equations in n-dimensional bounded domains with the velocity specified only at the inflow boundary are considered. The existence and uniqueness of L p solutions are proved for p > n. For time-discretized steady flows, results of Kweon and Kellogg and of Kweon and Song are extended in a manner that allows for more general domains and for density-dependent viscosity coefficients. Moreover, we only require p > n which is a critical barrier in the previous works.

Unusual concentration-dependent microscopic dynamics of dendrimers in aqueous solution

NASA Astrophysics Data System (ADS)

Wong, Kaikin; Wu, Chin Ming; Lam, Hak Fai; Chathoth, Suresh M.

2016-05-01

Dendrimers are novel three-dimensional, hyperbranched globular nanopolymeric macromolecules. The nanoscopic size, narrow polydispersity index, excellent control over molecular structure, availability of multiple functional groups at the periphery, and cavities in the interior made them very attractive candidate for drug delivery. In this communication, we have studied the microscopic dynamics of tetra-acid and pentaerythritol glycidyl ether dendrimers dissolved in aqueous solution with different concentrations. The effects of concentration and temperature to their long-range diffusion process are investigated by dynamic light scattering. Experimental results show a huge variation in the translational diffusion coefficient for the two dendrimers samples. Besides, the dependence of diffusion coefficients on concentration is unusually different in these dendrimer samples. Although the diffusion process follows Arrhenius relation with the temperature in both systems, the activation energy for the diffusion process has a distinct concentration dependence.

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

NASA Astrophysics Data System (ADS)

Toth, G.; Keppens, R.; Botchev, M. A.

1998-04-01

We describe and evaluate various implicit and semi-implicit time integration schemes applied to the numerical simulation of hydrodynamical and magnetohydrodynamical problems. The schemes were implemented recently in the software package Versatile Advection Code, which uses modern shock capturing methods to solve systems of conservation laws with optional source terms. The main advantage of implicit solution strategies over explicit time integration is that the restrictive constraint on the allowed time step can be (partially) eliminated, thus the computational cost is reduced. The test problems cover one and two dimensional, steady state and time accurate computations, and the solutions contain discontinuities. For each test, we confront explicit with implicit solution strategies.

Quasi-static finite element modeling of seismic attenuation and dispersion due to wave-induced fluid flow in poroelastic media

NASA Astrophysics Data System (ADS)

Quintal, Beatriz; Steeb, Holger; Frehner, Marcel; Schmalholz, Stefan M.

2011-01-01

The finite element method is used to solve Biot's equations of consolidation in the displacement-pressure (u - p) formulation. We compute one-dimensional (1-D) and two-dimensional (2-D) numerical quasi-static creep tests with poroelastic media exhibiting mesoscopic-scale heterogeneities to calculate the complex and frequency-dependent P wave moduli from the modeled stress-strain relations. The P wave modulus is used to calculate the frequency-dependent attenuation (i.e., inverse of quality factor) and phase velocity of the medium. Attenuation and velocity dispersion are due to fluid flow induced by pressure differences between regions of different compressibilities, e.g., regions (or patches) saturated with different fluids (i.e., so-called patchy saturation). Comparison of our numerical results with analytical solutions demonstrates the accuracy and stability of the algorithm for a wide range of frequencies (six orders of magnitude). The algorithm employs variable time stepping and an unstructured mesh which make it efficient and accurate for 2-D simulations in media with heterogeneities of arbitrary geometries (e.g., curved shapes). We further numerically calculate the quality factor and phase velocity for 1-D layered patchy saturated porous media exhibiting random distributions of patch sizes. We show that the numerical results for the random distributions can be approximated using a volume average of White's analytical solution and the proposed averaging method is, therefore, suitable for a fast and transparent prediction of both quality factor and phase velocity. Application of our results to frequency-dependent reflection coefficients of hydrocarbon reservoirs indicates that attenuation due to wave-induced flow can increase the reflection coefficient at low frequencies, as is observed at some reservoirs.

Three-dimensional time-dependent computer modeling of the electrothermal atomizers for analytical spectrometry

NASA Astrophysics Data System (ADS)

Tsivilskiy, I. V.; Nagulin, K. Yu.; Gilmutdinov, A. Kh.

2016-02-01

A full three-dimensional nonstationary numerical model of graphite electrothermal atomizers of various types is developed. The model is based on solution of a heat equation within solid walls of the atomizer with a radiative heat transfer and numerical solution of a full set of Navier-Stokes equations with an energy equation for a gas. Governing equations for the behavior of a discrete phase, i.e., atomic particles suspended in a gas (including gas-phase processes of evaporation and condensation), are derived from the formal equations molecular kinetics by numerical solution of the Hertz-Langmuir equation. The following atomizers test the model: a Varian standard heated electrothermal vaporizer (ETV), a Perkin Elmer standard THGA transversely heated graphite tube with integrated platform (THGA), and the original double-stage tube-helix atomizer (DSTHA). The experimental verification of computer calculations is carried out by a method of shadow spectral visualization of the spatial distributions of atomic and molecular vapors in an analytical space of an atomizer.

Two dimensional kinetic analysis of electrostatic harmonic plasma waves

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

Fonseca-Pongutá, E. C.; Ziebell, L. F.; Gaelzer, R.

2016-06-15

Electrostatic harmonic Langmuir waves are virtual modes excited in weakly turbulent plasmas, first observed in early laboratory beam-plasma experiments as well as in rocket-borne active experiments in space. However, their unequivocal presence was confirmed through computer simulated experiments and subsequently theoretically explained. The peculiarity of harmonic Langmuir waves is that while their existence requires nonlinear response, their excitation mechanism and subsequent early time evolution are governed by essentially linear process. One of the unresolved theoretical issues regards the role of nonlinear wave-particle interaction process over longer evolution time period. Another outstanding issue is that existing theories for these modes aremore » limited to one-dimensional space. The present paper carries out two dimensional theoretical analysis of fundamental and (first) harmonic Langmuir waves for the first time. The result shows that harmonic Langmuir wave is essentially governed by (quasi)linear process and that nonlinear wave-particle interaction plays no significant role in the time evolution of the wave spectrum. The numerical solutions of the two-dimensional wave spectra for fundamental and harmonic Langmuir waves are also found to be consistent with those obtained by direct particle-in-cell simulation method reported in the literature.« less

Langevin synchronization in a time-dependent, harmonic basin: An exact solution in 1D

NASA Astrophysics Data System (ADS)

Cadilhe, A.; Voter, Arthur F.

2018-02-01

The trajectories of two particles undergoing Langevin dynamics while sharing a common noise sequence can merge into a single (master) trajectory. Here, we present an exact solution for a particle undergoing Langevin dynamics in a harmonic, time-dependent potential, thus extending the idea of synchronization to nonequilibrium systems. We calculate the synchronization level, i.e., the mismatch between two trajectories sharing a common noise sequence, in the underdamped, critically damped, and overdamped regimes. Finally, we provide asymptotic expansions in various limiting cases and compare to the time independent case.

Advances in three-dimensional field analysis and evaluation of performance parameters of electrical machines

NASA Astrophysics Data System (ADS)

Sivasubramaniam, Kiruba

This thesis makes advances in three dimensional finite element analysis of electrical machines and the quantification of their parameters and performance. The principal objectives of the thesis are: (1)the development of a stable and accurate method of nonlinear three-dimensional field computation and application to electrical machinery and devices; and (2)improvement in the accuracy of determination of performance parameters, particularly forces and torque computed from finite elements. Contributions are made in two general areas: a more efficient formulation for three dimensional finite element analysis which saves time and improves accuracy, and new post-processing techniques to calculate flux density values from a given finite element solution. A novel three-dimensional magnetostatic solution based on a modified scalar potential method is implemented. This method has significant advantages over the traditional total scalar, reduced scalar or vector potential methods. The new method is applied to a 3D geometry of an iron core inductor and a permanent magnet motor. The results obtained are compared with those obtained from traditional methods, in terms of accuracy and speed of computation. A technique which has been observed to improve force computation in two dimensional analysis using a local solution of Laplace's equation in the airgap of machines is investigated and a similar method is implemented in the three dimensional analysis of electromagnetic devices. A new integral formulation to improve force calculation from a smoother flux-density profile is also explored and implemented. Comparisons are made and conclusions drawn as to how much improvement is obtained and at what cost. This thesis also demonstrates the use of finite element analysis to analyze torque ripples due to rotor eccentricity in permanent magnet BLDC motors. A new method for analyzing torque harmonics based on data obtained from a time stepping finite element analysis of the machine is explored and implemented.

A highly sensitive and temporal visualization system for gaseous ethanol with chemiluminescence enhancer.

PubMed

Arakawa, Takahiro; Ando, Eri; Wang, Xin; Kumiko, Miyajima; Kudo, Hiroyuki; Saito, Hirokazu; Mitani, Tomoyo; Takahashi, Mitsuo; Mitsubayashi, Kohji

2012-01-01

A two-dimensional gaseous ethanol visualization system has been developed and demonstrated using a horseradish peroxidase-luminol-hydrogen peroxide system with high-purity luminol solution and a chemiluminescence (CL) enhancer. This system measures ethanol concentrations as intensities of CL via the luminol reaction. CL was emitted when the gaseous ethanol was injected onto an enzyme-immobilized membrane, which was employed as a screen for two-dimensional gas visualization. The average intensity of CL on the substrate was linearly related to the concentration of standard ethanol gas. These results were compared with the CL intensity of the CCD camera recording image in the visualization system. This system is available for gas components not only for spatial but also for temporal analysis in real time. A high-purity sodium salt HG solution (L-HG) instead of standard luminol solution and an enhancer, eosin Y (EY) solution, were adapted for improvement of CL intensity of the system. The visualization of gaseous ethanol was achieved at a detection limit of 3 ppm at optimized concentrations of L-HG solution and EY. Copyright © 2011 John Wiley & Sons, Ltd.

Emergence and space-time structure of lump solution to the (2+1)-dimensional generalized KP equation

NASA Astrophysics Data System (ADS)

Tan, Wei; Dai, Houping; Dai, Zhengde; Zhong, Wenyong

2017-11-01

A periodic breather-wave solution is obtained using homoclinic test approach and Hirota's bilinear method with a small perturbation parameter u0 for the (2+1)-dimensional generalized Kadomtsev-Petviashvili equation. Based on the periodic breather-wave, a lump solution is emerged by limit behaviour. Finally, three different forms of the space-time structure of the lump solution are investigated and discussed using the extreme value theory.

Incoherent population mixing contributions to phase-modulation two-dimensional coherent excitation spectra

NASA Astrophysics Data System (ADS)

Grégoire, Pascal; Srimath Kandada, Ajay Ram; Vella, Eleonora; Tao, Chen; Leonelli, Richard; Silva, Carlos

2017-09-01

We present theoretical and experimental results showing the effects of incoherent population mixing on two-dimensional (2D) coherent excitation spectra that are measured via a time-integrated population and phase-sensitive detection. The technique uses four collinear ultrashort pulses and phase modulation to acquire two-dimensional spectra by isolating specific nonlinear contributions to the photoluminescence or photocurrent excitation signal. We demonstrate that an incoherent contribution to the measured line shape, arising from nonlinear population dynamics over the entire photoexcitation lifetime, generates a similar line shape to the expected 2D coherent spectra in condensed-phase systems. In those systems, photoexcitations are mobile such that inter-particle interactions are important on any time scale, including those long compared with the 2D coherent experiment. Measurements on a semicrystalline polymeric semiconductor film at low temperatures show that, in some conditions in which multi-exciton interactions are suppressed, the technique predominantly detects coherent signals and can be used, in our example, to extract homogeneous line widths. The same method used on a lead-halide perovskite photovoltaic cell shows that incoherent population mixing of mobile photocarriers can dominate the measured signal since carrier-carrier bimolecular scattering is active even at low excitation densities, which hides the coherent contribution to the spectral line shape. In this example, the intensity dependence of the signal matches the theoretical predictions over more than two orders of magnitude, confirming the incoherent nature of the signal. While these effects are typically not significant in dilute solution environments, we demonstrate the necessity to characterize, in condensed-phase materials systems, the extent of nonlinear population dynamics of photoexcitations (excitons, charge carriers, etc.) in the execution of this powerful population-detected coherent spectroscopy technique.

The passage of an infinite swept airfoil through an oblique gust. [approximate solution for aerodynamic response

NASA Technical Reports Server (NTRS)

Adamczyk, J. L.

1974-01-01

An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C072)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C048)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

Attosecond pulse carrier-envelope phase effects on ionized electron momentum and energy distributions

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

Peng, L.-Y.; Starace, Anthony F.

2007-10-15

We analyze carrier-envelope phase (CEP) effects on electron wave-packet momentum and energy spectra produced by one or two few-cycle attosecond xuv pulses. The few-cycle attosecond pulses are assumed to have arbitrary phases. We predict CEP effects on ionized electron wave-packet momentum distributions produced by attosecond pulses having durations comparable to those obtained by Sansone et al. [Science 314, 443 (2006)]. The onset of significant CEP effects is predicted to occur for attosecond pulse field strengths close to those possible with current experimental capabilities. Our results are based on single-active-electron solutions of the three-dimensional, time-dependent Schroedinger equation including atomic potentials appropriatemore » for the H and He atoms.« less

Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

NASA Astrophysics Data System (ADS)

Chen, Shanzhen; Jiang, Xiaoyun

2012-08-01

In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.

Frequency mode excitations in two-dimensional Hindmarsh-Rose neural networks

NASA Astrophysics Data System (ADS)

Tabi, Conrad Bertrand; Etémé, Armand Sylvin; Mohamadou, Alidou

2017-05-01

In this work, we explicitly show the existence of two frequency regimes in a two-dimensional Hindmarsh-Rose neural network. Each of the regimes, through the semi-discrete approximation, is shown to be described by a two-dimensional complex Ginzburg-Landau equation. The modulational instability phenomenon for the two regimes is studied, with consideration given to the coupling intensities among neighboring neurons. Analytical solutions are also investigated, along with their propagation in the two frequency regimes. These waves, depending on the coupling strength, are identified as breathers, impulses and trains of soliton-like structures. Although the waves in two regimes appear in some common regions of parameters, some phase differences are noticed and the global dynamics of the system is highly influenced by the values of the coupling terms. For some values of such parameters, the high-frequency regime displays modulated trains of waves, while the low-frequency dynamics keeps the original asymmetric character of action potentials. We argue that in a wide range of pathological situations, strong interactions among neurons can be responsible for some pathological states, including schizophrenia and epilepsy.

Multiscale statistics of trajectories with applications to fluid particles in turbulence and football players

NASA Astrophysics Data System (ADS)

Schneider, Kai; Kadoch, Benjamin; Bos, Wouter

2017-11-01

The angle between two subsequent particle displacement increments is evaluated as a function of the time lag. The directional change of particles can thus be quantified at different scales and multiscale statistics can be performed. Flow dependent and geometry dependent features can be distinguished. The mean angle satisfies scaling behaviors for short time lags based on the smoothness of the trajectories. For intermediate time lags a power law behavior can be observed for some turbulent flows, which can be related to Kolmogorov scaling. The long time behavior depends on the confinement geometry of the flow. We show that the shape of the probability distribution function of the directional change can be well described by a Fischer distribution. Results for two-dimensional (direct and inverse cascade) and three-dimensional turbulence with and without confinement, illustrate the properties of the proposed multiscale statistics. The presented Monte-Carlo simulations allow disentangling geometry dependent and flow independent features. Finally, we also analyze trajectories of football players, which are, in general, not randomly spaced on a field.

Phase transition of traveling waves in bacterial colony pattern

NASA Astrophysics Data System (ADS)

Wakano, Joe Yuichiro; Komoto, Atsushi; Yamaguchi, Yukio

2004-05-01

Depending on the growth condition, bacterial colonies can exhibit different morphologies. Many previous studies have used reaction diffusion equations to reproduce spatial patterns. They have revealed that nonlinear reaction term can produce diverse patterns as well as nonlinear diffusion coefficient. Typical reaction term consists of nutrient consumption, bacterial reproduction, and sporulation. Among them, the functional form of sporulation rate has not been biologically investigated. Here we report experimentally measured sporulation rate. Then, based on the result, a reaction diffusion model is proposed. One-dimensional simulation showed the existence of traveling wave solution. We study the wave form as a function of the initial nutrient concentration and find two distinct types of solution. Moreover, transition between them is very sharp, which is analogous to phase transition. The velocity of traveling wave also shows sharp transition in nonlinear diffusion model, which is consistent with the previous experimental result. The phenomenon can be explained by separatrix in reaction term dynamics. Results of two-dimensional simulation are also shown and discussed.

Origin of vertical orientation in two-dimensional metal halide perovskites and its effect on photovoltaic performance.

PubMed

Chen, Alexander Z; Shiu, Michelle; Ma, Jennifer H; Alpert, Matthew R; Zhang, Depei; Foley, Benjamin J; Smilgies, Detlef-M; Lee, Seung-Hun; Choi, Joshua J

2018-04-06

Thin films based on two-dimensional metal halide perovskites have achieved exceptional performance and stability in numerous optoelectronic device applications. Simple solution processing of the 2D perovskite provides opportunities for manufacturing devices at drastically lower cost compared to current commercial technologies. A key to high device performance is to align the 2D perovskite layers, during the solution processing, vertical to the electrodes to achieve efficient charge transport. However, it is yet to be understood how the counter-intuitive vertical orientations of 2D perovskite layers on substrates can be obtained. Here we report a formation mechanism of such vertically orientated 2D perovskite in which the nucleation and growth arise from the liquid-air interface. As a consequence, choice of substrates can be liberal from polymers to metal oxides depending on targeted application. We also demonstrate control over the degree of preferential orientation of the 2D perovskite layers and its drastic impact on device performance.

Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem

PubMed Central

Schilde, M.; Doerner, K.F.; Hartl, R.F.

2014-01-01

In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches. PMID:25844013

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Distributed Two-Dimensional Fourier Transforms on DSPs with an Application for Phase Retrieval

NASA Technical Reports Server (NTRS)

Smith, Jeffrey Scott

2006-01-01

Many applications of two-dimensional Fourier Transforms require fixed timing as defined by system specifications. One example is image-based wavefront sensing. The image-based approach has many benefits, yet it is a computational intensive solution for adaptive optic correction, where optical adjustments are made in real-time to correct for external (atmospheric turbulence) and internal (stability) aberrations, which cause image degradation. For phase retrieval, a type of image-based wavefront sensing, numerous two-dimensional Fast Fourier Transforms (FFTs) are used. To meet the required real-time specifications, a distributed system is needed, and thus, the 2-D FFT necessitates an all-to-all communication among the computational nodes. The 1-D floating point FFT is very efficient on a digital signal processor (DSP). For this study, several architectures and analysis of such are presented which address the all-to-all communication with DSPs. Emphasis of this research is on a 64-node cluster of Analog Devices TigerSharc TS-101 DSPs.

Dynamic colloidal assembly pathways via low dimensional models

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

Yang, Yuguang; Bevan, Michael A., E-mail: mabevan@jhu.edu; Thyagarajan, Raghuram

2016-05-28

Here we construct a low-dimensional Smoluchowski model for electric field mediated colloidal crystallization using Brownian dynamic simulations, which were previously matched to experiments. Diffusion mapping is used to infer dimensionality and confirm the use of two order parameters, one for degree of condensation and one for global crystallinity. Free energy and diffusivity landscapes are obtained as the coefficients of a low-dimensional Smoluchowski equation to capture the thermodynamics and kinetics of microstructure evolution. The resulting low-dimensional model quantitatively captures the dynamics of different assembly pathways between fluid, polycrystal, and single crystals states, in agreement with the full N-dimensional data as characterizedmore » by first passage time distributions. Numerical solution of the low-dimensional Smoluchowski equation reveals statistical properties of the dynamic evolution of states vs. applied field amplitude and system size. The low-dimensional Smoluchowski equation and associated landscapes calculated here can serve as models for predictive control of electric field mediated assembly of colloidal ensembles into two-dimensional crystalline objects.« less

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

Low-field one-dimensional and direction-dependent relaxation imaging of bovine articular cartilage

NASA Astrophysics Data System (ADS)

Rössler, Erik; Mattea, Carlos; Mollova, Ayret; Stapf, Siegfried

2011-12-01

The structure of articular cartilage is separated into three layers of differently oriented collagen fibers, which is accompanied by a gradient of increasing glycosaminoglycan (GAG) and decreasing water concentration from the top layer towards the bone interface. The combined effect of these structural variations results in a change of the longitudinal and transverse relaxation times as a function of the distance from the cartilage surface. In this paper, this dependence is investigated at a magnetic field strength of 0.27 T with a one-dimensional depth resolution of 50 μm on bovine hip and stifle joint articular cartilage. By employing this method, advantage is taken of the increasing contrast of the longitudinal relaxation rate found at lower magnetic field strengths. Furthermore, evidence for an orientational dependence of relaxation times with respect to an axis normal to the surface plane is given, an observation that has recently been reported using high-field MRI and that was explained by preferential orientations of collagen bundles in each of the three cartilage zones. In order to quantify the extent of a further contrast mechanism and to estimate spatially dependent glycosaminoglycan concentrations, the data are supplemented by proton relaxation times that were acquired in bovine articular cartilage that was soaked in a 0.8 mM aqueous Gd ++ solution.

Propagation of Boundary-Induced Discontinuity in Stationary Radiative Transfer

NASA Astrophysics Data System (ADS)

Kawagoe, Daisuke; Chen, I.-Kun

2018-01-01

We consider the boundary value problem of the stationary transport equation in the slab domain of general dimensions. In this paper, we discuss the relation between discontinuity of the incoming boundary data and that of the solution to the stationary transport equation. We introduce two conditions posed on the boundary data so that discontinuity of the boundary data propagates along positive characteristic lines as that of the solution to the stationary transport equation. Our analysis does not depend on the celebrated velocity averaging lemma, which is different from previous works. We also introduce an example in two dimensional case which shows that piecewise continuity of the boundary data is not a sufficient condition for the main result.

BPS equations and non-trivial compactifications

NASA Astrophysics Data System (ADS)

Tyukov, Alexander; Warner, Nicholas P.

2018-05-01

We consider the problem of finding exact, eleven-dimensional, BPS supergravity solutions in which the compactification involves a non-trivial Calabi-Yau manifold, Y , as opposed to simply a T 6. Since there are no explicitly-known metrics on non-trivial, compact Calabi-Yau manifolds, we use a non-compact "local model" and take the compactification manifold to be Y={M}_{GH}× {T}^2 , where ℳGH is a hyper-Kähler, Gibbons-Hawking ALE space. We focus on backgrounds with three electric charges in five dimensions and find exact families of solutions to the BPS equations that have the same four supersymmetries as the three-charge black hole. Our exact solution to the BPS system requires that the Calabi-Yau manifold be fibered over the space-time using compensators on Y . The role of the compensators is to ensure smoothness of the eleven-dimensional metric when the moduli of Y depend on the space-time. The Maxwell field Ansatz also implicitly involves the compensators through the frames of the fibration. We examine the equations of motion and discuss the brane distributions on generic internal manifolds that do not have enough symmetry to allow smearing.

A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems

NASA Astrophysics Data System (ADS)

Liu, Hailiang; Wang, Zhongming

2017-01-01

We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for solving time-dependent Poisson-Nernst-Planck systems. Both the semi-discrete and fully discrete DG methods are shown to satisfy the corresponding discrete free energy dissipation law for positive numerical solutions. Positivity of numerical solutions is enforced by an accuracy-preserving limiter in reference to positive cell averages. Numerical examples are presented to demonstrate the high resolution of the numerical algorithm and to illustrate the proven properties of mass conservation, free energy dissipation, as well as the preservation of steady states.

Direct computation of turbulence and noise

NASA Technical Reports Server (NTRS)

Berman, C.; Gordon, G.; Karniadakis, G.; Batcho, P.; Jackson, E.; Orszag, S.

1991-01-01

Jet exhaust turbulence noise is computed using a time dependent solution of the three dimensional Navier-Stokes equations to supply the source terms for an acoustic computation based on the Phillips convected wave equation. An extrapolation procedure is then used to determine the far field noise spectrum in terms of the near field sound. This will lay the groundwork for studies of more complex flows typical of noise suppression nozzles.

Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti-de Sitter Space

NASA Astrophysics Data System (ADS)

Crisford, Toby; Santos, Jorge E.

2017-05-01

We consider time-dependent solutions of the Einstein-Maxwell equations using anti-de Sitter (AdS) boundary conditions, and provide the first counterexample to the weak cosmic censorship conjecture in four spacetime dimensions. Our counterexample is entirely formulated in the Poincaré patch of AdS. We claim that our results have important consequences for quantum gravity, most notably to the weak gravity conjecture.

Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti-de Sitter Space.

PubMed

Crisford, Toby; Santos, Jorge E

2017-05-05

We consider time-dependent solutions of the Einstein-Maxwell equations using anti-de Sitter (AdS) boundary conditions, and provide the first counterexample to the weak cosmic censorship conjecture in four spacetime dimensions. Our counterexample is entirely formulated in the Poincaré patch of AdS. We claim that our results have important consequences for quantum gravity, most notably to the weak gravity conjecture.

Computer model of two-dimensional solute transport and dispersion in ground water

USGS Publications Warehouse

Konikow, Leonard F.; Bredehoeft, J.D.

1978-01-01

This report presents a model that simulates solute transport in flowing ground water. The model is both general and flexible in that it can be applied to a wide range of problem types. It is applicable to one- or two-dimensional problems involving steady-state or transient flow. The model computes changes in concentration over time caused by the processes of convective transport, hydrodynamic dispersion, and mixing (or dilution) from fluid sources. The model assumes that the solute is non-reactive and that gradients of fluid density, viscosity, and temperature do not affect the velocity distribution. However, the aquifer may be heterogeneous and (or) anisotropic. The model couples the ground-water flow equation with the solute-transport equation. The digital computer program uses an alternating-direction implicit procedure to solve a finite-difference approximation to the ground-water flow equation, and it uses the method of characteristics to solve the solute-transport equation. The latter uses a particle- tracking procedure to represent convective transport and a two-step explicit procedure to solve a finite-difference equation that describes the effects of hydrodynamic dispersion, fluid sources and sinks, and divergence of velocity. This explicit procedure has several stability criteria, but the consequent time-step limitations are automatically determined by the program. The report includes a listing of the computer program, which is written in FORTRAN IV and contains about 2,000 lines. The model is based on a rectangular, block-centered, finite difference grid. It allows the specification of any number of injection or withdrawal wells and of spatially varying diffuse recharge or discharge, saturated thickness, transmissivity, boundary conditions, and initial heads and concentrations. The program also permits the designation of up to five nodes as observation points, for which a summary table of head and concentration versus time is printed at the end of the calculations. The data input formats for the model require three data cards and from seven to nine data sets to describe the aquifer properties, boundaries, and stresses. The accuracy of the model was evaluated for two idealized problems for which analytical solutions could be obtained. In the case of one-dimensional flow the agreement was nearly exact, but in the case of plane radial flow a small amount of numerical dispersion occurred. An analysis of several test problems indicates that the error in the mass balance will be generally less than 10 percent. The test problems demonstrated that the accuracy and precision of the numerical solution is sensitive to the initial number of particles placed in each cell and to the size of the time increment, as determined by the stability criteria. Mass balance errors are commonly the greatest during the first several time increments, but tend to decrease and stabilize with time.

Reaction time for trimolecular reactions in compartment-based reaction-diffusion models

NASA Astrophysics Data System (ADS)

Li, Fei; Chen, Minghan; Erban, Radek; Cao, Yang

2018-05-01

Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.

A comparison of artificial compressibility and fractional step methods for incompressible flow computations

NASA Technical Reports Server (NTRS)

Chan, Daniel C.; Darian, Armen; Sindir, Munir

1992-01-01

We have applied and compared the efficiency and accuracy of two commonly used numerical methods for the solution of Navier-Stokes equations. The artificial compressibility method augments the continuity equation with a transient pressure term and allows one to solve the modified equations as a coupled system. Due to its implicit nature, one can have the luxury of taking a large temporal integration step at the expense of higher memory requirement and larger operation counts per step. Meanwhile, the fractional step method splits the Navier-Stokes equations into a sequence of differential operators and integrates them in multiple steps. The memory requirement and operation count per time step are low, however, the restriction on the size of time marching step is more severe. To explore the strengths and weaknesses of these two methods, we used them for the computation of a two-dimensional driven cavity flow with Reynolds number of 100 and 1000, respectively. Three grid sizes, 41 x 41, 81 x 81, and 161 x 161 were used. The computations were considered after the L2-norm of the change of the dependent variables in two consecutive time steps has fallen below 10(exp -5).

Self-Similar Compressible Free Vortices

NASA Technical Reports Server (NTRS)

vonEllenrieder, Karl

1998-01-01

Lie group methods are used to find both exact and numerical similarity solutions for compressible perturbations to all incompressible, two-dimensional, axisymmetric vortex reference flow. The reference flow vorticity satisfies an eigenvalue problem for which the solutions are a set of two-dimensional, self-similar, incompressible vortices. These solutions are augmented by deriving a conserved quantity for each eigenvalue, and identifying a Lie group which leaves the reference flow equations invariant. The partial differential equations governing the compressible perturbations to these reference flows are also invariant under the action of the same group. The similarity variables found with this group are used to determine the decay rates of the velocities and thermodynamic variables in the self-similar flows, and to reduce the governing partial differential equations to a set of ordinary differential equations. The ODE's are solved analytically and numerically for a Taylor vortex reference flow, and numerically for an Oseen vortex reference flow. The solutions are used to examine the dependencies of the temperature, density, entropy, dissipation and radial velocity on the Prandtl number. Also, experimental data on compressible free vortex flow are compared to the analytical results, the evolution of vortices from initial states which are not self-similar is discussed, and the energy transfer in a slightly-compressible vortex is considered.

Identification of the heat transfer coefficient in the two-dimensional model of binary alloy solidification

NASA Astrophysics Data System (ADS)

Hetmaniok, Edyta; Hristov, Jordan; Słota, Damian; Zielonka, Adam

2017-05-01

The paper presents the procedure for solving the inverse problem for the binary alloy solidification in a two-dimensional space. This is a continuation of some previous works of the authors investigating a similar problem but in the one-dimensional domain. Goal of the problem consists in identification of the heat transfer coefficient on boundary of the region and in reconstruction of the temperature distribution inside the considered region in case when the temperature measurements in selected points of the alloy are known. Mathematical model of the problem is based on the heat conduction equation with the substitute thermal capacity and with the liquidus and solidus temperatures varying in dependance on the concentration of the alloy component. For describing this concentration the Scheil model is used. Investigated procedure involves also the parallelized Ant Colony Optimization algorithm applied for minimizing a functional expressing the error of approximate solution.

Direct numerical simulation of axisymmetric turbulence

NASA Astrophysics Data System (ADS)

Qu, Bo; Bos, Wouter J. T.; Naso, Aurore

2017-09-01

The dynamics of decaying, strictly axisymmetric, incompressible turbulence is investigated using direct numerical simulations. It is found that the angular momentum is a robust invariant of the system. It is further shown that long-lived coherent structures are generated by the flow. These structures can be associated with stationary solutions of the Euler equations. The structures obey relations in agreement with predictions from selective decay principles, compatible with the decay laws of the system. Two different types of decay scenarios are highlighted. The first case results in a quasi-two-dimensional flow with a dynamical behavior in the poloidal plane similar to freely decaying two-dimensional turbulence. In a second regime, the long-time dynamics is dominated by a single three-dimensional mode.

User's Guide for ECAP2D: an Euler Unsteady Aerodynamic and Aeroelastic Analysis Program for Two Dimensional Oscillating Cascades, Version 1.0

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.

1995-01-01

This guide describes the input data required for using ECAP2D (Euler Cascade Aeroelastic Program-Two Dimensional). ECAP2D can be used for steady or unsteady aerodynamic and aeroelastic analysis of two dimensional cascades. Euler equations are used to obtain aerodynamic forces. The structural dynamic equations are written for a rigid typical section undergoing pitching (torsion) and plunging (bending) motion. The solution methods include harmonic oscillation method, influence coefficient method, pulse response method, and time integration method. For harmonic oscillation method, example inputs and outputs are provided for pitching motion and plunging motion. For the rest of the methods, input and output for pitching motion only are given.

The Time Course of Explicit and Implicit Categorization

PubMed Central

Zakrzewski, Alexandria C.; Herberger, Eric; Boomer, Joseph; Roeder, Jessica; Ashby, F. Gregory; Church, Barbara A.

2015-01-01

Contemporary theory in cognitive neuroscience distinguishes, among the processes and utilities that serve categorization, explicit and implicit systems of category learning that learn, respectively, category rules by active hypothesis testing or adaptive behaviors by association and reinforcement. Little is known about the time course of categorization within these systems. Accordingly, the present experiments contrasted tasks that fostered explicit categorization (because they had a one-dimensional, rule-based solution) or implicit categorization (because they had a two-dimensional, information-integration solution). In Experiment 1, participants learned categories under unspeeded or speeded conditions. In Experiment 2, they applied previously trained category knowledge under unspeeded or speeded conditions. Speeded conditions selectively impaired implicit category learning and implicit mature categorization. These results illuminate the processing dynamics of explicit/implicit categorization. PMID:26025556

Cosmic Ray Hysteresis as Evidence for Time-dependent Diffusive Processes in the Long Term Solar Modulation

NASA Technical Reports Server (NTRS)

Ogallagher, J. J.

1973-01-01

A simple one-dimensional time-dependent diffusion-convection model for the modulation of cosmic rays is presented. This model predicts that the observed intensity at a given time is approximately equal to the intensity given by the time independent diffusion convection solution under interplanetary conditions which existed a time iota in the past, (U(t sub o) = U sub s(t sub o - tau)) where iota is the average time spent by a particle inside the modulating cavity. Delay times in excess of several hundred days are possible with reasonable modulation parameters. Interpretation of phase lags observed during the 1969 to 1970 solar maximum in terms of this model suggests that the modulating region is probably not less than 10 a.u. and maybe as much as 35 a.u. in extent.

Comparison Between Laser Scanning and Automated 3d Modelling Techniques to Reconstruct Complex and Extensive Cultural Heritage Areas

NASA Astrophysics Data System (ADS)

Fassi, F.; Fregonese, L.; Ackermann, S.; De Troia, V.

2013-02-01

In Cultural Heritage field, the necessity to survey objects in a fast manner, with the ability to repeat the measurements several times for deformation or degradation monitoring purposes, is increasing. In this paper, two significant cases, an architectonical one and an archaeological one, are presented. Due to different reasons and emergency situations, the finding of the optimal solution to enable quick and well-timed survey for a complete digital reconstruction of the object is required. In both cases, two survey methods have been tested and used: a laser scanning approach that allows to obtain high-resolution and complete scans within a short time and a photogrammetric one that allows the three-dimensional reconstruction of the object from images. In the last months, several methodologies, including free or low cost techniques, have arisen. These kinds of software allow the fully automatically three-dimensional reconstruction of objects from images, giving back a dense point cloud and, in some case, a surfaced mesh model. In this paper some comparisons between the two methodologies above mentioned are presented, using the example of some real cases of study. The surveys have been performed by employing both photogrammetry and laser scanner techniques. The methodological operational choices, depending on the required goal, the difficulties encountered during the survey with these methods, the execution time (that is the key parameter), and finally the obtained results, are fully described and examinated. On the final 3D model, an analytical comparison has been made, to analyse the differences, the tolerances, the possibility of accuracy improvement and the future developments.

Flow through three-dimensional arrangements of cylinders with alternating streamwise planar tilt

NASA Astrophysics Data System (ADS)

Sahraoui, M.; Marshall, H.; Kaviany, M.

1993-09-01

In this report, fluid flow through a three-dimensional model for the fibrous filters is examined. In this model, the three-dimensional Stokes equation with the appropriate periodic boundary conditions is solved using the finite volume method. In addition to the numerical solution, we attempt to model this flow analytically by using the two-dimensional extended analytic solution in each of the unit cells of the three-dimensional structure. Particle trajectories computed using the superimposed analytic solution of the flow field are closed to those computed using the numerical solution of the flow field. The numerical results show that the pressure drop is not affected significantly by the relative angle of rotation of the cylinders for the high porosity used in this study (epsilon = 0.8 and epsilon = 0.95). The numerical solution and the superimposed analytic solution are also compared in terms of the particle capture efficiency. The results show that the efficiency predictions using the two methods are within 10% for St = 0.01 and 5% for St = 100. As the the porosity decreases, the three-dimensional effect becomes more significant and a difference of 35% is obtained for epsilon = 0.8.

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules

1999-01-01

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity

NASA Astrophysics Data System (ADS)

Feijoo, David; Zezyulin, Dmitry A.; Konotop, Vladimir V.

2015-12-01

We analyze a system of three two-dimensional nonlinear Schrödinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time (PT ) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the PT -symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and PT -symmetric cases. Interactions and collisions between the conservative and PT -symmetric solitons are briefly investigated, as well.

A novel potential/viscous flow coupling technique for computing helicopter flow fields

NASA Technical Reports Server (NTRS)

Summa, J. Michael; Strash, Daniel J.; Yoo, Sungyul

1993-01-01

The primary objective of this work was to demonstrate the feasibility of a new potential/viscous flow coupling procedure for reducing computational effort while maintaining solution accuracy. This closed-loop, overlapped velocity-coupling concept has been developed in a new two-dimensional code, ZAP2D (Zonal Aerodynamics Program - 2D), a three-dimensional code for wing analysis, ZAP3D (Zonal Aerodynamics Program - 3D), and a three-dimensional code for isolated helicopter rotors in hover, ZAPR3D (Zonal Aerodynamics Program for Rotors - 3D). Comparisons with large domain ARC3D solutions and with experimental data for a NACA 0012 airfoil have shown that the required domain size can be reduced to a few tenths of a percent chord for the low Mach and low angle of attack cases and to less than 2-5 chords for the high Mach and high angle of attack cases while maintaining solution accuracies to within a few percent. This represents CPU time reductions by a factor of 2-4 compared with ARC2D. The current ZAP3D calculation for a rectangular plan-form wing of aspect ratio 5 with an outer domain radius of about 1.2 chords represents a speed-up in CPU time over the ARC3D large domain calculation by about a factor of 2.5 while maintaining solution accuracies to within a few percent. A ZAPR3D simulation for a two-bladed rotor in hover with a reduced grid domain of about two chord lengths was able to capture the wake effects and compared accurately with the experimental pressure data. Further development is required in order to substantiate the promise of computational improvements due to the ZAPR3D coupling concept.

Dynamics of curved fronts in systems with power-law memory

NASA Astrophysics Data System (ADS)

Abu Hamed, M.; Nepomnyashchy, A. A.

2016-08-01

The dynamics of a curved front in a plane between two stable phases with equal potentials is modeled via two-dimensional fractional in time partial differential equation. A closed equation governing a slow motion of a small-curvature front is derived and applied for two typical examples of the potential function. Approximate axisymmetric and non-axisymmetric solutions are obtained.

Neutron star dynamics under time-dependent external torques

NASA Astrophysics Data System (ADS)

Gügercinoǧlu, Erbil; Alpar, M. Ali

2017-11-01

The two-component model describes neutron star dynamics incorporating the response of the superfluid interior. Conventional solutions and applications involve constant external torques, as appropriate for radio pulsars on dynamical time-scales. We present the general solution of two-component dynamics under arbitrary time-dependent external torques, with internal torques that are linear in the rotation rates, or with the extremely non-linear internal torques due to vortex creep. The two-component model incorporating the response of linear or non-linear internal torques can now be applied not only to radio pulsars but also to magnetars and to neutron stars in binary systems, with strong observed variability and noise in the spin-down or spin-up rates. Our results allow the extraction of the time-dependent external torques from the observed spin-down (or spin-up) time series, \\dot{Ω }(t). Applications are discussed.

Several reverse-time integrable nonlocal nonlinear equations: Rogue-wave solutions

NASA Astrophysics Data System (ADS)

Yang, Bo; Chen, Yong

2018-05-01

A study of rogue-wave solutions in the reverse-time nonlocal nonlinear Schrödinger (NLS) and nonlocal Davey-Stewartson (DS) equations is presented. By using Darboux transformation (DT) method, several types of rogue-wave solutions are constructed. Dynamics of these rogue-wave solutions are further explored. It is shown that the (1 + 1)-dimensional fundamental rogue-wave solutions in the reverse-time NLS equation can be globally bounded or have finite-time blowing-ups. It is also shown that the (2 + 1)-dimensional line rogue waves in the reverse-time nonlocal DS equations can be bounded for all space and time or develop singularities in critical time. In addition, the multi- and higher-order rogue waves exhibit richer structures, most of which have no counterparts in the corresponding local nonlinear equations.

Size-Dependent Biexciton Quantum Yields and Carrier Dynamics of Quasi-Two-Dimensional Core/Shell Nanoplatelets

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

Ma, Xuedan; Diroll, Benjamin T.; Cho, Wooje

Quasi-two-dimensional nanoplatelets (NPLs) possess fundamentally different excitonic properties from zero-dimensional quantum dots. We study lateral size-dependent photon emission statistics and carrier dynamics of individual NPLs using second-order photon correlation (g( 2)(τ)) spectroscopy and photoluminescence (PL) intensity-dependent lifetime analysis. Room-temperature radiative lifetimes of NPLs can be derived from maximum PL intensity periods in PL time traces. It first decreases with NPL lateral size and then stays constant, deviating from the electric dipole approximation. Analysis of the PL time traces further reveals that the single exciton quantum yield in NPLs decreases with NPL lateral size and increases with protecting shell thickness, indicatingmore » the importance of surface passivation on NPL emission quality. Second-order photon correlation (g( 2)(τ)) studies of single NPLs show that the biexciton quantum yield is strongly dependent on the lateral size and single exciton quantum yield of the NPLs. In large NPLs with unity single exciton quantum yield, the corresponding biexciton quantum yield can reach unity. In conclusion, these findings reveal that by careful growth control and core–shell material engineering, NPLs can be of great potential for light amplification and integrated quantum photonic applications.« less

Size-Dependent Biexciton Quantum Yields and Carrier Dynamics of Quasi-Two-Dimensional Core/Shell Nanoplatelets

DOE PAGES

Ma, Xuedan; Diroll, Benjamin T.; Cho, Wooje; ...

2017-08-08

Quasi-two-dimensional nanoplatelets (NPLs) possess fundamentally different excitonic properties from zero-dimensional quantum dots. We study lateral size-dependent photon emission statistics and carrier dynamics of individual NPLs using second-order photon correlation (g( 2)(τ)) spectroscopy and photoluminescence (PL) intensity-dependent lifetime analysis. Room-temperature radiative lifetimes of NPLs can be derived from maximum PL intensity periods in PL time traces. It first decreases with NPL lateral size and then stays constant, deviating from the electric dipole approximation. Analysis of the PL time traces further reveals that the single exciton quantum yield in NPLs decreases with NPL lateral size and increases with protecting shell thickness, indicatingmore » the importance of surface passivation on NPL emission quality. Second-order photon correlation (g( 2)(τ)) studies of single NPLs show that the biexciton quantum yield is strongly dependent on the lateral size and single exciton quantum yield of the NPLs. In large NPLs with unity single exciton quantum yield, the corresponding biexciton quantum yield can reach unity. In conclusion, these findings reveal that by careful growth control and core–shell material engineering, NPLs can be of great potential for light amplification and integrated quantum photonic applications.« less

A note on blowup of smooth solutions for relativistic Euler equations with infinite initial energy

NASA Astrophysics Data System (ADS)

Dong, Jianwei; Zhu, Junhui

2018-04-01

We study the singularity formation of smooth solutions of the relativistic Euler equations in (3+1)-dimensional spacetime for infinite initial energy. We prove that the smooth solution blows up in finite time provided that the radial component of the initial generalized momentum is sufficiently large without the conditions M(0)>0 and s2<1/3c2 , which were two key constraints stated in Pan and Smoller (Commun Math Phys 262:729-755, 2006).

Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II

NASA Astrophysics Data System (ADS)

Kazeykina, Anna; Muñoz, Claudio

2018-04-01

We continue our study on the Cauchy problem for the two-dimensional Novikov-Veselov (NV) equation, integrable via the inverse scattering transform for the two dimensional Schrödinger operator at a fixed energy parameter. This work is concerned with the more involved case of a positive energy parameter. For the solution of the linearized equation we derive smoothing and Strichartz estimates by combining new estimates for two different frequency regimes, extending our previous results for the negative energy case [18]. The low frequency regime, which our previous result was not able to treat, is studied in detail. At non-low frequencies we also derive improved smoothing estimates with gain of almost one derivative. Then we combine the linear estimates with a Fourier decomposition method and Xs,b spaces to obtain local well-posedness of NV at positive energy in Hs, s > 1/2. Our result implies, in particular, that at least for s > 1/2, NV does not change its behavior from semilinear to quasilinear as energy changes sign, in contrast to the closely related Kadomtsev-Petviashvili equations. As a complement to our LWP results, we also provide some new explicit solutions of NV at zero energy, generalizations of the lumps solutions, which exhibit new and nonstandard long time behavior. In particular, these solutions blow up in infinite time in L2.

One-Dimensional and Two-Dimensional Analytical Solutions for Functionally Graded Beams with Different Moduli in Tension and Compression

PubMed Central

Li, Xue; Dong, Jiao

2018-01-01

The material considered in this study not only has a functionally graded characteristic but also exhibits different tensile and compressive moduli of elasticity. One-dimensional and two-dimensional mechanical models for a functionally graded beam with a bimodular effect were established first. By taking the grade function as an exponential expression, the analytical solutions of a bimodular functionally graded beam under pure bending and lateral-force bending were obtained. The regression from a two-dimensional solution to a one-dimensional solution is verified. The physical quantities in a bimodular functionally graded beam are compared with their counterparts in a classical problem and a functionally graded beam without a bimodular effect. The validity of the plane section assumption under pure bending and lateral-force bending is analyzed. Three typical cases that the tensile modulus is greater than, equal to, or less than the compressive modulus are discussed. The result indicates that due to the introduction of the bimodular functionally graded effect of the materials, the maximum tensile and compressive bending stresses may not take place at the bottom and top of the beam. The real location at which the maximum bending stress takes place is determined via the extreme condition for the analytical solution. PMID:29772835

Low-dimensional manifold of actin polymerization dynamics

NASA Astrophysics Data System (ADS)

Floyd, Carlos; Jarzynski, Christopher; Papoian, Garegin

2017-12-01

Actin filaments are critical components of the eukaryotic cytoskeleton, playing important roles in a number of cellular functions, such as cell migration, organelle transport, and mechanosensation. They are helical polymers with a well-defined polarity, composed of globular subunits that bind nucleotides in one of three hydrolysis states (ATP, ADP-Pi, or ADP). Mean-field models of the dynamics of actin polymerization have succeeded in, among other things, determining the nucleotide profile of an average filament and resolving the mechanisms of accessory proteins. However, these models require numerical solution of a high-dimensional system of nonlinear ordinary differential equations. By truncating a set of recursion equations, the Brooks-Carlsson (BC) model reduces dimensionality to 11, but it still remains nonlinear and does not admit an analytical solution, hence, significantly hindering understanding of its resulting dynamics. In this work, by taking advantage of the fast timescales of the hydrolysis states of the filament tips, we propose two model reduction schemes: the quasi steady-state approximation model is five-dimensional and nonlinear, whereas the constant tip (CT) model is five-dimensional and linear, resulting from the approximation that the tip states are not dynamic variables. We provide an exact solution of the CT model and use it to shed light on the dynamical behaviors of the full BC model, highlighting the relative ordering of the timescales of various collective processes, and explaining some unusual dependence of the steady-state behavior on initial conditions.

Double ionization of neon in elliptically polarized femtosecond laser fields

NASA Astrophysics Data System (ADS)

Kang, HuiPeng; Henrichs, Kevin; Wang, YanLan; Hao, XiaoLei; Eckart, Sebastian; Kunitski, Maksim; Schöffler, Markus; Jahnke, Till; Liu, XiaoJun; Dörner, Reinhard

2018-06-01

We present a joint experimental and theoretical investigation of the correlated electron momentum spectra from strong-field double ionization of neon induced by elliptically polarized laser pulses. A significant asymmetry of the electron momentum distributions along the major polarization axis is reported. This asymmetry depends sensitively on the laser ellipticity. Using a three-dimensional semiclassical model, we attribute this asymmetry pattern to the ellipticity-dependent probability distributions of recollision time. Our work demonstrates that, by simply varying the ellipticity, the correlated electron emission can be two-dimensionally controlled and the recolliding electron trajectories can be steered on a subcycle time scale.