Transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation under the influence of nonlinear gain and higher-order effects

NASA Astrophysics Data System (ADS)

Uzunov, Ivan M.; Georgiev, Zhivko D.; Arabadzhiev, Todor N.

2018-05-01

In this paper we study the transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation (CCQGLE) under the influence of nonlinear gain, its saturation, and higher-order effects: self-steepening, third-order of dispersion, and intrapulse Raman scattering in the anomalous dispersion region. The variation method and the method of moments are applied in order to obtain the dynamic models with finite degrees of freedom for the description of stationary and pulsating solutions. Having applied the first model and its bifurcation analysis we have discovered the existence of families of subcritical Poincaré-Andronov-Hopf bifurcations due to the intrapulse Raman scattering, as well as some small nonlinear gain and the saturation of the nonlinear gain. A phenomenon of nonlinear stability has been studied and it has been shown that long living pulsating solutions with relatively small fluctuations of amplitude and frequencies exist at the bifurcation point. The numerical analysis of the second model has revealed the existence of Poincaré-Andronov-Hopf bifurcations of Raman dissipative soliton under the influence of the self-steepening effect and large nonlinear gain. All our theoretical predictions have been confirmed by the direct numerical solution of the full perturbed CCQGLE. The detailed comparison between the results obtained by both dynamic models and the direct numerical solution of the perturbed CCQGLE has proved the applicability of the proposed models in the investigation of the solutions of the perturbed CCQGLE.

A review on the solution of Grad-Shafranov equation in the cylindrical coordinates based on the Chebyshev collocation technique

NASA Astrophysics Data System (ADS)

Amerian, Z.; Salem, M. K.; Salar Elahi, A.; Ghoranneviss, M.

2017-03-01

Equilibrium reconstruction consists of identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad-Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the Grad-Shafranov equation (an axisymmetric, magnetic field transformed in cylindrical coordinates solved with the Chebyshev collocation method) when the source term (current density function) on the right-hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of differential equations. We describe a circular cross-section of the tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.

The stagnation-point flow towards a shrinking sheet with homogeneous - heterogeneous reactions effects: A stability analysis

NASA Astrophysics Data System (ADS)

Ismail, Nurul Syuhada; Arifin, Norihan Md.; Bachok, Norfifah; Mahiddin, Norhasimah

2017-01-01

A numerical study is performed to evaluate the problem of stagnation - point flow towards a shrinking sheet with homogeneous - heterogeneous reaction effects. By using non-similar transformation, the governing equations be able to reduced to an ordinary differential equation. Then, results of the equations can be obtained numerically by shooting method with maple implementation. Based on the numerical results obtained, the velocity ratio parameter λ< 0, the dual solutions do exist. Then, the stability analysis is carried out to determine which solution is more stable between both of the solutions by bvp4c solver in Matlab.

Modified harmonic balance method for the solution of nonlinear jerk equations

NASA Astrophysics Data System (ADS)

Rahman, M. Saifur; Hasan, A. S. M. Z.

2018-03-01

In this paper, a second approximate solution of nonlinear jerk equations (third order differential equation) can be obtained by using modified harmonic balance method. The method is simpler and easier to carry out the solution of nonlinear differential equations due to less number of nonlinear equations are required to solve than the classical harmonic balance method. The results obtained from this method are compared with those obtained from the other existing analytical methods that are available in the literature and the numerical method. The solution shows a good agreement with the numerical solution as well as the analytical methods of the available literature.

Flow to a well in a water-table aquifer: An improved laplace transform solution

USGS Publications Warehouse

Moench, A.F.

1996-01-01

An alternative Laplace transform solution for the problem, originally solved by Neuman, of constant discharge from a partially penetrating well in a water-table aquifer was obtained. The solution differs from existing solutions in that it is simpler in form and can be numerically inverted without the need for time-consuming numerical integration. The derivation invloves the use of the Laplace transform and a finite Fourier cosine series and avoids the Hankel transform used in prior derivations. The solution allows for water in the overlying unsaturated zone to be released either instantaneously in response to a declining water table as assumed by Neuman, or gradually as approximated by Boulton's convolution integral. Numerical evaluation yields results identical with results obtained by previously published methods with the advantage, under most well-aquifer configurations, of much reduced computation time.

Evidence for a scaling solution in cosmic-string evolution

NASA Technical Reports Server (NTRS)

Bennett, David P.; Bouchet, Francois R.

1988-01-01

Numerical simulations are used to study the most fundamental issue of cosmic-string evolution: the existence of a scaling solution. Strong evidence is found that a scaling solution does indeed exist. This justifies the main assumption on which the cosmic-string theories of galaxy formation is based. The main conclusion coincides with that of Albrecht and Turok (1985) but the results are not consistent with theirs. In fact, the results indicate that the details of string evolution are very different from the standard dogma.

The Forced Soft Spring Equation

ERIC Educational Resources Information Center

Fay, T. H.

2006-01-01

Through numerical investigations, this paper studies examples of the forced Duffing type spring equation with [epsilon] negative. By performing trial-and-error numerical experiments, the existence is demonstrated of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions. Subharmonic boundaries are…

Numerical simulations of an elastica pendulum

NASA Astrophysics Data System (ADS)

Sinclair, R.

Folklore would have it that a massless clamped-free elastica undergoing planar motion with a point end mass possesses periodic solutions corresponding to a single mode of oscillation. We present a battery of numerical simulations leading to the single conclusion that these supposed periodic solutions do not exist, due to a strong nonlinear coupling of two modes, the frequency of one of which is apparently inversely proportional to the magnitude of the force acting on the elastica.

A Quadratic Spring Equation

ERIC Educational Resources Information Center

Fay, Temple H.

2010-01-01

Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

Fundamental Solution For The Self-healing Fracture Pulse

NASA Astrophysics Data System (ADS)

Nielsen, S.; Madariaga, R.

We find the analytical solution for a fundamental fracture mode in the form of a self- similar, self-healing pulse. The existence of such a fracture mode was strongly sug- gested by recent numerical findings but, to our knwledge, no formal proof had been proposed up to date. We present a two dimensional, anti-plane solution for fixed rup- ture and healing velocities, that satisfies both wave equation and stress conditions; we argue that such a solution is plausible even in the absence of rate-weakening in the friction, as an alternative to the classic crack solution. In practice, the impulsive mode rather than the expanding crack mode is selected depending on details of fracture initiation, and is therafter self-maintained. We discuss stress concentration, fracture energy, rupture velocity and compare them to the case of a crack. The analytical study is complemented by various numerical examples and comparisons. On more general grounds, we argue that an infinity of marginally stable fracture modes may exist other than the crack solution or the impulseive fracture described here.

MHD stagnation-point flow over a nonlinearly shrinking sheet with suction effect

NASA Astrophysics Data System (ADS)

Awaludin, Izyan Syazana; Ahmad, Rokiah; Ishak, Anuar

2018-04-01

The stagnation point flow over a shrinking permeable sheet in the existence of magnetic field is numerically investigated in this paper. The system of partial differential equations are transformed to a nonlinear ordinary differential equation using similarity transformation and is solved numerically using the boundary value problem solver, bvp4c, in Matlab software. It is found that dual solutions exist for a certain range of the shrinking strength.

Existence and stability of periodic solution of a Lotka-Volterra predator-prey model with state dependent impulsive effects

NASA Astrophysics Data System (ADS)

Nie, Linfei; Peng, Jigen; Teng, Zhidong; Hu, Lin

2009-02-01

According to biological and chemical control strategy for pest, we investigate the dynamic behavior of a Lotka-Volterra predator-prey state-dependent impulsive system by releasing natural enemies and spraying pesticide at different thresholds. By using Poincaré map and the properties of the Lambert W function, we prove that the sufficient conditions for the existence and stability of semi-trivial solution and positive periodic solution. Numerical simulations are carried out to illustrate the feasibility of our main results.

Survey of three-dimensional numerical estuarine models

USGS Publications Warehouse

Cheng, Ralph T.; Smith, Peter E.

1989-01-01

This paper surveys the existing 3-D estuarine hydrodynamic and solute transport models by a review of the commonly used assumptions and approximations, and by an examination of the methods of solution. The model formulations, methods of solution, and known applications are surveyed and summarized in tables. In conclusion, the authors present their modeling philosophy and suggest future research needs.

Integrability and structural stability of solutions to the Ginzburg-Landau equation

NASA Technical Reports Server (NTRS)

Keefe, Laurence R.

1986-01-01

The integrability of the Ginzburg-Landau equation is studied to investigate if the existence of chaotic solutions found numerically could have been predicted a priori. The equation is shown not to possess the Painleveproperty, except for a special case of the coefficients that corresponds to the integrable, nonlinear Schroedinger (NLS) equation. Regarding the Ginzburg-Landau equation as a dissipative perturbation of the NLS, numerical experiments show all but one of a family of two-tori solutions, possessed by the NLS under particular conditions, to disappear under real perturbations to the NLS coefficients of O(10 to the -6th).

Parametric symplectic partitioned Runge-Kutta methods with energy-preserving properties for Hamiltonian systems

NASA Astrophysics Data System (ADS)

Wang, Dongling; Xiao, Aiguo; Li, Xueyang

2013-02-01

Based on W-transformation, some parametric symplectic partitioned Runge-Kutta (PRK) methods depending on a real parameter α are developed. For α=0, the corresponding methods become the usual PRK methods, including Radau IA-IA¯ and Lobatto IIIA-IIIB methods as examples. For any α≠0, the corresponding methods are symplectic and there exists a value α∗ such that energy is preserved in the numerical solution at each step. The existence of the parameter and the order of the numerical methods are discussed. Some numerical examples are presented to illustrate these results.

Use of multivariable asymptotic expansions in a satellite theory

NASA Technical Reports Server (NTRS)

Dallas, S. S.

1973-01-01

Initial conditions and perturbative force of satellite are restricted to yield motion of equatorial satellite about oblate body. In this manner, exact analytic solution exists and can be used as standard of comparison in numerical accuracy comparisons. Detailed numerical accuracy studies of uniformly valid asymptotic expansions were made.

Cosmic strings - A problem or a solution?

NASA Technical Reports Server (NTRS)

Bennett, David P.; Bouchet, Francois R.

1988-01-01

The most fundamental issue in the theory of cosmic strings is addressed by means of Numerical Simulations: the existence of a scaling solution. The resolution of this question will determine whether cosmic strings can form the basis of an attractive theory of galaxy formation or prove to be a cosmological disaster like magnetic monopoles or domain walls. After a brief discussion of our numerical technique, results are presented which, though still preliminary, offer the best support to date of this scaling hypothesis.

A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

PubMed

Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

2016-01-01

This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model

NASA Astrophysics Data System (ADS)

Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled

2017-02-01

We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer-Nunziato model, namely Schwendeman-Wahle-Kapila's Godunov-type scheme [39] and Tokareva-Toro's HLLC scheme [44]. The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.

A positive and entropy-satisfying finite volume scheme for the Baer–Nunziato model

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

Coquel, Frédéric, E-mail: frederic.coquel@cmap.polytechnique.fr; Hérard, Jean-Marc, E-mail: jean-marc.herard@edf.fr; Saleh, Khaled, E-mail: saleh@math.univ-lyon1.fr

We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer–Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in for the isentropic Baer–Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound aremore » also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer–Nunziato model, namely Schwendeman–Wahle–Kapila's Godunov-type scheme and Tokareva–Toro's HLLC scheme . The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.« less

A new numerical approach for uniquely solvable exterior Riemann-Hilbert problem on region with corners

NASA Astrophysics Data System (ADS)

Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira

2014-06-01

Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.

Boundary enhanced effects on the existence of quadratic solitons

NASA Astrophysics Data System (ADS)

Chen, Manna; Zhang, Ting; Li, Wenjie; Lu, Daquan; Guo, Qi; Hu, Wei

2018-05-01

We investigate, both analytically and numerically, the boundary enhanced effects exerted on the quadratic solitons consisting of fundamental waves and oscillatory second harmonics in the presence of boundary conditions. The nonlocal analogy predicts that the soliton for fundamental wave is supported by the balance between equivalent nonlinear confinement and diffraction (or dispersion). Under Snyder and Mitchell's strongly nonlocal approximation, we obtain the analytical soliton solutions both with and without the boundary conditions to show the impact of boundary conditions. We can distinguish explicitly the nonlinear confinement between the second harmonic mutual interaction and the enhanced effects caused by remote boundaries. Those boundary enhanced effects on the existence of solitons can be positive or negative, which depend on both sample size and nonlocal parameter. The piecewise existence regime of solitons can be explained analytically. The analytical soliton solutions are verified by the numerical ones and the discrepancy between them is also discussed.

Numerical study of fractional nonlinear Schrödinger equations.

PubMed

Klein, Christian; Sparber, Christof; Markowich, Peter

2014-12-08

Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.

Numerical study of fractional nonlinear Schrödinger equations

PubMed Central

Klein, Christian; Sparber, Christof; Markowich, Peter

2014-01-01

Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation. PMID:25484604

Singular perturbation of smoothly evolving Hele-Shaw solutions

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

Siegel, M.; Tanveer, S.

1996-01-01

We present analytical scaling results, confirmed by accurate numerics, to show that there exists a class of smoothly evolving zero surface tension solutions to the Hele-Shaw problem that are significantly perturbed by an arbitrarily small amount of surface tension in order one time. {copyright} {ital 1996 The American Physical Society.}

Singular perturbation solutions of steady-state Poisson-Nernst-Planck systems.

PubMed

Wang, Xiang-Sheng; He, Dongdong; Wylie, Jonathan J; Huang, Huaxiong

2014-02-01

We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively studied, the uniqueness of the solution has been proved, and an explicit expression for the solution has been obtained. However, the case of three or more ions has received significantly less attention. Previous work has indicated that the solution may be nonunique and that even obtaining numerical solutions is a difficult task since one must solve complicated systems of nonlinear equations. By adopting a methodology that preserves the symmetries of the PNP system, we show that determining the outer solution effectively reduces to solving a single scalar transcendental equation. Due to the simple form of the transcendental equation, it can be solved numerically in a straightforward manner. Our methodology thus provides a standard procedure for solving the PNP system and we illustrate this by solving some practical examples. Despite the fact that for three ions, previous studies have indicated that multiple solutions may exist, we show that all except for one of these solutions are unphysical and thereby prove the existence and uniqueness for the three-ion case.

ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

NASA Astrophysics Data System (ADS)

Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

2018-04-01

In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis.

PubMed

Faye, Grégory; Rankin, James; Chossat, Pascal

2013-05-01

The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize working (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spatial connectivity. Noting that stationary solutions of our neural field equation are equivalent to homoclinic orbits in a related fourth order ordinary differential equation, we apply normal form theory for a reversible Hopf bifurcation to prove the existence of localized solutions; further, we present results concerning their stability. Numerical continuation is used to compute branches of localized solution that exhibit snaking-type behaviour. We describe in terms of three parameters the exact regions for which localized solutions persist.

Existence of almost periodic solutions for forced perturbed systems with piecewise constant argument

NASA Astrophysics Data System (ADS)

Xia, Yonghui; Huang, Zhenkun; Han, Maoan

2007-09-01

Certain almost periodic forced perturbed systems with piecewise argument are considered in this paper. By using the contraction mapping principle and some new analysis technique, some sufficient conditions are obtained for the existence and uniqueness of almost periodic solution of these systems. Furthermore, we study the harmonic and subharmonic solutions of these systems. The obtained results generalize the previous known results such as [A.M. Fink, Almost Periodic Differential Equation, Lecture Notes in Math., volE 377, Springer-Verlag, Berlin, 1974; C.Y. He, Almost Periodic Differential Equations, Higher Education Press, Beijing, 1992 (in Chinese); Z.S. Lin, The existence of almost periodic solution of linear system, Acta Math. Sinica 22 (5) (1979) 515-528 (in Chinese); C.Y. He, Existence of almost periodic solutions of perturbation systems, Ann. Differential Equations 9 (2) (1992) 173-181; Y.H. Xia, M. Lin, J. Cao, The existence of almost periodic solutions of certain perturbation system, J. Math. Anal. Appl. 310 (1) (2005) 81-96]. Finally, a tangible example and its numeric simulations show the feasibility of our results, the comparison between non-perturbed system and perturbed system, the relation between systems with and without piecewise argument.

A new model for volume recombination in plane-parallel chambers in pulsed fields of high dose-per-pulse

NASA Astrophysics Data System (ADS)

Gotz, M.; Karsch, L.; Pawelke, J.

2017-11-01

In order to describe the volume recombination in a pulsed radiation field of high dose-per-pulse this study presents a numerical solution of a 1D transport model of the liberated charges in a plane-parallel ionization chamber. In addition, measurements were performed on an Advanced Markus ionization chamber in a pulsed electron beam to obtain suitable data to test the calculation. The experiment used radiation pulses of 4 μs duration and variable dose-per-pulse values up to about 1 Gy, as well as pulses of variable duration up to 308 μs at constant dose-per-pulse values between 85 mGy and 400 mGy. Those experimental data were compared to the developed numerical model and existing descriptions of volume recombination. At low collection voltages the observed dose-per-pulse dependence of volume recombination can be approximated by the existing theory using effective parameters. However, at high collection voltages large discrepancies are observed. The developed numerical model shows much better agreement with the observations and is able to replicate the observed behavior over the entire range of dose-per-pulse values and collection voltages. Using the developed numerical model, the differences between observation and existing theory are shown to be the result of a large fraction of the charge being collected as free electrons and the resultant distortion of the electric field inside the chamber. Furthermore, the numerical solution is able to calculate recombination losses for arbitrary pulse durations in good agreement with the experimental data, an aspect not covered by current theory. Overall, the presented numerical solution of the charge transport model should provide a more flexible tool to describe volume recombination for high dose-per-pulse values as well as for arbitrary pulse durations and repetition rates.

A new model for volume recombination in plane-parallel chambers in pulsed fields of high dose-per-pulse.

PubMed

Gotz, M; Karsch, L; Pawelke, J

2017-11-01

In order to describe the volume recombination in a pulsed radiation field of high dose-per-pulse this study presents a numerical solution of a 1D transport model of the liberated charges in a plane-parallel ionization chamber. In addition, measurements were performed on an Advanced Markus ionization chamber in a pulsed electron beam to obtain suitable data to test the calculation. The experiment used radiation pulses of 4 μs duration and variable dose-per-pulse values up to about 1 Gy, as well as pulses of variable duration up to 308 [Formula: see text] at constant dose-per-pulse values between 85 mGy and 400 mGy. Those experimental data were compared to the developed numerical model and existing descriptions of volume recombination. At low collection voltages the observed dose-per-pulse dependence of volume recombination can be approximated by the existing theory using effective parameters. However, at high collection voltages large discrepancies are observed. The developed numerical model shows much better agreement with the observations and is able to replicate the observed behavior over the entire range of dose-per-pulse values and collection voltages. Using the developed numerical model, the differences between observation and existing theory are shown to be the result of a large fraction of the charge being collected as free electrons and the resultant distortion of the electric field inside the chamber. Furthermore, the numerical solution is able to calculate recombination losses for arbitrary pulse durations in good agreement with the experimental data, an aspect not covered by current theory. Overall, the presented numerical solution of the charge transport model should provide a more flexible tool to describe volume recombination for high dose-per-pulse values as well as for arbitrary pulse durations and repetition rates.

Implicity restarted Arnoldi/Lanczos methods for large scale eigenvalue calculations

NASA Technical Reports Server (NTRS)

Sorensen, Danny C.

1996-01-01

Eigenvalues and eigenfunctions of linear operators are important to many areas of applied mathematics. The ability to approximate these quantities numerically is becoming increasingly important in a wide variety of applications. This increasing demand has fueled interest in the development of new methods and software for the numerical solution of large-scale algebraic eigenvalue problems. In turn, the existence of these new methods and software, along with the dramatically increased computational capabilities now available, has enabled the solution of problems that would not even have been posed five or ten years ago. Until very recently, software for large-scale nonsymmetric problems was virtually non-existent. Fortunately, the situation is improving rapidly. The purpose of this article is to provide an overview of the numerical solution of large-scale algebraic eigenvalue problems. The focus will be on a class of methods called Krylov subspace projection methods. The well-known Lanczos method is the premier member of this class. The Arnoldi method generalizes the Lanczos method to the nonsymmetric case. A recently developed variant of the Arnoldi/Lanczos scheme called the Implicitly Restarted Arnoldi Method is presented here in some depth. This method is highlighted because of its suitability as a basis for software development.

Application of a flux-split algorithm to chemically relaxing, hypervelocity blunt-body flows

NASA Technical Reports Server (NTRS)

Balakrishnan, A.

1987-01-01

Viscous, nonequilibrium, hypervelocity flow fields over two axisymmetric configurations are numerically simulated using a factored, implicit, flux-split algorithm. The governing gas-dynamic and species-continuity equations for laminar flow are presented. The gas-dynamics/nonequilibrium-chemistry coupling procedure is developed as part of the solution procedure and is described in detail. Numerical solutions are presented for hypervelocity flows over a hemisphere and over an axisymmetric aeroassisted orbital transfer vehicle using three different chemistry models. The gas models considered are those for an ideal gas, for a frozen gas, and for chemically relaxing air consisting of five species. The calculated results are compared with existing numerical solutions in the literature along the stagnation line of the hemisphere. The effects of free-stream Reynolds number on the nonequilibrium flow field are discussed.

Co-existence and switching between fast and Ω-slow wind solutions in rapidly rotating massive stars

NASA Astrophysics Data System (ADS)

Araya, I.; Curé, M.; ud-Doula, A.; Santillán, A.; Cidale, L.

2018-06-01

Most radiation-driven winds of massive stars can be modelled with m-CAK theory, resulting in the so-called fast solution. However, the most rapidly rotating stars among them, especially when the rotational speed is higher than {˜ } 75 per cent of the critical rotational speed, can adopt a different solution, the so-called Ω-slow solution, characterized by a dense and slow wind. Here, we study the transition region of the solutions where the fast solution changes to the Ω-slow solution. Using both time-steady and time-dependent numerical codes, we study this transition region for various equatorial models of B-type stars. In all cases, in a certain range of rotational speeds we find a region where the fast and the Ω-slow solution can co-exist. We find that the type of solution obtained in this co-existence region depends stongly on the initial conditions of our models. We also test the stability of the solutions within the co-existence region by performing base-density perturbations in the wind. We find that under certain conditions, the fast solution can switch to the Ω-slow solution, or vice versa. Such solution-switching may be a possible contributor of material injected into the circumstellar environment of Be stars, without requiring rotational speeds near critical values.

Solution of quadratic matrix equations for free vibration analysis of structures.

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1973-01-01

An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures. The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures - a cantilever beam and a semicircular arch.

The dynamics of a delayed predator-prey model with state dependent feedback control

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

Singh, Anuraj; Gakkhar, Sunita

2011-11-30

A delayed prey-predator model with state-dependent impulses is investigated. The sufficient conditions of existence and stability of semi-trivial solution and positive period-1 solution are obtained by using the Poincare map and analogue of the Poincare Criterion. The qualitative analysis shows that the positive period-one solution bifurcates from the semi-trivial solution through a fold bifurcation. The complex dynamics including chaos is obtained and numerical simulations substantiate the analytical results.

A Numerical Study of Coupled Non-Linear Equations of Thermo-Viscous Fluid Flow in Cylindrical Geometry

NASA Astrophysics Data System (ADS)

Pothanna, N.; Aparna, P.; Gorla, R. S. R.

2017-12-01

In this paper we present numerical solutions to coupled non-linear governing equations of thermo-viscous fluid flow in cylindrical geometry using MATHEMATICA software solver. The numerical results are presented in terms of velocity, temperature and pressure distribution for various values of the material parameters such as the thermo-mechanical stress coefficient, thermal conductivity coefficient, Reiner Rivlin cross viscosity coefficient and the Prandtl number in the form of tables and graphs. Also, the solutions to governing equations for slow steady motion of a fluid have been obtained numerically and compared with the existing analytical results and are found to be in excellent agreement. The results of the present study will hopefully enable a better understanding applications of the flow under consideration.

New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics

NASA Astrophysics Data System (ADS)

Xie, Dexuan

2014-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model in the calculation of electrostatic potential energy for biomolecules in ionic solvent, but its numerical solution remains a challenge due to its strong singularity and nonlinearity caused by its singular distribution source terms and exponential nonlinear terms. To effectively deal with such a challenge, in this paper, new solution decomposition and minimization schemes are proposed, together with a new PBE analysis on solution existence and uniqueness. Moreover, a PBE finite element program package is developed in Python based on the FEniCS program library and GAMer, a molecular surface and volumetric mesh generation program package. Numerical tests on proteins and a nonlinear Born ball model with an analytical solution validate the new solution decomposition and minimization schemes, and demonstrate the effectiveness and efficiency of the new PBE finite element program package.

New analytical solutions to the two-phase water faucet problem

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-06-17

Here, the one-dimensional water faucet problem is one of the classical benchmark problems originally proposed by Ransom to study the two-fluid two-phase flow model. With certain simplifications, such as massless gas phase and no wall and interfacial frictions, analytical solutions had been previously obtained for the transient liquid velocity and void fraction distribution. The water faucet problem and its analytical solutions have been widely used for the purposes of code assessment, benchmark and numerical verifications. In our previous study, the Ransom’s solutions were used for the mesh convergence study of a high-resolution spatial discretization scheme. It was found that, atmore » the steady state, an anticipated second-order spatial accuracy could not be achieved, when compared to the existing Ransom’s analytical solutions. A further investigation showed that the existing analytical solutions do not actually satisfy the commonly used two-fluid single-pressure two-phase flow equations. In this work, we present a new set of analytical solutions of the water faucet problem at the steady state, considering the gas phase density’s effect on pressure distribution. This new set of analytical solutions are used for mesh convergence studies, from which anticipated second-order of accuracy is achieved for the 2nd order spatial discretization scheme. In addition, extended Ransom’s transient solutions for the gas phase velocity and pressure are derived, with the assumption of decoupled liquid and gas pressures. Numerical verifications on the extended Ransom’s solutions are also presented.« less

Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage

NASA Astrophysics Data System (ADS)

Han, Weimin; Shillor, Meir; Sofonea, Mircea

2001-12-01

We consider a model for quasistatic frictional contact between a viscoelastic body and a foundation. The material constitutive relation is assumed to be nonlinear. The mechanical damage of the material, caused by excessive stress or strain, is described by the damage function, the evolution of which is determined by a parabolic inclusion. The contact is modeled with the normal compliance condition and the associated version of Coulomb's law of dry friction. We derive a variational formulation for the problem and prove the existence of its unique weak solution. We then study a fully discrete scheme for the numerical solutions of the problem and obtain error estimates on the approximate solutions.

Divergent expansion, Borel summability and three-dimensional Navier-Stokes equation.

PubMed

Costin, Ovidiu; Luo, Guo; Tanveer, Saleh

2008-08-13

We describe how the Borel summability of a divergent asymptotic expansion can be expanded and applied to nonlinear partial differential equations (PDEs). While Borel summation does not apply for non-analytic initial data, the present approach generates an integral equation (IE) applicable to much more general data. We apply these concepts to the three-dimensional Navier-Stokes (NS) system and show how the IE approach can give rise to local existence proofs. In this approach, the global existence problem in three-dimensional NS systems, for specific initial condition and viscosity, becomes a problem of asymptotics in the variable p (dual to 1/t or some positive power of 1/t). Furthermore, the errors in numerical computations in the associated IE can be controlled rigorously, which is very important for nonlinear PDEs such as NS when solutions are not known to exist globally.Moreover, computation of the solution of the IE over an interval [0,p0] provides sharper control of its p-->infinity behaviour. Preliminary numerical computations give encouraging results.

Numerical Analysis of Intra-Cavity and Power-Stream Flow Interaction in Multiple Gas-Turbine Disk-Cavities

NASA Technical Reports Server (NTRS)

Athavale, M. M.; Przekwas, A. J.; Hendricks, R. C.; Steinetz, B. M.

1995-01-01

A numerical analysis methodology and solutions of the interaction between the power stream and multiply-connected multi-cavity sealed secondary flow fields are presented. Flow solutions for a multi-cavity experimental rig were computed and compared with experimental data of Daniels and Johnson. The flow solutions illustrate the complex coupling between the main-path and the cavity flows as well as outline the flow thread that exists throughout the subplatform multiple cavities and seals. The analysis also shows that the de-coupled solutions on single cavities is inadequate. The present results show trends similar to the T-700 engine data that suggests the changes in the CDP seal altered the flow fields throughout the engine and affected the engine performance.

The effect of surface tension on steadily translating bubbles in an unbounded Hele-Shaw cell

PubMed Central

2017-01-01

New numerical solutions to the so-called selection problem for one and two steadily translating bubbles in an unbounded Hele-Shaw cell are presented. Our approach relies on conformal mapping which, for the two-bubble problem, involves the Schottky-Klein prime function associated with an annulus. We show that a countably infinite number of solutions exist for each fixed value of dimensionless surface tension, with the bubble shapes becoming more exotic as the solution branch number increases. Our numerical results suggest that a single solution is selected in the limit that surface tension vanishes, with the scaling between the bubble velocity and surface tension being different to the well-studied problems for a bubble or a finger propagating in a channel geometry. PMID:28588410

On the limits of numerical astronomical solutions used in paleoclimate studies

NASA Astrophysics Data System (ADS)

Zeebe, Richard E.

2017-04-01

Numerical solutions of the equations of the Solar System estimate Earth's orbital parameters in the past and represent the backbone of cyclostratigraphy and astrochronology, now widely applied in geology and paleoclimatology. Given one numerical realization of a Solar System model (i.e., obtained using one code or integrator package), various parameters determine the properties of the solution and usually limit its validity to a certain time period. Such limitations are denoted here as "internal" and include limitations due to (i) the underlying physics/physical model and (ii) numerics. The physics include initial coordinates and velocities of Solar System bodies, treatment of the Moon and asteroids, the Sun's quadrupole moment, and the intrinsic dynamics of the Solar System itself, i.e., its chaotic nature. Numerical issues include solver algorithm, numerical accuracy (e.g., time step), and round-off errors. At present, internal limitations seem to restrict the validity of astronomical solutions to perhaps the past 50 or 60 myr. However, little is currently known about "external" limitations, that is, how do different numerical realizations compare, say, between different investigators using different codes and integrators? Hitherto only two solutions for Earth's eccentricity appear to be used in paleoclimate studies, provided by two different groups that integrated the full Solar System equations over the past >100 myr (Laskar and coworkers and Varadi et al. 2003). In this contribution, I will present results from new Solar System integrations for Earth's eccentricity obtained using the integrator package HNBody (Rauch and Hamilton 2002). I will discuss the various internal limitations listed above within the framework of the present simulations. I will also compare the results to the existing solutions, the details of which are still being sorted out as several simulations are still running at the time of writing.

A Numerical Simulation of Scattering from One-Dimensional Inhomogeneous Dielectric Random Surfaces

NASA Technical Reports Server (NTRS)

Sarabandi, Kamal; Oh, Yisok; Ulaby, Fawwaz T.

1996-01-01

In this paper, an efficient numerical solution for the scattering problem of inhomogeneous dielectric rough surfaces is presented. The inhomogeneous dielectric random surface represents a bare soil surface and is considered to be comprised of a large number of randomly positioned dielectric humps of different sizes, shapes, and dielectric constants above an impedance surface. Clods with nonuniform moisture content and rocks are modeled by inhomogeneous dielectric humps and the underlying smooth wet soil surface is modeled by an impedance surface. In this technique, an efficient numerical solution for the constituent dielectric humps over an impedance surface is obtained using Green's function derived by the exact image theory in conjunction with the method of moments. The scattered field from a sample of the rough surface is obtained by summing the scattered fields from all the individual humps of the surface coherently ignoring the effect of multiple scattering between the humps. The statistical behavior of the scattering coefficient sigma(sup 0) is obtained from the calculation of scattered fields of many different realizations of the surface. Numerical results are presented for several different roughnesses and dielectric constants of the random surfaces. The numerical technique is verified by comparing the numerical solution with the solution based on the small perturbation method and the physical optics model for homogeneous rough surfaces. This technique can be used to study the behavior of scattering coefficient and phase difference statistics of rough soil surfaces for which no analytical solution exists.

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

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

Here, the one-dimensional water faucet problem is one of the classical benchmark problems originally proposed by Ransom to study the two-fluid two-phase flow model. With certain simplifications, such as massless gas phase and no wall and interfacial frictions, analytical solutions had been previously obtained for the transient liquid velocity and void fraction distribution. The water faucet problem and its analytical solutions have been widely used for the purposes of code assessment, benchmark and numerical verifications. In our previous study, the Ransom’s solutions were used for the mesh convergence study of a high-resolution spatial discretization scheme. It was found that, atmore » the steady state, an anticipated second-order spatial accuracy could not be achieved, when compared to the existing Ransom’s analytical solutions. A further investigation showed that the existing analytical solutions do not actually satisfy the commonly used two-fluid single-pressure two-phase flow equations. In this work, we present a new set of analytical solutions of the water faucet problem at the steady state, considering the gas phase density’s effect on pressure distribution. This new set of analytical solutions are used for mesh convergence studies, from which anticipated second-order of accuracy is achieved for the 2nd order spatial discretization scheme. In addition, extended Ransom’s transient solutions for the gas phase velocity and pressure are derived, with the assumption of decoupled liquid and gas pressures. Numerical verifications on the extended Ransom’s solutions are also presented.« less

MHD stagnation point flow and heat transfer of a nanofluid over a permeable nonlinear stretching/shrinking sheet with viscous dissipation effect

NASA Astrophysics Data System (ADS)

Jusoh, Rahimah; Nazar, Roslinda

2018-04-01

The magnetohydrodynamic (MHD) stagnation point flow and heat transfer of an electrically conducting nanofluid over a nonlinear stretching/shrinking sheet is studied numerically. Mathematical modelling and analysis are attended in the presence of viscous dissipation. Appropriate similarity transformations are used to reduce the boundary layer equations for momentum, energy and concentration into a set of ordinary differential equations. The reduced equations are solved numerically using the built in bvp4c function in Matlab. The numerical and graphical results on the effects of various parameters on the velocity and temperature profiles as well as the skin friction coefficient and the local Nusselt number are analyzed and discussed in this paper. The study discovers the existence of dual solutions for a certain range of the suction parameter. The conducted stability analysis reveals that the first solution is stable and feasible, while the second solution is unstable.

The role of membrane-like stresses in determining the stability and sensitivity of the Antarctic ice sheets: back pressure and grounding line motion.

PubMed

Hindmarsh, Richard C A

2006-07-15

Membrane stresses act along thin bodies which are relatively well lubricated on both surfaces. They operate in ice sheets because the bottom is either sliding, or is much less viscous than the top owing to stress and heat softening of the basal ice. Ice streams flow over very well lubricated beds, and are restrained at their sides. The ideal of the perfectly slippery bed is considered in this paper, and the propagation of mechanical effects along an ice stream considered by applying spatially varying horizontal body forces. Propagation distances depend sensitively on the rheological index, and can be very large for ice-type rheologies.A new analytical solution for ice-shelf profiles and grounded tractionless stream profiles is presented, which show blow up of the profile in a finite distance upstream at locations where the flux is non-zero. This is a feature of an earlier analytical solution for a floating shelf.The length scale of decay of membrane stresses from the grounding line is investigated through scale analysis. In ice sheets, such effects decay over distances of several tens of kilometres, creating a vertical boundary layer between sheet flow and shelf flow, where membrane stresses adjust. Bounded, physically reasonable steady surface profiles only exist conditionally in this boundary layer. Where bounded steady profiles exist, adjacent profile equilibria for the whole ice sheet corresponding to different grounded areas occur (neutral equilibrium). If no solution in the boundary layer can exist, the ice-sheet profile must change.The conditions for existence can be written in terms of whether the basal rate factor (sliding or internal deformation) is too large to permit a steady solution. The critical value depends extremely sensitively on ice velocity and the back stress applied at the grounding line. High ice velocity and high stress both favour the existence of solutions and stability. Changes in these parameters can cause the steady solution existence criterion to be traversed, and the ice-sheet dynamics to change.A finite difference model which represents both neutral equilibrium and the dynamical transition is presented, and preliminary investigations into its numerical sensitivity are carried out. Evidence for the existence of a long wavelength instability is presented through the solution of a numerical eigenproblem, which will hamper predictability.

Evaluation of Proteus as a Tool for the Rapid Development of Models of Hydrologic Systems

NASA Astrophysics Data System (ADS)

Weigand, T. M.; Farthing, M. W.; Kees, C. E.; Miller, C. T.

2013-12-01

Models of modern hydrologic systems can be complex and involve a variety of operators with varying character. The goal is to implement approximations of such models that are both efficient for the developer and computationally efficient, which is a set of naturally competing objectives. Proteus is a Python-based toolbox that supports prototyping of model formulations as well as a wide variety of modern numerical methods and parallel computing. We used Proteus to develop numerical approximations for three models: Richards' equation, a brine flow model derived using the Thermodynamically Constrained Averaging Theory (TCAT), and a multiphase TCAT-based tumor growth model. For Richards' equation, we investigated discontinuous Galerkin solutions with higher order time integration based on the backward difference formulas. The TCAT brine flow model was implemented using Proteus and a variety of numerical methods were compared to hand coded solutions. Finally, an existing tumor growth model was implemented in Proteus to introduce more advanced numerics and allow the code to be run in parallel. From these three example models, Proteus was found to be an attractive open-source option for rapidly developing high quality code for solving existing and evolving computational science models.

Numerical solutions of the macroscopic Maxwell equations for scattering by non-spherical particles: A tutorial review

NASA Astrophysics Data System (ADS)

Kahnert, Michael

2016-07-01

Numerical solution methods for electromagnetic scattering by non-spherical particles comprise a variety of different techniques, which can be traced back to different assumptions and solution strategies applied to the macroscopic Maxwell equations. One can distinguish between time- and frequency-domain methods; further, one can divide numerical techniques into finite-difference methods (which are based on approximating the differential operators), separation-of-variables methods (which are based on expanding the solution in a complete set of functions, thus approximating the fields), and volume integral-equation methods (which are usually solved by discretisation of the target volume and invoking the long-wave approximation in each volume cell). While existing reviews of the topic often tend to have a target audience of program developers and expert users, this tutorial review is intended to accommodate the needs of practitioners as well as novices to the field. The required conciseness is achieved by limiting the presentation to a selection of illustrative methods, and by omitting many technical details that are not essential at a first exposure to the subject. On the other hand, the theoretical basis of numerical methods is explained with little compromises in mathematical rigour; the rationale is that a good grasp of numerical light scattering methods is best achieved by understanding their foundation in Maxwell's theory.

Dispersive models describing mosquitoes’ population dynamics

NASA Astrophysics Data System (ADS)

Yamashita, W. M. S.; Takahashi, L. T.; Chapiro, G.

2016-08-01

The global incidences of dengue and, more recently, zica virus have increased the interest in studying and understanding the mosquito population dynamics. Understanding this dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. This work is based on the study of nonlinear mathematical models dealing with the life cycle of the dengue mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through numerical simulations using finite difference schemes.

Analytical formulation of selected activities of the remote manipulator system

NASA Technical Reports Server (NTRS)

Zimmerman, K. J.

1977-01-01

Existing analysis of Orbiter-RMS-Payload kinematics were surveyed, including equations dealing with the two body kinematics in the presence of a massless RMS and compares analytical explicit solutions with numerical solutions. For the following operational phases of the RMS numerical demonstration, problems are provided: (1) payload capture; (2) payload stowage and removal from cargo bay; and (3) payload deployment. The equation of motion provided accounted for RMS control forces and torque moments and could be extended to RMS flexibility and control loop simulation without increasing the degrees of freedom of the two body system.

Salty popcorn in a homogeneous low-dimensional toy model of holographic QCD

NASA Astrophysics Data System (ADS)

Elliot-Ripley, Matthew

2017-04-01

Recently, a homogeneous ansatz has been used to study cold dense nuclear matter in the Sakai-Sugimoto model of holographic QCD. To justify this homogeneous approximation we here investigate a homogeneous ansatz within a low-dimensional toy version of Sakai-Sugimoto to study finite baryon density configurations and compare it to full numerical solutions. We find the ansatz corresponds to enforcing a dyon salt arrangement in which the soliton solutions are split into half-soliton layers. Within this ansatz we find analogues of the proposed baryonic popcorn transitions, in which solutions split into multiple layers in the holographic direction. The homogeneous results are found to qualitatively match the full numerical solutions, lending confidence to the homogeneous approximations of the full Sakai-Sugimoto model. In addition, we find exact compact solutions in the high density, flat space limit which demonstrate the existence of further popcorn transitions to three layers and beyond.

Assessment Processes to Increase the Burden of Existing Buildings Using BIM

NASA Astrophysics Data System (ADS)

Szeląg, Romuald

2017-10-01

The process of implementation of the reconstruction of buildings is often associated with the need to adapt them to increased loads. In the restricted access to the archive project documentation it is necessary to use technical solutions to obtain a fairly short period of time necessary to implement the technical parameters of such processes. Dissemination of BIM in the design process can also be used effectively in the processes of identification of existing facilities for the implementation of the work of strengthening or adapting objects to the increased load requirements. Obtained in the process of research and macroscopic data is then used in the processes of numerical processing aimed at developing a numerical model reflects the actual parameters of the structure of the existing structure and, therefore, allows a better look at the object and the execution of the process to strengthen future. This article will identify possibilities for the use of BIM in processes of identification technology buildings and structures and indicated the necessary data to be obtained during the preliminary work. Introduced in model solutions enable the use of multi-criteria analysis of the choice of the most optimal solutions in terms of costs or expenditures of time during the process of construction. Taking the above work by building a numerical model of the object allows every step of verification by authorized person inventoried solutions and enables tracking and changes in the situation of those found derogations in relation to the parameters established at the primary stage. In the event of significant deviations, there is the possibility of rapid changes to the completed process of calculation and presentation of alternative solutions. Availability software using BIM technology is increasingly common here knowledge of the implementation of such solutions will become in a short time, the standard for most objects or engineering structures. The use of modern solutions using the described processes will be discussed on the example of an industrial facility where there was a need for installation of new equipment and adapt it to the technical parameters.

Numerical simulations of three-dimensional laminar flow over a backward facing step; flow near side walls

NASA Technical Reports Server (NTRS)

Steinthorsson, Erlendur; Liou, Meng-Sing; Povinelli, Louis A.; Arnone, Andrea

1993-01-01

This paper reports the results of numerical simulations of steady, laminar flow over a backward-facing step. The governing equations used in the simulations are the full 'compressible' Navier-Stokes equations, solutions to which were computed by using a cell-centered, finite volume discretization. The convection terms of the governing equations were discretized by using the Advection Upwind Splitting Method (AUSM), whereas the diffusion terms were discretized using central differencing formulas. The validity and accuracy of the numerical solutions were verified by comparing the results to existing experimental data for flow at identical Reynolds numbers in the same back step geometry. The paper focuses attention on the details of the flow field near the side wall of the geometry.

Localized solutions of Lugiato-Lefever equations with focused pump.

PubMed

Cardoso, Wesley B; Salasnich, Luca; Malomed, Boris A

2017-12-04

Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too-in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.

Novel approach for dam break flow modeling using computational intelligence

NASA Astrophysics Data System (ADS)

Seyedashraf, Omid; Mehrabi, Mohammad; Akhtari, Ali Akbar

2018-04-01

A new methodology based on the computational intelligence (CI) system is proposed and tested for modeling the classic 1D dam-break flow problem. The reason to seek for a new solution lies in the shortcomings of the existing analytical and numerical models. This includes the difficulty of using the exact solutions and the unwanted fluctuations, which arise in the numerical results. In this research, the application of the radial-basis-function (RBF) and multi-layer-perceptron (MLP) systems is detailed for the solution of twenty-nine dam-break scenarios. The models are developed using seven variables, i.e. the length of the channel, the depths of the up-and downstream sections, time, and distance as the inputs. Moreover, the depths and velocities of each computational node in the flow domain are considered as the model outputs. The models are validated against the analytical, and Lax-Wendroff and MacCormack FDM schemes. The findings indicate that the employed CI models are able to replicate the overall shape of the shock- and rarefaction-waves. Furthermore, the MLP system outperforms RBF and the tested numerical schemes. A new monolithic equation is proposed based on the best fitting model, which can be used as an efficient alternative to the existing piecewise analytic equations.

Rupture dynamics along bimaterial interfaces: a parametric study of the coupling between interfacial sliding and normal traction perturbation

NASA Astrophysics Data System (ADS)

Scala, Antonio; Festa, Gaetano; Vilotte, Jean-Pierre

2017-04-01

Earthquake ruptures often develop along faults separating materials with dissimilar elastic properties. Due to the broken symmetry, the propagation of the rupture along the bimaterial interface is driven by the coupling between interfacial sliding and normal traction perturbations. We numerically investigate in-plane rupture growth along a planar interface, under slip weakening friction, separating two dissimilar isotropic linearly elastic half-spaces. We perform a parametric study of the classical Prakash-Clifton regularisation for different material contrasts. In particular mesh-dependence and regularisation-dependence of the numerical solutions are analysed in this parameter space. When regularisation involves a slip-rate dependent relaxation time, a characteristic sliding distance is identified below which numerical solutions no longer depend on the regularisation parameter, i.e. they are consistent solutions of the same physical problem. Such regularisation provides an adaptive high-frequency filter of the slip-induced normal traction perturbations, following the dynamic shrinking of the dissipation zone during the acceleration phase. In contrast, regularisation involving a constant relaxation time leads to numerical solutions that always depend on the regularisation parameter since it fails adapting to the shrinking of the process zone. Dynamic regularisation is further investigated using a non-local regularisation based on a relaxation time that depends on the dynamic length of the dissipation zone. Such reformulation is shown to provide similar results as the dynamic time scale regularisation proposed by Prakash-Clifton when slip rate is replaced by the maximum slip rate along the sliding interface. This leads to the identification of a dissipative length scale associated with the coupling between interfacial sliding and normal traction perturbations, together with a scaling law between the maximum slip rate and the dynamic size of the process zone during the rupture propagation. Dynamic time scale regularisation is show to provide mesh-independent and physically well-posed numerical solutions during the acceleration phase toward an asymptotic speed. When generalised Rayleigh wave does not exist, numerical solutions are shown to tend toward an asymptotic velocity higher than the slowest shear wave speed. When generalised Rayleigh wave speed exists, as numerical solutions tend toward this velocity, increasing spurious oscillations develop and solutions become unstable. In this regime regularisation dependent and unstable finite-size pulses may be generated. This instability is associated with the singular behaviour of the slip-induced normal traction perturbations, and of the slip rate at the rupture front, in relation with complete shrinking of the dissipation zone. This phase requires to be modelled either by more complex interface constitutive laws involving velocity-strengthening effects that may stabilize short wavelength interfacial propagating modes or by considering non-ideal interfaces that introduce a new length scale in the problem that may promote selection and stabilization of the slip pulses.

Asymptotic traveling wave solution for a credit rating migration problem

NASA Astrophysics Data System (ADS)

Liang, Jin; Wu, Yuan; Hu, Bei

2016-07-01

In this paper, an asymptotic traveling wave solution of a free boundary model for pricing a corporate bond with credit rating migration risk is studied. This is the first study to associate the asymptotic traveling wave solution to the credit rating migration problem. The pricing problem with credit rating migration risk is modeled by a free boundary problem. The existence, uniqueness and regularity of the solution are obtained. Under some condition, we proved that the solution of our credit rating problem is convergent to a traveling wave solution, which has an explicit form. Furthermore, numerical examples are presented.

Group invariant solution for a pre-existing fracture driven by a power-law fluid in permeable rock

NASA Astrophysics Data System (ADS)

Fareo, A. G.; Mason, D. P.

2016-06-01

Group invariant analytical and numerical solutions for the evolution of a two-dimensional fracture with nonzero initial length in permeable rock and driven by an incompressible non-Newtonian fluid of power-law rheology are obtained. The effect of fluid leak-off on the evolution of the power-law fluid fracture is investigated.

Phases and stability of non-uniform black strings

NASA Astrophysics Data System (ADS)

Emparan, Roberto; Luna, Raimon; Martínez, Marina; Suzuki, Ryotaku; Tanabe, Kentaro

2018-05-01

We construct solutions of non-uniform black strings in dimensions from D ≈ 9 all the way up to D = ∞, and investigate their thermodynamics and dynamical stability. Our approach employs the large- D perturbative expansion beyond the leading order, including corrections up to 1 /D 4. Combining both analytical techniques and relatively simple numerical solution of ODEs, we map out the ranges of parameters in which non-uniform black strings exist in each dimension and compute their thermodynamics and quasinormal modes with accuracy. We establish with very good precision the existence of Sorkin's critical dimension and we prove that not only the thermodynamic stability, but also the dynamic stability of the solutions changes at it.

Dynamics of climate-based malaria transmission model with age-structured human population

NASA Astrophysics Data System (ADS)

Addawe, Joel; Pajimola, Aprimelle Kris

2016-10-01

In this paper, we proposed to study the dynamics of malaria transmission with periodic birth rate of the vector and an age-structure for the human population. The human population is divided into two compartments: pre-school (0-5 years) and the rest of the human population. We showed the existence of a disease-free equilibrium point. Using published epidemiological parameters, we use numerical simulations to show potential effect of climate change in the dynamics of age-structured malaria transmission. Numerical simulations suggest that there exists an asymptotically attractive solution that is positive and periodic.

Numerical solution of the electron transport equation

NASA Astrophysics Data System (ADS)

Woods, Mark

The electron transport equation has been solved many times for a variety of reasons. The main difficulty in its numerical solution is that it is a very stiff boundary value problem. The most common numerical methods for solving boundary value problems are symmetric collocation methods and shooting methods. Both of these types of methods can only be applied to the electron transport equation if the boundary conditions are altered with unrealistic assumptions because they require too many points to be practical. Further, they result in oscillating and negative solutions, which are physically meaningless for the problem at hand. For these reasons, all numerical methods for this problem to date are a bit unusual because they were designed to try and avoid the problem of extreme stiffness. This dissertation shows that there is no need to introduce spurious boundary conditions or invent other numerical methods for the electron transport equation. Rather, there already exists methods for very stiff boundary value problems within the numerical analysis literature. We demonstrate one such method in which the fast and slow modes of the boundary value problem are essentially decoupled. This allows for an upwind finite difference method to be applied to each mode as is appropriate. This greatly reduces the number of points needed in the mesh, and we demonstrate how this eliminates the need to define new boundary conditions. This method is verified by showing that under certain restrictive assumptions, the electron transport equation has an exact solution that can be written as an integral. We show that the solution from the upwind method agrees with the quadrature evaluation of the exact solution. This serves to verify that the upwind method is properly solving the electron transport equation. Further, it is demonstrated that the output of the upwind method can be used to compute auroral light emissions.

Structure of field rotating disturbances in warm plasma

NASA Technical Reports Server (NTRS)

Wolfson, R.

1982-01-01

A model in which thermal effects are simulated through use of a multibeam plasma distribution function is developed and investigated to see if solutions which take an initially uniform magnetized plasma to a new uniform state with different field orientation are possible. The momentum conservation integrals are found to admit two classes of such solutions, but only one class exhibits appropriate asymptotic behavior. Extensive numerical integrations have failed to demonstrate the existence of the desired solutions.

Formalism for calculation of polymer-solvent-mediated potential

NASA Astrophysics Data System (ADS)

Zhou, Shiqi

2006-07-01

A simple theoretical approach is proposed for calculation of a solvent-mediated potential (SMP) between two colloid particles immersed in a polymer solvent bath in which the polymer is modeled as a chain with intramolecular degrees of freedom. The present recipe is only concerned with the estimation of the density profile of a polymer site around a single solute colloid particle instead of two solute colloid particles separated by a varying distance as done in existing calculational methods for polymer-SMP. Therefore the present recipe is far simpler for numerical implementation than the existing methods. The resultant predictions for the polymer-SMP and polymer solvent-mediated mean force (polymer-SMMF) are in very good agreement with available simulation data. With the present recipe, change tendencies of the contact value and second virial coefficiency of the SMP as a function of size ratio between the colloid particle and polymer site, the number of sites per chain, and the polymer concentration are investigated in detail. The metastable critical polymer concentration as a function of size ratio and the number of sites per chain is also reported for the first time. To yield the numerical solution of the present recipe at less than 1min on a personal computer, a rapid and accurate algorithm for the numerical solution of the classical density functional theory is proposed to supply rapid and accurate estimation of the density profile of the polymer site as an input into the present formalism.

Multiple stationary solutions of an irradiated slab

NASA Astrophysics Data System (ADS)

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

2005-04-01

A mathematical model describing the heat budget of an irradiated medium is introduced. The one-dimensional form of the equations and boundary conditions are presented and analysed. Heat transport at one face of the slab occurs by absorption (and reflection) of an incoming beam of short-wave radiation with a fraction of this radiation penetrating into the body of the slab, a diffusive heat flux in the slab and a prescribed incoming heat flux term. The other face of the slab is immersed in its own melt and is considered to be a free surface. Here, temperature continuity is prescribed and evolution of the surface is determined by a Stefan condition. These boundary conditions are flexible enough to describe a range of situations such as a laser shining on an opaque medium, or the natural environment of polar sea ice or lake ice. A two-stream radiation model is used which replaces the simple Beer's law of radiation attenuation frequently used for semi-infinite domains. The stationary solutions of the governing equations are sought and it is found that there exists two possible stationary solutions for a given set of boundary conditions and a range of parameter choices. It is found that the existence of two stationary solutions is a direct result of the model of radiation absorption, due to its effect on the albedo of the medium. A linear stability analysis and numerical calculations indicate that where two stationary solutions exist, the solution corresponding to a larger thickness is always stable and the solution corresponding to a smaller thickness is unstable. Numerical simulations reveal that when there are two solutions, if the slab is thinner than the smaller stationary thickness it will melt completely, whereas if the slab is thicker than the smaller stationary thickness it will evolve toward the larger stationary thickness. These results indicate that other mechanisms (e.g. wave-induced agglomeration of crystals) are necessary to grow a slab from zero initial thickness in the parameter regime that yields two stationary solutions.

Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

PubMed Central

Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui

2014-01-01

Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904

Anisotropic cosmological solutions in R + R^2 gravity

NASA Astrophysics Data System (ADS)

Müller, Daniel; Ricciardone, Angelo; Starobinsky, Alexei A.; Toporensky, Aleksey

2018-04-01

In this paper we investigate the past evolution of an anisotropic Bianchi I universe in R+R^2 gravity. Using the dynamical system approach we show that there exists a new two-parameter set of solutions that includes both an isotropic "false radiation" solution and an anisotropic generalized Kasner solution, which is stable. We derive the analytic behavior of the shear from a specific property of f( R) gravity and the analytic asymptotic form of the Ricci scalar when approaching the initial singularity. Finally, we numerically check our results.

Multiple branches of travelling waves for the Gross–Pitaevskii equation

NASA Astrophysics Data System (ADS)

Chiron, David; Scheid, Claire

2018-06-01

Explicit solitary waves are known to exist for the Kadomtsev–Petviashvili-I (KP-I) equation in dimension 2. We first address numerically the question of their Morse index. The results confirm that the lump solitary wave has Morse index one and that the other explicit solutions correspond to excited states. We then turn to the 2D Gross–Pitaevskii (GP) equation, which in some long wave regime converges to the KP-I equation. Numerical simulations have already shown that a branch of travelling waves of GP converges to a ground state of KP-I, expected to be the lump. In this work, we perform numerical simulations showing that other explicit solitary waves solutions to the KP-I equation give rise to new branches of travelling waves of GP corresponding to excited states.

Fredholm-Volterra Integral Equation with a Generalized Singular Kernel and its Numerical Solutions

NASA Astrophysics Data System (ADS)

El-Kalla, I. L.; Al-Bugami, A. M.

2010-11-01

In this paper, the existence and uniqueness of solution of the Fredholm-Volterra integral equation (F-VIE), with a generalized singular kernel, are discussed and proved in the spaceL2(Ω)×C(0,T). The Fredholm integral term (FIT) is considered in position while the Volterra integral term (VIT) is considered in time. Using a numerical technique we have a system of Fredholm integral equations (SFIEs). This system of integral equations can be reduced to a linear algebraic system (LAS) of equations by using two different methods. These methods are: Toeplitz matrix method and Product Nyström method. A numerical examples are considered when the generalized kernel takes the following forms: Carleman function, logarithmic form, Cauchy kernel, and Hilbert kernel.

Solid state light engines for bioanalytical instruments and biomedical devices

NASA Astrophysics Data System (ADS)

Jaffe, Claudia B.; Jaffe, Steven M.

2010-02-01

Lighting subsystems to drive 21st century bioanalysis and biomedical diagnostics face stringent requirements. Industrywide demands for speed, accuracy and portability mean illumination must be intense as well as spectrally pure, switchable, stable, durable and inexpensive. Ideally a common lighting solution could service these needs for numerous research and clinical applications. While this is a noble objective, the current technology of arc lamps, lasers, LEDs and most recently light pipes have intrinsic spectral and angular traits that make a common solution untenable. Clearly a hybrid solution is required to service the varied needs of the life sciences. Any solution begins with a critical understanding of the instrument architecture and specifications for illumination regarding power, illumination area, illumination and emission wavelengths and numerical aperture. Optimizing signal to noise requires careful optimization of these parameters within the additional constraints of instrument footprint and cost. Often the illumination design process is confined to maximizing signal to noise without the ability to adjust any of the above parameters. A hybrid solution leverages the best of the existing lighting technologies. This paper will review the design process for this highly constrained, but typical optical optimization scenario for numerous bioanalytical instruments and biomedical devices.

Numerical Validation of Chemical Compositional Model for Wettability Alteration Processes

NASA Astrophysics Data System (ADS)

Bekbauov, Bakhbergen; Berdyshev, Abdumauvlen; Baishemirov, Zharasbek; Bau, Domenico

2017-12-01

Chemical compositional simulation of enhanced oil recovery and surfactant enhanced aquifer remediation processes is a complex task that involves solving dozens of equations for all grid blocks representing a reservoir. In the present work, we perform a numerical validation of the newly developed mathematical formulation which satisfies the conservation laws of mass and energy and allows applying a sequential solution approach to solve the governing equations separately and implicitly. Through its application to the numerical experiment using a wettability alteration model and comparisons with existing chemical compositional model's numerical results, the new model has proven to be practical, reliable and stable.

Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays.

PubMed

Li, Hongfei; Jiang, Haijun; Hu, Cheng

2016-03-01

In this paper, we investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks are guaranteed by Chain rule and inequalities technique. Moreover, a new method involving Yoshizawa-like theorem is favorably employed to acquire the existence of periodic solution. By applying the theory of set-valued maps and functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks. The obtained results expand and complement some previous work on memristor-based BAM neural networks. Finally, a numerical example is provided to show the applicability and effectiveness of our theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Homotopy perturbation method: a versatile tool to evaluate linear and nonlinear fuzzy Volterra integral equations of the second kind.

PubMed

Narayanamoorthy, S; Sathiyapriya, S P

2016-01-01

In this article, we focus on linear and nonlinear fuzzy Volterra integral equations of the second kind and we propose a numerical scheme using homotopy perturbation method (HPM) to obtain fuzzy approximate solutions to them. To facilitate the benefits of this proposal, an algorithmic form of the HPM is also designed to handle the same. In order to illustrate the potentiality of the approach, two test problems are offered and the obtained numerical results are compared with the existing exact solutions and are depicted in terms of plots to reveal its precision and reliability.

On the solution of two-point linear differential eigenvalue problems. [numerical technique with application to Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Antar, B. N.

1976-01-01

A numerical technique is presented for locating the eigenvalues of two point linear differential eigenvalue problems. The technique is designed to search for complex eigenvalues belonging to complex operators. With this method, any domain of the complex eigenvalue plane could be scanned and the eigenvalues within it, if any, located. For an application of the method, the eigenvalues of the Orr-Sommerfeld equation of the plane Poiseuille flow are determined within a specified portion of the c-plane. The eigenvalues for alpha = 1 and R = 10,000 are tabulated and compared for accuracy with existing solutions.

New solutions for steady bubbles in a Hele-Shaw cell

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

Tanveer, S.

1987-03-01

Exact solutions are presented for steadily moving bubbles in a Hele--Shaw cell when the effect of surface tension is neglected. These solutions form a three-parameter family. For specified area, both the speed of the bubble and the distance of its centroid from the channel centerline remain arbitrary when surface tension is ignored. However, numerical evidence suggests that this twofold arbitrariness is removed by the effect of surface tension, i.e., for given bubble area and surface tension, solutions exist only when the bubble velocity and the centroid distance from the channel centerline attain one or more isolated values. From a limitedmore » numerical search, no nonsymmetric solutions could be found; however, a branch of symmetric bubble solutions that was not found in earlier work was found. This branch corresponds to one of the Romero-Vanden-Broeck branch of finger solutions when the bubble size is large. A new procedure for numerical calculations of bubble solutions in the presence of surface tension is presented and is found to work very well for reasonably large bubbles, unlike the previous method of Tanveer (Phys. Fluids 29, 3537 (1986)). The precise power law dependence of bubble velocity on surface tension for small surface tension is explored for bubbles of different area. Agreement is noted with recent analytical results for a finger.« less

Elegant Ince—Gaussian breathers in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Bai, Zhi-Yong; Deng, Dong-Mei; Guo, Qi

2012-06-01

A novel class of optical breathers, called elegant Ince—Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell's mode in an elliptic coordinate system, and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function. We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear Schrödinger equation.

Existence and discrete approximation for optimization problems governed by fractional differential equations

NASA Astrophysics Data System (ADS)

Bai, Yunru; Baleanu, Dumitru; Wu, Guo-Cheng

2018-06-01

We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe ´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.

Stochastic weighted particle methods for population balance equations with coagulation, fragmentation and spatial inhomogeneity

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

Lee, Kok Foong; Patterson, Robert I.A.; Wagner, Wolfgang

2015-12-15

Graphical abstract: -- Highlights: •Problems concerning multi-compartment population balance equations are studied. •A class of fragmentation weight transfer functions is presented. •Three stochastic weighted algorithms are compared against the direct simulation algorithm. •The numerical errors of the stochastic solutions are assessed as a function of fragmentation rate. •The algorithms are applied to a multi-dimensional granulation model. -- Abstract: This paper introduces stochastic weighted particle algorithms for the solution of multi-compartment population balance equations. In particular, it presents a class of fragmentation weight transfer functions which are constructed such that the number of computational particles stays constant during fragmentation events. Themore » weight transfer functions are constructed based on systems of weighted computational particles and each of it leads to a stochastic particle algorithm for the numerical treatment of population balance equations. Besides fragmentation, the algorithms also consider physical processes such as coagulation and the exchange of mass with the surroundings. The numerical properties of the algorithms are compared to the direct simulation algorithm and an existing method for the fragmentation of weighted particles. It is found that the new algorithms show better numerical performance over the two existing methods especially for systems with significant amount of large particles and high fragmentation rates.« less

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 third-order computational method for numerical fluxes to guarantee nonnegative difference coefficients for advection-diffusion equations in a semi-conservative form

NASA Astrophysics Data System (ADS)

Sakai, K.; Watabe, D.; Minamidani, T.; Zhang, G. S.

2012-10-01

According to Godunov theorem for numerical calculations of advection equations, there exist no higher-order schemes with constant positive difference coefficients in a family of polynomial schemes with an accuracy exceeding the first-order. We propose a third-order computational scheme for numerical fluxes to guarantee the non-negative difference coefficients of resulting finite difference equations for advection-diffusion equations in a semi-conservative form, in which there exist two kinds of numerical fluxes at a cell surface and these two fluxes are not always coincident in non-uniform velocity fields. The present scheme is optimized so as to minimize truncation errors for the numerical fluxes while fulfilling the positivity condition of the difference coefficients which are variable depending on the local Courant number and diffusion number. The feature of the present optimized scheme consists in keeping the third-order accuracy anywhere without any numerical flux limiter. We extend the present method into multi-dimensional equations. Numerical experiments for advection-diffusion equations showed nonoscillatory solutions.

Gram-Schmidt Orthogonalization by Gauss Elimination.

ERIC Educational Resources Information Center

Pursell, Lyle; Trimble, S. Y.

1991-01-01

Described is the hand-calculation method for the orthogonalization of a given set of vectors through the integration of Gaussian elimination with existing algorithms. Although not numerically preferable, this method adds increased precision as well as organization to the solution process. (JJK)

Complexity of the laminar-turbulent boundary in pipe flow

NASA Astrophysics Data System (ADS)

Budanur, Nazmi Burak; Hof, Björn

2018-05-01

Over the past decade, the edge of chaos has proven to be a fruitful starting point for investigations of shear flows when the laminar base flow is linearly stable. Numerous computational studies of shear flows demonstrated the existence of states that separate laminar and turbulent regions of the state space. In addition, some studies determined invariant solutions that reside on this edge. In this paper, we study the unstable manifold of one such solution with the aid of continuous symmetry reduction, which we formulate here for the simultaneous quotiening of axial and azimuthal symmetries. Upon our investigation of the unstable manifold, we discover a previously unknown traveling-wave solution on the laminar-turbulent boundary with a relatively complex structure. By means of low-dimensional projections, we visualize different dynamical paths that connect these solutions to the turbulence. Our numerical experiments demonstrate that the laminar-turbulent boundary exhibits qualitatively different regions whose properties are influenced by the nearby invariant solutions.

Mathematical formulation and numerical simulation of bird flu infection process within a poultry farm

NASA Astrophysics Data System (ADS)

Putri, Arrival Rince; Nova, Tertia Delia; Watanabe, M.

2016-02-01

Bird flu infection processes within a poultry farm are formulated mathematically. A spatial effect is taken into account for the virus concentration with a diffusive term. An infection process is represented in terms of a traveling wave solutions. For a small removal rate, a singular perturbation analysis lead to existence of traveling wave solutions, that correspond to progressive infection in one direction.

Locations of stationary/periodic solutions in mean motion resonances according to the properties of dust grains

NASA Astrophysics Data System (ADS)

Pástor, P.

2016-07-01

The equations of secular evolution for dust grains in mean motion resonances with a planet are solved for stationary points. Non-gravitational effects caused by stellar radiation (the Poynting-Robertson effect and the stellar wind) are taken into account. The solutions are stationary in the semimajor axis, eccentricity and resonant angle, but allow the pericentre to advance. The semimajor axis of stationary solutions can be slightly shifted from the exact resonant value. The periodicity of the stationary solutions in a reference frame orbiting with the planet is proved analytically. The existence of periodic solutions in mean motion resonances means that analytical theory enables infinitely long capture times for dust particles. The stationary solutions are periodic motions to which the eccentricity asymptotically approaches and around which the libration occurs. Initial conditions corresponding to the stationary solutions are successfully found by numerically integrating the equation of motion. Numerically and analytically determined shifts of the semimajor axis from the exact resonance for the stationary solutions are in excellent agreement. The stationary solutions can be plotted by the locations of pericentres in the reference frame orbiting with the planet. The pericentres are distributed in space according to the properties of the dust particles.

Three Dimensional Grid Generation for Complex Configurations - Recent Progress

DTIC Science & Technology

1988-03-01

Navier/Stokes finite difference calculations currently of interest. It has been amply demonstrated that the viability of a numerical solution depends...such as advanced fighters or logistic transports, where a multiblock mesh, for example, is necessary. There exist numerous reports and books on the...MESHES I 3.10 ADAPTIVE GRID SCHEMES 10 3.11 REFERENCES 12 4. CONTRIBUTIONS 13 4.1 SOLICITATION AND OVERVIEW 13 4.2 LESSONS LEARNED IN THE MESH

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.

Numerical analysis for trajectory controllability of a coupled multi-order fractional delay differential system via the shifted Jacobi method

NASA Astrophysics Data System (ADS)

Priya, B. Ganesh; Muthukumar, P.

2018-02-01

This paper deals with the trajectory controllability for a class of multi-order fractional linear systems subject to a constant delay in state vector. The solution for the coupled fractional delay differential equation is established by the Mittag-Leffler function. The necessary and sufficient condition for the trajectory controllability is formulated and proved by the generalized Gronwall's inequality. The approximate trajectory for the proposed system is obtained through the shifted Jacobi operational matrix method. The numerical simulation of the approximate solution shows the theoretical results. Finally, some remarks and comments on the existing results of constrained controllability for the fractional dynamical system are also presented.

Poisson-Nernst-Planck equations with steric effects - non-convexity and multiple stationary solutions

NASA Astrophysics Data System (ADS)

Gavish, Nir

2018-04-01

We study the existence and stability of stationary solutions of Poisson-Nernst-Planck equations with steric effects (PNP-steric equations) with two counter-charged species. We show that within a range of parameters, steric effects give rise to multiple solutions of the corresponding stationary equation that are smooth. The PNP-steric equation, however, is found to be ill-posed at the parameter regime where multiple solutions arise. Following these findings, we introduce a novel PNP-Cahn-Hilliard model, show that it is well-posed and that it admits multiple stationary solutions that are smooth and stable. The various branches of stationary solutions and their stability are mapped utilizing bifurcation analysis and numerical continuation methods.

Physics of heat pipe rewetting

NASA Technical Reports Server (NTRS)

Chan, S. H.

1992-01-01

Although several studies have been made to determine the rewetting characteristics of liquid films on heated rods, tubes, and flat plates, no solutions are yet available to describe the rewetting process of a hot plate subjected to a uniform heating. A model is presented to analyze the rewetting process of such plates with and without grooves. Approximate analytical solutions are presented for the prediction of the rewetting velocity and the transient temperature profiles of the plates. It is shown that the present rewetting velocity solution reduces correctly to the existing solution for the rewetting of an initially hot isothermal plate without heating from beneath the plate. Numerical solutions have also been obtained to validate the analytical solutions.

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

Afonso, V.I.; Olmo, Gonzalo J.; Rubiera-Garcia, D., E-mail: viafonso@df.ufcg.edu.br, E-mail: gonzalo.olmo@uv.es, E-mail: drgarcia@fc.ul.pt

The existence of static, spherically symmetric, self-gravitating scalar field solutions in the context of Born-Infeld gravity is explored. Upon a combination of analytical approximations and numerical methods, the equations for a free scalar field (without a potential term) are solved, verifying that the solutions recover the predictions of General Relativity far from the center but finding important new effects in the central regions. We find two classes of objects depending on the ratio between the Schwarzschild radius and a length scale associated to the Born-Infeld theory: massive solutions have a wormhole structure, with their throat at r ≈ 2 Mmore » , while for the lighter configurations the topology is Euclidean. The total energy density of these solutions exhibits a solitonic profile with a maximum peaked away from the center, and located at the throat whenever a wormhole exists. The geodesic structure and curvature invariants are analyzed for the various configurations considered.« less

Bright discrete solitons in spatially modulated DNLS systems

DOE PAGES

Kevrekidis, P. G.; Horne, R. L.; Whitaker, N.; ...

2015-08-04

In the present work, we revisit the highly active research area of inhomogeneously nonlinear defocusing media and consider the existence, spectral stability and nonlinear dynamics of bright solitary waves in them. We use the anti-continuum limit of vanishing coupling as the starting point of our analysis, enabling in this way a systematic characterization of the branches of solutions. Our stability findings and bifurcation characteristics reveal the enhanced robustness and wider existence intervals of solutions with a broader support, culminating in the 'extended' solution in which all sites are excited. Our eigenvalue predictions are corroborated by numerical linear stability analysis. Inmore » conclusion, the dynamics also reveal a tendency of the solution profiles to broaden, in line with the above findings. These results pave the way for further explorations of such states in discrete systems, including in higher dimensional settings.« less

Euclidean black hole vortices

NASA Technical Reports Server (NTRS)

Dowker, Fay; Gregory, Ruth; Traschen, Jennie

1991-01-01

We argue the existence of solutions of the Euclidean Einstein equations that correspond to a vortex sitting at the horizon of a black hole. We find the asymptotic behaviors, at the horizon and at infinity, of vortex solutions for the gauge and scalar fields in an abelian Higgs model on a Euclidean Schwarzschild background and interpolate between them by integrating the equations numerically. Calculating the backreaction shows that the effect of the vortex is to cut a slice out of the Schwarzschild geometry. Consequences of these solutions for black hole thermodynamics are discussed.

A limiting analysis for edge effects in angle-ply laminates

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1976-01-01

A zeroth order solution for edge effects in angle ply composite laminates using perturbation techniques and a limiting free body approach was developed. The general method of solution for laminates is developed and then applied to the special case of a graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness to width ratio h/b and compared to existing numerical results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress for two laminates, and provides mathematical evidence for singular interlaminar shear stresses.

The solution of the dam-break problem in the Porous Shallow water Equations

NASA Astrophysics Data System (ADS)

Cozzolino, Luca; Pepe, Veronica; Cimorelli, Luigi; D'Aniello, Andrea; Della Morte, Renata; Pianese, Domenico

2018-04-01

The Porous Shallow water Equations are commonly used to evaluate the propagation of flooding waves in the urban environment. These equations may exhibit not only classic shocks, rarefactions, and contact discontinuities, as in the ordinary two-dimensional Shallow water Equations, but also special discontinuities at abrupt porosity jumps. In this paper, an appropriate parameterization of the stationary weak solutions of one-dimensional Porous Shallow water Equations supplies the inner structure of the porosity jumps. The exact solution of the corresponding dam-break problem is presented, and six different wave configurations are individuated, proving that the solution exists and it is unique for given initial conditions and geometric characteristics. These results can be used as a benchmark in order to validate one- and two-dimensional numerical models for the solution of the Porous Shallow water Equations. In addition, it is presented a novel Finite Volume scheme where the porosity jumps are taken into account by means of a variables reconstruction approach. The dam-break results supplied by this numerical scheme are compared with the exact dam-break results, showing the promising capabilities of this numerical approach. Finally, the advantages of the novel porosity jump definition are shown by comparison with other definitions available in the literature, demonstrating its advantages, and the issues raising in real world applications are discussed.

A time-accurate high-resolution TVD scheme for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Kim, Hyun Dae; Liu, Nan-Suey

1992-01-01

A total variation diminishing (TVD) scheme has been developed and incorporated into an existing time-accurate high-resolution Navier-Stokes code. The accuracy and the robustness of the resulting solution procedure have been assessed by performing many calculations in four different areas: shock tube flows, regular shock reflection, supersonic boundary layer, and shock boundary layer interactions. These numerical results compare well with corresponding exact solutions or experimental data.

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; D'Costa, Joseph F.

1991-01-01

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves

NASA Technical Reports Server (NTRS)

Fibich, G.; Ilan, B.; Tsynkov, S.

2002-01-01

The critical nonlinear Schrodinger equation (NLS) models the propagation of intense laser light in Kerr media. This equation is derived from the more comprehensive nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. It is known that if the input power of the laser beam (i.e., L(sub 2) norm of the initial solution) is sufficiently high, then the NLS model predicts that the beam will self-focus to a point (i.e.. collapse) at a finite propagation distance. Mathematically, this behavior corresponds to the formation of a singularity in the solution of the NLS. A key question which has been open for many years is whether the solution to the NLH, i.e., the 'parent' equation, may nonetheless exist and remain regular everywhere, in particular for those initial conditions (input powers) that lead to blowup in the NLS. In the current study, we address this question by introducing linear damping into both models and subsequently comparing the numerical solutions of the damped NLH (boundary-value problem) with the corresponding solutions of the damped NLS (initial-value problem). Linear damping is introduced in much the same way as done when analyzing the classical constant-coefficient Helmholtz equation using the limiting absorption principle. Numerically, we have found that it provides a very efficient tool for controlling the solutions of both the NLH and NHS. In particular, we have been able to identify initial conditions for which the NLS solution does become singular. whereas the NLH solution still remains regular everywhere. We believe that our finding of a larger domain of existence for the NLH than that for the NLS is accounted for by precisely those mechanisms, that have been neglected when deriving the NLS from the NLH, i.e., nonparaxiality and backscattering.

Stationary and moving solitons in spin-orbit-coupled spin-1 Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Li, Yu-E.; Xue, Ju-Kui

2018-04-01

We investigate the matter-wave solitons in a spin-orbit-coupled spin-1 Bose-Einstein condensate using a multiscale perturbation method. Beginning with the one-dimensional spin-orbit-coupled threecomponent Gross-Pitaevskii equations, we derive a single nonlinear Schrödinger equation, which allows determination of the analytical soliton solutions of the system. Stationary and moving solitons in the system are derived. In particular, a parameter space for different existing soliton types is provided. It is shown that there exist only dark or bright solitons when the spin-orbit coupling is weak, with the solitons depending on the atomic interactions. However, when the spin-orbit coupling is strong, both dark and bright solitons exist, being determined by the Raman coupling. Our analytical solutions are confirmed by direct numerical simulations.

Black-hole solutions with scalar hair in Einstein-scalar-Gauss-Bonnet theories

NASA Astrophysics Data System (ADS)

Antoniou, G.; Bakopoulos, A.; Kanti, P.

2018-04-01

In the context of the Einstein-scalar-Gauss-Bonnet theory, with a general coupling function between the scalar field and the quadratic Gauss-Bonnet term, we investigate the existence of regular black-hole solutions with scalar hair. Based on a previous theoretical analysis, which studied the evasion of the old and novel no-hair theorems, we consider a variety of forms for the coupling function (exponential, even and odd polynomial, inverse polynomial, and logarithmic) that, in conjunction with the profile of the scalar field, satisfy a basic constraint. Our numerical analysis then always leads to families of regular, asymptotically flat black-hole solutions with nontrivial scalar hair. The solution for the scalar field and the profile of the corresponding energy-momentum tensor, depending on the value of the coupling constant, may exhibit a nonmonotonic behavior, an unusual feature that highlights the limitations of the existing no-hair theorems. We also determine and study in detail the scalar charge, horizon area, and entropy of our solutions.

Periodic waves in fiber Bragg gratings

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

Chow, K. W.; Merhasin, Ilya M.; Malomed, Boris A.

2008-02-15

We construct two families of exact periodic solutions to the standard model of fiber Bragg grating (FBG) with Kerr nonlinearity. The solutions are named ''sn'' and ''cn'' waves, according to the elliptic functions used in their analytical representation. The sn wave exists only inside the FBG's spectral bandgap, while waves of the cn type may only exist at negative frequencies ({omega}<0), both inside and outside the bandgap. In the long-wave limit, the sn and cn families recover, respectively, the ordinary gap solitons, and (unstable) antidark and dark solitons. Stability of the periodic solutions is checked by direct numerical simulations and,more » in the case of the sn family, also through the calculation of instability growth rates for small perturbations. Although, rigorously speaking, all periodic solutions are unstable, a subfamily of practically stable sn waves, with a sufficiently large spatial period and {omega}>0, is identified. However, the sn waves with {omega}<0, as well as all cn solutions, are strongly unstable.« less

D3-Equivariant coupled advertising oscillators model

NASA Astrophysics Data System (ADS)

Zhang, Chunrui; Zheng, Huifeng

2011-04-01

A ring of three coupled advertising oscillators with delay is considered. Using the symmetric functional differential equation theories, the multiple Hopf bifurcations of the equilibrium at the origin are demonstrated. The existence of multiple branches of bifurcating periodic solution is obtained. Numerical simulation supports our analysis results.

Numerical modeling of runback water on ice protected aircraft surfaces

NASA Technical Reports Server (NTRS)

Al-Khalil, Kamel M.; Keith, Theo G., Jr.; Dewitt, Kenneth J.

1992-01-01

A numerical simulation for 'running wet' aircraft anti-icing systems is developed. The model includes breakup of the water film, which exists in regions of direct impingement, into individual rivulets. The wetness factor distribution resulting from the film breakup and the rivulet configuration on the surface are predicted in the numerical solution procedure. The solid wall is modeled as a multilayer structure and the anti-icing system used is of the thermal type utilizing hot air and/or electrical heating elements embedded with the layers. Details of the calculation procedure and the methods used are presented.

Symmetric tridiagonal structure preserving finite element model updating problem for the quadratic model

NASA Astrophysics Data System (ADS)

Rakshit, Suman; Khare, Swanand R.; Datta, Biswa Nath

2018-07-01

One of the most important yet difficult aspect of the Finite Element Model Updating Problem is to preserve the finite element inherited structures in the updated model. Finite element matrices are in general symmetric, positive definite (or semi-definite) and banded (tridiagonal, diagonal, penta-diagonal, etc.). Though a large number of papers have been published in recent years on various aspects of solutions of this problem, papers dealing with structure preservation almost do not exist. A novel optimization based approach that preserves the symmetric tridiagonal structures of the stiffness and damping matrices is proposed in this paper. An analytical expression for the global minimum solution of the associated optimization problem along with the results of numerical experiments obtained by both the analytical expressions and by an appropriate numerical optimization algorithm are presented. The results of numerical experiments support the validity of the proposed method.

Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Venkatachari, Balaji; Cheng, Gary C.

2015-01-01

Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the isotropic turbulent flow decay, at a relatively high turbulent Mach number, show a nicely behaved spectral decay rate for medium to high wave numbers. The high-order CESE schemes offer very robust solutions even with the presence of strong shocks or widespread shocklets. The explicit formulation in conjunction with a close to unity theoretical upper Courant number bound has the potential to offer an efficient numerical framework for general compressible turbulent flow simulations with unstructured meshes.

Transient well flow in leaky multiple-aquifer systems

NASA Astrophysics Data System (ADS)

Hemker, C. J.

1985-10-01

A previously developed eigenvalue analysis approach to groundwater flow in leaky multiple aquifers is used to derive exact solutions for transient well flow problems in leaky and confined systems comprising any number of aquifers. Equations are presented for the drawdown distribution in systems of infinite extent, caused by wells penetrating one or more of the aquifers completely and discharging each layer at a constant rate. Since the solution obtained may be regarded as a combined analytical-numerical technique, a type of one-dimensional modelling can be applied to find approximate solutions for several complicating conditions. Numerical evaluations are presented as time-drawdown curves and include effects of storage in the aquitard, unconfined conditions, partially penetrating wells and stratified aquifers. The outcome of calculations for relatively simple systems compares very well with published corresponding results. The proposed multilayer solution can be a valuable tool in aquifer test evaluation, as it provides the analytical expression required to enable the application of existing computer methods to the determination of aquifer characteristics.

Hydromagnetic flow of a Cu-water nanofluid past a moving wedge with viscous dissipation

NASA Astrophysics Data System (ADS)

M. Salem, A.; Galal, Ismail; Rania, Fathy

2014-04-01

A numerical study is performed to investigate the flow and heat transfer at the surface of a permeable wedge immersed in a copper (Cu)-water-based nanofluid in the presence of magnetic field and viscous dissipation using a nanofluid model proposed by Tiwari and Das (Tiwari I K and Das M K 2007 Int. J. Heat Mass Transfer 50 2002). A similarity solution for the transformed governing equation is obtained, and those equations are solved by employing a numerical shooting technique with a fourth-order Runge-Kutta integration scheme. A comparison with previously published work is carried out and shows that they are in good agreement with each other. The effects of velocity ratio parameter λ, solid volume fraction φ, magnetic field M, viscous dissipation Ec, and suction parameter Fw on the fluid flow and heat transfer characteristics are discussed. The unique and dual solutions for self-similar equations of the flow and heat transfer are analyzed numerically. Moreover, the range of the velocity ratio parameter for which the solution exists increases in the presence of magnetic field and suction parameter.

Modelling groundwater fractal flow with fractional differentiation via Mittag-Leffler law

NASA Astrophysics Data System (ADS)

Ahokposi, D. P.; Atangana, Abdon; Vermeulen, D. P.

2017-04-01

Modelling the flow of groundwater within a network of fractures is perhaps one of the most difficult exercises within the field of geohydrology. This physical problem has attracted the attention of several scientists across the globe. Already two different types of differentiations have been used to attempt modelling this problem including the classical and the fractional differentiation. In this paper, we employed the most recent concept of differentiation based on the non-local and non-singular kernel called the generalized Mittag-Leffler function, to reshape the model of groundwater fractal flow. We presented the existence of positive solution of the new model. Using the fixed-point approach, we established the uniqueness of the positive solution. We solve the new model with three different numerical schemes including implicit, explicit and Crank-Nicholson numerical methods. Experimental data collected from four constant discharge tests conducted in a typical fractured crystalline rock aquifer of the Northern Limb (Bushveld Complex) in the Limpopo Province (South Africa) are compared with the numerical solutions. It is worth noting that the four boreholes (BPAC1, BPAC2, BPAC3, and BPAC4) are located on Faults.

Almost periodic cellular neural networks with neutral-type proportional delays

NASA Astrophysics Data System (ADS)

Xiao, Songlin

2018-03-01

This paper presents a new result on the existence, uniqueness and generalised exponential stability of almost periodic solutions for cellular neural networks with neutral-type proportional delays and D operator. Based on some novel differential inequality techniques, a testable condition is derived to ensure that all the state trajectories of the system converge to an almost periodic solution with a positive exponential convergence rate. The effectiveness of the obtained result is illustrated by a numerical example.

Strongly nonlinear waves in locally resonant granular chains

DOE PAGES

Liu, Lifeng; James, Guillaume; Kevrekidis, Panayotis; ...

2016-09-23

In this paper, we explore a recently proposed locally resonant granular system bearing harmonic internal resonators in a chain of beads interacting via Hertzian elastic contacts. In this system, we propose the existence of two types of configurations: (a) small-amplitude periodic traveling waves and (b) dark-breather solutions, i.e. exponentially localized, time-periodic states mounted on top of a non-vanishing background. A remarkable feature distinguishing our results from other settings where dark breathers are observed is the complete absence of precompression in the system, i.e. the absence of a linear spectral band. We also identify conditions under which the system admits long-livedmore » bright breather solutions. Our results are obtained by means of an asymptotic reduction to a suitably modified version of the so-called discrete p-Schrödinger (DpS) equation, which is established as controllably approximating the solutions of the original system for large but finite times (under suitable assumptions on the solution amplitude and the resonator mass). The findings are also corroborated by detailed numerical computations. Long-lived bright breathers are proved to exist over long but finite times, after which numerical simulations indicate that the breathers disintegrate. Finally, in line with these results, we prove that the only exact time-periodic bright breathers consist of trivial linear oscillations, without contact interactions between discrete elements.« less

Analysis of user equilibrium for staggered shifts in a single-entry traffic corridor with no late arrivals

NASA Astrophysics Data System (ADS)

Li, Chuan-Yao; Huang, Hai-Jun; Tang, Tie-Qiao

2017-05-01

In this paper, we investigate the effects of staggered shifts on the user equilibrium (UE) state in a single-entry traffic corridor with no late arrivals from the analytical and numerical perspective. The LWR (Lighthill-Whitham-Richards) model and the Greenshields' velocity-density function are used to describe the dynamic properties of traffic flow. Propositions for the properties of flow patterns in UE, and the quasi-analytic solutions for three possible situations in UE are deduced. Numerical tests are carried out to testify the analytical results, where the three-dimensional evolution diagram of traffic flow illustrates that shock and rarefaction wave exist in UE and the space-time diagram indicates that UE solutions satisfy the propagation properties of traffic flow. In addition, the cost curves show that the UE solutions satisfy the UE trip-timing condition.

Dissipative discrete breathers: periodic, quasiperiodic, chaotic, and mobile.

PubMed

Martínez, P J; Meister, M; Floría, L M; Falo, F

2003-06-01

The properties of discrete breathers in dissipative one-dimensional lattices of nonlinear oscillators subject to periodic driving forces are reviewed. We focus on oscillobreathers in the Frenkel-Kontorova chain and rotobreathers in a ladder of Josephson junctions. Both types of exponentially localized solutions are easily obtained numerically using adiabatic continuation from the anticontinuous limit. Linear stability (Floquet) analysis allows the characterization of different types of bifurcations experienced by periodic discrete breathers. Some of these bifurcations produce nonperiodic localized solutions, namely, quasiperiodic and chaotic discrete breathers, which are generally impossible as exact solutions in Hamiltonian systems. Within a certain range of parameters, propagating breathers occur as attractors of the dissipative dynamics. General features of these excitations are discussed and the Peierls-Nabarro barrier is addressed. Numerical scattering experiments with mobile breathers reveal the existence of two-breather bound states and allow a first glimpse at the intricate phenomenology of these special multibreather configurations. (c) 2003 American Institute of Physics.

Boundary-layer effects in composite laminates. I - Free-edge stress singularities. II - Free-edge stress solutions and basic characteristics

NASA Technical Reports Server (NTRS)

Wang, S. S.; Choi, I.

1982-01-01

The fundamental nature of the boundary-layer effect in fiber-reinforced composite laminates is formulated in terms of the theory of anisotropic elasticity. The basic structure of the boundary-layer field solution is obtained by using Lekhnitskii's stress potentials (1963). The boundary-layer stress field is found to be singular at composite laminate edges, and the exact order or strength of the boundary layer stress singularity is determined using an eigenfunction expansion method. A complete solution to the boundary-layer problem is then derived, and the convergence and accuracy of the solution are analyzed, comparing results with existing approximate numerical solutions. The solution method is demonstrated for a symmetric graphite-epoxy composite.

Particlelike solutions of the Einstein-Dirac equations

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

1999-05-01

The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of solitonlike solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well behaved even for strong coupling.

A Numerical Investigation of the Burnett Equations Based on the Second Law

NASA Technical Reports Server (NTRS)

Comeaux, Keith A.; Chapman, Dean R.; MacCormack, Robert W.; Edwards, Thomas A. (Technical Monitor)

1995-01-01

The Burnett equations have been shown to potentially violate the second law of thermodynamics. The objective of this investigation is to correlate the numerical problems experienced by the Burnett equations to the negative production of entropy. The equations have had a long history of numerical instability to small wavelength disturbances. Recently, Zhong corrected the instability problem and made solutions attainable for one dimensional shock waves and hypersonic blunt bodies. Difficulties still exist when attempting to solve hypersonic flat plate boundary layers and blunt body wake flows, however. Numerical experiments will include one-dimensional shock waves, quasi-one dimensional nozzles, and expanding Prandlt-Meyer flows and specifically examine the entropy production for these cases.

A Study on Water Surface Profiles of Rivers with Constriction

NASA Astrophysics Data System (ADS)

Qian, Chaochao; Yamada, Tadashi

2013-04-01

Water surface profile of rivers with constrictions is precious in both classic hydraulics and river management practice. This study was conducted to clarify the essences of the water surface profiles. 3 cases of experiments and 1D numerical calculations with different discharges were made in the study and analysis solutions of the non-linear basic equation of surface profile in varied flow without considering friction were derived. The manning's number was kept in the same in each case by using crosspiece roughness. We found a new type of water surface profile of varied flow from the results of 1D numerical calculation and that of experiments and named it as Mc curve because of its mild condition with constriction segment. This kind of curves appears as a nature phenomenon ubiquitously. The process of water surface forming is dynamic and bore occurs at the upper side of constriction during increasing discharge before the surface profile formed. As a theoretical work, 3 analysis solutions were derived included 2 physical-meaning solutions in the study by using Man-Machine system. One of the derived physical-meaning solutions was confirmed that it is validity by comparing to the results of 1D numerical calculation and that of experiments. The solution represents a flow profile from under critical condition at the upper side to super critical condition at the down side of constriction segment. The other derived physical-meaning solution represents a flow profile from super critical condition at the upper side to under critical condition at the down side of constriction segment. These two kinds of flow profiles exist in the nature but no theoretical solution can express the phenomenon. We find the depth distribution only concerned with unit width discharge distribution and critical depth under a constant discharge from the derived solutions. Therefor, the profile can be gained simply and precisely by using the theoretical solutions instead of numerical calculation even in practice.

Quantification of mixing in vesicle suspensions using numerical simulations in two dimensions.

PubMed

Kabacaoğlu, G; Quaife, B; Biros, G

2017-02-01

We study mixing in Stokesian vesicle suspensions in two dimensions on a cylindrical Couette apparatus using numerical simulations. The vesicle flow simulation is done using a boundary integral method, and the advection-diffusion equation for the mixing of the solute is solved using a pseudo-spectral scheme. We study the effect of the area fraction, the viscosity contrast between the inside (the vesicles) and the outside (the bulk) fluid, the initial condition of the solute, and the mixing metric. We compare mixing in the suspension with mixing in the Couette apparatus without vesicles. On the one hand, the presence of vesicles in most cases slightly suppresses mixing. This is because the solute can be only diffused across the vesicle interface and not advected. On the other hand, there exist spatial distributions of the solute for which the unperturbed Couette flow completely fails to mix whereas the presence of vesicles enables mixing. We derive a simple condition that relates the velocity and solute and can be used to characterize the cases in which the presence of vesicles promotes mixing.

Quantification of mixing in vesicle suspensions using numerical simulations in two dimensions

PubMed Central

Quaife, B.; Biros, G.

2017-01-01

We study mixing in Stokesian vesicle suspensions in two dimensions on a cylindrical Couette apparatus using numerical simulations. The vesicle flow simulation is done using a boundary integral method, and the advection-diffusion equation for the mixing of the solute is solved using a pseudo-spectral scheme. We study the effect of the area fraction, the viscosity contrast between the inside (the vesicles) and the outside (the bulk) fluid, the initial condition of the solute, and the mixing metric. We compare mixing in the suspension with mixing in the Couette apparatus without vesicles. On the one hand, the presence of vesicles in most cases slightly suppresses mixing. This is because the solute can be only diffused across the vesicle interface and not advected. On the other hand, there exist spatial distributions of the solute for which the unperturbed Couette flow completely fails to mix whereas the presence of vesicles enables mixing. We derive a simple condition that relates the velocity and solute and can be used to characterize the cases in which the presence of vesicles promotes mixing. PMID:28344432

Bifurcation structure of a wind-driven shallow water model with layer-outcropping

NASA Astrophysics Data System (ADS)

Primeau, François W.; Newman, David

The steady state bifurcation structure of the double-gyre wind-driven ocean circulation is examined in a shallow water model where the upper layer is allowed to outcrop at the sea surface. In addition to the classical jet-up and jet-down multiple equilibria, we find a new regime in which one of the equilibrium solutions has a large outcropping region in the subpolar gyre. Time dependent simulations show that the outcropping solution equilibrates to a stable periodic orbit with a period of 8 months. Co-existing with the periodic solution is a stable steady state solution without outcropping. A numerical scheme that has the unique advantage of being differentiable while still allowing layers to outcrop at the sea surface is used for the analysis. In contrast, standard schemes for solving layered models with outcropping are non-differentiable and have an ill-defined Jacobian making them unsuitable for solution using Newton's method. As such, our new scheme expands the applicability of numerical bifurcation techniques to an important class of ocean models whose bifurcation structure had hitherto remained unexplored.

Numerical continuation and bifurcation analysis in aircraft design: an industrial perspective.

PubMed

Sharma, Sanjiv; Coetzee, Etienne B; Lowenberg, Mark H; Neild, Simon A; Krauskopf, Bernd

2015-09-28

Bifurcation analysis is a powerful method for studying the steady-state nonlinear dynamics of systems. Software tools exist for the numerical continuation of steady-state solutions as parameters of the system are varied. These tools make it possible to generate 'maps of solutions' in an efficient way that provide valuable insight into the overall dynamic behaviour of a system and potentially to influence the design process. While this approach has been employed in the military aircraft control community to understand the effectiveness of controllers, the use of bifurcation analysis in the wider aircraft industry is yet limited. This paper reports progress on how bifurcation analysis can play a role as part of the design process for passenger aircraft. © 2015 The Author(s).

Wave propagation in predator-prey systems

NASA Astrophysics Data System (ADS)

Fu, Sheng-Chen; Tsai, Je-Chiang

2015-12-01

In this paper, we study a class of predator-prey systems of reaction-diffusion type. Specifically, we are interested in the dynamical behaviour for the solution with the initial distribution where the prey species is at the level of the carrying capacity, and the density of the predator species has compact support, or exponentially small tails near x=+/- ∞ . Numerical evidence suggests that this will lead to the formation of a pair of diverging waves propagating outwards from the initial zone. Motivated by this phenomenon, we establish the existence of a family of travelling waves with the minimum speed. Unlike the previous studies, we do not use the shooting argument to show this. Instead, we apply an iteration process based on Berestycki et al 2005 (Math Comput. Modelling 50 1385-93) to construct a set of super/sub-solutions. Since the underlying system does not enjoy the comparison principle, such a set of super/sub-solutions is not based on travelling waves, and in fact the super/sub-solutions depend on each other. With the aid of the set of super/sub-solutions, we can construct the solution of the truncated problem on the finite interval, which, via the limiting argument, can in turn generate the wave solution. There are several advantages to this approach. First, it can remove the technical assumptions on the diffusivities of the species in the existing literature. Second, this approach is of PDE type, and hence it can shed some light on the spreading phenomenon indicated by numerical simulation. In fact, we can compute the spreading speed of the predator species for a class of biologically acceptable initial distributions. Third, this approach might be applied to the study of waves in non-cooperative systems (i.e. a system without a comparison principle).

The Equilibrium State of Colliding Electron Beams

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

Warnock, R

2003-12-12

We study a nonlinear integral equation that is a necessary condition on the equilibrium phase space distribution function of stored, colliding electron beams. It is analogous to the Haissinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. The equation is analyzed for the case of the Chao-Ruth model of the beam-beam interaction in one degree of freedom, a so-called strong-strong model with nonlinear beam-beam force. We prove existence of a unique solution, for sufficiently small beam current, by an application of the implicit function theorem. We have not yet proved that this solution is positive, asmore » would be required to establish existence of an equilibrium. There is, however, numerical evidence of a positive solution. We expect that our analysis can be extended to more realistic models.« less

Simultaneous computation of jet turbulence and noise

NASA Technical Reports Server (NTRS)

Berman, C. H.; Ramos, J. I.

1989-01-01

The existing flow computation methods, wave computation techniques, and theories based on noise source models are reviewed in order to assess the capabilities of numerical techniques to compute jet turbulence noise and understand the physical mechanisms governing it over a range of subsonic and supersonic nozzle exit conditions. In particular, attention is given to (1) methods for extrapolating near field information, obtained from flow computations, to the acoustic far field and (2) the numerical solution of the time-dependent Lilley equation.

Transient three-dimensional thermal-hydraulic analysis of nuclear reactor fuel rod arrays: general equations and numerical scheme

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

Wnek, W.J.; Ramshaw, J.D.; Trapp, J.A.

1975-11-01

A mathematical model and a numerical solution scheme for thermal- hydraulic analysis of fuel rod arrays are given. The model alleviates the two major deficiencies associated with existing rod array analysis models, that of a correct transverse momentum equation and the capability of handling reversing and circulatory flows. Possible applications of the model include steady state and transient subchannel calculations as well as analysis of flows in heat exchangers, other engineering equipment, and porous media. (auth)

The effect of intra-wellbore head losses in a vertical well

NASA Astrophysics Data System (ADS)

Wang, Quanrong; Zhan, Hongbin

2017-05-01

Flow to a partially penetrating vertical well is made more complex by intra-wellbore losses. These are caused not only by the frictional effect, but also by the kinematic effect, which consists of the accelerational and fluid inflow effects inside a wellbore. Existing models of flow to a partially penetrating vertical well assume either a uniform-flux boundary condition (UFBC) or a uniform-head boundary condition (UHBC) for treating the flow into the wellbore. Neither approach considers intra-wellbore losses. In this study a new general solution, named the mixed-type boundary condition (MTBC) solution, is introduced to include intra-wellbore losses. It is developed from the existing solutions using a hybrid analytical-numerical method. The MTBC solution is capable of modeling various types of aquifer tests (constant-head tests, constant-rate tests, and slug tests) for partially or fully penetrating vertical wells in confined aquifers. Results show that intra-wellbore losses (both frictional and kinematic) can be significant in the early pumping stage. At later pumping times the UHBC solution is adequate because the difference between the MTBC and UHBC solutions becomes negligible.

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems. Task 4: Advanced fan section aerodynamic analysis

NASA Technical Reports Server (NTRS)

Crook, Andrew J.; Delaney, Robert A.

1992-01-01

The purpose of this study is the development of a three-dimensional Euler/Navier-Stokes flow analysis for fan section/engine geometries containing multiple blade rows and multiple spanwise flow splitters. An existing procedure developed by Dr. J. J. Adamczyk and associates and the NASA Lewis Research Center was modified to accept multiple spanwise splitter geometries and simulate engine core conditions. The procedure was also modified to allow coarse parallelization of the solution algorithm. This document is a final report outlining the development and techniques used in the procedure. The numerical solution is based upon a finite volume technique with a four stage Runge-Kutta time marching procedure. Numerical dissipation is used to gain solution stability but is reduced in viscous dominated flow regions. Local time stepping and implicit residual smoothing are used to increase the rate of convergence. Multiple blade row solutions are based upon the average-passage system of equations. The numerical solutions are performed on an H-type grid system, with meshes being generated by the system (TIGG3D) developed earlier under this contract. The grid generation scheme meets the average-passage requirement of maintaining a common axisymmetric mesh for each blade row grid. The analysis was run on several geometry configurations ranging from one to five blade rows and from one to four radial flow splitters. Pure internal flow solutions were obtained as well as solutions with flow about the cowl/nacelle and various engine core flow conditions. The efficiency of the solution procedure was shown to be the same as the original analysis.

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

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

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

2016-07-15

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

Black holes in higher derivative gravity.

PubMed

Lü, H; Perkins, A; Pope, C N; Stelle, K S

2015-05-01

Extensions of Einstein gravity with higher-order derivative terms arise in string theory and other effective theories, as well as being of interest in their own right. In this Letter we study static black-hole solutions in the example of Einstein gravity with additional quadratic curvature terms. A Lichnerowicz-type theorem simplifies the analysis by establishing that they must have vanishing Ricci scalar curvature. By numerical methods we then demonstrate the existence of further black-hole solutions over and above the Schwarzschild solution. We discuss some of their thermodynamic properties, and show that they obey the first law of thermodynamics.

Heat Source/Sink in a Magneto-Hydrodynamic Non-Newtonian Fluid Flow in a Porous Medium: Dual Solutions.

PubMed

Hayat, Tasawar; Awais, Muhammad; Imtiaz, Amna

2016-01-01

This communication deals with the properties of heat source/sink in a magneto-hydrodynamic flow of a non-Newtonian fluid immersed in a porous medium. Shrinking phenomenon along with the permeability of the wall is considered. Mathematical modelling is performed to convert the considered physical process into set of coupled nonlinear mathematical equations. Suitable transformations are invoked to convert the set of partial differential equations into nonlinear ordinary differential equations which are tackled numerically for the solution computations. It is noted that dual solutions for various physical parameters exist which are analyzed in detail.

Orientation of doubly rotated quartz plates.

PubMed

Sherman, J R

1989-01-01

A derivation from classical spherical trigonometry of equations to compute the orientation of doubly-rotated quartz blanks from Bragg X-ray data is discussed. These are usually derived by compact and efficient vector methods, which are reviewed briefly. They are solved by generating a quadratic equation with numerical coefficients. Two methods exist for performing the computation from measurements against two planes: a direct solution by a quadratic equation and a process of convergent iteration. Both have a spurious solution. Measurement against three lattice planes yields a set of three linear equations the solution of which is an unambiguous result.

Lax-Wendroff and TVD finite volume methods for unidimensional thermomechanical numerical simulations of impacts on elastic-plastic solids

NASA Astrophysics Data System (ADS)

Heuzé, Thomas

2017-10-01

We present in this work two finite volume methods for the simulation of unidimensional impact problems, both for bars and plane waves, on elastic-plastic solid media within the small strain framework. First, an extension of Lax-Wendroff to elastic-plastic constitutive models with linear and nonlinear hardenings is presented. Second, a high order TVD method based on flux-difference splitting [1] and Superbee flux limiter [2] is coupled with an approximate elastic-plastic Riemann solver for nonlinear hardenings, and follows that of Fogarty [3] for linear ones. Thermomechanical coupling is accounted for through dissipation heating and thermal softening, and adiabatic conditions are assumed. This paper essentially focuses on one-dimensional problems since analytical solutions exist or can easily be developed. Accordingly, these two numerical methods are compared to analytical solutions and to the explicit finite element method on test cases involving discontinuous and continuous solutions. This allows to study in more details their respective performance during the loading, unloading and reloading stages. Particular emphasis is also paid to the accuracy of the computed plastic strains, some differences being found according to the numerical method used. Lax-Wendoff two-dimensional discretization of a one-dimensional problem is also appended at the end to demonstrate the extensibility of such numerical scheme to multidimensional problems.

Multi-hump bright solitons in a Schrödinger-mKdV system

NASA Astrophysics Data System (ADS)

Cisneros-Ake, Luis A.; Parra Prado, Hugo; López Villatoro, Diego Joselito; Carretero-González, R.

2018-03-01

We consider the problem of energy transport in a Davydov model along an anharmonic crystal medium obeying quartic longitudinal interactions corresponding to rigid interacting particles. The Zabusky and Kruskal unidirectional continuum limit of the original discrete equations reduces, in the long wave approximation, to a coupled system between the linear Schrödinger (LS) equation and the modified Korteweg-de Vries (mKdV) equation. Single- and two-hump bright soliton solutions for this LS-mKdV system are predicted to exist by variational means and numerically confirmed. The one-hump bright solitons are found to be the anharmonic supersonic analogue of the Davydov's solitons while the two-hump (in both components) bright solitons are found to be a novel type of soliton consisting of a two-soliton solution of mKdV trapped by the wave function associated to the LS equation. This two-hump soliton solution, as a two component solution, represents a new class of polaron solution to be contrasted with the two-soliton interaction phenomena from soliton theory, as revealed by a variational approach and direct numerical results for the two-soliton solution.

Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators

NASA Astrophysics Data System (ADS)

Koca, Ilknur

2018-03-01

The model of Ebola spread within a targeted population is extended to the concept of fractional differentiation and integration with non-local and non-singular fading memory introduced by Atangana and Baleanu. It is expected that the proposed model will show better approximation than the models established before. The existence and uniqueness of solutions for the spread of Ebola disease model is given via the Picard-Lindelof method. Finally, numerical solutions for the model are given by using different parameter values.

Dynamics of the stochastic low concentration trimolecular oscillatory chemical system with jumps

NASA Astrophysics Data System (ADS)

Wei, Yongchang; Yang, Qigui

2018-06-01

This paper is devoted to discern long time dynamics through the stochastic low concentration trimolecular oscillatory chemical system with jumps. By Lyapunov technique, this system is proved to have a unique global positive solution, and the asymptotic stability in mean square of such model is further established. Moreover, the existence of random attractor and Lyapunov exponents are obtained for the stochastic homeomorphism flow generated by the corresponding global positive solution. And some numerical simulations are given to illustrate the presented results.

Recent developments in chaotic dynamics

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

Ott, E.

1994-02-01

Before the relatively recent wide acceptance of the existence of chaotic dynamics, many physicists and engineers were under the impression that simple systems could necessarily only display simple solutions. This feeling had been unintentionally reinforced by conventional college courses which emphasize linear dynamics (partly because that is the only case with nice general solutions). More recently, physical experiments and numerical examples have abundantly demonstrated how wrong this feeling is. A brief review of chaotic dynamics is presented. Topics discussed include basic concepts, recent developments, and applications.

Nonideal isentropic gas flow through converging-diverging nozzles

NASA Technical Reports Server (NTRS)

Bober, W.; Chow, W. L.

1990-01-01

A method for treating nonideal gas flows through converging-diverging nozzles is described. The method incorporates the Redlich-Kwong equation of state. The Runge-Kutta method is used to obtain a solution. Numerical results were obtained for methane gas. Typical plots of pressure, temperature, and area ratios as functions of Mach number are given. From the plots, it can be seen that there exists a range of reservoir conditions that require the gas to be treated as nonideal if an accurate solution is to be obtained.

Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem.

PubMed

Altürk, Ahmet

2016-01-01

Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some existing techniques.

Elementary wave interactions in blood flow through artery

NASA Astrophysics Data System (ADS)

Raja Sekhar, T.; Minhajul

2017-10-01

In this paper, we consider the Riemann problem and interaction of elementary waves for the quasilinear hyperbolic system of conservation laws that arises in blood flow through arteries. We study the properties of solution involving shocks and rarefaction waves and establish the existence and uniqueness conditions. We show that the Riemann problem is solvable for arbitrary initial data under certain condition and construct the condition for no-feasible solution. Finally, we present numerical examples with different initial data and discuss all possible interactions of elementary waves.

Iterative discrete ordinates solution of the equation for surface-reflected radiance

NASA Astrophysics Data System (ADS)

Radkevich, Alexander

2017-11-01

This paper presents a new method of numerical solution of the integral equation for the radiance reflected from an anisotropic surface. The equation relates the radiance at the surface level with BRDF and solutions of the standard radiative transfer problems for a slab with no reflection on its surfaces. It is also shown that the kernel of the equation satisfies the condition of the existence of a unique solution and the convergence of the successive approximations to that solution. The developed method features two basic steps: discretization on a 2D quadrature, and solving the resulting system of algebraic equations with successive over-relaxation method based on the Gauss-Seidel iterative process. Presented numerical examples show good coincidence between the surface-reflected radiance obtained with DISORT and the proposed method. Analysis of contributions of the direct and diffuse (but not yet reflected) parts of the downward radiance to the total solution is performed. Together, they represent a very good initial guess for the iterative process. This fact ensures fast convergence. The numerical evidence is given that the fastest convergence occurs with the relaxation parameter of 1 (no relaxation). An integral equation for BRDF is derived as inversion of the original equation. The potential of this new equation for BRDF retrievals is analyzed. The approach is found not viable as the BRDF equation appears to be an ill-posed problem, and it requires knowledge the surface-reflected radiance on the entire domain of both Sun and viewing zenith angles.

Synchrony, waves and ripple in spatially coupled Kuramoto oscillators with Mexican hat connectivity.

PubMed

Heitmann, Stewart; Ermentrout, G Bard

2015-06-01

Spatiotemporal waves of synchronized activity are known to arise in oscillatory neural networks with lateral inhibitory coupling. How such patterns respond to dynamic changes in coupling strength is largely unexplored. The present study uses analysis and simulation to investigate the evolution of wave patterns when the strength of lateral inhibition is varied dynamically. Neural synchronization was modeled by a spatial ring of Kuramoto oscillators with Mexican hat lateral coupling. Broad bands of coexisting stable wave solutions were observed at all levels of inhibition. The stability of these waves was formally analyzed in both the infinite ring and the finite ring. The broad range of multi-stability predicted hysteresis in transitions between neighboring wave solutions when inhibition is slowly varied. Numerical simulation confirmed the predicted transitions when inhibition was ramped down from a high initial value. However, non-wave solutions emerged from the uniform solution when inhibition was ramped upward from zero. These solutions correspond to spatially periodic deviations of phase that we call ripple states. Numerical continuation showed that stable ripple states emerge from synchrony via a supercritical pitchfork bifurcation. The normal form of this bifurcation was derived analytically, and its predictions compared against the numerical results. Ripple states were also found to bifurcate from wave solutions, but these were locally unstable. Simulation also confirmed the existence of hysteresis and ripple states in two spatial dimensions. Our findings show that spatial synchronization patterns can remain structurally stable despite substantial changes in network connectivity.

Shock formation in the dispersionless Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Grava, T.; Klein, C.; Eggers, J.

2016-04-01

The dispersionless Kadomtsev-Petviashvili (dKP) equation {{≤ft({{u}t}+u{{u}x}\\right)}x}={{u}yy} is one of the simplest nonlinear wave equations describing two-dimensional shocks. To solve the dKP equation numerically we use a coordinate transformation inspired by the method of characteristics for the one-dimensional Hopf equation {{u}t}+u{{u}x}=0 . We show numerically that the solutions to the transformed equation stays regular for longer times than the solution of the dKP equation. This permits us to extend the dKP solution as the graph of a multivalued function beyond the critical time when the gradients blow up. This overturned solution is multivalued in a lip shape region in the (x, y) plane, where the solution of the dKP equation exists in a weak sense only, and a shock front develops. A local expansion reveals the universal scaling structure of the shock, which after a suitable change of coordinates corresponds to a generic cusp catastrophe. We provide a heuristic derivation of the shock front position near the critical point for the solution of the dKP equation, and study the solution of the dKP equation when a small amount of dissipation is added. Using multiple-scale analysis, we show that in the limit of small dissipation and near the critical point of the dKP solution, the solution of the dissipative dKP equation converges to a Pearcey integral. We test and illustrate our results by detailed comparisons with numerical simulations of both the regularized equation, the dKP equation, and the asymptotic description given in terms of the Pearcey integral.

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.

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

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

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

Front and pulse solutions for the complex Ginzburg-Landau equation with higher-order terms.

PubMed

Tian, Huiping; Li, Zhonghao; Tian, Jinping; Zhou, Guosheng

2002-12-01

We investigate one-dimensional complex Ginzburg-Landau equation with higher-order terms and discuss their influences on the multiplicity of solutions. An exact analytic front solution is presented. By stability analysis for the original partial differential equation, we derive its necessary stability condition for amplitude perturbations. This condition together with the exact front solution determine the region of parameter space where the uniformly translating front solution can exist. In addition, stable pulses, chaotic pulses, and attenuation pulses appear generally if the parameters are out of the range. Finally, applying these analysis into the optical transmission system numerically we find that the stable transmission of optical pulses can be achieved if the parameters are appropriately chosen.

Dual Solutions for Nonlinear Flow Using Lie Group Analysis

PubMed Central

Awais, Muhammad; Hayat, Tasawar; Irum, Sania; Saleem, Salman

2015-01-01

`The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD) flow of an upper-convected Maxwell (UCM) fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and computed the absolute invariants explicitly. An efficient numerical technique namely the shooting method has been employed for the constructions of solutions. Dual solutions are computed for velocity profile of an upper-convected Maxwell (UCM) fluid flow. Plots reflecting the impact of dual solutions for the variations of Deborah number, Hartman number, wall mass transfer are presented and analyzed. Streamlines are also plotted for the wall mass transfer effects when suction and blowing situations are considered. PMID:26575996

Singular eigenstates in the even(odd) length Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Ranjan Giri, Pulak; Deguchi, Tetsuo

2015-05-01

We study the implications of the regularization for the singular solutions on the even(odd) length spin-1/2 XXX chains in some specific down-spin sectors. In particular, the analytic expressions of the Bethe eigenstates for three down-spin sector have been obtained along with their numerical forms in some fixed length chains. For an even-length chain if the singular solutions \\{{{λ }α }\\} are invariant under the sign changes of their rapidities \\{{{λ }α }\\}=\\{-{{λ }α }\\}, then the Bethe ansatz equations are reduced to a system of (M-2)/2((M-3)/2) equations in an even (odd) down-spin sector. For an odd N length chain in the three down-spin sector, it has been analytically shown that there exist singular solutions in any finite length of the spin chain of the form N=3(2k+1) with k=1,2,3,\\cdots . It is also shown that there exist no singular solutions in the four down-spin sector for some odd-length spin-1/2 XXX chains.

Terahertz response of dipolar impurities in polar liquids: On anomalous dielectric absorption of protein solutions

NASA Astrophysics Data System (ADS)

Matyushov, Dmitry V.

2010-02-01

A theory of radiation absorption by dielectric mixtures is presented. The coarse-grained formulation is based on the wave-vector-dependent correlation functions of molecular dipoles of the host polar liquid and a density structure factor of the solutes. A nonlinear dependence of the dielectric absorption coefficient on the solute concentration is predicted and originates from the mutual polarization of the liquid surrounding the solutes by the collective field of the solute dipoles aligned along the radiation field. The theory is applied to terahertz absorption of hydrated saccharides and proteins. While the theory gives an excellent account of the observations for saccharides, without additional assumptions and fitting parameters, experimental absorption coefficient of protein solutions significantly exceeds theoretical calculations with dipole moment of the bare protein assigned to the solute and shows a peak against the protein concentration. A substantial polarization of protein’s hydration shell, resulting in a net dipole moment, is required to explain the disagreement between theory and experiment. When the correlation function of the total dipole moment of the protein with its hydration shell from numerical simulations is used in the analytical model, an absorption peak, qualitatively similar to that seen in experiment, is obtained. The existence and position of the peak are sensitive to the specifics of the protein-protein interactions. Numerical testing of the theory requires the combination of dielectric and small-angle scattering measurements. The calculations confirm that “elastic ferroelectric bag” of water shells observed in previous numerical simulations is required to explain terahertz dielectric measurements.

Nonlocal dark solitons under competing cubic-quintic nonlinearities.

PubMed

Chen, L; Wang, Q; Shen, M; Zhao, H; Lin, Y-Y; Jeng, C-C; Lee, R-K; Krolikowski, W

2013-01-01

We investigate properties of dark solitons under competing nonlocal cubic-local quintic nonlinearities. Analytical results, based on a variational approach and confirmed by direct numerical simulations, reveal the existence of a unique dark soliton solutions with their width being independent of the degree of nonlocality, due to the competing cubic-quintic nonlinearities.

A Mathematical Model of Anthrax Transmission in Animal Populations.

PubMed

Saad-Roy, C M; van den Driessche, P; Yakubu, Abdul-Aziz

2017-02-01

A general mathematical model of anthrax (caused by Bacillus anthracis) transmission is formulated that includes live animals, infected carcasses and spores in the environment. The basic reproduction number [Formula: see text] is calculated, and existence of a unique endemic equilibrium is established for [Formula: see text] above the threshold value 1. Using data from the literature, elasticity indices for [Formula: see text] and type reproduction numbers are computed to quantify anthrax control measures. Including only herbivorous animals, anthrax is eradicated if [Formula: see text]. For these animals, oscillatory solutions arising from Hopf bifurcations are numerically shown to exist for certain parameter values with [Formula: see text] and to have periodicity as observed from anthrax data. Including carnivores and assuming no disease-related death, anthrax again goes extinct below the threshold. Local stability of the endemic equilibrium is established above the threshold; thus, periodic solutions are not possible for these populations. It is shown numerically that oscillations in spore growth may drive oscillations in animal populations; however, the total number of infected animals remains about the same as with constant spore growth.

Recovery of time-dependent volatility in option pricing model

NASA Astrophysics Data System (ADS)

Deng, Zui-Cha; Hon, Y. C.; Isakov, V.

2016-11-01

In this paper we investigate an inverse problem of determining the time-dependent volatility from observed market prices of options with different strikes. Due to the non linearity and sparsity of observations, an analytical solution to the problem is generally not available. Numerical approximation is also difficult to obtain using most of the existing numerical algorithms. Based on our recent theoretical results, we apply the linearisation technique to convert the problem into an inverse source problem from which recovery of the unknown volatility function can be achieved. Two kinds of strategies, namely, the integral equation method and the Landweber iterations, are adopted to obtain the stable numerical solution to the inverse problem. Both theoretical analysis and numerical examples confirm that the proposed approaches are effective. The work described in this paper was partially supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region (Project No. CityU 101112) and grants from the NNSF of China (Nos. 11261029, 11461039), and NSF grants DMS 10-08902 and 15-14886 and by Emylou Keith and Betty Dutcher Distinguished Professorship at the Wichita State University (USA).

Numerical equilibrium analysis for structured consumer resource models.

PubMed

de Roos, A M; Diekmann, O; Getto, P; Kirkilionis, M A

2010-02-01

In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries can be defined in the (two-parameter) plane. We numerically trace these implicitly defined curves using alternatingly tangent prediction and Newton correction. Evaluation of the maps defining the curves involves integration over individual size and individual survival probability (and their derivatives) as functions of individual age. Such ingredients are often defined as solutions of ODE, i.e., in general only implicitly. In our case, the right-hand sides of these ODE feature discontinuities that are caused by an abrupt change of behavior at the size where juveniles are assumed to turn adult. So, we combine the numerical solution of these ODE with curve tracing methods. We have implemented the algorithms for "Daphnia consuming algae" models in C-code. The results obtained by way of this implementation are shown in the form of graphs.

Travelling Wave Solutions in Multigroup Age-Structured Epidemic Models

NASA Astrophysics Data System (ADS)

Ducrot, Arnaut; Magal, Pierre; Ruan, Shigui

2010-01-01

Age-structured epidemic models have been used to describe either the age of individuals or the age of infection of certain diseases and to determine how these characteristics affect the outcomes and consequences of epidemiological processes. Most results on age-structured epidemic models focus on the existence, uniqueness, and convergence to disease equilibria of solutions. In this paper we investigate the existence of travelling wave solutions in a deterministic age-structured model describing the circulation of a disease within a population of multigroups. Individuals of each group are able to move with a random walk which is modelled by the classical Fickian diffusion and are classified into two subclasses, susceptible and infective. A susceptible individual in a given group can be crisscross infected by direct contact with infective individuals of possibly any group. This process of transmission can depend upon the age of the disease of infected individuals. The goal of this paper is to provide sufficient conditions that ensure the existence of travelling wave solutions for the age-structured epidemic model. The case of two population groups is numerically investigated which applies to the crisscross transmission of feline immunodeficiency virus (FIV) and some sexual transmission diseases.

On plane submerged laminar jets

NASA Astrophysics Data System (ADS)

Coenen, Wilfried; Sanchez, Antonio L.

2016-11-01

We address the laminar flow generated when a developed stream of liquid of kinematic viscosity ν flowing along channel of width 2 h discharges into an open space bounded by two symmetric plane walls departing from the channel rim with an angle α 1 . Attention is focused on values of the jet volume flux 2 Q such that the associated Reynolds number Re = Qh / ν is of order unity. The formulation requires specification of the boundary conditions far from the channel exit. If the flow is driven by the volume flux, then the far-field solution corresponds to Jeffery-Hamel self-similar flow. However, as noted by Fraenkel (1962), such solutions exist only for α <129o in a limited range of Reynolds numbers 0 <=Re <=Rec (α) (e.g. Rec = 1 . 43 for α = π / 2). It is reasoned that an alternative solution, driven by a fraction of the momentum flux of the feed stream, may also exist for all values of Re and α, including a near-centerline Bickley jet, a surrounding Taylor potential flow driven by the jet entrainment, and a Falkner-Skan near-wall boundary layer. Numerical integrations of the Navier-Stokes equations are used to ascertain the existence of these different solutions.

Quantifying errors in trace species transport modeling.

PubMed

Prather, Michael J; Zhu, Xin; Strahan, Susan E; Steenrod, Stephen D; Rodriguez, Jose M

2008-12-16

One expectation when computationally solving an Earth system model is that a correct answer exists, that with adequate physical approximations and numerical methods our solutions will converge to that single answer. With such hubris, we performed a controlled numerical test of the atmospheric transport of CO(2) using 2 models known for accurate transport of trace species. Resulting differences were unexpectedly large, indicating that in some cases, scientific conclusions may err because of lack of knowledge of the numerical errors in tracer transport models. By doubling the resolution, thereby reducing numerical error, both models show some convergence to the same answer. Now, under realistic conditions, we identify a practical approach for finding the correct answer and thus quantifying the advection error.

Global existence and energy decay rates for a Kirchhoff-type wave equation with nonlinear dissipation.

PubMed

Kim, Daewook; Kim, Dojin; Hong, Keum-Shik; Jung, Il Hyo

2014-01-01

The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku'' + M(|A (1/2) u|(2))Au + g(u') = 0 under suitable assumptions on K, A, M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations in order to verify the analytical results are given.

Analysis of Classes of Superlinear Semipositone Problems with Nonlinear Boundary Conditions

NASA Astrophysics Data System (ADS)

Morris, Quinn A.

We study positive radial solutions for classes of steady state reaction diffusion problems on the exterior of a ball with both Dirichlet and nonlinear boundary conditions. We consider p-Laplacian problems (p > 1) with reaction terms which are superlinear at infinity and semipositone. In the case p = 2, using variational methods, we establish the existence of a solution, and via detailed analysis of the Green's function, we prove the positivity of the solution. In the case p ≠ 2, we again use variational methods to establish the existence of a solution, but the positivity of the solution is achieved via sophisticated a priori estimates. In the case p ≠ 2, the Green's function analysis is no longer available. Our results significantly enhance the literature on superlinear semipositone problems. Finally, we provide algorithms for the numerical generation of exact bifurcation curves for one-dimensional problems. In the autonomous case, we extend and analyze a quadrature method, and using nonlinear solvers in Mathematica, generate bifurcation curves. In the nonautonomous case, we employ shooting methods in Mathematica to generate bifurcation curves.

Semianalytical solutions for transport in aquifer and fractured clay matrix system

NASA Astrophysics Data System (ADS)

Huang, Junqi; Goltz, Mark N.

2015-09-01

A three-dimensional mathematical model that describes transport of contaminant in a horizontal aquifer with simultaneous diffusion into a fractured clay formation is proposed. A group of semianalytical solutions is derived based on specific initial and boundary conditions as well as various source functions. The analytical model solutions are evaluated by numerical Laplace inverse transformation and analytical Fourier inverse transformation. The model solutions can be used to study the fate and transport in a three-dimensional spatial domain in which a nonaqueous phase liquid exists as a pool atop a fractured low-permeability clay layer. The nonaqueous phase liquid gradually dissolves into the groundwater flowing past the pool, while simultaneously diffusing into the fractured clay formation below the aquifer. Mass transfer of the contaminant into the clay formation is demonstrated to be significantly enhanced by the existence of the fractures, even though the volume of fractures is relatively small compared to the volume of the clay matrix. The model solution is a useful tool in assessing contaminant attenuation processes in a confined aquifer underlain by a fractured clay formation.

Trapped Modes in a Three-Layer Fluid

NASA Astrophysics Data System (ADS)

Saha, Sunanda; Bora, Swaroop Nandan

2018-03-01

In this work, trapped mode frequencies are computed for a submerged horizontal circular cylinder with the hydrodynamic set-up involving an infinite depth three-layer incompressible fluid with layer-wise different densities. The impermeable cylinder is fully immersed in either the bottom layer or the upper layer. The effect of surface tension at the surface of separation is neglected. In this set-up, there exist three wave numbers: the lowest one on the free surface and the other two on the internal interfaces. For each wave number, there exist two modes for which trapped waves exist. The existence of these trapped modes is shown by numerical evidence. We investigate the variation of these trapped modes subject to change in the depth of the middle layer as well as the submergence depth. We show numerically that two-layer and single-layer results cannot be recovered in the double and single limiting cases of the density ratios tending to unity. The existence of trapped modes shows that in general, a radiation condition for the waves at infinity is insufficient for the uniqueness of the solution of the scattering problem.

Exploring the spectrum of planar AdS4 /CFT3 at finite coupling

NASA Astrophysics Data System (ADS)

Bombardelli, Diego; Cavaglià, Andrea; Conti, Riccardo; Tateo, Roberto

2018-04-01

The Quantum Spectral Curve (QSC) equations for planar N=6 super-conformal Chern-Simons (SCS) are solved numerically at finite values of the coupling constant for states in the sl(2\\Big|1) sector. New weak coupling results for conformal dimensions of operators outside the sl(2) -like sector are obtained by adapting a recently proposed algorithm for the QSC perturbative solution. Besides being interesting in their own right, these perturbative results are necessary initial inputs for the numerical algorithm to converge on the correct solution. The non-perturbative numerical outcomes nicely interpolate between the weak coupling and the known semiclassical expansions, and novel strong coupling exact results are deduced from the numerics. Finally, the existence of contour crossing singularities in the TBA equations for the operator 20 is ruled out by our analysis. The results of this paper are an important test of the QSC formalism for this model, open the way to new quantitative studies and provide further evidence in favour of the conjectured weak/strong coupling duality between N=6 SCS and type IIA superstring theory on AdS4 × CP 3. Attached to the arXiv submission, a Mathematica implementation of the numerical method and ancillary files containing the numerical results are provided.

Automatic differentiation for Fourier series and the radii polynomial approach

NASA Astrophysics Data System (ADS)

Lessard, Jean-Philippe; Mireles James, J. D.; Ransford, Julian

2016-11-01

In this work we develop a computer-assisted technique for proving existence of periodic solutions of nonlinear differential equations with non-polynomial nonlinearities. We exploit ideas from the theory of automatic differentiation in order to formulate an augmented polynomial system. We compute a numerical Fourier expansion of the periodic orbit for the augmented system, and prove the existence of a true solution nearby using an a-posteriori validation scheme (the radii polynomial approach). The problems considered here are given in terms of locally analytic vector fields (i.e. the field is analytic in a neighborhood of the periodic orbit) hence the computer-assisted proofs are formulated in a Banach space of sequences satisfying a geometric decay condition. In order to illustrate the use and utility of these ideas we implement a number of computer-assisted existence proofs for periodic orbits of the Planar Circular Restricted Three-Body Problem (PCRTBP).

Stability analysis on the flow and heat transfer of nanofluid past a stretching/shrinking cylinder with suction effect

NASA Astrophysics Data System (ADS)

Bakar, Nor Ashikin Abu; Bachok, Norfifah; Arifin, Norihan Md.; Pop, Ioan

2018-06-01

The steady boundary layer flow over a stretching/shrinking cylinder with suction effect is numerically studied. Using a similarity transformations, the governing partial differential equations are transformed into a set of nonlinear differential equations and have been solved numerically using a bvp4c code in Matlab software. The nanofluid model used is taking into account the effects of Brownian motion and thermophoresis. The influences of the governing parameters namely the curvature parameter γ, mass suction parameter S, Brownian motion parameter Nb and thermophoresis parameter Nt on the flow, heat and mass transfers characteristics are presented graphically. The numerical results obtained for the skin friction coefficient, local Nusselt number and local Sherwood number are thoroughly determined and presented graphically for several values of the governing parameters. From our investigation, it is found that the non-unique (dual) solutions exist for a certain range of mass suction parameter. It is observed that as curvature parameter increases, the skin friction coefficient and heat transfer rate decrease, meanwhile the mass transfer rates increase. Moreover, the stability analysis showed that the first solution is linearly stable, while the second solution is linearly unstable.

Numerical simulation of advective-dispersive multisolute transport with sorption, ion exchange and equilibrium chemistry

USGS Publications Warehouse

Lewis, F.M.; Voss, C.I.; Rubin, Jacob

1986-01-01

A model was developed that can simulate the effect of certain chemical and sorption reactions simultaneously among solutes involved in advective-dispersive transport through porous media. The model is based on a methodology that utilizes physical-chemical relationships in the development of the basic solute mass-balance equations; however, the form of these equations allows their solution to be obtained by methods that do not depend on the chemical processes. The chemical environment is governed by the condition of local chemical equilibrium, and may be defined either by the linear sorption of a single species and two soluble complexation reactions which also involve that species, or binary ion exchange and one complexation reaction involving a common ion. Partial differential equations that describe solute mass balance entirely in the liquid phase are developed for each tenad (a chemical entity whose total mass is independent of the reaction process) in terms of their total dissolved concentration. These equations are solved numerically in two dimensions through the modification of an existing groundwater flow/transport computer code. (Author 's abstract)

Hierarchical matrices implemented into the boundary integral approaches for gravity field modelling

NASA Astrophysics Data System (ADS)

Čunderlík, Róbert; Vipiana, Francesca

2017-04-01

Boundary integral approaches applied for gravity field modelling have been recently developed to solve the geodetic boundary value problems numerically, or to process satellite observations, e.g. from the GOCE satellite mission. In order to obtain numerical solutions of "cm-level" accuracy, such approaches require very refined level of the disretization or resolution. This leads to enormous memory requirements that need to be reduced. An implementation of the Hierarchical Matrices (H-matrices) can significantly reduce a numerical complexity of these approaches. A main idea of the H-matrices is based on an approximation of the entire system matrix that is split into a family of submatrices. Large submatrices are stored in factorized representation, while small submatrices are stored in standard representation. This allows reducing memory requirements significantly while improving the efficiency. The poster presents our preliminary results of implementations of the H-matrices into the existing boundary integral approaches based on the boundary element method or the method of fundamental solution.

Cylindrical and spherical Akhmediev breather and freak waves in ultracold neutral plasmas

NASA Astrophysics Data System (ADS)

El-Tantawy, S. A.; El-Awady, E. I.

2018-01-01

The properties of cylindrical and spherical ion-acoustic breathers Akhmediev breather and freak waves in strongly coupled ultracold neutral plasmas (UNPs), whose constituents are inertial strongly coupled ions and weakly coupled Maxwellian electrons, are investigated numerically. Using the derivative expansion method, the basic set of fluid equations is reduced to a nonplanar (cylindrical and spherical)/modified nonlinear Schrödinger equation (mNLSE). The analytical solutions of the mNLSE were not possible until now, so their numerical solutions are obtained using the finite difference scheme with the help of the Dirichlet boundary conditions. Moreover, the criteria for the existence and propagation of breathers are discussed in detail. The geometrical effects due to the cylindrical and spherical geometries on the breather profile are studied numerically. It is found that the propagation of the ion-acoustic breathers in one-dimensional planar and nonplanar geometries is very different. Finally, our results may help to manipulate matter breathers experimentally in UNPs.

Accuracy Study of the Space-Time CE/SE Method for Computational Aeroacoustics Problems Involving Shock Waves

NASA Technical Reports Server (NTRS)

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

1999-01-01

The space-time conservation element and solution element(CE/SE) method is used to study the sound-shock interaction problem. The order of accuracy of numerical schemes is investigated. The linear model problem.govemed by the 1-D scalar convection equation, sound-shock interaction problem governed by the 1-D Euler equations, and the 1-D shock-tube problem which involves moving shock waves and contact surfaces are solved to investigate the order of accuracy of numerical schemes. It is concluded that the accuracy of the CE/SE numerical scheme with designed 2nd-order accuracy becomes 1st order when a moving shock wave exists. However, the absolute error in the CE/SE solution downstream of the shock wave is on the same order as that obtained using a fourth-order accurate essentially nonoscillatory (ENO) scheme. No special techniques are used for either high-frequency low-amplitude waves or shock waves.

Numerical studies of the fluid and optical fields associated with complex cavity flows

NASA Technical Reports Server (NTRS)

Atwood, Christopher A.

1992-01-01

Numerical solutions for the flowfield about several cavity configurations have been computed using the Reynolds averaged Navier-Stokes equations. Comparisons between numerical and experimental results are made in two dimensions for free shear layers and a rectangular cavity, and in three dimensions for the transonic aero-window problem of the Stratospheric Observatory for Infrared Astronomy (SOFIA). Results show that dominant acoustic frequencies and magnitudes of the self excited resonant cavity flows compare well with the experiment. In addition, solution sensitivity to artificial dissipation and grid resolution levels are determined. Optical path distortion due to the flow field is modelled geometrically and is found to match the experiment. The fluid field was computed using a diagonalized scheme within an overset mesh framework. An existing code, OVERFLOW, was utilized with the additions of characteristic boundary condition and output routines required for reduction of the unsteady data. The newly developed code is directly applicable to a generalized three dimensional structured grid zone. Details are provided in a paper included in Appendix A.

Heat Source/Sink in a Magneto-Hydrodynamic Non-Newtonian Fluid Flow in a Porous Medium: Dual Solutions

PubMed Central

Hayat, Tasawar; Awais, Muhammad; Imtiaz, Amna

2016-01-01

This communication deals with the properties of heat source/sink in a magneto-hydrodynamic flow of a non-Newtonian fluid immersed in a porous medium. Shrinking phenomenon along with the permeability of the wall is considered. Mathematical modelling is performed to convert the considered physical process into set of coupled nonlinear mathematical equations. Suitable transformations are invoked to convert the set of partial differential equations into nonlinear ordinary differential equations which are tackled numerically for the solution computations. It is noted that dual solutions for various physical parameters exist which are analyzed in detail. PMID:27598314

Control optimization of a lifting body entry problem by an improved and a modified method of perturbation function. Ph.D. Thesis - Houston Univ.

NASA Technical Reports Server (NTRS)

Garcia, F., Jr.

1974-01-01

A study of the solution problem of a complex entry optimization was studied. The problem was transformed into a two-point boundary value problem by using classical calculus of variation methods. Two perturbation methods were devised. These methods attempted to desensitize the contingency of the solution of this type of problem on the required initial co-state estimates. Also numerical results are presented for the optimal solution resulting from a number of different initial co-states estimates. The perturbation methods were compared. It is found that they are an improvement over existing methods.

Long-time behavior and Turing instability induced by cross-diffusion in a three species food chain model with a Holling type-II functional response.

PubMed

Haile, Dawit; Xie, Zhifu

2015-09-01

In this paper, we study a strongly coupled reaction-diffusion system describing three interacting species in a food chain model, where the third species preys on the second one and simultaneously the second species preys on the first one. An intra-species competition b2 among the second predator is introduced to the food chain model. This parameter produces some very interesting result in linear stability and Turing instability. We first show that the unique positive equilibrium solution is locally asymptotically stable for the corresponding ODE system when the intra-species competition exists among the second predator. The positive equilibrium solution remains linearly stable for the reaction diffusion system without cross diffusion, hence it does not belong to the classical Turing instability scheme. But it becomes linearly unstable only when cross-diffusion also plays a role in the reaction-diffusion system, hence the instability is driven solely from the effect of cross diffusion. Our results also exhibit some interesting combining effects of cross-diffusion, intra-species competitions and inter-species interactions. Numerically, we conduct a one parameter analysis which illustrate how the interactions change the existence of stable equilibrium, limit cycle, and chaos. Some interesting dynamical phenomena occur when we perform analysis of interactions in terms of self-production of prey and intra-species competition of the middle predator. By numerical simulations, it illustrates the existence of nonuniform steady solutions and new patterns such as spot patterns, strip patterns and fluctuations due to the diffusion and cross diffusion in two-dimension. Published by Elsevier Inc.

A nonequilibrium model for reactive contaminant transport through fractured porous media: Model development and semianalytical solution

NASA Astrophysics Data System (ADS)

Joshi, Nitin; Ojha, C. S. P.; Sharma, P. K.

2012-10-01

In this study a conceptual model that accounts for the effects of nonequilibrium contaminant transport in a fractured porous media is developed. Present model accounts for both physical and sorption nonequilibrium. Analytical solution was developed using the Laplace transform technique, which was then numerically inverted to obtain solute concentration in the fracture matrix system. The semianalytical solution developed here can incorporate both semi-infinite and finite fracture matrix extent. In addition, the model can account for flexible boundary conditions and nonzero initial condition in the fracture matrix system. The present semianalytical solution was validated against the existing analytical solutions for the fracture matrix system. In order to differentiate between various sorption/transport mechanism different cases of sorption and mass transfer were analyzed by comparing the breakthrough curves and temporal moments. It was found that significant differences in the signature of sorption and mass transfer exists. Applicability of the developed model was evaluated by simulating the published experimental data of Calcium and Strontium transport in a single fracture. The present model simulated the experimental data reasonably well in comparison to the model based on equilibrium sorption assumption in fracture matrix system, and multi rate mass transfer model.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves.

PubMed

Tsitoura, F; Gietz, U; Chabchoub, A; Hoffmann, N

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves

NASA Astrophysics Data System (ADS)

Tsitoura, F.; Gietz, U.; Chabchoub, A.; Hoffmann, N.

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Structure of two-dimensional solitons in the context of a generalized Kadomtsev-Petviashvili equation

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

Abramyan, L.A.; Stepanyants, Yu.A.

1988-04-01

The structure of steady-state two-dimensional solutions of the soliton type with quadratic and cubic nonlinearities and power-law dispersion is analyzed numerically. It is shown that steadily coupled two-dimensional multisolitons can exist for positive dispersion in a broad class of equations, which generalize the Kadomtsev-Petviashvili equation.

A new analysis of the Fornberg-Whitham equation pertaining to a fractional derivative with Mittag-Leffler-type kernel

NASA Astrophysics Data System (ADS)

Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru

2018-02-01

The mathematical model of breaking of non-linear dispersive water waves with memory effect is very important in mathematical physics. In the present article, we examine a novel fractional extension of the non-linear Fornberg-Whitham equation occurring in wave breaking. We consider the most recent theory of differentiation involving the non-singular kernel based on the extended Mittag-Leffler-type function to modify the Fornberg-Whitham equation. We examine the existence of the solution of the non-linear Fornberg-Whitham equation of fractional order. Further, we show the uniqueness of the solution. We obtain the numerical solution of the new arbitrary order model of the non-linear Fornberg-Whitham equation with the aid of the Laplace decomposition technique. The numerical outcomes are displayed in the form of graphs and tables. The results indicate that the Laplace decomposition algorithm is a very user-friendly and reliable scheme for handling such type of non-linear problems of fractional order.

On similarity solutions of a boundary layer problem with an upstream moving wall

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Lakin, W. D.; Nachman, A.

1986-01-01

The problem of a boundary layer on a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream is examined. It was previously shown that the solution of this boundary value problem is crucially dependent on the parameter which is the ratio of the velocity of the plate to the velocity of the free stream. In particular, it was proved that a solution exists only if this parameter does not exceed a certain critical value, and numerical evidence was adduced to show that this solution is nonunique. Using Crocco formulation the present work proves this nonuniqueness. Also considered are the analyticity of solutions and the derivation of upper bounds on the critical value of wall velocity parameter.

Large Black Holes in the Randall-Sundrum II Model

NASA Astrophysics Data System (ADS)

Yaghoobpour Tari, Shima

The Einstein equation with a negative cosmological constant ! in the five dimensions for the Randall-Sundrum II model, which includes a black hole, has been solved numerically. We have constructed an AdS5-CFT 4 solution numerically, using a spectral method to minimize the integral of the square of the error of the Einstein equation, with 210 parameters to be determined by optimization. This metric is conformal to the Schwarzschild metric at an AdS5 boundary with an infinite scale factor. So, we consider this solution as an infinite-mass black hole solution. We have rewritten the infinite-mass black hole in the Fefferman-Graham form and obtained the numerical components of the CFT energy-momentum tensor. Using them, we have perturbed the metric to relocate the brane from infinity and obtained a large static black hole solution for the Randall- Sundrum II model. The changes of mass, entropy, temperature and area of the large black hole from the Schwarzschild metric are studied up to the first order for the perturbation parameter 1/(-Λ5M 2). The Hawking temperature and entropy for our large black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(-Λ5). Figueras, Lucietti, and Wiseman found an AdS5-CFT4 solution using an independent and different method from us, called the Ricci-DeTurck-flow method. Then, Figueras and Wiseman perturbed this solution in a same way as we have done and obtained the solution for the large black hole in the Randall-Sundrum II model. These two numerical solutions are the first mathematical proofs for having a large black hole in the Randall-Sundrum II. We have compared their results with ours for the CFT energy-momentum tensor components and the perturbed metric. We have shown that the results are closely in agreement, which can be considered as evidence that the solution for the large black hole in the Randall-Sundrum II model exists.

Asymptotic behaviors of a cell-to-cell HIV-1 infection model perturbed by white noise

NASA Astrophysics Data System (ADS)

Liu, Qun

2017-02-01

In this paper, we analyze a mathematical model of cell-to-cell HIV-1 infection to CD4+ T cells perturbed by stochastic perturbations. First of all, we investigate that there exists a unique global positive solution of the system for any positive initial value. Then by using Lyapunov analysis methods, we study the asymptotic property of this solution. Moreover, we discuss whether there is a stationary distribution for this system and if it owns the ergodic property. Numerical simulations are presented to illustrate the theoretical results.

A stage structure pest management model with impulsive state feedback control

NASA Astrophysics Data System (ADS)

Pang, Guoping; Chen, Lansun; Xu, Weijian; Fu, Gang

2015-06-01

A stage structure pest management model with impulsive state feedback control is investigated. We get the sufficient condition for the existence of the order-1 periodic solution by differential equation geometry theory and successor function. Further, we obtain a new judgement method for the stability of the order-1 periodic solution of the semi-continuous systems by referencing the stability analysis for limit cycles of continuous systems, which is different from the previous method of analog of Poincarè criterion. Finally, we analyze numerically the theoretical results obtained.

Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Singhal, A. K.; Tam, L. T.

1984-01-01

The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.

Bifurcation Analysis and Chaos Control in a Modified Finance System with Delayed Feedback

NASA Astrophysics Data System (ADS)

Yang, Jihua; Zhang, Erli; Liu, Mei

2016-06-01

We investigate the effect of delayed feedback on the finance system, which describes the time variation of the interest rate, for establishing the fiscal policy. By local stability analysis, we theoretically prove the existences of Hopf bifurcation and Hopf-zero bifurcation. By using the normal form method and center manifold theory, we determine the stability and direction of a bifurcating periodic solution. Finally, we give some numerical solutions, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable equilibrium or periodic orbit.

Approximate solutions to Mathieu's equation

NASA Astrophysics Data System (ADS)

Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

2018-06-01

Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

NASA Astrophysics Data System (ADS)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

An efficient numerical solution of the transient storage equations for solute transport in small streams

USGS Publications Warehouse

Runkel, Robert L.; Chapra, Steven C.

1993-01-01

Several investigators have proposed solute transport models that incorporate the effects of transient storage. Transient storage occurs in small streams when portions of the transported solute become isolated in zones of water that are immobile relative to water in the main channel (e.g., pools, gravel beds). Transient storage is modeled by adding a storage term to the advection-dispersion equation describing conservation of mass for the main channel. In addition, a separate mass balance equation is written for the storage zone. Although numerous applications of the transient storage equations may be found in the literature, little attention has been paid to the numerical aspects of the approach. Of particular interest is the coupled nature of the equations describing mass conservation for the main channel and the storage zone. In the work described herein, an implicit finite difference technique is developed that allows for a decoupling of the governing differential equations. This decoupling method may be applied to other sets of coupled equations such as those describing sediment-water interactions for toxic contaminants. For the case at hand, decoupling leads to a 50% reduction in simulation run time. Computational costs may be further reduced through efficient application of the Thomas algorithm. These techniques may be easily incorporated into existing codes and new applications in which simulation run time is of concern.

Some exact velocity profiles for granular flow in converging hoppers

NASA Astrophysics Data System (ADS)

Cox, Grant M.; Hill, James M.

2005-01-01

Gravity flow of granular materials through hoppers occurs in many industrial processes. For an ideal cohesionless granular material, which satisfies the Coulomb-Mohr yield condition, the number of known analytical solutions is limited. However, for the special case of the angle of internal friction δ equal to ninety degrees, there exist exact parametric solutions for the governing coupled ordinary differential equations for both two-dimensional wedges and three-dimensional cones, both of which involve two arbitrary constants of integration. These solutions are the only known analytical solutions of this generality. Here, we utilize the double-shearing theory of granular materials to determine the velocity field corresponding to these exact parametric solutions for the two problems of gravity flow through converging wedge and conical hoppers. An independent numerical solution for other angles of internal friction is shown to coincide with the analytical solution.

A numerical scheme for the identification of hybrid systems describing the vibration of flexible beams with tip bodies

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

A cubic spline based Galerkin-like method is developed for the identification of a class of hybrid systems which describe the transverse vibration to flexible beams with attached tip bodies. The identification problem is formulated as a least squares fit to data subject to the system dynamics given by a coupled system of ordnary and partial differential equations recast as an abstract evolution equation (AEE) in an appropriate infinite dimensional Hilbert space. Projecting the AEE into spline-based subspaces leads naturally to a sequence of approximating finite dimensional identification problems. The solutions to these problems are shown to exist, are relatively easily computed, and are shown to, in some sense, converge to solutions to the original identification problem. Numerical results for a variety of examples are discussed.

Optimal policy for profit maximising in an EOQ model under non-linear holding cost and stock-dependent demand rate

NASA Astrophysics Data System (ADS)

Pando, V.; García-Laguna, J.; San-José, L. A.

2012-11-01

In this article, we integrate a non-linear holding cost with a stock-dependent demand rate in a maximising profit per unit time model, extending several inventory models studied by other authors. After giving the mathematical formulation of the inventory system, we prove the existence and uniqueness of the optimal policy. Relying on this result, we can obtain the optimal solution using different numerical algorithms. Moreover, we provide a necessary and sufficient condition to determine whether a system is profitable, and we establish a rule to check when a given order quantity is the optimal lot size of the inventory model. The results are illustrated through numerical examples and the sensitivity of the optimal solution with respect to changes in some values of the parameters is assessed.

Nash equilibrium and multi criterion aerodynamic optimization

NASA Astrophysics Data System (ADS)

Tang, Zhili; Zhang, Lianhe

2016-06-01

Game theory and its particular Nash Equilibrium (NE) are gaining importance in solving Multi Criterion Optimization (MCO) in engineering problems over the past decade. The solution of a MCO problem can be viewed as a NE under the concept of competitive games. This paper surveyed/proposed four efficient algorithms for calculating a NE of a MCO problem. Existence and equivalence of the solution are analyzed and proved in the paper based on fixed point theorem. Specific virtual symmetric Nash game is also presented to set up an optimization strategy for single objective optimization problems. Two numerical examples are presented to verify proposed algorithms. One is mathematical functions' optimization to illustrate detailed numerical procedures of algorithms, the other is aerodynamic drag reduction of civil transport wing fuselage configuration by using virtual game. The successful application validates efficiency of algorithms in solving complex aerodynamic optimization problem.

A linear stability analysis for nonlinear, grey, thermal radiative transfer problems

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

Wollaber, Allan B., E-mail: wollaber@lanl.go; Larsen, Edward W., E-mail: edlarsen@umich.ed

2011-02-20

We present a new linear stability analysis of three time discretizations and Monte Carlo interpretations of the nonlinear, grey thermal radiative transfer (TRT) equations: the widely used 'Implicit Monte Carlo' (IMC) equations, the Carter Forest (CF) equations, and the Ahrens-Larsen or 'Semi-Analog Monte Carlo' (SMC) equations. Using a spatial Fourier analysis of the 1-D Implicit Monte Carlo (IMC) equations that are linearized about an equilibrium solution, we show that the IMC equations are unconditionally stable (undamped perturbations do not exist) if {alpha}, the IMC time-discretization parameter, satisfies 0.5 < {alpha} {<=} 1. This is consistent with conventional wisdom. However, wemore » also show that for sufficiently large time steps, unphysical damped oscillations can exist that correspond to the lowest-frequency Fourier modes. After numerically confirming this result, we develop a method to assess the stability of any time discretization of the 0-D, nonlinear, grey, thermal radiative transfer problem. Subsequent analyses of the CF and SMC methods then demonstrate that the CF method is unconditionally stable and monotonic, but the SMC method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium. This stability theory provides new conditions on the time step to guarantee monotonicity of the IMC solution, although they are likely too conservative to be used in practice. Theoretical predictions are tested and confirmed with numerical experiments.« less

A linear stability analysis for nonlinear, grey, thermal radiative transfer problems

NASA Astrophysics Data System (ADS)

Wollaber, Allan B.; Larsen, Edward W.

2011-02-01

We present a new linear stability analysis of three time discretizations and Monte Carlo interpretations of the nonlinear, grey thermal radiative transfer (TRT) equations: the widely used “Implicit Monte Carlo” (IMC) equations, the Carter Forest (CF) equations, and the Ahrens-Larsen or “Semi-Analog Monte Carlo” (SMC) equations. Using a spatial Fourier analysis of the 1-D Implicit Monte Carlo (IMC) equations that are linearized about an equilibrium solution, we show that the IMC equations are unconditionally stable (undamped perturbations do not exist) if α, the IMC time-discretization parameter, satisfies 0.5 < α ⩽ 1. This is consistent with conventional wisdom. However, we also show that for sufficiently large time steps, unphysical damped oscillations can exist that correspond to the lowest-frequency Fourier modes. After numerically confirming this result, we develop a method to assess the stability of any time discretization of the 0-D, nonlinear, grey, thermal radiative transfer problem. Subsequent analyses of the CF and SMC methods then demonstrate that the CF method is unconditionally stable and monotonic, but the SMC method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium. This stability theory provides new conditions on the time step to guarantee monotonicity of the IMC solution, although they are likely too conservative to be used in practice. Theoretical predictions are tested and confirmed with numerical experiments.

Numerical Investigation of the Interaction of Counterflowing Jets and Supersonic Capsule Flows

NASA Technical Reports Server (NTRS)

Venkatachari, Balaji Shankar; Ito, Yasushi; Cheng, Gary; Chang, Chau-Lyan

2011-01-01

Use of counterflowing jets ejected into supersonic freestreams as a flow control concept to modify the external flowfield has gained renewed interest with regards to potential retropropulsion applications pertinent to entry, descent, and landing investigations. This study describes numerical computations of such a concept for a scaled wind-tunnel capsule model by employing the space-time conservation element solution element viscous flow solver with unstructured meshes. Both steady-state and time-accurate computations are performed for several configurations with different counterflowing jet Mach numbers. Axisymmetric computations exploring the effect of the jet flow rate and jet Mach number on the flow stability, jet interaction with the bow shock and its subsequent impact on the aerodynamic and aerothermal loads on the capsule body are carried out. Similar to previous experimental findings, both long and short penetration modes exist at a windtunnel Mach number of 3.48. It was found that both modes exhibit non-stationary behavior and the former is much more unstable than the latter. It was also found that the unstable long penetration mode only exists in a relatively small range of the jet mass flow rate. Solution-based mesh refinement procedures are used to improve solution accuracy and provide guidelines for a more effective mesh generation procedure for parametric studies. Details of the computed flowfields also serve as a means to broaden the knowledge base for future retropropulsion design studies.

Embedded WENO: A design strategy to improve existing WENO schemes

NASA Astrophysics Data System (ADS)

van Lith, Bart S.; ten Thije Boonkkamp, Jan H. M.; IJzerman, Wilbert L.

2017-02-01

Embedded WENO methods utilise all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for constructing embedded versions of existing WENO schemes. Embedded methods based on the WENO schemes of Jiang and Shu [1] and on the WENO-Z scheme of Borges et al. [2] are explicitly constructed. Several possible choices are presented that result in either better spectral properties or a higher order of convergence for sufficiently smooth solutions. However, these improvements carry over to discontinuous solutions. The embedded methods are demonstrated to be indeed improvements over their standard counterparts by several numerical examples. All the embedded methods presented have no added computational effort compared to their standard counterparts.

Surface plasmons for doped graphene

NASA Astrophysics Data System (ADS)

Bordag, M.; Pirozhenko, I. G.

2015-04-01

Within the Dirac model for the electronic excitations of graphene, we calculate the full polarization tensor with finite mass and chemical potential. It has, besides the (00)-component, a second form factor, which must be accounted for. We obtain explicit formulas for both form factors and for the reflection coefficients. Using these, we discuss the regions in the momentum-frequency plane where plasmons may exist and give numeric solutions for the plasmon dispersion relations. It turns out that plasmons exist for both, transverse electric and transverse magnetic polarizations over the whole range of the ratio of mass to chemical potential, except for zero chemical potential, where only a TE plasmon exists.

Numerical Modeling in Geodynamics: Success, Failure and Perspective

NASA Astrophysics Data System (ADS)

Ismail-Zadeh, A.

2005-12-01

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

Standards and Guidelines for Numerical Models for Tsunami Hazard Mitigation

NASA Astrophysics Data System (ADS)

Titov, V.; Gonzalez, F.; Kanoglu, U.; Yalciner, A.; Synolakis, C. E.

2006-12-01

An increased number of nations around the workd need to develop tsunami mitigation plans which invariably involve inundation maps for warning guidance and evacuation planning. There is the risk that inundation maps may be produced with older or untested methodology, as there are currently no standards for modeling tools. In the aftermath of the 2004 megatsunami, some models were used to model inundation for Cascadia events with results much larger than sediment records and existing state-of-the-art studies suggest leading to confusion among emergency management. Incorrectly assessing tsunami impact is hazardous, as recent events in 2006 in Tonga, Kythira, Greece and Central Java have suggested (Synolakis and Bernard, 2006). To calculate tsunami currents, forces and runup on coastal structures, and inundation of coastlines one must calculate the evolution of the tsunami wave from the deep ocean to its target site, numerically. No matter what the numerical model, validation (the process of ensuring that the model solves the parent equations of motion accurately) and verification (the process of ensuring that the model used represents geophysical reality appropriately) both are an essential. Validation ensures that the model performs well in a wide range of circumstances and is accomplished through comparison with analytical solutions. Verification ensures that the computational code performs well over a range of geophysical problems. A few analytic solutions have been validated themselves with laboratory data. Even fewer existing numerical models have been both validated with the analytical solutions and verified with both laboratory measurements and field measurements, thus establishing a gold standard for numerical codes for inundation mapping. While there is in principle no absolute certainty that a numerical code that has performed well in all the benchmark tests will also produce correct inundation predictions with any given source motions, validated codes reduce the level of uncertainty in their results to the uncertainty in the geophysical initial conditions. Further, when coupled with real--time free--field tsunami measurements from tsunameters, validated codes are the only choice for realistic forecasting of inundation; the consequences of failure are too ghastly to take chances with numerical procedures that have not been validated. We discuss a ten step process of benchmark tests for models used for inundation mapping. The associated methodology and algorithmes have to first be validated with analytical solutions, then verified with laboratory measurements and field data. The models need to be published in the scientific literature in peer-review journals indexed by ISI. While this process may appear onerous, it reflects our state of knowledge, and is the only defensible methodology when human lives are at stake. Synolakis, C.E., and Bernard, E.N, Tsunami science before and beyond Boxing Day 2004, Phil. Trans. R. Soc. A 364 1845, 2231--2263, 2005.

Aggregation work at polydisperse micellization: ideal solution and "dressed micelle" models comparing to molecular dynamics simulations.

PubMed

Burov, S V; Shchekin, A K

2010-12-28

General thermodynamic relations for the work of polydisperse micelle formation in the model of ideal solution of molecular aggregates in nonionic surfactant solution and the model of "dressed micelles" in ionic solution have been considered. In particular, the dependence of the aggregation work on the total concentration of nonionic surfactant has been analyzed. The analogous dependence for the work of formation of ionic aggregates has been examined with regard to existence of two variables of a state of an ionic aggregate, the aggregation numbers of surface active ions and counterions. To verify the thermodynamic models, the molecular dynamics simulations of micellization in nonionic and ionic surfactant solutions at two total surfactant concentrations have been performed. It was shown that for nonionic surfactants, even at relatively high total surfactant concentrations, the shape and behavior of the work of polydisperse micelle formation found within the model of the ideal solution at different total surfactant concentrations agrees fairly well with the numerical experiment. For ionic surfactant solutions, the numerical results indicate a strong screening of ionic aggregates by the bound counterions. This fact as well as independence of the coefficient in the law of mass action for ionic aggregates on total surfactant concentration and predictable behavior of the "waterfall" lines of surfaces of the aggregation work upholds the model of "dressed" ionic aggregates.

On the existence of mosaic-skeleton approximations for discrete analogues of integral operators

NASA Astrophysics Data System (ADS)

Kashirin, A. A.; Taltykina, M. Yu.

2017-09-01

Exterior three-dimensional Dirichlet problems for the Laplace and Helmholtz equations are considered. By applying methods of potential theory, they are reduced to equivalent Fredholm boundary integral equations of the first kind, for which discrete analogues, i.e., systems of linear algebraic equations (SLAEs) are constructed. The existence of mosaic-skeleton approximations for the matrices of the indicated systems is proved. These approximations make it possible to reduce the computational complexity of an iterative solution of the SLAEs. Numerical experiments estimating the capabilities of the proposed approach are described.

Dynamics of an advertising competition model with sales promotion

NASA Astrophysics Data System (ADS)

Jiang, Hui; Feng, Zhaosheng; Jiang, Guirong

2017-01-01

In this paper, an advertising competition model with sales promotion is constructed and investigated. Conditions of the existence and stability of period-T solutions are obtained by means of the discrete map. Flip bifurcation is analyzed by using the center manifold theory and three sales promotion strategies are discussed. Example and numerical simulations are illustrated which agree well with our theoretical analysis.

Chandrasekhar equations and computational algorithms for distributed parameter systems

NASA Technical Reports Server (NTRS)

Burns, J. A.; Ito, K.; Powers, R. K.

1984-01-01

The Chandrasekhar equations arising in optimal control problems for linear distributed parameter systems are considered. The equations are derived via approximation theory. This approach is used to obtain existence, uniqueness, and strong differentiability of the solutions and provides the basis for a convergent computation scheme for approximating feedback gain operators. A numerical example is presented to illustrate these ideas.

Reinforcement learning for resource allocation in LEO satellite networks.

PubMed

Usaha, Wipawee; Barria, Javier A

2007-06-01

In this paper, we develop and assess online decision-making algorithms for call admission and routing for low Earth orbit (LEO) satellite networks. It has been shown in a recent paper that, in a LEO satellite system, a semi-Markov decision process formulation of the call admission and routing problem can achieve better performance in terms of an average revenue function than existing routing methods. However, the conventional dynamic programming (DP) numerical solution becomes prohibited as the problem size increases. In this paper, two solution methods based on reinforcement learning (RL) are proposed in order to circumvent the computational burden of DP. The first method is based on an actor-critic method with temporal-difference (TD) learning. The second method is based on a critic-only method, called optimistic TD learning. The algorithms enhance performance in terms of requirements in storage, computational complexity and computational time, and in terms of an overall long-term average revenue function that penalizes blocked calls. Numerical studies are carried out, and the results obtained show that the RL framework can achieve up to 56% higher average revenue over existing routing methods used in LEO satellite networks with reasonable storage and computational requirements.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Hixon, Duane; Sankar, L. N.

1993-01-01

During the past two decades, there has been significant progress in the field of numerical simulation of unsteady compressible viscous flows. At present, a variety of solution techniques exist such as the transonic small disturbance analyses (TSD), transonic full potential equation-based methods, unsteady Euler solvers, and unsteady Navier-Stokes solvers. These advances have been made possible by developments in three areas: (1) improved numerical algorithms; (2) automation of body-fitted grid generation schemes; and (3) advanced computer architectures with vector processing and massively parallel processing features. In this work, the GMRES scheme has been considered as a candidate for acceleration of a Newton iteration time marching scheme for unsteady 2-D and 3-D compressible viscous flow calculation; from preliminary calculations, this will provide up to a 65 percent reduction in the computer time requirements over the existing class of explicit and implicit time marching schemes. The proposed method has ben tested on structured grids, but is flexible enough for extension to unstructured grids. The described scheme has been tested only on the current generation of vector processor architecture of the Cray Y/MP class, but should be suitable for adaptation to massively parallel machines.

Numerical solution of modified differential equations based on symmetry preservation.

PubMed

Ozbenli, Ersin; Vedula, Prakash

2017-12-01

In this paper, we propose a method to construct invariant finite-difference schemes for solution of partial differential equations (PDEs) via consideration of modified forms of the underlying PDEs. The invariant schemes, which preserve Lie symmetries, are obtained based on the method of equivariant moving frames. While it is often difficult to construct invariant numerical schemes for PDEs due to complicated symmetry groups associated with cumbersome discrete variable transformations, we note that symmetries associated with more convenient transformations can often be obtained by appropriately modifying the original PDEs. In some cases, modifications to the original PDEs are also found to be useful in order to avoid trivial solutions that might arise from particular selections of moving frames. In our proposed method, modified forms of PDEs can be obtained either by addition of perturbation terms to the original PDEs or through defect correction procedures. These additional terms, whose primary purpose is to enable symmetries with more convenient transformations, are then removed from the system by considering moving frames for which these specific terms go to zero. Further, we explore selection of appropriate moving frames that result in improvement in accuracy of invariant numerical schemes based on modified PDEs. The proposed method is tested using the linear advection equation (in one- and two-dimensions) and the inviscid Burgers' equation. Results obtained for these tests cases indicate that numerical schemes derived from the proposed method perform significantly better than existing schemes not only by virtue of improvement in numerical accuracy but also due to preservation of qualitative properties or symmetries of the underlying differential equations.

Revealing Numerical Solutions of a Differential Equation

ERIC Educational Resources Information Center

Glaister, P.

2006-01-01

In this article, the author considers a student exercise that involves determining the exact and numerical solutions of a particular differential equation. He shows how a typical student solution is at variance with a numerical solution, suggesting that the numerical solution is incorrect. However, further investigation shows that this numerical…

Hopf Bifurcation Analysis of a Gene Regulatory Network Mediated by Small Noncoding RNA with Time Delays and Diffusion

NASA Astrophysics Data System (ADS)

Li, Chengxian; Liu, Haihong; Zhang, Tonghua; Yan, Fang

2017-12-01

In this paper, a gene regulatory network mediated by small noncoding RNA involving two time delays and diffusion under the Neumann boundary conditions is studied. Choosing the sum of delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of spatially homogeneous and spatially inhomogeneous periodic solutions are investigated by analyzing the corresponding characteristic equation. It is shown that the sum of delays can induce Hopf bifurcation and the diffusion incorporated into the system can effect the amplitude of periodic solutions. Furthermore, the spatially homogeneous periodic solution always exists and the spatially inhomogeneous periodic solution will arise when the diffusion coefficients of protein and mRNA are suitably small. Particularly, the small RNA diffusion coefficient is more robust and its effect on model is much less than protein and mRNA. Finally, the explicit formulae for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by employing the normal form theory and center manifold theorem for partial functional differential equations. Finally, numerical simulations are carried out to illustrate our theoretical analysis.

Stability analysis and nonstandard Grünwald-Letnikov scheme for a fractional order predator-prey model with ratio-dependent functional response

NASA Astrophysics Data System (ADS)

Suryanto, Agus; Darti, Isnani

2017-12-01

In this paper we discuss a fractional order predator-prey model with ratio-dependent functional response. The dynamical properties of this model is analyzed. Here we determine all equilibrium points of this model including their existence conditions and their stability properties. It is found that the model has two type of equilibria, namely the predator-free point and the co-existence point. If there is no co-existence equilibrium, i.e. when the coefficient of conversion from the functional response into the growth rate of predator is less than the death rate of predator, then the predator-free point is asymptotically stable. On the other hand, if the co-existence point exists then this equilibrium is conditionally stable. We also construct a nonstandard Grnwald-Letnikov (NSGL) numerical scheme for the propose model. This scheme is a combination of the Grnwald-Letnikov approximation and the nonstandard finite difference scheme. This scheme is implemented in MATLAB and used to perform some simulations. It is shown that our numerical solutions are consistent with the dynamical properties of our fractional predator-prey model.

Finite-amplitude pressure waves in the radial mode of a cylinder

NASA Technical Reports Server (NTRS)

Kubo, I.; Moore, F. K.

1972-01-01

A numerical study of finite-strength, isentropic pressure waves transverse to the axis of a circular cylinder was made for the radial resonant mode. The waves occur in a gas otherwise at rest, filling the cylinder. A method of characteristics was used for the numerical solution. For small but finite amplitudes, calculations indicate the existence of waves of permanent potential form. For larger amplitudes, a shock is indicated to occur. The critical value of the initial amplitude parameter in the power series is found to be 0.06 to 0.08, under various types of initial conditions.

Strongly localized dark modes in binary discrete media with cubic-quintic nonlinearity within the anti-continuum limit

NASA Astrophysics Data System (ADS)

Taib, L. Abdul; Hadi, M. S. Abdul; Umarov, B. A.

2017-12-01

The existence of dark strongly localized modes of binary discrete media with cubic-quintic nonlinearity is numerically demonstrated by solving the relevant discrete nonlinear Schrödinger equations. In the model, the coupling coefficients between adjacent sites are set to be relatively small representing the anti-continuum limit. In addition, approximated analytical solutions for vectorial solitons with various topologies are derived. Stability analysis of the localized states was performed using the standard linearized eigenfrequency problem. The prediction from the stability analysis are furthermore verified by direct numerical integrations.

An efficient numerical scheme for the study of equal width equation

NASA Astrophysics Data System (ADS)

Ghafoor, Abdul; Haq, Sirajul

2018-06-01

In this work a new numerical scheme is proposed in which Haar wavelet method is coupled with finite difference scheme for the solution of a nonlinear partial differential equation. The scheme transforms the partial differential equation to a system of algebraic equations which can be solved easily. The technique is applied to equal width equation in order to study the behaviour of one, two, three solitary waves, undular bore and soliton collision. For efficiency and accuracy of the scheme, L2 and L∞ norms and invariants are computed. The results obtained are compared with already existing results in literature.

Analytical Solution for Flow to a Partially Penetrating Well with Storage in a Confined Aquifer

NASA Astrophysics Data System (ADS)

Vesselinov, V. V.; Mishra, P. K.; Neuman, S. P.

2009-12-01

Analytical solutions for radial flow toward a pumping well are commonly applied to analyze pumping tests conducted in confined aquifers. However, the existing analytical solutions are not capable to simultaneously take into account aquifer anisotropy, partial penetration, and wellbore storage capacity of pumping well. Ignoring these effects may have important impact on the estimated aquifer properties. We present a new analytical solution for three-dimensional, axially symmetric flow to a pumping well in confined aquifer that accouts for aquifer anisotropy, partial penetration and wellbore storage capacity of pumping well. Our analytical reduces to that of Papadopulos et.al. [1967] when the pumping well is fully penetrating, Hantush [1964] when the pumping well has no wellbore storage, and Theis [1935] when both conditions are fulfilled. The solution is evaluated through numerical inversion of its Laplace transform. We use our new solution to analyze data from synthetic and real pumping tests.

Development of solute transport models in YMPYRÄ framework to simulate solute migration in military shooting and training areas

NASA Astrophysics Data System (ADS)

Warsta, L.; Karvonen, T.

2017-12-01

There are currently 25 shooting and training areas in Finland managed by The Finnish Defence Forces (FDF), where military activities can cause contamination of open waters and groundwater reservoirs. In the YMPYRÄ project, a computer software framework is being developed that combines existing open environmental data and proprietary information collected by FDF with computational models to investigate current and prevent future environmental problems. A data centric philosophy is followed in the development of the system, i.e. the models are updated and extended to handle available data from different areas. The results generated by the models are summarized as easily understandable flow and risk maps that can be opened in GIS programs and used in environmental assessments by experts. Substances investigated with the system include explosives and metals such as lead, and both surface and groundwater dominated areas can be simulated. The YMPYRÄ framework is composed of a three dimensional soil and groundwater flow model, several solute transport models and an uncertainty assessment system. Solute transport models in the framework include particle based, stream tube and finite volume based approaches. The models can be used to simulate solute dissolution from source area, transport in the unsaturated layers to groundwater and finally migration in groundwater to water extraction wells and springs. The models can be used to simulate advection, dispersion, equilibrium adsorption on soil particles, solubility and dissolution from solute phase and dendritic solute decay chains. Correct numerical solutions were confirmed by comparing results to analytical 1D and 2D solutions and by comparing the numerical solutions to each other. The particle based and stream tube type solute transport models were useful as they could complement the traditional finite volume based approach which in certain circumstances produced numerical dispersion due to piecewise solution of the governing equations in computational grids and included computationally intensive and in some cases unstable iterative solutions. The YMPYRÄ framework is being developed by WaterHope, Gain Oy, and SITO Oy consulting companies and funded by FDF.

Advances in mosquito dynamics modeling

NASA Astrophysics Data System (ADS)

Wijaya, Karunia Putra; Götz, Thomas; Soewono, Edy

2016-11-01

It is preliminarily known that Aedes mosquitoes are very close to humans and their dwellings, also give rises to a broad spectrum of diseases: dengue, yellow fever, chikungunya. In this paper, we explore a multi-age-class model for mosquito population secondarily classified into indoor-outdoor dynamics. We accentuate a novel design for the model in which periodicity of the affecting time-varying environmental condition is taken into account. Application of the optimal control with collocated measure as apposed to the widely-used prototypic smooth time-continuous measure is also considered. Using two approaches: least-square and maximum likelihood, we estimate several involving undetermined parameters. We analyze the model enforceability to biological point of view such as existence, uniqueness, positivity and boundedness of solution trajectory, also existence and stability of (non)trivial periodic solution(s) by means of the basic mosquito offspring number. Some numerical tests are brought along at the rest of the paper as a compact realistic visualization of the model.

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems. Task 4: Advanced fan section aerodynamic analysis computer program user's manual

NASA Technical Reports Server (NTRS)

Crook, Andrew J.; Delaney, Robert A.

1992-01-01

The computer program user's manual for the ADPACAPES (Advanced Ducted Propfan Analysis Code-Average Passage Engine Simulation) program is included. The objective of the computer program is development of a three-dimensional Euler/Navier-Stokes flow analysis for fan section/engine geometries containing multiple blade rows and multiple spanwise flow splitters. An existing procedure developed by Dr. J. J. Adamczyk and associates at the NASA Lewis Research Center was modified to accept multiple spanwise splitter geometries and simulate engine core conditions. The numerical solution is based upon a finite volume technique with a four stage Runge-Kutta time marching procedure. Multiple blade row solutions are based upon the average-passage system of equations. The numerical solutions are performed on an H-type grid system, with meshes meeting the requirement of maintaining a common axisymmetric mesh for each blade row grid. The analysis was run on several geometry configurations ranging from one to five blade rows and from one to four radial flow splitters. The efficiency of the solution procedure was shown to be the same as the original analysis.

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

PubMed Central

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

2016-01-01

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

New algorithms to compute the nearness symmetric solution of the matrix equation.

PubMed

Peng, Zhen-Yun; Fang, Yang-Zhi; Xiao, Xian-Wei; Du, Dan-Dan

2016-01-01

In this paper we consider the nearness symmetric solution of the matrix equation AXB = C to a given matrix [Formula: see text] in the sense of the Frobenius norm. By discussing equivalent form of the considered problem, we derive some necessary and sufficient conditions for the matrix [Formula: see text] is a solution of the considered problem. Based on the idea of the alternating variable minimization with multiplier method, we propose two iterative methods to compute the solution of the considered problem, and analyze the global convergence results of the proposed algorithms. Numerical results illustrate the proposed methods are more effective than the existing two methods proposed in Peng et al. (Appl Math Comput 160:763-777, 2005) and Peng (Int J Comput Math 87: 1820-1830, 2010).

Numerical Asymptotic Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1992-01-01

Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

Non-Abelian clouds around Reissner-Nordström black holes: The existence line

NASA Astrophysics Data System (ADS)

Radu, Eugen; Tchrakian, D. H.; Yang, Yisong

2016-06-01

A known feature of electrically charged Reissner-Nordström-anti-de Sitter planar black holes is that they can become unstable when considered as solutions of Einstein-Yang-Mills theory. The mechanism for this is that the linearized Yang-Mills equations in the background of the Reissner-Nordström (RN) black holes possess a normalizable zero mode, resulting in non-Abelian (nA) magnetic clouds near the horizon. In this work we show that the same pattern may occur also for asymptotically flat RN black holes. Different from the anti-de Sitter case, in the Minkowskian background the prerequisites for the existence of the nA clouds are (i) a large enough gauge group, and (ii) the presence of some extra interaction terms in the matter Lagrangian. To illustrate this mechanism we present two specific examples, one in four- and the other in five-dimensional asymptotically flat spacetime. In the first case, we augment the usual S U (3 ) Yang-Mills Lagrangian with a higher-order (quartic) curvature term, while for the second one we add the Chern-Simons density to the S O (6 ) Yang-Mills system. In both cases, an Abelian gauge symmetry is spontaneously broken near a RN black hole horizon with the appearance of a condensate of nA gauge fields. In addition to these two examples, we review the corresponding picture for anti-de Sitter black holes. All these solutions are studied both analytically and numerically, existence proofs being provided for nA clouds in the background of RN black holes. The proofs use shooting techniques which are suggested by and in turn offer insights for our numerical methods. They indicate that, for a black hole of given mass, appropriate electric charge values are required to ensure the existence of solutions interpolating desired boundary behavior at the horizons and spatial infinity.

A Computational Study of Shear Layer Receptivity

NASA Astrophysics Data System (ADS)

Barone, Matthew; Lele, Sanjiva

2002-11-01

The receptivity of two-dimensional, compressible shear layers to local and external excitation sources is examined using a computational approach. The family of base flows considered consists of a laminar supersonic stream separated from nearly quiescent fluid by a thin, rigid splitter plate with a rounded trailing edge. The linearized Euler and linearized Navier-Stokes equations are solved numerically in the frequency domain. The flow solver is based on a high order finite difference scheme, coupled with an overset mesh technique developed for computational aeroacoustics applications. Solutions are obtained for acoustic plane wave forcing near the most unstable shear layer frequency, and are compared to the existing low frequency theory. An adjoint formulation to the present problem is developed, and adjoint equation calculations are performed using the same numerical methods as for the regular equation sets. Solutions to the adjoint equations are used to shed light on the mechanisms which control the receptivity of finite-width compressible shear layers.

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.

Prediction-Correction Algorithms for Time-Varying Constrained Optimization

DOE PAGES

Simonetto, Andrea; Dall'Anese, Emiliano

2017-07-26

This article develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do notmore » require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.« less

Extending BPM Environments of Your Choice with Performance Related Decision Support

NASA Astrophysics Data System (ADS)

Fritzsche, Mathias; Picht, Michael; Gilani, Wasif; Spence, Ivor; Brown, John; Kilpatrick, Peter

What-if Simulations have been identified as one solution for business performance related decision support. Such support is especially useful in cases where it can be automatically generated out of Business Process Management (BPM) Environments from the existing business process models and performance parameters monitored from the executed business process instances. Currently, some of the available BPM Environments offer basic-level performance prediction capabilities. However, these functionalities are normally too limited to be generally useful for performance related decision support at business process level. In this paper, an approach is presented which allows the non-intrusive integration of sophisticated tooling for what-if simulations, analytic performance prediction tools, process optimizations or a combination of such solutions into already existing BPM environments. The approach abstracts from process modelling techniques which enable automatic decision support spanning processes across numerous BPM Environments. For instance, this enables end-to-end decision support for composite processes modelled with the Business Process Modelling Notation (BPMN) on top of existing Enterprise Resource Planning (ERP) processes modelled with proprietary languages.

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

Simonetto, Andrea; Dall'Anese, Emiliano

This article develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do notmore » require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.« less

Ferrofluids: Modeling, numerical analysis, and scientific computation

NASA Astrophysics Data System (ADS)

Tomas, Ignacio

This dissertation presents some developments in the Numerical Analysis of Partial Differential Equations (PDEs) describing the behavior of ferrofluids. The most widely accepted PDE model for ferrofluids is the Micropolar model proposed by R.E. Rosensweig. The Micropolar Navier-Stokes Equations (MNSE) is a subsystem of PDEs within the Rosensweig model. Being a simplified version of the much bigger system of PDEs proposed by Rosensweig, the MNSE are a natural starting point of this thesis. The MNSE couple linear velocity u, angular velocity w, and pressure p. We propose and analyze a first-order semi-implicit fully-discrete scheme for the MNSE, which decouples the computation of the linear and angular velocities, is unconditionally stable and delivers optimal convergence rates under assumptions analogous to those used for the Navier-Stokes equations. Moving onto the much more complex Rosensweig's model, we provide a definition (approximation) for the effective magnetizing field h, and explain the assumptions behind this definition. Unlike previous definitions available in the literature, this new definition is able to accommodate the effect of external magnetic fields. Using this definition we setup the system of PDEs coupling linear velocity u, pressure p, angular velocity w, magnetization m, and magnetic potential ϕ We show that this system is energy-stable and devise a numerical scheme that mimics the same stability property. We prove that solutions of the numerical scheme always exist and, under certain simplifying assumptions, that the discrete solutions converge. A notable outcome of the analysis of the numerical scheme for the Rosensweig's model is the choice of finite element spaces that allow the construction of an energy-stable scheme. Finally, with the lessons learned from Rosensweig's model, we develop a diffuse-interface model describing the behavior of two-phase ferrofluid flows and present an energy-stable numerical scheme for this model. For a simplified version of this model and the corresponding numerical scheme we prove (in addition to stability) convergence and existence of solutions as by-product . Throughout this dissertation, we will provide numerical experiments, not only to validate mathematical results, but also to help the reader gain a qualitative understanding of the PDE models analyzed in this dissertation (the MNSE, the Rosenweig's model, and the Two-phase model). In addition, we also provide computational experiments to illustrate the potential of these simple models and their ability to capture basic phenomenological features of ferrofluids, such as the Rosensweig instability for the case of the two-phase model. In this respect, we highlight the incisive numerical experiments with the two-phase model illustrating the critical role of the demagnetizing field to reproduce physically realistic behavior of ferrofluids.

A New Homotopy Perturbation Scheme for Solving Singular Boundary Value Problems Arising in Various Physical Models

NASA Astrophysics Data System (ADS)

Roul, Pradip; Warbhe, Ujwal

2017-08-01

The classical homotopy perturbation method proposed by J. H. He, Comput. Methods Appl. Mech. Eng. 178, 257 (1999) is useful for obtaining the approximate solutions for a wide class of nonlinear problems in terms of series with easily calculable components. However, in some cases, it has been found that this method results in slowly convergent series. To overcome the shortcoming, we present a new reliable algorithm called the domain decomposition homotopy perturbation method (DDHPM) to solve a class of singular two-point boundary value problems with Neumann and Robin-type boundary conditions arising in various physical models. Five numerical examples are presented to demonstrate the accuracy and applicability of our method, including thermal explosion, oxygen-diffusion in a spherical cell and heat conduction through a solid with heat generation. A comparison is made between the proposed technique and other existing seminumerical or numerical techniques. Numerical results reveal that only two or three iterations lead to high accuracy of the solution and this newly improved technique introduces a powerful improvement for solving nonlinear singular boundary value problems (SBVPs).

Applications of MMPBSA to Membrane Proteins I: Efficient Numerical Solutions of Periodic Poisson-Boltzmann Equation

PubMed Central

Botello-Smith, Wesley M.; Luo, Ray

2016-01-01

Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membrane into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multi-grid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations. PMID:26389966

Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution

NASA Astrophysics Data System (ADS)

Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

2012-10-01

A singular boundary value problem for a second-order linear integrodifferential equation with Volterra and non-Volterra integral operators is formulated and analyzed. The equation is defined on ℝ+, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given limit boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deterministic premiums is given.

Study of tethered satellite active attitude control

NASA Technical Reports Server (NTRS)

Colombo, G.

1982-01-01

Existing software was adapted for the study of tethered subsatellite rotational dynamics, an analytic solution for a stable configuration of a tethered subsatellite was developed, the analytic and numerical integrator (computer) solutions for this "test case' was compared in a two mass tether model program (DUMBEL), the existing multiple mass tether model (SKYHOOK) was modified to include subsatellite rotational dynamics, the analytic "test case,' was verified, and the use of the SKYHOOK rotational dynamics capability with a computer run showing the effect of a single off axis thruster on the behavior of the subsatellite was demonstrated. Subroutines for specific attitude control systems are developed and applied to the study of the behavior of the tethered subsatellite under realistic on orbit conditions. The effect of all tether "inputs,' including pendular oscillations, air drag, and electrodynamic interactions, on the dynamic behavior of the tether are included.

Addition of Improved Shock-Capturing Schemes to OVERFLOW 2.1

NASA Technical Reports Server (NTRS)

Burning, Pieter G.; Nichols, Robert H.; Tramel, Robert W.

2009-01-01

Existing approximate Riemann solvers do not perform well when the grid is not aligned with strong shocks in the flow field. Three new approximate Riemann algorithms are investigated to improve solution accuracy and stability in the vicinity of strong shocks. The new algorithms are compared to the existing upwind algorithms in OVERFLOW 2.1. The new algorithms use a multidimensional pressure gradient based switch to transition to a more numerically dissipative algorithm in the vicinity of strong shocks. One new algorithm also attempts to artificially thicken captured shocks in order to alleviate the errors in the solution introduced by "stair-stepping" of the shock resulting from the approximate Riemann solver. This algorithm performed well for all the example cases and produced results that were almost insensitive to the alignment of the grid and the shock.

An improved, robust, axial line singularity method for bodies of revolution

NASA Technical Reports Server (NTRS)

Hemsch, Michael J.

1989-01-01

The failures encountered in attempts to increase the range of applicability of the axial line singularity method for representing incompressible, inviscid flow about an inclined and slender body-of-revolution are presently noted to be common to all efforts to solve Fredholm equations of the first kind. It is shown that a previously developed smoothing technique yields a robust method for numerical solution of the governing equations; this technique is easily retrofitted to existing codes, and allows the number of circularities to be increased until the most accurate line singularity solution is obtained.

Solution of Einsteins Equation for Deformation of a Magnetized Neutron Star

NASA Astrophysics Data System (ADS)

Rizaldy, R.; Sulaksono, A.

2018-04-01

We studied the effect of very large and non-uniform magnetic field existed in the neutron star on the deformation of the neutron star. We used in our analytical calculation, multipole expansion of the tensor metric and the momentum-energy tensor in Legendre polynomial expansion up to the quadrupole order. In this way we obtain the solutions of Einstein’s equation with the correction factors due to the magnetic field are taken into account. We obtain from our numerical calculation that the degree of deformation (ellipticity) is increased when the the mass is decreased.

Endogenous population growth may imply chaos.

PubMed

Prskawetz, A; Feichtinger, G

1995-01-01

The authors consider a discrete-time neoclassical growth model with an endogenous rate of population growth. The resulting one-dimensional map for the capital intensity has a tilted z-shape. Using the theory of nonlinear dynamical systems, they obtain numerical results on the qualitative behavior of time paths for changing parameter values. Besides stable and periodic solutions, erratic time paths may result. In particular, myopic and far-sighted economies--assumed to be characterized by low and high savings rate respectively--are characterized by stable per capita capital stocks, while solutions with chaotic windows exist between these two extremes.

Identifying the principal coefficient of parabolic equations with non-divergent form

NASA Astrophysics Data System (ADS)

Jiang, L. S.; Bian, B. J.

2005-01-01

We deal with an inverse problem of determining a coefficient a(x, t) of principal part for second order parabolic equations with non-divergent form when the solution is known. Such a problem has important applications in a large fields of applied science. We propose a well-posed approximate algorithm to identify the coefficient. The existence, uniqueness and stability of such solutions a(x, t) are proved. A necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced. Our numerical simulations show that the coefficient is recovered very well.

Laplace-transform-based method to calculate back-reflected radiance from an isotropically scattering half-space

NASA Astrophysics Data System (ADS)

Rinzema, K.; Hoenders, B. J.; Ferwerda, H. A.

1997-07-01

We present a method to determine the back-reflected radiance from an isotropically scattering half-space with matched boundary. This method has the advantage that it leads very quickly to the relevant equations, the numerical solution of which is also quite easy. Essentially, the method is derived from a mathematical criterion that effectively forbids the existence of solutions to the transport equation which grow exponentially as one moves away from the surface and deeper into the medium. Preliminary calculations for infinitely wide beams yield results which agree very well with what is found in the literature.

Nonlocal systems of balance laws in several space dimensions with applications to laser technology

NASA Astrophysics Data System (ADS)

Colombo, Rinaldo M.; Marcellini, Francesca

2015-12-01

For a class of systems of nonlinear and nonlocal balance laws in several space dimensions, we prove the local in time existence of solutions and their continuous dependence on the initial datum. The choice of this class is motivated by a new model devoted to the description of a metal plate being cut by a laser beam. Using realistic parameters, solutions to this model obtained through numerical integrations meet qualitative properties of real cuts. Moreover, the class of equations considered comprises a model describing the dynamics of solid particles along a conveyor belt.

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

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Quasi-integrability in deformed sine-Gordon models and infinite towers of conserved charges

NASA Astrophysics Data System (ADS)

Blas, Harold; Callisaya, Hector Flores

2018-02-01

We have studied the space-reflection symmetries of some soliton solutions of deformed sine-Gordon models in the context of the quasi-integrability concept. Considering a dual pair of anomalous Lax representations of the deformed model we compute analytically and numerically an infinite number of alternating conserved and asymptotically conserved charges through a modification of the usual techniques of integrable field theories. The charges associated to two-solitons with a definite parity under space-reflection symmetry, i.e. kink-kink (odd parity) and kink-antikink (even parity) scatterings with equal and opposite velocities, split into two infinite towers of conserved and asymptotically conserved charges. For two-solitons without definite parity under space-reflection symmetry (kink-kink and kink-antikink scatterings with unequal and opposite velocities) our numerical results show the existence of the asymptotically conserved charges only. However, we show that in the center-of-mass reference frame of the two solitons the parity symmetries and their associated set of exactly conserved charges can be restored. Moreover, the positive parity breather-like (kink-antikink bound state) solution exhibits a tower of exactly conserved charges and a subset of charges which are periodic in time. We back up our results with extensive numerical simulations which also demonstrate the existence of long lived breather-like states in these models. The time evolution has been simulated by the 4th order Runge-Kutta method supplied with non-reflecting boundary conditions.

Research on Aero-Thermodynamic Distortion Induced Structural Dynamic Response of Multi-Stage Compressor Blading.

DTIC Science & Technology

1988-01-15

However. only very engineering limited experimental data exists to assess the Director, Thermal Sciences and range of validity and to direct the... experimental results of Goldstein et. al. "A 1111 and also the Navier Stokes numerical solutions of Morihara 1121. Diffuser The predicted stream function...Unsteady Aerodynamic Interactions in a Multistage Compressor............................................................ 53 I APPENDIX VI. Experimental

Structure of solar coronal streamers

NASA Astrophysics Data System (ADS)

Schultz, C. G.

The present, direct method for the solution of generalized potential problems works outward from an O-point, under an assumption of the existence of flux surfaces. At each flux surface, a Fourier filter is used for the flux surface length variable to prevent numerical error amplifications, and the value of the inverse curvature radius and the normal direction are filtered to avoid the effects of local wrinkles.

Updates to Simulation of a Single-Element Lean-Direct Injection Combustor Using a Polyhedral Mesh Derived From Hanging-Node Elements

NASA Technical Reports Server (NTRS)

Wey, Changju Thomas; Liu, Nan-Suey

2014-01-01

This paper summarizes the procedures of inserting a thin-layer mesh to existing inviscid polyhedral mesh either with or without hanging-node elements as well as presents sample results from its applications to the numerical solution of a single-element LDI combustor using a releasable edition of the National Combustion Code (NCC).

Updates to Simulation of a Single-Element Lean-Direct Injection Combustor Using a Polyhedral Mesh Derived from Hanging-Node Elements

NASA Technical Reports Server (NTRS)

Wey, Thomas; Liu, Nan-Suey

2014-01-01

This paper summarizes the procedures of inserting a thin-layer mesh to existing inviscid polyhedral mesh either with or without hanging-node elements as well as presents sample results from its applications to the numerical solution of a single-element LDI combustor using a releasable edition of the National Combustion Code (NCC).

Enhanced verification test suite for physics simulation codes

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

Kamm, James R.; Brock, Jerry S.; Brandon, Scott T.

2008-09-01

This document discusses problems with which to augment, in quantity and in quality, the existing tri-laboratory suite of verification problems used by Los Alamos National Laboratory (LANL), Lawrence Livermore National Laboratory (LLNL), and Sandia National Laboratories (SNL). The purpose of verification analysis is demonstrate whether the numerical results of the discretization algorithms in physics and engineering simulation codes provide correct solutions of the corresponding continuum equations.

Bifurcation analysis of a photoreceptor interaction model for Retinitis Pigmentosa

NASA Astrophysics Data System (ADS)

Camacho, Erika T.; Radulescu, Anca; Wirkus, Stephen

2016-09-01

Retinitis Pigmentosa (RP) is the term used to describe a diverse set of degenerative eye diseases affecting the photoreceptors (rods and cones) in the retina. This work builds on an existing mathematical model of RP that focused on the interaction of the rods and cones. We non-dimensionalize the model and examine the stability of the equilibria. We then numerically investigate other stable modes that are present in the system for various parameter values and relate these modes to the original problem. Our results show that stable modes exist for a wider range of parameter values than the stability of the equilibrium solutions alone, suggesting that additional approaches to preventing cone death may exist.

Numerical solutions of Navier-Stokes equations for a Butler wing

NASA Technical Reports Server (NTRS)

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

1985-01-01

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, 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 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 parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

Validation of Groundwater Models: Meaningful or Meaningless?

NASA Astrophysics Data System (ADS)

Konikow, L. F.

2003-12-01

Although numerical simulation models are valuable tools for analyzing groundwater systems, their predictive accuracy is limited. People who apply groundwater flow or solute-transport models, as well as those who make decisions based on model results, naturally want assurance that a model is "valid." To many people, model validation implies some authentication of the truth or accuracy of the model. History matching is often presented as the basis for model validation. Although such model calibration is a necessary modeling step, it is simply insufficient for model validation. Because of parameter uncertainty and solution non-uniqueness, declarations of validation (or verification) of a model are not meaningful. Post-audits represent a useful means to assess the predictive accuracy of a site-specific model, but they require the existence of long-term monitoring data. Model testing may yield invalidation, but that is an opportunity to learn and to improve the conceptual and numerical models. Examples of post-audits and of the application of a solute-transport model to a radioactive waste disposal site illustrate deficiencies in model calibration, prediction, and validation.

Stability and bifurcation analysis of three-species predator-prey model with non-monotonic delayed predator response

NASA Astrophysics Data System (ADS)

Balilo, Aldrin T.; Collera, Juancho A.

2018-03-01

In this paper, we consider delayed three-species predator-prey model with non-monotonic functional response where two predator populations feed on a single prey population. Response function in both predator populations includes a time delay which represents the gestation period of the predator populations. We call a positive equlibrium solution of the form E*S=(x*,y*,y*) as a symmetric equilibrium. The goal of this paper is to determine the effect of the difference in gestation periods of predator populations to the local dynamics of symmetric equilibria. Our results include conditions on the existence of equilibrium solutions, and stability and bifurcations of symmetric equilibria as the gestation periods of predator populations are varied. A numerical bifurcation analysis tool is also used to illustrate our results. Stability switch occurs at a Hopf bifurcation. Moreover, a branch of stable periodic solutions, obtained using numerical continuation, emerges from the Hopf bifurcation. This shows that the predator population with longer gestation period oscillates higher than the predator population with shorter gestation period.

Solutions of interval type-2 fuzzy polynomials using a new ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim; Ghani, Ahmad Termimi Ab.; Ahmad, Noor'Ani

2015-10-01

A few years ago, a ranking method have been introduced in the fuzzy polynomial equations. Concept of the ranking method is proposed to find actual roots of fuzzy polynomials (if exists). Fuzzy polynomials are transformed to system of crisp polynomials, performed by using ranking method based on three parameters namely, Value, Ambiguity and Fuzziness. However, it was found that solutions based on these three parameters are quite inefficient to produce answers. Therefore in this study a new ranking method have been developed with the aim to overcome the inherent weakness. The new ranking method which have four parameters are then applied in the interval type-2 fuzzy polynomials, covering the interval type-2 of fuzzy polynomial equation, dual fuzzy polynomial equations and system of fuzzy polynomials. The efficiency of the new ranking method then numerically considered in the triangular fuzzy numbers and the trapezoidal fuzzy numbers. Finally, the approximate solutions produced from the numerical examples indicate that the new ranking method successfully produced actual roots for the interval type-2 fuzzy polynomials.

Chemotaxis with logistic source

NASA Astrophysics Data System (ADS)

Winkler, Michael

2008-12-01

We consider the chemotaxis system in a smooth bounded domain , where [chi]>0 and g generalizes the logistic function g(u)=Au-bu[alpha] with [alpha]>1, A[greater-or-equal, slanted]0 and b>0. A concept of very weak solutions is introduced, and global existence of such solutions for any nonnegative initial data u0[set membership, variant]L1([Omega]) is proved under the assumption that . Moreover, boundedness properties of the constructed solutions are studied. Inter alia, it is shown that if b is sufficiently large and u0[set membership, variant]L[infinity]([Omega]) has small norm in L[gamma]([Omega]) for some then the solution is globally bounded. Finally, in the case that additionally holds, a bounded set in L[infinity]([Omega]) can be found which eventually attracts very weak solutions emanating from arbitrary L1 initial data. The paper closes with numerical experiments that illustrate some of the theoretically established results.

Stability analysis of the Peregrine solution via squared eigenfunctions

NASA Astrophysics Data System (ADS)

Schober, C. M.; Strawn, M.

2017-10-01

A preliminary numerical investigation involving ensembles of perturbed initial data for the Peregrine soliton (the lowest order rational solution of the nonlinear Schrödinger equation) indicates that it is unstable [16]. In this paper we analytically investigate the linear stability of the Peregrine soliton, appealing to the fact that the Peregrine solution can be viewed as the singular limit of a single mode spatially periodic breathers (SPB). The "squared eigenfunction" connection between the Zakharov-Shabat (Z-S) system and the linearized NLS equation is employed in the stability analysis. Specifically, we determine the eigenfunctions of the Z-S system associated with the Peregrine soliton and construct a family of solutions of the associated linearized NLS (about the Peregrine) in terms of quadratic products of components of the eigenfunctions (i.e., the squared eigenfunction). We find there exist solutions of the linearization that grow exponentially in time, thus showing the Peregrine soliton is linearly unstable.

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.

On the Hosoya index of a family of deterministic recursive trees

NASA Astrophysics Data System (ADS)

Chen, Xufeng; Zhang, Jingyuan; Sun, Weigang

2017-01-01

In this paper, we calculate the Hosoya index in a family of deterministic recursive trees with a special feature that includes new nodes which are connected to existing nodes with a certain rule. We then obtain a recursive solution of the Hosoya index based on the operations of a determinant. The computational complexity of our proposed algorithm is O(log2 n) with n being the network size, which is lower than that of the existing numerical methods. Finally, we give a weighted tree shrinking method as a graphical interpretation of the recurrence formula for the Hosoya index.

Coexistence of collapse and stable spatiotemporal solitons in multimode fibers

NASA Astrophysics Data System (ADS)

Shtyrina, Olga V.; Fedoruk, Mikhail P.; Kivshar, Yuri S.; Turitsyn, Sergei K.

2018-01-01

We analyze spatiotemporal solitons in multimode optical fibers and demonstrate the existence of stable solitons, in a sharp contrast to earlier predictions of collapse of multidimensional solitons in three-dimensional media. We discuss the coexistence of blow-up solutions and collapse stabilization by a low-dimensional external potential in graded-index media, and also predict the existence of stable higher-order nonlinear waves such as dipole-mode spatiotemporal solitons. To support the main conclusions of our numerical studies we employ a variational approach and derive analytically the stability criterion for input powers for the collapse stabilization.

Existence, uniqueness and regularity of a time-periodic probability density distribution arising in a sedimentation-diffusion problem

NASA Technical Reports Server (NTRS)

Nitsche, Ludwig C.; Nitsche, Johannes M.; Brenner, Howard

1988-01-01

The sedimentation and diffusion of a nonneutrally buoyant Brownian particle in vertical fluid-filled cylinder of finite length which is instantaneously inverted at regular intervals are investigated analytically. A one-dimensional convective-diffusive equation is derived to describe the temporal and spatial evolution of the probability density; a periodicity condition is formulated; the applicability of Fredholm theory is established; and the parameter-space regions are determined within which the existence and uniqueness of solutions are guaranteed. Numerical results for sample problems are presented graphically and briefly characterized.

Wakes and precursor soliton excitations by a moving charged object in a plasma

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

Kumar Tiwari, Sanat, E-mail: sanat-tiwari@uiowa.edu; Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242; Sen, Abhijit, E-mail: senabhijit@gmail.com

2016-02-15

We study the evolution of nonlinear ion acoustic wave excitations due to a moving charged source in a plasma. Our numerical investigations of the full set of cold fluid equations go beyond the usual weak nonlinearity approximation and show the existence of a rich variety of solutions including wakes, precursor solitons, and “pinned” solitons that travel with the source velocity. These solutions represent a large amplitude generalization of solutions obtained in the past for the forced Korteweg deVries equation and can find useful applications in a variety of situations in the laboratory and in space, wherever there is a largemore » relative velocity between the plasma and a charged object.« less

Machining Chatter Analysis for High Speed Milling Operations

NASA Astrophysics Data System (ADS)

Sekar, M.; Kantharaj, I.; Amit Siddhappa, Savale

2017-10-01

Chatter in high speed milling is characterized by time delay differential equations (DDE). Since closed form solution exists only for simple cases, the governing non-linear DDEs of chatter problems are solved by various numerical methods. Custom codes to solve DDEs are tedious to build, implement and not error free and robust. On the other hand, software packages provide solution to DDEs, however they are not straight forward to implement. In this paper an easy way to solve DDE of chatter in milling is proposed and implemented with MATLAB. Time domain solution permits the study and model of non-linear effects of chatter vibration with ease. Time domain results are presented for various stable and unstable conditions of cut and compared with stability lobe diagrams.

Stress waves in transversely isotropic media: The homogeneous problem

NASA Technical Reports Server (NTRS)

Marques, E. R. C.; Williams, J. H., Jr.

1986-01-01

The homogeneous problem of stress wave propagation in unbounded transversely isotropic media is analyzed. By adopting plane wave solutions, the conditions for the existence of the solution are established in terms of phase velocities and directions of particle displacements. Dispersion relations and group velocities are derived from the phase velocity expressions. The deviation angles (e.g., angles between the normals to the adopted plane waves and the actual directions of their propagation) are numerically determined for a specific fiber-glass epoxy composite. A graphical method is introduced for the construction of the wave surfaces using magnitudes of phase velocities and deviation angles. The results for the case of isotropic media are shown to be contained in the solutions for the transversely isotropic media.

Analytic theory of photoacoustic wave generation from a spheroidal droplet.

PubMed

Li, Yong; Fang, Hui; Min, Changjun; Yuan, Xiaocong

2014-08-25

In this paper, we develop an analytic theory for describing the photoacoustic wave generation from a spheroidal droplet and derive the first complete analytic solution. Our derivation is based on solving the photoacoustic Helmholtz equation in spheroidal coordinates with the separation-of-variables method. As the verification, besides carrying out the asymptotic analyses which recover the standard solutions for a sphere, an infinite cylinder and an infinite layer, we also confirm that the partial transmission and reflection model previously demonstrated for these three geometries still stands. We expect that this analytic solution will find broad practical uses in interpreting experiment results, considering that its building blocks, the spheroidal wave functions (SWFs), can be numerically calculated by the existing computer programs.

Optimal trace inequality constants for interior penalty discontinuous Galerkin discretisations of elliptic operators using arbitrary elements with non-constant Jacobians

NASA Astrophysics Data System (ADS)

Owens, A. R.; Kópházi, J.; Eaton, M. D.

2017-12-01

In this paper, a new method to numerically calculate the trace inequality constants, which arise in the calculation of penalty parameters for interior penalty discretisations of elliptic operators, is presented. These constants are provably optimal for the inequality of interest. As their calculation is based on the solution of a generalised eigenvalue problem involving the volumetric and face stiffness matrices, the method is applicable to any element type for which these matrices can be calculated, including standard finite elements and the non-uniform rational B-splines of isogeometric analysis. In particular, the presented method does not require the Jacobian of the element to be constant, and so can be applied to a much wider variety of element shapes than are currently available in the literature. Numerical results are presented for a variety of finite element and isogeometric cases. When the Jacobian is constant, it is demonstrated that the new method produces lower penalty parameters than existing methods in the literature in all cases, which translates directly into savings in the solution time of the resulting linear system. When the Jacobian is not constant, it is shown that the naive application of existing approaches can result in penalty parameters that do not guarantee coercivity of the bilinear form, and by extension, the stability of the solution. The method of manufactured solutions is applied to a model reaction-diffusion equation with a range of parameters, and it is found that using penalty parameters based on the new trace inequality constants result in better conditioned linear systems, which can be solved approximately 11% faster than those produced by the methods from the literature.

An Artificial Neural Networks Method for Solving Partial Differential Equations

NASA Astrophysics Data System (ADS)

Alharbi, Abir

2010-09-01

While there already exists many analytical and numerical techniques for solving PDEs, this paper introduces an approach using artificial neural networks. The approach consists of a technique developed by combining the standard numerical method, finite-difference, with the Hopfield neural network. The method is denoted Hopfield-finite-difference (HFD). The architecture of the nets, energy function, updating equations, and algorithms are developed for the method. The HFD method has been used successfully to approximate the solution of classical PDEs, such as the Wave, Heat, Poisson and the Diffusion equations, and on a system of PDEs. The software Matlab is used to obtain the results in both tabular and graphical form. The results are similar in terms of accuracy to those obtained by standard numerical methods. In terms of speed, the parallel nature of the Hopfield nets methods makes them easier to implement on fast parallel computers while some numerical methods need extra effort for parallelization.

Numerical Simulation of Black Holes

NASA Astrophysics Data System (ADS)

Teukolsky, Saul

2003-04-01

Einstein's equations of general relativity are prime candidates for numerical solution on supercomputers. There is some urgency in being able to carry out such simulations: Large-scale gravitational wave detectors are now coming on line, and the most important expected signals cannot be predicted except numerically. Problems involving black holes are perhaps the most interesting, yet also particularly challenging computationally. One difficulty is that inside a black hole there is a physical singularity that cannot be part of the computational domain. A second difficulty is the disparity in length scales between the size of the black hole and the wavelength of the gravitational radiation emitted. A third difficulty is that all existing methods of evolving black holes in three spatial dimensions are plagued by instabilities that prohibit long-term evolution. I will describe the ideas that are being introduced in numerical relativity to deal with these problems, and discuss the results of recent calculations of black hole collisions.

An analysis of the vapor flow and the heat conduction through the liquid-wick and pipe wall in a heat pipe with single or multiple heat sources

NASA Technical Reports Server (NTRS)

Chen, Ming-Ming; Faghri, Amir

1990-01-01

A numerical analysis is presented for the overall performance of heat pipes with single or multiple heat sources. The analysis includes the heat conduction in the wall and liquid-wick regions as well as the compressibility effect of the vapor inside the heat pipe. The two-dimensional elliptic governing equations in conjunction with the thermodynamic equilibrium relation and appropriate boundary conditions are solved numerically. The solutions are in agreement with existing experimental data for the vapor and wall temperatures at both low and high operating temperatures.

Modelling migration in multilayer systems by a finite difference method: the spherical symmetry case

NASA Astrophysics Data System (ADS)

Hojbotǎ, C. I.; Toşa, V.; Mercea, P. V.

2013-08-01

We present a numerical model based on finite differences to solve the problem of chemical impurity migration within a multilayer spherical system. Migration here means diffusion of chemical species in conditions of concentration partitioning at layer interfaces due to different solubilities of the migrant in different layers. We detail here the numerical model and discuss the results of its implementation. To validate the method we compare it with cases where an analytic solution exists. We also present an application of our model to a practical problem in which we compute the migration of caprolactam from the packaging multilayer foil into the food.

Unsteady boundary layer rotating flow and heat transfer in a copper-water nanofluid over a shrinking sheet

NASA Astrophysics Data System (ADS)

Dzulkifli, Nor Fadhilah; Bachok, Norfifah; Yacob, Nor Azizah; Arifin, Norihan Md; Rosali, Haliza

2017-04-01

The study of unsteady three-dimensional boundary layer rotating flow with heat transfer in Copper-water nanofluid over a shrinking sheet is discussed. The governing equations in terms of partial differential equations are transformed to ordinary differential equations by introducing the appropriate similarity variables which are then solved numerically by a shooting method with Maple software. The numerical results of velocity gradient in x and y directions, skin friction coefficient and local Nusselt number as well as dual velocity and temperature profiles are shown graphically. The study revealed that dual solutions exist in certain range of s > 0.

A numerical analysis of high-temperature heat pipe startup from the frozen state

NASA Technical Reports Server (NTRS)

Cao, Y.; Faghri, A.

1993-01-01

Continuum and rarefied vapor flows co-exist along the heat pipe length for most of the startup period. A two-region model is proposed in which the vapor flow in the continuum region is modeled by the compressible Navier-Stokes equations, and the vapor flow in the rarefied region is simulated by a self-diffusion model. The two vapor regions are linked with appropriate boundary conditions, and heat pipe wail, wick, and vapor flow are solved as a conjugate problem. The numerical solutions for the entire heat pipe startup process from the frozen state are compared with the corresponding experimental data with good agreement.

Influence of Non-linear Radiation Heat Flux on Rotating Maxwell Fluid over a Deformable Surface: A Numerical Study

NASA Astrophysics Data System (ADS)

Mustafa, M.; Mushtaq, A.; Hayat, T.; Alsaedi, A.

2018-04-01

Mathematical model for Maxwell fluid flow in rotating frame induced by an isothermal stretching wall is explored numerically. Scale analysis based boundary layer approximations are applied to simplify the conservation relations which are later converted to similar forms via appropriate substitutions. A numerical approach is utilized to derive similarity solutions for broad range of Deborah number. The results predict that velocity distributions are inversely proportional to the stress relaxation time. This outcome is different from that observed for the elastic parameter of second grade fluid. Unlike non-rotating frame, the solution curves are oscillatory decaying functions of similarity variable. As angular velocity enlarges, temperature rises and significant drop in the heat transfer coefficient occurs. We note that the wall slope of temperature has an asymptotically decaying profile against the wall to ambient ratio parameter. From the qualitative view point, temperature ratio parameter and radiation parameter have similar effect on the thermal boundary layer. Furthermore, radiation parameter has a definite role in improving the cooling process of the stretching boundary. A comparative study of current numerical computations and those from the existing studies is also presented in a limiting case. To our knowledge, the phenomenon of non-linear radiation in rotating viscoelastic flow due to linearly stretched plate is just modeled here.

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

Brihaye, Yves; Delsate, Terence; Kodama, Yuta

We consider a six-dimensional brane world model, where the brane is described by a localized solution to the baby-Skyrme model extending in the extra dimensions. The branes have a cosmological constant modeled by inflating four-dimensional slices, and we further consider a bulk cosmological constant. We construct solutions numerically and present evidence that the solutions cease to exist for large values of the brane cosmological constant in some particular case. Then we study the stability of the model by considering perturbation of the gravitational part (resp. baby Skyrmion) with fixed matter fields (resp. gravitational background). Our results indicate that the perturbationmore » equations do not admit localized solutions for certain type of perturbation. The stability analysis can be alternatively seen as leading to a particle spectrum; we give mass estimations for the baby-Skyrme perturbation and for the graviton.« less

Development of comprehensive numerical schemes for predicting evaporating gas-droplets flow processes of a liquid-fueled combustor

NASA Technical Reports Server (NTRS)

Chen, C. P.

1990-01-01

An existing Computational Fluid Dynamics code for simulating complex turbulent flows inside a liquid rocket combustion chamber was validated and further developed. The Advanced Rocket Injector/Combustor Code (ARICC) is simplified and validated against benchmark flow situations for laminar and turbulent flows. The numerical method used in ARICC Code is re-examined for incompressible flow calculations. For turbulent flows, both the subgrid and the two equation k-epsilon turbulence models are studied. Cases tested include idealized Burger's equation in complex geometries and boundaries, a laminar pipe flow, a high Reynolds number turbulent flow, and a confined coaxial jet with recirculations. The accuracy of the algorithm is examined by comparing the numerical results with the analytical solutions as well as experimented data with different grid sizes.

Mean Field Type Control with Congestion (II): An Augmented Lagrangian Method

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

Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Laurière, Mathieu

This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential equations arising from the model were discussed and existence and uniqueness were proved. Here, the focus is put on numerical methods: a monotone finite difference scheme is proposed and shown to have a variational interpretation. Then an Alternating Direction Method of Multipliers for solving the variational problem is addressed. It is based on an augmented Lagrangian. Two kinds of boundary conditionsmore » are considered: periodic conditions and more realistic boundary conditions associated to state constrained problems. Various test cases and numerical results are presented.« less

Semianalytical solutions for contaminant transport under variable velocity field in a coastal aquifer

NASA Astrophysics Data System (ADS)

Koohbor, Behshad; Fahs, Marwan; Ataie-Ashtiani, Behzad; Simmons, Craig T.; Younes, Anis

2018-05-01

Existing closed-form solutions of contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. These solutions cannot be used to investigate contaminant transport in coastal aquifers where seawater intrusion induces a variable velocity field. An adaptation of the Fourier-Galerkin method is introduced to obtain semi-analytical solutions for contaminant transport in a confined coastal aquifer in which the saltwater wedge is in equilibrium with a freshwater discharge flow. Two scenarios dealing with contaminant leakage from the aquifer top surface and contaminant migration from a source at the landward boundary are considered. Robust implementation of the Fourier-Galerkin method is developed to efficiently solve the coupled flow, salt and contaminant transport equations. Various illustrative examples are generated and the semi-analytical solutions are compared against an in-house numerical code. The Fourier series are used to evaluate relevant metrics characterizing contaminant transport such as the discharge flux to the sea, amount of contaminant persisting in the groundwater and solute flux from the source. These metrics represent quantitative data for numerical code validation and are relevant to understand the effect of seawater intrusion on contaminant transport. It is observed that, for the surface contamination scenario, seawater intrusion limits the spread of the contaminant but intensifies the contaminant discharge to the sea. For the landward contamination scenario, moderate seawater intrusion affects only the spatial distribution of the contaminant plume while extreme seawater intrusion can increase the contaminant discharge to the sea. The developed semi-analytical solution presents an efficient tool for the verification of numerical models. It provides a clear interpretation of the contaminant transport processes in coastal aquifers subject to seawater intrusion. For practical usage in further studies, the full open source semi-analytical codes are made available at the website https://lhyges.unistra.fr/FAHS-Marwan.

Laboratory measurement of tip and global behavior for zero-toughness hydraulic fractures with circular and blade-shaped (PKN) geometry

NASA Astrophysics Data System (ADS)

Xing, Pengju; Yoshioka, Keita; Adachi, Jose; El-Fayoumi, Amr; Bunger, Andrew P.

2017-07-01

The tip behavior of hydraulic fractures is characterized by a rich nesting of asymptotic solutions, comprising a formidable challenge for the development of efficient and accurate numerical simulators. We present experimental validation of several theoretically-predicted asymptotic behaviors, namely for hydraulic fracture growth under conditions of negligible fracture toughness, with growth progressing from early-time radial geometry to large-time blade-like (PKN) geometry. Our experimental results demonstrate: 1) existence of a asymptotic solution of the form w ∼ s3/2 (LEFM) in the near tip region, where w is the crack opening and s is the distance from the crack tip, 2) transition to an asymptotic solution of the form w ∼ s2/3 away from the near-tip region, with the transition length scale also consistent with theory, 3) transition to an asymptotic solution of the form w ∼ s1/3 after the fracture attains blade-like (PKN) geometry, and 4) existence of a region near the tip of a blade-like (PKN) hydraulic fracture in which plane strain conditions persist, with the thickness of this region of the same order as the crack height.

Splash singularity for water waves.

PubMed

Castro, Angel; Córdoba, Diego; Fefferman, Charles L; Gancedo, Francisco; Gómez-Serrano, Javier

2012-01-17

We exhibit smooth initial data for the two-dimensional (2D) water-wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water-wave equation that start from a graph, turn over, and collapse in a splash singularity (self-intersecting curve in one point) in finite time.

Splash singularity for water waves

PubMed Central

Castro, Angel; Córdoba, Diego; Fefferman, Charles L.; Gancedo, Francisco; Gómez-Serrano, Javier

2012-01-01

We exhibit smooth initial data for the two-dimensional (2D) water-wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water-wave equation that start from a graph, turn over, and collapse in a splash singularity (self-intersecting curve in one point) in finite time. PMID:22219372

Nonperturbative confinement in quantum chromodynamics. I. Study of an approximate equation of Mandelstam

NASA Astrophysics Data System (ADS)

Atkinson, D.; Drohm, J. K.; Johnson, P. W.; Stam, K.

1981-11-01

An approximated form of the Dyson-Schwinger equation for the gluon propagator in quarkless QCD is subjected to nonlinear functional and numerical analysis. It is found that solutions exist, and that these have a double pole at the origin of the square of the propagator momentum, together with an accumulation of soft branch points. This analytic structure is strongly suggestive of confinement by infrared slavery.

Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

PubMed

Predoi, Mihai Valentin

2014-09-01

The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.

New non-linear model of groundwater recharge: Inclusion of memory, heterogeneity and visco-elasticity

NASA Astrophysics Data System (ADS)

Spannenberg, Jescica; Atangana, Abdon; Vermeulen, P. D.

2017-09-01

Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.

Algorithms for the computation of solutions of the Ornstein-Zernike equation.

PubMed

Peplow, A T; Beardmore, R E; Bresme, F

2006-10-01

We introduce a robust and efficient methodology to solve the Ornstein-Zernike integral equation using the pseudoarc length (PAL) continuation method that reformulates the integral equation in an equivalent but nonstandard form. This enables the computation of solutions in regions where the compressibility experiences large changes or where the existence of multiple solutions and so-called branch points prevents Newton's method from converging. We illustrate the use of the algorithm with a difficult problem that arises in the numerical solution of integral equations, namely the evaluation of the so-called no-solution line of the Ornstein-Zernike hypernetted chain (HNC) integral equation for the Lennard-Jones potential. We are able to use the PAL algorithm to solve the integral equation along this line and to connect physical and nonphysical solution branches (both isotherms and isochores) where appropriate. We also show that PAL continuation can compute solutions within the no-solution region that cannot be computed when Newton and Picard methods are applied directly to the integral equation. While many solutions that we find are new, some correspond to states with negative compressibility and consequently are not physical.

Development of Numerical Tools for the Investigation of Plasma Detachment from Magnetic Nozzles

NASA Technical Reports Server (NTRS)

Sankaran, Kamesh; Polzin, Kurt A.

2007-01-01

A multidimensional numerical simulation framework aimed at investigating the process of plasma detachment from a magnetic nozzle is introduced. An existing numerical code based on a magnetohydrodynamic formulation of the plasma flow equations that accounts for various dispersive and dissipative processes in plasmas was significantly enhanced to allow for the modeling of axisymmetric domains containing three.dimensiunai momentum and magnetic flux vectors. A separate magnetostatic solver was used to simulate the applied magnetic field topologies found in various nozzle experiments. Numerical results from a magnetic diffusion test problem in which all three components of the magnetic field were present exhibit excellent quantitative agreement with the analytical solution, and the lack of numerical instabilities due to fluctuations in the value of del(raised dot)B indicate that the conservative MHD framework with dissipative effects is well-suited for multi-dimensional analysis of magnetic nozzles. Further studies will focus on modeling literature experiments both for the purpose of code validation and to extract physical insight regarding the mechanisms driving detachment.

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 conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

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

Gamba, Irene M.; ICES, The University of Texas at Austin, 201 E. 24th St., Stop C0200, Austin, TX 78712; Haack, Jeffrey R.

2014-08-01

We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit tomore » the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation.« less

The inverse Numerical Computer Program FLUX-BOT for estimating Vertical Water Fluxes from Temperature Time-Series.

NASA Astrophysics Data System (ADS)

Trauth, N.; Schmidt, C.; Munz, M.

2016-12-01

Heat as a natural tracer to quantify water fluxes between groundwater and surface water has evolved to a standard hydrological method. Typically, time series of temperatures in the surface water and in the sediment are observed and are subsequently evaluated by a vertical 1D representation of heat transport by advection and dispersion. Several analytical solutions as well as their implementation into user-friendly software exist in order to estimate water fluxes from the observed temperatures. Analytical solutions can be easily implemented but assumptions on the boundary conditions have to be made a priori, e.g. sinusoidal upper temperature boundary. Numerical models offer more flexibility and can handle temperature data which is characterized by irregular variations such as storm-event induced temperature changes and thus cannot readily be incorporated in analytical solutions. This also reduced the effort of data preprocessing such as the extraction of the diurnal temperature variation. We developed a software to estimate water FLUXes Based On Temperatures- FLUX-BOT. FLUX-BOT is a numerical code written in MATLAB which is intended to calculate vertical water fluxes in saturated sediments, based on the inversion of measured temperature time series observed at multiple depths. It applies a cell-centered Crank-Nicolson implicit finite difference scheme to solve the one-dimensional heat advection-conduction equation. Besides its core inverse numerical routines, FLUX-BOT includes functions visualizing the results and functions for performing uncertainty analysis. We provide applications of FLUX-BOT to generic as well as to measured temperature data to demonstrate its performance.

Protostellar Collapse with a Shock

NASA Technical Reports Server (NTRS)

Tsai, John C.; Hsu, Juliana J.

1995-01-01

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(exp -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Protostellar Collapse with a Shock

NASA Technical Reports Server (NTRS)

Tsai, John C.; Hsu, Juliana J. L.

1995-01-01

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(sup -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Root finding in the complex plane for seismo-acoustic propagation scenarios with Green's function solutions.

PubMed

McCollom, Brittany A; Collis, Jon M

2014-09-01

A normal mode solution to the ocean acoustic problem of the Pekeris waveguide with an elastic bottom using a Green's function formulation for a compressional wave point source is considered. Analytic solutions to these types of waveguide propagation problems are strongly dependent on the eigenvalues of the problem; these eigenvalues represent horizontal wavenumbers, corresponding to propagating modes of energy. The eigenvalues arise as singularities in the inverse Hankel transform integral and are specified by roots to a characteristic equation. These roots manifest themselves as poles in the inverse transform integral and can be both subtle and difficult to determine. Following methods previously developed [S. Ivansson et al., J. Sound Vib. 161 (1993)], a root finding routine has been implemented using the argument principle. Using the roots to the characteristic equation in the Green's function formulation, full-field solutions are calculated for scenarios where an acoustic source lies in either the water column or elastic half space. Solutions are benchmarked against laboratory data and existing numerical solutions.

Multigrid methods for a semilinear PDE in the theory of pseudoplastic fluids

NASA Technical Reports Server (NTRS)

Henson, Van Emden; Shaker, A. W.

1993-01-01

We show that by certain transformations the boundary layer equations for the class of non-Newtonian fluids named pseudoplastic can be generalized in the form the vector differential operator(u) + p(x)u(exp -lambda) = 0, where x is a member of the set Omega and Omega is a subset of R(exp n), n is greater than or equal to 1 under the classical conditions for steady flow over a semi-infinite flat plate. We provide a survey of the existence, uniqueness, and analyticity of the solutions for this problem. We also establish numerical solutions in one- and two-dimensional regions using multigrid methods.

Longtime dynamics of the PDE model for the motion toward light of bacterial colonies

NASA Astrophysics Data System (ADS)

Taranets, R.; Chugunova, M.

2018-03-01

We study stationary solutions and longtime dynamics of the PDE model for cyanobacteria motion, which was recently proposed by Chavy-Waddy and Kolokolnikov (2016 Nonlinearity 29 3174). For different values of the parameter α, which controls the extent of the aggregate, we analyse a family of corresponding steady states and their stability (considering symmetric and non-symmetric cases separately). We derive the rate of convergence toward steady states, show existence of weak nonnegative solutions, and we also discover that the value α = 3 is a special case for this PDE model. Using numerical simulations we compare different regimes and illustrate convergence toward steady states.

Modeling the state dependent impulse control for computer virus propagation under media coverage

NASA Astrophysics Data System (ADS)

Liang, Xiyin; Pei, Yongzhen; Lv, Yunfei

2018-02-01

A state dependent impulsive control model is proposed to model the spread of computer virus incorporating media coverage. By the successor function, the sufficient conditions for the existence and uniqueness of order-1 periodic solution are presented first. Secondly, for two classes of periodic solutions, the geometric property of successor function and the analogue of the Poincaré criterion are employed to obtain the stability results. These results show that the number of the infective computers is under the threshold all the time. Finally, the theoretic and numerical analysis show that media coverage can delay the spread of computer virus.

Numerical solution of the stochastic parabolic equation with the dependent operator coefficient

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

Ashyralyev, Allaberen; Department of Mathematics, ITTU, Ashgabat; Okur, Ulker

2015-09-18

In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.

Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon min-max optimal control problems with uncertainty

NASA Astrophysics Data System (ADS)

Nikooeinejad, Z.; Delavarkhalafi, A.; Heydari, M.

2018-03-01

The difficulty of solving the min-max optimal control problems (M-MOCPs) with uncertainty using generalised Euler-Lagrange equations is caused by the combination of split boundary conditions, nonlinear differential equations and the manner in which the final time is treated. In this investigation, the shifted Jacobi pseudospectral method (SJPM) as a numerical technique for solving two-point boundary value problems (TPBVPs) in M-MOCPs for several boundary states is proposed. At first, a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented. Then, by applying the generalised Euler-Lagrange equations and expanding the required approximate solutions as elements of shifted Jacobi polynomials, finding a solution of TPBVPs in nonlinear M-MOCPs with uncertainty is reduced to the solution of a system of algebraic equations. Moreover, the Jacobi polynomials are particularly useful for boundary value problems in unbounded domain, which allow us to solve infinite- as well as finite and free final time problems by domain truncation method. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. A comparative study between the proposed method and other existing methods shows that the SJPM is simple and accurate.

Magnetization-induced dynamics of a Josephson junction coupled to a nanomagnet

NASA Astrophysics Data System (ADS)

Ghosh, Roopayan; Maiti, Moitri; Shukrinov, Yury M.; Sengupta, K.

2017-11-01

We study the superconducting current of a Josephson junction (JJ) coupled to an external nanomagnet driven by a time-dependent magnetic field both without and in the presence of an external ac drive. We provide an analytic, albeit perturbative, solution for the Landau-Lifshitz (LL) equations governing the coupled JJ-nanomagnet system in the presence of a magnetic field with arbitrary time dependence oriented along the easy axis of the nanomagnet's magnetization and in the limit of weak dimensionless coupling ɛ0 between the JJ and the nanomagnet. We show the existence of Shapiro-type steps in the I -V characteristics of the JJ subjected to a voltage bias for a constant or periodically varying magnetic field and explore the effect of rotation of the magnetic field and the presence of an external ac drive on these steps. We support our analytic results with exact numerical solution of the LL equations. We also extend our results to dissipative nanomagnets by providing a perturbative solution to the Landau-Lifshitz-Gilbert (LLG) equations for weak dissipation. We study the fate of magnetization-induced Shapiro steps in the presence of dissipation both from our analytical results and via numerical solution of the coupled LLG equations. We discuss experiments which can test our theory.

Sedimentary Geothermal Feasibility Study: October 2016

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

Augustine, Chad; Zerpa, Luis

The objective of this project is to analyze the feasibility of commercial geothermal projects using numerical reservoir simulation, considering a sedimentary reservoir with low permeability that requires productivity enhancement. A commercial thermal reservoir simulator (STARS, from Computer Modeling Group, CMG) is used in this work for numerical modeling. In the first stage of this project (FY14), a hypothetical numerical reservoir model was developed, and validated against an analytical solution. The following model parameters were considered to obtain an acceptable match between the numerical and analytical solutions: grid block size, time step and reservoir areal dimensions; the latter related to boundarymore » effects on the numerical solution. Systematic model runs showed that insufficient grid sizing generates numerical dispersion that causes the numerical model to underestimate the thermal breakthrough time compared to the analytic model. As grid sizing is decreased, the model results converge on a solution. Likewise, insufficient reservoir model area introduces boundary effects in the numerical solution that cause the model results to differ from the analytical solution.« less

Numerical framework for the modeling of electrokinetic flows

NASA Astrophysics Data System (ADS)

Deshpande, Manish; Ghaddar, Chahid; Gilbert, John R.; St. John, Pamela M.; Woudenberg, Timothy M.; Connell, Charles R.; Molho, Joshua; Herr, Amy; Mungal, Godfrey; Kenny, Thomas W.

1998-09-01

This paper presents a numerical framework for design-based analyses of electrokinetic flow in interconnects. Electrokinetic effects, which can be broadly divided into electrophoresis and electroosmosis, are of importance in providing a transport mechanism in microfluidic devices for both pumping and separation. Models for the electrokinetic effects can be derived and coupled to the fluid dynamic equations through appropriate source terms. In the design of practical microdevices, however, accurate coupling of the electrokinetic effects requires the knowledge of several material and physical parameters, such as the diffusivity and the mobility of the solute in the solvent. Additionally wall-based effects such as chemical binding sites might exist that affect the flow patterns. In this paper, we address some of these issues by describing a synergistic numerical/experimental process to extract the parameters required. Experiments were conducted to provide the numerical simulations with a mechanism to extract these parameters based on quantitative comparisons with each other. These parameters were then applied in predicting further experiments to validate the process. As part of this research, we have created NetFlow, a tool for micro-fluid analyses. The tool can be validated and applied in existing technologies by first creating test structures to extract representations of the physical phenomena in the device, and then applying them in the design analyses to predict correct behavior.

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.

Computation of molecular vibrational frequencies using anomalous harmoniclike potentials.

PubMed

Li, Xiangzhu; Paldus, Josef

2009-07-28

The instabilities of Hartree-Fock (HF) solutions at or near the equilibrium geometry of symmetric molecular species imply the existence of broken-symmetry solutions having a lower energy than the corresponding symmetry-adapted ones. Moreover, the distortion of the nuclear framework along the normal modes that are implied by such broken-symmetry solutions results in an anomalous or even singular behavior in the corresponding cuts of the potential energy surface (PES). Using such HF solutions as a reference, these anomalies propagate to a post-HF level and make it impossible to determine reliable harmonic or fundamental vibrational frequencies for such modes by relying on either numerical or analytical differentiation of the PES, requiring instead a numerical integration of the Schrodinger equation for the nuclear motion. This, in turn, requires a detailed knowledge on the PES in a wide range of geometries, necessitating a computation of the potential energy function in a large number of points. We present an alternative approach to this problem, referred to as the integral averaging method (IAM), which facilitates this task by significantly reducing the number of geometries for which one has to compute the potential energy while yielding results of practically the same accuracy as the solution of the Schrodinger equation. The IAM is applied to several ABA-type triatomics and to the allyl radical, whose asymmetric stretching mode potential suffers from an anomalous behavior due to the spin-preserving instabilities in restricted open-shell HF solutions.

Variational data assimilation for limited-area models: solution of the open boundary control problem and its application for the Gulf of Finland

NASA Astrophysics Data System (ADS)

Sheloput, Tatiana; Agoshkov, Valery

2017-04-01

The problem of modeling water areas with `liquid' (open) lateral boundaries is discussed. There are different known methods dealing with open boundaries in limited-area models, and one of the most efficient is data assimilation. Although this method is popular, there are not so many articles concerning its implementation for recovering boundary functions. However, the problem of specifying boundary conditions at the open boundary of a limited area is still actual and important. The mathematical model of the Baltic Sea circulation, developed in INM RAS, is considered. It is based on the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations. The splitting method that is used for time approximation in the model allows to consider the data assimilation problem as a sequence of linear problems. One of such `simple' temperature (salinity) assimilation problem is investigated in the study. Using well known techniques of study and solution of inverse problems and optimal control problems [1], we propose an iterative solution algorithm and we obtain conditions for existence of the solution, for unique and dense solvability of the problem and for convergence of the iterative algorithm. The investigation shows that if observations satisfy certain conditions, the proposed algorithm converges to the solution of the boundary control problem. Particularly, it converges when observational data are given on the `liquid' boundary [2]. Theoretical results are confirmed by the results of numerical experiments. The numerical algorithm was implemented to water area of the Baltic Sea. Two numerical experiments were carried out in the Gulf of Finland: one with the application of the assimilation procedure and the other without. The analyses have shown that the surface temperature field in the first experiment is close to the observed one, while the result of the second experiment misfits. Number of iterations depends on the regularisation parameter, but generally the algorithm converges after 10 iterations. The results of the numerical experiments show that the usage of the proposed method makes sense. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments) and by the Russian Foundation for Basic Research (project 16-01-00548, the formulation of the problem and its study). [1] Agoshkov V. I. Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian). [2] Agoshkov V.I., Sheloput T.O. The study and numerical solution of the problem of heat and salinity transfer assuming 'liquid' boundaries // Russ. J. Numer. Anal. Math. Modelling. 2016. Vol. 31, No. 2. P. 71-80.

Development of a defect stream function, law of the wall/wake method for compressible turbulent boundary layers. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Wahls, Richard A.

1990-01-01

The method presented is designed to improve the accuracy and computational efficiency of existing numerical methods for the solution of flows with compressible turbulent boundary layers. A compressible defect stream function formulation of the governing equations assuming an arbitrary turbulence model is derived. This formulation is advantageous because it has a constrained zero-order approximation with respect to the wall shear stress and the tangential momentum equation has a first integral. Previous problems with this type of formulation near the wall are eliminated by using empirically based analytic expressions to define the flow near the wall. The van Driest law of the wall for velocity and the modified Crocco temperature-velocity relationship are used. The associated compressible law of the wake is determined and it extends the valid range of the analytical expressions beyond the logarithmic region of the boundary layer. The need for an inner-region eddy viscosity model is completely avoided. The near-wall analytic expressions are patched to numerically computed outer region solutions at a point determined during the computation. A new boundary condition on the normal derivative of the tangential velocity at the surface is presented; this condition replaces the no-slip condition and enables numerical integration to the surface with a relatively coarse grid using only an outer region turbulence model. The method was evaluated for incompressible and compressible equilibrium flows and was implemented into an existing Navier-Stokes code using the assumption of local equilibrium flow with respect to the patching. The method has proven to be accurate and efficient.

Numerical integration of asymptotic solutions of ordinary differential equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

High-order scheme for the source-sink term in a one-dimensional water temperature model

PubMed Central

Jing, Zheng; Kang, Ling

2017-01-01

The source-sink term in water temperature models represents the net heat absorbed or released by a water system. This term is very important because it accounts for solar radiation that can significantly affect water temperature, especially in lakes. However, existing numerical methods for discretizing the source-sink term are very simplistic, causing significant deviations between simulation results and measured data. To address this problem, we present a numerical method specific to the source-sink term. A vertical one-dimensional heat conduction equation was chosen to describe water temperature changes. A two-step operator-splitting method was adopted as the numerical solution. In the first step, using the undetermined coefficient method, a high-order scheme was adopted for discretizing the source-sink term. In the second step, the diffusion term was discretized using the Crank-Nicolson scheme. The effectiveness and capability of the numerical method was assessed by performing numerical tests. Then, the proposed numerical method was applied to a simulation of Guozheng Lake (located in central China). The modeling results were in an excellent agreement with measured data. PMID:28264005

High-order scheme for the source-sink term in a one-dimensional water temperature model.

PubMed

Jing, Zheng; Kang, Ling

2017-01-01

The source-sink term in water temperature models represents the net heat absorbed or released by a water system. This term is very important because it accounts for solar radiation that can significantly affect water temperature, especially in lakes. However, existing numerical methods for discretizing the source-sink term are very simplistic, causing significant deviations between simulation results and measured data. To address this problem, we present a numerical method specific to the source-sink term. A vertical one-dimensional heat conduction equation was chosen to describe water temperature changes. A two-step operator-splitting method was adopted as the numerical solution. In the first step, using the undetermined coefficient method, a high-order scheme was adopted for discretizing the source-sink term. In the second step, the diffusion term was discretized using the Crank-Nicolson scheme. The effectiveness and capability of the numerical method was assessed by performing numerical tests. Then, the proposed numerical method was applied to a simulation of Guozheng Lake (located in central China). The modeling results were in an excellent agreement with measured data.

Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

NASA Astrophysics Data System (ADS)

Minesaki, Yukitaka

2018-04-01

We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.

Special discontinuities in nonlinearly elastic media

NASA Astrophysics Data System (ADS)

Chugainova, A. P.

2017-06-01

Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.

Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.

DTIC Science & Technology

1983-12-01

numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numer- ical evaluation of any partial differential...emphasis is being placed on numerical solution of the governing differential equations by finite difference methods . In the past two decades, considerable...original equations presented in that paper. The solution of the second problem is more difficult. 2 The method of Thompson et al. provides control for

Alternative formulations of the Laplace transform boundary element (LTBE) numerical method for the solution of diffusion-type equations

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

Moridis, G.

1992-03-01

The Laplace Transform Boundary Element (LTBE) method is a recently introduced numerical method, and has been used for the solution of diffusion-type PDEs. It completely eliminates the time dependency of the problem and the need for time discretization, yielding solutions numerical in space and semi-analytical in time. In LTBE solutions are obtained in the Laplace spare, and are then inverted numerically to yield the solution in time. The Stehfest and the DeHoog formulations of LTBE, based on two different inversion algorithms, are investigated. Both formulations produce comparable, extremely accurate solutions.

Novel asymmetric representation method for solving the higher-order Ginzburg-Landau equation

PubMed Central

Wong, Pring; Pang, Lihui; Wu, Ye; Lei, Ming; Liu, Wenjun

2016-01-01

In ultrafast optics, optical pulses are generated to be of shorter pulse duration, which has enormous significance to industrial applications and scientific research. The ultrashort pulse evolution in fiber lasers can be described by the higher-order Ginzburg-Landau (GL) equation. However, analytic soliton solutions for this equation have not been obtained by use of existing methods. In this paper, a novel method is proposed to deal with this equation. The analytic soliton solution is obtained for the first time, and is proved to be stable against amplitude perturbations. Through the split-step Fourier method, the bright soliton solution is studied numerically. The analytic results here may extend the integrable methods, and could be used to study soliton dynamics for some equations in other disciplines. It may also provide the other way to obtain two-soliton solutions for higher-order GL equations. PMID:27086841

A duality theorem-based algorithm for inexact quadratic programming problems: Application to waste management under uncertainty

NASA Astrophysics Data System (ADS)

Kong, X. M.; Huang, G. H.; Fan, Y. R.; Li, Y. P.

2016-04-01

In this study, a duality theorem-based algorithm (DTA) for inexact quadratic programming (IQP) is developed for municipal solid waste (MSW) management under uncertainty. It improves upon the existing numerical solution method for IQP problems. The comparison between DTA and derivative algorithm (DAM) shows that the DTA method provides better solutions than DAM with lower computational complexity. It is not necessary to identify the uncertain relationship between the objective function and decision variables, which is required for the solution process of DAM. The developed method is applied to a case study of MSW management and planning. The results indicate that reasonable solutions have been generated for supporting long-term MSW management and planning. They could provide more information as well as enable managers to make better decisions to identify desired MSW management policies in association with minimized cost under uncertainty.

A semi-analytical solution for elastic analysis of rotating thick cylindrical shells with variable thickness using disk form multilayers.

PubMed

Zamani Nejad, Mohammad; Jabbari, Mehdi; Ghannad, Mehdi

2014-01-01

Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations. Given that the cylinder is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM) is also presented and good agreement was found.

A Semi-Analytical Solution for Elastic Analysis of Rotating Thick Cylindrical Shells with Variable Thickness Using Disk Form Multilayers

PubMed Central

Zamani Nejad, Mohammad; Jabbari, Mehdi; Ghannad, Mehdi

2014-01-01

Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations. Given that the cylinder is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM) is also presented and good agreement was found. PMID:24719582

Saturated-unsaturated flow in a compressible leaky-unconfined aquifer

NASA Astrophysics Data System (ADS)

Mishra, Phoolendra K.; Vesselinov, Velimir V.; Kuhlman, Kristopher L.

2012-06-01

An analytical solution is developed for three-dimensional flow towards a partially penetrating large-diameter well in an unconfined aquifer bounded below by a leaky aquitard of finite or semi-infinite extent. The analytical solution is derived using Laplace and Hankel transforms, then inverted numerically. Existing solutions for flow in leaky unconfined aquifers neglect the unsaturated zone following an assumption of instantaneous drainage due to Neuman. We extend the theory of leakage in unconfined aquifers by (1) including water flow and storage in the unsaturated zone above the water table, and (2) allowing the finite-diameter pumping well to partially penetrate the aquifer. The investigation of model-predicted results shows that aquitard leakage leads to significant departure from the unconfined solution without leakage. The investigation of dimensionless time-drawdown relationships shows that the aquitard drawdown also depends on unsaturated zone properties and the pumping-well wellbore storage effects.

Radial flow towards well in leaky unconfined aquifer

NASA Astrophysics Data System (ADS)

Mishra, P. K.; Kuhlman, K. L.

2012-12-01

An analytical solution is developed for three-dimensional flow towards a partially penetrating large- diameter well in an unconfined aquifer bounded below by a leaky aquitard of finite or semi-infinite extent. The analytical solution is derived using Laplace and Hankel transforms, then inverted numerically. Existing solutions for flow in leaky unconfined aquifers neglect the unsaturated zone following an assumption of instantaneous drainage due to Neuman. We extend the theory of leakage in unconfined aquifers by (1) including water flow and storage in the unsaturated zone above the water table, and (2) allowing the finite-diameter pumping well to partially penetrate the aquifer. The investigation of model-predicted results shows that aquitard leakage leads to significant departure from the unconfined solution without leakage. The investigation of dimensionless time-drawdown relationships shows that the aquitard drawdown also depends on unsaturated zone properties and the pumping-well wellbore storage effects.

A family of conjugate gradient methods for large-scale nonlinear equations.

PubMed

Feng, Dexiang; Sun, Min; Wang, Xueyong

2017-01-01

In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method.

Modelling and properties of a nonlinear autonomous switching system in fed-batch culture of glycerol

NASA Astrophysics Data System (ADS)

Wang, Juan; Sun, Qingying; Feng, Enmin

2012-11-01

A nonlinear autonomous switching system is proposed to describe the coupled fed-batch fermentation with the pH as the feedback parameter. We prove the non-Zeno behaviors of the switching system and some basic properties of its solution, including the existence, uniqueness, boundedness and regularity. Numerical simulation is also carried out, which reveals that the proposed system can describe the factual fermentation process properly.

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).

Numerical solution of potential flow about arbitrary 2-dimensional multiple bodies

NASA Technical Reports Server (NTRS)

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

1982-01-01

A procedure for the finite-difference numerical solution of the lifting potential flow about any number of arbitrarily shaped bodies is given. The solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having coordinate lines coincident with the contours of all bodies in the field, regardless of their shapes and number. The effects of all numerical parameters involved are analyzed and appropriate values are recommended. Comparisons with analytic solutions for single Karman-Trefftz airfoils and a circular cylinder pair show excellent agreement. The technique of application of the boundary-fitted coordinate systems to the numerical solution of partial differential equations is illustrated.

Bounded energy states in homogeneous turbulent shear flow - An alternative view

NASA Technical Reports Server (NTRS)

Bernard, P. S.; Speziale, C. G.

1992-01-01

The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if a residual vortex stretching term is maintained in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are presented for a k-epsilon model modified to account for net vortex stretching.

A Discrete Velocity Kinetic Model with Food Metric: Chemotaxis Traveling Waves.

PubMed

Choi, Sun-Ho; Kim, Yong-Jung

2017-02-01

We introduce a mesoscopic scale chemotaxis model for traveling wave phenomena which is induced by food metric. The organisms of this simplified kinetic model have two discrete velocity modes, [Formula: see text] and a constant tumbling rate. The main feature of the model is that the speed of organisms is constant [Formula: see text] with respect to the food metric, not the Euclidean metric. The uniqueness and the existence of the traveling wave solution of the model are obtained. Unlike the classical logarithmic model case there exist traveling waves under super-linear consumption rates and infinite population pulse-type traveling waves are obtained. Numerical simulations are also provided.

Global Mittag-Leffler stability analysis of fractional-order impulsive neural networks with one-side Lipschitz condition.

PubMed

Zhang, Xinxin; Niu, Peifeng; Ma, Yunpeng; Wei, Yanqiao; Li, Guoqiang

2017-10-01

This paper is concerned with the stability analysis issue of fractional-order impulsive neural networks. Under the one-side Lipschitz condition or the linear growth condition of activation function, the existence of solution is analyzed respectively. In addition, the existence, uniqueness and global Mittag-Leffler stability of equilibrium point of the fractional-order impulsive neural networks with one-side Lipschitz condition are investigated by the means of contraction mapping principle and Lyapunov direct method. Finally, an example with numerical simulation is given to illustrate the validity and feasibility of the proposed results. Copyright © 2017 Elsevier Ltd. All rights reserved.

The route to chaos for the Kuramoto-Sivashinsky equation

NASA Technical Reports Server (NTRS)

Papageorgiou, Demetrios T.; Smyrlis, Yiorgos

1990-01-01

The results of extensive numerical experiments of the spatially periodic initial value problem for the Kuramoto-Sivashinsky equation. This paper is concerned with the asymptotic nonlinear dynamics at the dissipation parameter decreases and spatio-temporal chaos sets in. To this end the initial condition is taken to be the same for all numerical experiments (a single sine wave is used) and the large time evolution of the system is followed numerically. Numerous computations were performed to establish the existence of windows, in parameter space, in which the solution has the following characteristics as the viscosity is decreased: a steady fully modal attractor to a steady bimodal attractor to another steady fully modal attractor to a steady trimodal attractor to a periodic attractor, to another steady fully modal attractor, to another periodic attractor, to a steady tetramodal attractor, to another periodic attractor having a full sequence of period-doublings (in parameter space) to chaos. Numerous solutions are presented which provide conclusive evidence of the period-doubling cascades which precede chaos for this infinite-dimensional dynamical system. These results permit a computation of the length of subwindows which in turn provide an estimate for their successive ratios as the cascade develops. A calculation based on the numerical results is also presented to show that the period doubling sequences found here for the Kuramoto-Sivashinsky equation, are in complete agreement with Feigenbaum's universal constant of 4,669201609... . Some preliminary work shows several other windows following the first chaotic one including periodic, chaotic, and a steady octamodal window; however, the windows shrink significantly in size to enable concrete quantitative conclusions to be made.

Time-Accurate Local Time Stepping and High-Order Time CESE Methods for Multi-Dimensional Flows Using Unstructured Meshes

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Venkatachari, Balaji Shankar; Cheng, Gary

2013-01-01

With the wide availability of affordable multiple-core parallel supercomputers, next generation numerical simulations of flow physics are being focused on unsteady computations for problems involving multiple time scales and multiple physics. These simulations require higher solution accuracy than most algorithms and computational fluid dynamics codes currently available. This paper focuses on the developmental effort for high-fidelity multi-dimensional, unstructured-mesh flow solvers using the space-time conservation element, solution element (CESE) framework. Two approaches have been investigated in this research in order to provide high-accuracy, cross-cutting numerical simulations for a variety of flow regimes: 1) time-accurate local time stepping and 2) highorder CESE method. The first approach utilizes consistent numerical formulations in the space-time flux integration to preserve temporal conservation across the cells with different marching time steps. Such approach relieves the stringent time step constraint associated with the smallest time step in the computational domain while preserving temporal accuracy for all the cells. For flows involving multiple scales, both numerical accuracy and efficiency can be significantly enhanced. The second approach extends the current CESE solver to higher-order accuracy. Unlike other existing explicit high-order methods for unstructured meshes, the CESE framework maintains a CFL condition of one for arbitrarily high-order formulations while retaining the same compact stencil as its second-order counterpart. For large-scale unsteady computations, this feature substantially enhances numerical efficiency. Numerical formulations and validations using benchmark problems are discussed in this paper along with realistic examples.

Automated Calibration For Numerical Models Of Riverflow

NASA Astrophysics Data System (ADS)

Fernandez, Betsaida; Kopmann, Rebekka; Oladyshkin, Sergey

2017-04-01

Calibration of numerical models is fundamental since the beginning of all types of hydro system modeling, to approximate the parameters that can mimic the overall system behavior. Thus, an assessment of different deterministic and stochastic optimization methods is undertaken to compare their robustness, computational feasibility, and global search capacity. Also, the uncertainty of the most suitable methods is analyzed. These optimization methods minimize the objective function that comprises synthetic measurements and simulated data. Synthetic measurement data replace the observed data set to guarantee an existing parameter solution. The input data for the objective function derivate from a hydro-morphological dynamics numerical model which represents an 180-degree bend channel. The hydro- morphological numerical model shows a high level of ill-posedness in the mathematical problem. The minimization of the objective function by different candidate methods for optimization indicates a failure in some of the gradient-based methods as Newton Conjugated and BFGS. Others reveal partial convergence, such as Nelder-Mead, Polak und Ribieri, L-BFGS-B, Truncated Newton Conjugated, and Trust-Region Newton Conjugated Gradient. Further ones indicate parameter solutions that range outside the physical limits, such as Levenberg-Marquardt and LeastSquareRoot. Moreover, there is a significant computational demand for genetic optimization methods, such as Differential Evolution and Basin-Hopping, as well as for Brute Force methods. The Deterministic Sequential Least Square Programming and the scholastic Bayes Inference theory methods present the optimal optimization results. keywords: Automated calibration of hydro-morphological dynamic numerical model, Bayesian inference theory, deterministic optimization methods.

A multi-scale residual-based anti-hourglass control for compatible staggered Lagrangian hydrodynamics

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

Kucharik, M.; Scovazzi, Guglielmo; Shashkov, Mikhail Jurievich

Hourglassing is a well-known pathological numerical artifact affecting the robustness and accuracy of Lagrangian methods. There exist a large number of hourglass control/suppression strategies. In the community of the staggered compatible Lagrangian methods, the approach of sub-zonal pressure forces is among the most widely used. However, this approach is known to add numerical strength to the solution, which can cause potential problems in certain types of simulations, for instance in simulations of various instabilities. To avoid this complication, we have adapted the multi-scale residual-based stabilization typically used in the finite element approach for staggered compatible framework. In this study, wemore » describe two discretizations of the new approach and demonstrate their properties and compare with the method of sub-zonal pressure forces on selected numerical problems.« less

A multi-scale residual-based anti-hourglass control for compatible staggered Lagrangian hydrodynamics

DOE PAGES

Kucharik, M.; Scovazzi, Guglielmo; Shashkov, Mikhail Jurievich; ...

2017-10-28

Hourglassing is a well-known pathological numerical artifact affecting the robustness and accuracy of Lagrangian methods. There exist a large number of hourglass control/suppression strategies. In the community of the staggered compatible Lagrangian methods, the approach of sub-zonal pressure forces is among the most widely used. However, this approach is known to add numerical strength to the solution, which can cause potential problems in certain types of simulations, for instance in simulations of various instabilities. To avoid this complication, we have adapted the multi-scale residual-based stabilization typically used in the finite element approach for staggered compatible framework. In this study, wemore » describe two discretizations of the new approach and demonstrate their properties and compare with the method of sub-zonal pressure forces on selected numerical problems.« less

Dynamic strain aging and plastic instabilities

NASA Astrophysics Data System (ADS)

Mesarovic, Sinisa Dj.

1995-05-01

A constitutive model proposed by McCormick [(1988) Theory of flow localization due to dynamic strain ageing. Acta. Metall.36, 3061-3067] based on dislocation-solute interaction and describing dynamic strain aging behavior, is analyzed for the simple loading case of uniaxial tension. The model is rate dependent and includes a time-varying state variable, representing the local concentration of the impurity atoms at dislocations. Stability of the system and its post-instability behavior are considered. The methods used include analytical and numerical stability and bifurcation analysis with a numerical continuation technique. Yield point behavior and serrated yielding are found to result for well defined intervals of temperature and strain rate. Serrated yielding emerges as a branch of periodic solutions of the relaxation oscillation type, similar to frictional stick-slip. The distinction between the temporal and spatial (loss of homogeneity of strain) instability is emphasized. It is found that a critical machine stiffness exists above which a purely temporal instability cannot occur. The results are compared to the available experimental data.

FASOR - A second generation shell of revolution code

NASA Technical Reports Server (NTRS)

Cohen, G. A.

1978-01-01

An integrated computer program entitled Field Analysis of Shells of Revolution (FASOR) currently under development for NASA is described. When completed, this code will treat prebuckling, buckling, initial postbuckling and vibrations under axisymmetric static loads as well as linear response and bifurcation under asymmetric static loads. Although these modes of response are treated by existing programs, FASOR extends the class of problems treated to include general anisotropy and transverse shear deformations of stiffened laminated shells. At the same time, a primary goal is to develop a program which is free of the usual problems of modeling, numerical convergence and ill-conditioning, laborious problem setup, limitations on problem size and interpretation of output. The field method is briefly described, the shell differential equations are cast in a suitable form for solution by this method and essential aspects of the input format are presented. Numerical results are given for both unstiffened and stiffened anisotropic cylindrical shells and compared with previously published analytical solutions.

Weibel instability for a streaming electron, counterstreaming e-e, and e-p plasmas with intrinsic temperature anisotropy

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

Ghorbanalilu, M.; Physics Department, Azarbaijan Shahid Madani University, Tabriz; Sadegzadeh, S.

2014-05-15

The existence of Weibel instability for a streaming electron, counterstreaming electron-electron (e-e), and electron-positron (e-p) plasmas with intrinsic temperature anisotropy is investigated. The temperature anisotropy is included in the directions perpendicular and parallel to the streaming direction. It is shown that the beam mean speed changes the instability mode, for a streaming electron beam, from the classic Weibel to the Weibel-like mode. The analytical and numerical solutions approved that Weibel-like modes are excited for both counterstreaming e-e and e-p plasmas. The growth rates of the instabilities in e-e and e-p plasmas are compared. The growth rate is larger for e-pmore » plasmas if the thermal anisotropy is small and the opposite is true for large thermal anisotropies. The analytical and numerical solutions are in good agreement only in the small parallel temperature and wave number limits, when the instability growth rate increases linearly with normalized wave number kc∕ω{sub p}.« less

Effective screening length and quasiuniversality for the restricted primitive model of an electrolyte solution.

PubMed

Janecek, Jirí; Netz, Roland R

2009-02-21

Monte Carlo simulations for the restricted primitive model of an electrolyte solution above the critical temperature are performed at a wide range of concentrations and temperatures. Thermodynamic properties such as internal energy, osmotic coefficient, activity coefficient, as well as spatial correlation functions are determined. These observables are used to investigate whether quasiuniversality in terms of an effective screening length exists, similar to the role played by the effective electron mass in solid-state physics. To that end, an effective screening length is extracted from the asymptotic behavior of the Fourier-transformed charge-correlation function and plugged into the Debye-Huckel limiting expressions for various thermodynamic properties. Comparison with numerical results is favorable, suggesting that correlation and other effects not captured on the Debye-Huckel limiting level can be successfully incorporated by a single effective parameter while keeping the functional form of Debye-Huckel expressions. We also compare different methods to determine mean ionic activity coefficient in molecular simulations and check the internal consistency of the numerical data.

Development of an upwind, finite-volume code with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Molvik, Gregory A.

1994-01-01

Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques, and a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical, and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data.

Numerical Modeling of High-Temperature Corrosion Processes

NASA Technical Reports Server (NTRS)

Nesbitt, James A.

1995-01-01

Numerical modeling of the diffusional transport associated with high-temperature corrosion processes is reviewed. These corrosion processes include external scale formation and internal subscale formation during oxidation, coating degradation by oxidation and substrate interdiffusion, carburization, sulfidation and nitridation. The studies that are reviewed cover such complexities as concentration-dependent diffusivities, cross-term effects in ternary alloys, and internal precipitation where several compounds of the same element form (e.g., carbides of Cr) or several compounds exist simultaneously (e.g., carbides containing varying amounts of Ni, Cr, Fe or Mo). In addition, the studies involve a variety of boundary conditions that vary with time and temperature. Finite-difference (F-D) techniques have been applied almost exclusively to model either the solute or corrodant transport in each of these studies. Hence, the paper first reviews the use of F-D techniques to develop solutions to the diffusion equations with various boundary conditions appropriate to high-temperature corrosion processes. The bulk of the paper then reviews various F-D modeling studies of diffusional transport associated with high-temperature corrosion.

Computational attributes of the integral form of the equation of transfer

NASA Technical Reports Server (NTRS)

Frankel, J. I.

1991-01-01

Difficulties can arise in radiative and neutron transport calculations when a highly anisotropic scattering phase function is present. In the presence of anisotropy, currently used numerical solutions are based on the integro-differential form of the linearized Boltzmann transport equation. This paper, departs from classical thought and presents an alternative numerical approach based on application of the integral form of the transport equation. Use of the integral formalism facilitates the following steps: a reduction in dimensionality of the system prior to discretization, the use of symbolic manipulation to augment the computational procedure, and the direct determination of key physical quantities which are derivable through the various Legendre moments of the intensity. The approach is developed in the context of radiative heat transfer in a plane-parallel geometry, and results are presented and compared with existing benchmark solutions. Encouraging results are presented to illustrate the potential of the integral formalism for computation. The integral formalism appears to possess several computational attributes which are well-suited to radiative and neutron transport calculations.

A Riccati solution for the ideal MHD plasma response with applications to real-time stability control

NASA Astrophysics Data System (ADS)

Glasser, Alexander; Kolemen, Egemen; Glasser, A. H.

2018-03-01

Active feedback control of ideal MHD stability in a tokamak requires rapid plasma stability analysis. Toward this end, we reformulate the δW stability method with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the generic tokamak ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD matrix Riccati differential equation. Since Riccati equations are prevalent in the control theory literature, such a shift in perspective brings to bear a range of numerical methods that are well-suited to the robust, fast solution of control problems. We discuss the usefulness of Riccati techniques in solving the stiff ordinary differential equations often encountered in ideal MHD stability analyses—for example, in tokamak edge and stellarator physics. We demonstrate the applicability of such methods to an existing 2D ideal MHD stability code—DCON [A. H. Glasser, Phys. Plasmas 23, 072505 (2016)]—enabling its parallel operation in near real-time, with wall-clock time ≪1 s . Such speed may help enable active feedback ideal MHD stability control, especially in tokamak plasmas whose ideal MHD equilibria evolve with inductive timescale τ≳ 1s—as in ITER.

A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

NASA Astrophysics Data System (ADS)

Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

2017-12-01

Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.

The PAC-MAN model: Benchmark case for linear acoustics in computational physics

NASA Astrophysics Data System (ADS)

Ziegelwanger, Harald; Reiter, Paul

2017-10-01

Benchmark cases in the field of computational physics, on the one hand, have to contain a certain complexity to test numerical edge cases and, on the other hand, require the existence of an analytical solution, because an analytical solution allows the exact quantification of the accuracy of a numerical simulation method. This dilemma causes a need for analytical sound field formulations of complex acoustic problems. A well known example for such a benchmark case for harmonic linear acoustics is the ;Cat's Eye model;, which describes the three-dimensional sound field radiated from a sphere with a missing octant analytically. In this paper, a benchmark case for two-dimensional (2D) harmonic linear acoustic problems, viz., the ;PAC-MAN model;, is proposed. The PAC-MAN model describes the radiated and scattered sound field around an infinitely long cylinder with a cut out sector of variable angular width. While the analytical calculation of the 2D sound field allows different angular cut-out widths and arbitrarily positioned line sources, the computational cost associated with the solution of this problem is similar to a 1D problem because of a modal formulation of the sound field in the PAC-MAN model.

On analyticity of linear waves scattered by a layered medium

NASA Astrophysics Data System (ADS)

Nicholls, David P.

2017-10-01

The scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering. In this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of High-Order Perturbation of Surfaces methods for simulating such waves. More specifically, we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a multiply layered periodic structure in three dimensions. This result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of Operator Expansions, Field Expansions, and Transformed Field Expansions.

A digital matched filter for reverse time chaos.

PubMed

Bailey, J Phillip; Beal, Aubrey N; Dean, Robert N; Hamilton, Michael C

2016-07-01

The use of reverse time chaos allows the realization of hardware chaotic systems that can operate at speeds equivalent to existing state of the art while requiring significantly less complex circuitry. Matched filter decoding is possible for the reverse time system since it exhibits a closed form solution formed partially by a linear basis pulse. Coefficients have been calculated and are used to realize the matched filter digitally as a finite impulse response filter. Numerical simulations confirm that this correctly implements a matched filter that can be used for detection of the chaotic signal. In addition, the direct form of the filter has been implemented in hardware description language and demonstrates performance in agreement with numerical results.

An implicit boundary integral method for computing electric potential of macromolecules in solvent

NASA Astrophysics Data System (ADS)

Zhong, Yimin; Ren, Kui; Tsai, Richard

2018-04-01

A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equation that arises in mathematical models for the electrostatics of molecules in solvent. The proposed method uses an implicit boundary integral formulation to derive a linear system defined on Cartesian nodes in a narrowband surrounding the closed surface that separates the molecule and the solvent. The needed implicit surface is constructed from the given atomic description of the molecules, by a sequence of standard level set algorithms. A fast multipole method is applied to accelerate the solution of the linear system. A few numerical studies involving some standard test cases are presented and compared to other existing results.

Multiple control strategies for prevention of avian influenza pandemic.

PubMed

Ullah, Roman; Zaman, Gul; Islam, Saeed

2014-01-01

We present the prevention of avian influenza pandemic by adjusting multiple control functions in the human-to-human transmittable avian influenza model. First we show the existence of the optimal control problem; then by using both analytical and numerical techniques, we investigate the cost-effective control effects for the prevention of transmission of disease. To do this, we use three control functions, the effort to reduce the number of contacts with human infected with mutant avian influenza, the antiviral treatment of infected individuals, and the effort to reduce the number of infected birds. We completely characterized the optimal control and compute numerical solution of the optimality system by using an iterative method.

Remarks on the maximum luminosity

NASA Astrophysics Data System (ADS)

Cardoso, Vitor; Ikeda, Taishi; Moore, Christopher J.; Yoo, Chul-Moon

2018-04-01

The quest for fundamental limitations on physical processes is old and venerable. Here, we investigate the maximum possible power, or luminosity, that any event can produce. We show, via full nonlinear simulations of Einstein's equations, that there exist initial conditions which give rise to arbitrarily large luminosities. However, the requirement that there is no past horizon in the spacetime seems to limit the luminosity to below the Planck value, LP=c5/G . Numerical relativity simulations of critical collapse yield the largest luminosities observed to date, ≈ 0.2 LP . We also present an analytic solution to the Einstein equations which seems to give an unboundedly large luminosity; this will guide future numerical efforts to investigate super-Planckian luminosities.

Numerical studies of the Bethe-Salpeter equation for a two-fermion bound state

NASA Astrophysics Data System (ADS)

de Paula, W.; Frederico, T.; Salmè, G.; Viviani, M.

2018-03-01

Some recent advances on the solution of the Bethe-Salpeter equation (BSE) for a two-fermion bound system directly in Minkowski space are presented. The calculations are based on the expression of the Bethe-Salpeter amplitude in terms of the so-called Nakanishi integral representation and on the light-front projection (i.e. the integration of the light-front variable k - = k 0 - k 3). The latter technique allows for the analytically exact treatment of the singularities plaguing the two-fermion BSE in Minkowski space. The good agreement observed between our results and those obtained using other existing numerical methods, based on both Minkowski and Euclidean space techniques, fully corroborate our analytical treatment.

A digital matched filter for reverse time chaos

NASA Astrophysics Data System (ADS)

Bailey, J. Phillip; Beal, Aubrey N.; Dean, Robert N.; Hamilton, Michael C.

2016-07-01

The use of reverse time chaos allows the realization of hardware chaotic systems that can operate at speeds equivalent to existing state of the art while requiring significantly less complex circuitry. Matched filter decoding is possible for the reverse time system since it exhibits a closed form solution formed partially by a linear basis pulse. Coefficients have been calculated and are used to realize the matched filter digitally as a finite impulse response filter. Numerical simulations confirm that this correctly implements a matched filter that can be used for detection of the chaotic signal. In addition, the direct form of the filter has been implemented in hardware description language and demonstrates performance in agreement with numerical results.

Grid adaption based on modified anisotropic diffusion equations formulated in the parametic domain

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

Hagmeijer, R.

1994-11-01

A new grid-adaption algorithm for problems in computational fluid dynamics is presented. The basic equations are derived from a variational problem formulated in the parametric domain of the mapping that defines the existing grid. Modification of the basic equations provides desirable properties in boundary layers. The resulting modified anisotropic diffusion equations are solved for the computational coordinates as functions of the parametric coordinates and these functions are numerically inverted. Numerical examples show that the algorithm is robust, that shocks and boundary layers are well-resolved on the adapted grid, and that the flow solution becomes a globally smooth function of themore » computational coordinates.« less

Spurious Numerical Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1995-01-01

Paper presents detailed study of spurious steady-state numerical solutions of differential equations that contain nonlinear source terms. Main objectives of this study are (1) to investigate how well numerical steady-state solutions of model nonlinear reaction/convection boundary-value problem mimic true steady-state solutions and (2) to relate findings of this investigation to implications for interpretation of numerical results from computational-fluid-dynamics algorithms and computer codes used to simulate reacting flows.

An approximate solution for a penny-shaped hydraulic fracture that accounts for fracture toughness, fluid viscosity and leak-off.

PubMed

Dontsov, E V

2016-12-01

This paper develops a closed-form approximate solution for a penny-shaped hydraulic fracture whose behaviour is determined by an interplay of three competing physical processes that are associated with fluid viscosity, fracture toughness and fluid leak-off. The primary assumption that permits one to construct the solution is that the fracture behaviour is mainly determined by the three-process multiscale tip asymptotics and the global fluid volume balance. First, the developed approximation is compared with the existing solutions for all limiting regimes of propagation. Then, a solution map, which indicates applicability regions of the limiting solutions, is constructed. It is also shown that the constructed approximation accurately captures the scaling that is associated with the transition from any one limiting solution to another. The developed approximation is tested against a reference numerical solution, showing that accuracy of the fracture width and radius predictions lie within a fraction of a per cent for a wide range of parameters. As a result, the constructed approximation provides a rapid solution for a penny-shaped hydraulic fracture, which can be used for quick fracture design calculations or as a reference solution to evaluate accuracy of various hydraulic fracture simulators.

An approximate solution for a penny-shaped hydraulic fracture that accounts for fracture toughness, fluid viscosity and leak-off

NASA Astrophysics Data System (ADS)

Dontsov, E. V.

2016-12-01

This paper develops a closed-form approximate solution for a penny-shaped hydraulic fracture whose behaviour is determined by an interplay of three competing physical processes that are associated with fluid viscosity, fracture toughness and fluid leak-off. The primary assumption that permits one to construct the solution is that the fracture behaviour is mainly determined by the three-process multiscale tip asymptotics and the global fluid volume balance. First, the developed approximation is compared with the existing solutions for all limiting regimes of propagation. Then, a solution map, which indicates applicability regions of the limiting solutions, is constructed. It is also shown that the constructed approximation accurately captures the scaling that is associated with the transition from any one limiting solution to another. The developed approximation is tested against a reference numerical solution, showing that accuracy of the fracture width and radius predictions lie within a fraction of a per cent for a wide range of parameters. As a result, the constructed approximation provides a rapid solution for a penny-shaped hydraulic fracture, which can be used for quick fracture design calculations or as a reference solution to evaluate accuracy of various hydraulic fracture simulators.

Advanced in Visualization of 3D Time-Dependent CFD Solutions

NASA Technical Reports Server (NTRS)

Lane, David A.; Lasinski, T. A. (Technical Monitor)

1995-01-01

Numerical simulations of complex 3D time-dependent (unsteady) flows are becoming increasingly feasible because of the progress in computing systems. Unfortunately, many existing flow visualization systems were developed for time-independent (steady) solutions and do not adequately depict solutions from unsteady flow simulations. Furthermore, most systems only handle one time step of the solutions individually and do not consider the time-dependent nature of the solutions. For example, instantaneous streamlines are computed by tracking the particles using one time step of the solution. However, for streaklines and timelines, particles need to be tracked through all time steps. Streaklines can reveal quite different information about the flow than those revealed by instantaneous streamlines. Comparisons of instantaneous streamlines with dynamic streaklines are shown. For a complex 3D flow simulation, it is common to generate a grid system with several millions of grid points and to have tens of thousands of time steps. The disk requirement for storing the flow data can easily be tens of gigabytes. Visualizing solutions of this magnitude is a challenging problem with today's computer hardware technology. Even interactive visualization of one time step of the flow data can be a problem for some existing flow visualization systems because of the size of the grid. Current approaches for visualizing complex 3D time-dependent CFD solutions are described. The flow visualization system developed at NASA Ames Research Center to compute time-dependent particle traces from unsteady CFD solutions is described. The system computes particle traces (streaklines) by integrating through the time steps. This system has been used by several NASA scientists to visualize their CFD time-dependent solutions. The flow visualization capabilities of this system are described, and visualization results are shown.

Ineffective higher derivative black hole hair

NASA Astrophysics Data System (ADS)

Goldstein, Kevin; Mashiyane, James Junior

2018-01-01

Inspired by the possibility that the Schwarzschild black hole may not be the unique spherically symmetric vacuum solution to generalizations of general relativity, we consider black holes in pure fourth order higher derivative gravity treated as an effective theory. Such solutions may be of interest in addressing the issue of higher derivative hair or during the later stages of black hole evaporation. Non-Schwarzschild solutions have been studied but we have put earlier results on a firmer footing by finding a systematic asymptotic expansion for the black holes and matching them with known numerical solutions obtained by integrating out from the near-horizon region. These asymptotic expansions can be cast in the form of trans-series expansions which we conjecture will be a generic feature of non-Schwarzschild higher derivative black holes. Excitingly we find a new branch of solutions with lower free energy than the Schwarzschild solution, but as found in earlier work, solutions only seem to exist for black holes with large curvatures, meaning that one should not generically neglect even higher derivative corrections. This suggests that one effectively recovers the nonhair theorems in this context.

A Planning Framework for the Deployment of Innovative Information and Communication Technologies in Procurement

NASA Astrophysics Data System (ADS)

Alard, Robert; Gustafsson, Martin; Nienhaus, Jörg

The management of buyer-supplier relations is a major topic for many enterprises today. Modern Information and Communication Technologies (ICT) offer interesting perspectives on opportunities and implementation approaches. Today, logistics and procurement departments of numerous enterprises are evaluating the possibilities and opportunities of new ICT solutions and especially of internet-based electronic procurement solutions for the optimisation and re-engineering of their buyer-supplier relationships. Due to the highly innovative character of the new ICT solutions and the scarcely available operational examples in the industry, only little guidance exists to support responsible managers during the evaluation, planning and designing of internet-based electronic procurement solutions. This paper describes a framework for the strategic evaluation and planning of the deployment of internet-based procurement solutions for direct materials. The presented approach supports enterprises in the analysis of procurement objects and procurement structuring, in the definition and management of buyer-supplier-relationships, in the requirements analysis of ICT solutions as well as the assessment of the potential to support procurement with innovative ICT and internet-based electronic procurement solutions.

The use of multigrid techniques in the solution of the Elrod algorithm for a dynamically loaded journal bearing. M.S. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Woods, Claudia M.

1988-01-01

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed, utilizing a multigrid iterative technique. The code is compared with a presently existing direct solution in terms of computational time and accuracy. The model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobssen-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via liquid striations. The mixed nature of the equations (elliptic in the full film zone and nonelliptic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

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.

Group invariant solution for a pre-existing fracture driven by a power-law fluid in impermeable rock

NASA Astrophysics Data System (ADS)

Fareo, A. G.; Mason, D. P.

2013-12-01

The effect of power-law rheology on hydraulic fracturing is investigated. The evolution of a two-dimensional fracture with non-zero initial length and driven by a power-law fluid is analyzed. Only fluid injection into the fracture is considered. The surrounding rock mass is impermeable. With the aid of lubrication theory and the PKN approximation a partial differential equation for the fracture half-width is derived. Using a linear combination of the Lie-point symmetry generators of the partial differential equation, the group invariant solution is obtained and the problem is reduced to a boundary value problem for an ordinary differential equation. Exact analytical solutions are derived for hydraulic fractures with constant volume and with constant propagation speed. The asymptotic solution near the fracture tip is found. The numerical solution for general working conditions is obtained by transforming the boundary value problem to a pair of initial value problems. Throughout the paper, hydraulic fracturing with shear thinning, Newtonian and shear thickening fluids are compared.

Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations

PubMed Central

Zhou, Shenggao; Sun, Hui; Cheng, Li-Tien; Dzubiella, Joachim; McCammon, J. Andrew

2016-01-01

Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the “normal velocity” that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach. PMID:27497546

CSR Fields: Direct Numerical Solution of the Maxwell___s Equation

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

Novokhatski, A.; /SLAC

2011-06-22

We discuss the properties of the coherent electromagnetic fields of a very short, ultra-relativistic bunch in a rectangular vacuum chamber inside a bending magnet. The analysis is based on the results of a direct numerical solution of Maxwell's equations together with Newton's equations. We use a new dispersion-free time-domain algorithm which employs a more efficient use of finite element mesh techniques and hence produces self-consistent and stable solutions for very short bunches. We investigate the fine structure of the CSR fields including coherent edge radiation. This approach should be useful in the study of existing and future concepts of particlemore » accelerators and ultrafast coherent light sources. The coherent synchrotron radiation (CSR) fields have a strong action on the beam dynamics of very short bunches, which are moving in the bends of all kinds of magnetic elements. They are responsible for additional energy loss and energy spread; micro bunching and beam emittance growth. These fields may bound the efficiency of damping rings, electron-positron colliders and ultrafast coherent light sources, where high peak currents and very short bunches are envisioned. This is relevant to most high-brightness beam applications. On the other hand these fields together with transition radiation fields can be used for beam diagnostics or even as a powerful resource of THz radiation. A history of the study of CSR and a good collection of references can be found in [1]. Electromagnetic theory suggests several methods on how to calculate CSR fields. The most popular method is to use Lienard-Wiechert potentials. Other approach is to solve numerically the approximate equations, which are a Schrodinger type equation. These numerical methods are described in [2]. We suggest that a direct solution of Maxwell's equations together with Newton's equations can describe the detailed structure of the CSR fields [3].« less

Multiple Steady States of Buoyancy Induced Flow in Cold Water and Their Stability.

NASA Astrophysics Data System (ADS)

El-Henawy, Ibrahim Mahmoud

In Chapters 1 and 2 the physical background and the literature related to buoyancy-induced flows are reviewed. An accurate representation, based upon experimental data, of the motion-causing buoyancy force, in the vicinity of maximum density in pure water at low temperatures, is used. This representation is an accurate and quite simple formulation due to Gebhart and Mollendorf (1977). Using the representation, we study, numerically, Chapter 3, a model for the laminar, boundary-layer flow arising from natural convection adjacent to a vertical isothermal flat surface submerged in quiescent cold water. The results demonstrate for the first time the existence of multiple steady-state solutions in a natural convection flow. The existence of these new multiple steady-state solutions led to an investigation of their stability. This is carried out in Chapter 4 by a mathematical method, different from that of the usual hydrodynamic stability approach, Lin (1955) and Razinand and Reid (1982). Three real eigenvalue and eigenvector pairs corresponding to the new steady-state -solutions were found. Each of these eigenvalues changes its algebraic sign at a particular limit point (point of vertical tangency, nose, knee) in the bifurcation diagrams found in Chapter 3. The results indicate that the new steady-state solutions are unstable and that the previously found steady-state solutions, Carey, Gebhart, and Mollendorf (1980), may be stable.

Computation in Classical Mechanics with Easy Java Simulations (EJS)

NASA Astrophysics Data System (ADS)

Cox, Anne J.

2006-12-01

Let your students enjoy creating animations and incorporating some computational physics into your Classical Mechanics course. This talk will demonstrate the use of an Open Source Physics package, Easy Java Simulations (EJS), in an already existing sophomore/junior level Classical Mechanics course. EJS allows for incremental introduction of computational physics into existing courses because it is easy to use (for instructors and students alike) and it is open source. Students can use this tool for numerical solutions to problems (as they can with commercial systems: Mathcad and Mathematica), but they can also generate their own animations. For example, students in Classical Mechanics use Lagrangian mechanics to solve a problem, and then use EJS not only to numerically solve the differential equations, but to show the associated motion (and check their answers). EJS, developed by Francisco Esquembre (http://fem.um.es/Ejs/), is built on the OpenSource Physics framework (http://www.opensourcephysics.org/) supported through NSF DUE0442581.

On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach

NASA Astrophysics Data System (ADS)

Gerstmayr, Johannes; Irschik, Hans

2008-12-01

In finite element methods that are based on position and slope coordinates, a representation of axial and bending deformation by means of an elastic line approach has become popular. Such beam and plate formulations based on the so-called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories. Examining the existing planar absolute nodal coordinate element, which uses a curvature proportional bending strain expression, it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and, even more serious, the normal force is incorrect. A correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived. The strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the St. Venant-Kirchhoff material: therefore, the strain energy is derived for the latter case and compared to classical nonlinear rod theories. The error in the original absolute nodal coordinate formulation is documented by numerical examples. The numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach, while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications. The numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre-curved static and dynamic problems, including buckling and eigenvalue analysis. The resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy-momentum conservation.

Dynamics of temporally localized states in passively mode-locked semiconductor lasers

NASA Astrophysics Data System (ADS)

Schelte, C.; Javaloyes, J.; Gurevich, S. V.

2018-05-01

We study the emergence and the stability of temporally localized structures in the output of a semiconductor laser passively mode locked by a saturable absorber in the long-cavity regime. For large yet realistic values of the linewidth enhancement factor, we disclose the existence of secondary dynamical instabilities where the pulses develop regular and subsequent irregular temporal oscillations. By a detailed bifurcation analysis we show that additional solution branches that consist of multipulse (molecules) solutions exist. We demonstrate that the various solution curves for the single and multipeak pulses can splice and intersect each other via transcritical bifurcations, leading to a complex web of solutions. Our analysis is based on a generic model of mode locking that consists of a time-delayed dynamical system, but also on a much more numerically efficient, yet approximate, partial differential equation. We compare the results of the bifurcation analysis of both models in order to assess up to which point the two approaches are equivalent. We conclude our analysis by the study of the influence of group velocity dispersion, which is only possible in the framework of the partial differential equation model, and we show that it may have a profound impact on the dynamics of the localized states.

Magnetic resonance electrical impedance tomography (MREIT) based on the solution of the convection equation using FEM with stabilization.

PubMed

Oran, Omer Faruk; Ider, Yusuf Ziya

2012-08-21

Most algorithms for magnetic resonance electrical impedance tomography (MREIT) concentrate on reconstructing the internal conductivity distribution of a conductive object from the Laplacian of only one component of the magnetic flux density (∇²B(z)) generated by the internal current distribution. In this study, a new algorithm is proposed to solve this ∇²B(z)-based MREIT problem which is mathematically formulated as the steady-state scalar pure convection equation. Numerical methods developed for the solution of the more general convection-diffusion equation are utilized. It is known that the solution of the pure convection equation is numerically unstable if sharp variations of the field variable (in this case conductivity) exist or if there are inconsistent boundary conditions. Various stabilization techniques, based on introducing artificial diffusion, are developed to handle such cases and in this study the streamline upwind Petrov-Galerkin (SUPG) stabilization method is incorporated into the Galerkin weighted residual finite element method (FEM) to numerically solve the MREIT problem. The proposed algorithm is tested with simulated and also experimental data from phantoms. Successful conductivity reconstructions are obtained by solving the related convection equation using the Galerkin weighted residual FEM when there are no sharp variations in the actual conductivity distribution. However, when there is noise in the magnetic flux density data or when there are sharp variations in conductivity, it is found that SUPG stabilization is beneficial.

Numerical solutions of acoustic wave propagation problems using Euler computations

NASA Technical Reports Server (NTRS)

Hariharan, S. I.

1984-01-01

This paper reports solution procedures for problems arising from the study of engine inlet wave propagation. The first problem is the study of sound waves radiated from cylindrical inlets. The second one is a quasi-one-dimensional problem to study the effect of nonlinearities and the third one is the study of nonlinearities in two dimensions. In all three problems Euler computations are done with a fourth-order explicit scheme. For the first problem results are shown in agreement with experimental data and for the second problem comparisons are made with an existing asymptotic theory. The third problem is part of an ongoing work and preliminary results are presented for this case.

A spatially homogeneous and isotropic Einstein-Dirac cosmology

NASA Astrophysics Data System (ADS)

Finster, Felix; Hainzl, Christian

2011-04-01

We consider a spatially homogeneous and isotropic cosmological model where Dirac spinors are coupled to classical gravity. For the Dirac spinors we choose a Hartree-Fock ansatz where all one-particle wave functions are coherent and have the same momentum. If the scale function is large, the universe behaves like the classical Friedmann dust solution. If however the scale function is small, quantum effects lead to oscillations of the energy-momentum tensor. It is shown numerically and proven analytically that these quantum oscillations can prevent the formation of a big bang or big crunch singularity. The energy conditions are analyzed. We prove the existence of time-periodic solutions which go through an infinite number of expansion and contraction cycles.

Global stability and periodic solution of the viral dynamics

NASA Astrophysics Data System (ADS)

Song, Xinyu; Neumann, Avidan U.

2007-05-01

It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.

Robust iterative method for nonlinear Helmholtz equation

NASA Astrophysics Data System (ADS)

Yuan, Lijun; Lu, Ya Yan

2017-08-01

A new iterative method is developed for solving the two-dimensional nonlinear Helmholtz equation which governs polarized light in media with the optical Kerr nonlinearity. In the strongly nonlinear regime, the nonlinear Helmholtz equation could have multiple solutions related to phenomena such as optical bistability and symmetry breaking. The new method exhibits a much more robust convergence behavior than existing iterative methods, such as frozen-nonlinearity iteration, Newton's method and damped Newton's method, and it can be used to find solutions when good initial guesses are unavailable. Numerical results are presented for the scattering of light by a nonlinear circular cylinder based on the exact nonlocal boundary condition and a pseudospectral method in the polar coordinate system.

Long-time predictions in nonlinear dynamics

NASA Technical Reports Server (NTRS)

Szebehely, V.

1980-01-01

It is known that nonintegrable dynamical systems do not allow precise predictions concerning their behavior for arbitrary long times. The available series solutions are not uniformly convergent according to Poincare's theorem and numerical integrations lose their meaningfulness after the elapse of arbitrary long times. Two approaches are the use of existing global integrals and statistical methods. This paper presents a generalized method along the first approach. As examples long-time predictions in the classical gravitational satellite and planetary problems are treated.

Stability Analysis of Distributed Order Fractional Chen System

PubMed Central

Aminikhah, H.; Refahi Sheikhani, A.; Rezazadeh, H.

2013-01-01

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results. PMID:24489508

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1984-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Teglas, Russell

1987-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Late-time behaviour of the tilted Bianchi type VIh models

NASA Astrophysics Data System (ADS)

Hervik, S.; van den Hoogen, R. J.; Lim, W. C.; Coley, A. A.

2007-08-01

We study tilted perfect fluid cosmological models with a constant equation of state parameter in spatially homogeneous models of Bianchi type VIh using dynamical systems methods and numerical experimentation, with an emphasis on their future asymptotic evolution. We determine all of the equilibrium points of the type VIh state space (which correspond to exact self-similar solutions of the Einstein equations, some of which are new), and their stability is investigated. We find that there are vacuum plane-wave solutions that act as future attractors. In the parameter space, a 'loophole' is shown to exist in which there are no stable equilibrium points. We then show that a Hopf-bifurcation can occur resulting in a stable closed orbit (which we refer to as the Mussel attractor) corresponding to points both inside the loophole and points just outside the loophole; in the former case the closed curves act as late-time attractors while in the latter case these attracting curves will co-exist with attracting equilibrium points. In the special Bianchi type III case, centre manifold theory is required to determine the future attractors. Comprehensive numerical experiments are carried out to complement and confirm the analytical results presented. We note that the Bianchi type VIh case is of particular interest in that it contains many different subcases which exhibit many of the different possible future asymptotic behaviours of Bianchi cosmological models.

Numerical Algorithm for Delta of Asian Option

PubMed Central

Zhang, Boxiang; Yu, Yang; Wang, Weiguo

2015-01-01

We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options. PMID:26266271

Early Paleogene Orbital Variations in Atmospheric CO2 and New Astronomical Solutions

NASA Astrophysics Data System (ADS)

Zeebe, R. E.

2017-12-01

Geologic records across the globe show prominent variations on orbital time scales during numerous epochs going back hundreds of millions of years. The origin of the Milankovic cycles are variations in orbital parameters of the bodies of the Solar System. On long time scales, the orbital variations can not be computed analytically because of the chaotic nature of the Solar System. Thus, numerical solutions are used to estimate changes in, e.g., Earth's orbital parameters in the past. The orbital solutions represent the backbone of cyclostratigraphy and astrochronology, now widely used in geology and paleoclimatology. Hitherto only two solutions for Earth's eccentricity appear to be used in paleoclimate studies, provided by two different groups that integrated the full Solar System equations over the past >100 Myr. In this presentation, I will touch on the basic physics behind, and present new results of, accurate Solar System integrations for Earth's eccentricity over the past hundred million years. I will discuss various limitations within the framework of the present simulations and compare the results to existing solutions. Furthermore, I will present new results from practical applications of such orbital solutions, including effects of orbital forcing on coupled climate- and carbon cycle variations. For instance, we have recently revealed a mechanism for a large lag between changes in carbon isotope ratios and eccentricity at the 400-kyr period, which has been observed in Paleocene, Oligocene, and Miocene sections. Finally, I will present the first estimates of orbital-scale variations in atmospheric CO2 during the early Paleogene.

Numerical simulation of KdV equation by finite difference method

NASA Astrophysics Data System (ADS)

Yokus, A.; Bulut, H.

2018-05-01

In this study, the numerical solutions to the KdV equation with dual power nonlinearity by using the finite difference method are obtained. Discretize equation is presented in the form of finite difference operators. The numerical solutions are secured via the analytical solution to the KdV equation with dual power nonlinearity which is present in the literature. Through the Fourier-Von Neumann technique and linear stable, we have seen that the FDM is stable. Accuracy of the method is analyzed via the L2 and L_{∞} norm errors. The numerical, exact approximations and absolute error are presented in tables. We compare the numerical solutions with the exact solutions and this comparison is supported with the graphic plots. Under the choice of suitable values of parameters, the 2D and 3D surfaces for the used analytical solution are plotted.

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

NASA Technical Reports Server (NTRS)

Chen, C.-J.; Naseri-Neshat, H.; Ho, K.-S.

1981-01-01

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

Numerical Technology for Large-Scale Computational Electromagnetics

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

Sharpe, R; Champagne, N; White, D

The key bottleneck of implicit computational electromagnetics tools for large complex geometries is the solution of the resulting linear system of equations. The goal of this effort was to research and develop critical numerical technology that alleviates this bottleneck for large-scale computational electromagnetics (CEM). The mathematical operators and numerical formulations used in this arena of CEM yield linear equations that are complex valued, unstructured, and indefinite. Also, simultaneously applying multiple mathematical modeling formulations to different portions of a complex problem (hybrid formulations) results in a mixed structure linear system, further increasing the computational difficulty. Typically, these hybrid linear systems aremore » solved using a direct solution method, which was acceptable for Cray-class machines but does not scale adequately for ASCI-class machines. Additionally, LLNL's previously existing linear solvers were not well suited for the linear systems that are created by hybrid implicit CEM codes. Hence, a new approach was required to make effective use of ASCI-class computing platforms and to enable the next generation design capabilities. Multiple approaches were investigated, including the latest sparse-direct methods developed by our ASCI collaborators. In addition, approaches that combine domain decomposition (or matrix partitioning) with general-purpose iterative methods and special purpose pre-conditioners were investigated. Special-purpose pre-conditioners that take advantage of the structure of the matrix were adapted and developed based on intimate knowledge of the matrix properties. Finally, new operator formulations were developed that radically improve the conditioning of the resulting linear systems thus greatly reducing solution time. The goal was to enable the solution of CEM problems that are 10 to 100 times larger than our previous capability.« less

A stability analysis on forced convection boundary layer stagnation-point slip flow in Darcy-Forchheimer porous medium towards a shrinking sheet

NASA Astrophysics Data System (ADS)

Bakar, Shahirah Abu; Arifin, Norihan Md; Ali, Fadzilah Md; Bachok, Norfifah; Nazar, Roslinda

2017-08-01

The stagnation-point flow over a shrinking sheet in Darcy-Forchheimer porous medium is numerically studied. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, and then solved numerically by using shooting technique method with Maple implementation. Dual solutions are observed in a certain range of the shrinking parameter. Regarding on numerical solutions, we prepared stability analysis to identify which solution is stable between non-unique solutions by bvp4c solver in Matlab. Further we obtain numerical results or each solution, which enable us to discuss the features of the respective solutions.

Scalar hairy black holes and scalarons in the isolated horizons formalism

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

Corichi, Alejandro; Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, A. Postal 61-3, Morelia, Michoacan, 58090; Nucamendi, Ulises

The Isolated Horizons (IH) formalism, together with a simple phenomenological model for colored black holes has been used to predict nontrivial formulas that relate the ADM mass of the solitons and hairy Black Holes of Gravity-Matter system on the one hand, and several horizon properties of the black holes in the other. In this article, the IH formalism is tested numerically for spherically symmetric solutions to an Einstein-Higgs system where hairy black holes were recently found to exist. It is shown that the mass formulas still hold and that, by appropriately extending the current model, one can account for themore » behavior of the horizon properties of these new solutions. An empirical formula that approximates the ADM mass of hairy solutions is put forward, and some of its properties are analyzed.« less

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.

Noise reduction in urban LRT networks by combining track based solutions.

PubMed

Vogiatzis, Konstantinos; Vanhonacker, Patrick

2016-10-15

The overall objective of the Quiet-Track project is to provide step-changing track based noise mitigation and maintenance schemes for railway rolling noise in LRT (Light Rail Transit) networks. WP 4 in particular focuses on the combination of existing track based solutions to yield a global performance of at least 6dB(A). The validation was carried out using a track section in the network of Athens Metro Line 1 with an existing outside concrete slab track (RHEDA track) where high airborne rolling noise was observed. The procedure for the selection of mitigation measures is based on numerical simulations, combining WRNOISE and IMMI software tools for noise prediction with experimental determination of the required track and vehicle parameters (e.g., rail and wheel roughness). The availability of a detailed rolling noise calculation procedure allows for detailed designing of measures and of ranking individual measures. It achieves this by including the modelling of the wheel/rail source intensity and of the noise propagation with the ability to evaluate the effect of modifications at source level (e.g., grinding, rail dampers, wheel dampers, change in resiliency of wheels and/or rail fixation) and of modifications in the propagation path (absorption at the track base, noise barriers, screening). A relevant combination of existing solutions was selected in the function of the simulation results. Three distinct existing solutions were designed in detail aiming at a high rolling noise attenuation and not affecting the normal operation of the metro system: Action 1: implementation of sound absorbing precast elements (panel type) on the track bed, Action 2: implementation of an absorbing noise barrier with a height of 1.10-1.20m above rail level, and Action 3: installation of rail dampers. The selected solutions were implemented on site and the global performance was measured step by step for comparison with simulations. Copyright © 2015 Elsevier B.V. All rights reserved.

A Variational Reduction and the Existence of a Fully Localised Solitary Wave for the Three-Dimensional Water-Wave Problem with Weak Surface Tension

NASA Astrophysics Data System (ADS)

Buffoni, Boris; Groves, Mark D.; Wahlén, Erik

2017-12-01

Fully localised solitary waves are travelling-wave solutions of the three- dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence has been predicted on the basis of numerical simulations and model equations (in which context they are usually referred to as `lumps'), and a mathematically rigorous existence theory for strong surface tension (Bond number {β} greater than {1/3} ) has recently been given. In this article we present an existence theory for the physically more realistic case {0 < β < 1/3} . A classical variational principle for fully localised solitary waves is reduced to a locally equivalent variational principle featuring a perturbation of the functional associated with the Davey-Stewartson equation. A nontrivial critical point of the reduced functional is found by minimising it over its natural constraint set.

A Variational Reduction and the Existence of a Fully Localised Solitary Wave for the Three-Dimensional Water-Wave Problem with Weak Surface Tension

NASA Astrophysics Data System (ADS)

Buffoni, Boris; Groves, Mark D.; Wahlén, Erik

2018-06-01

Fully localised solitary waves are travelling-wave solutions of the three- dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence has been predicted on the basis of numerical simulations and model equations (in which context they are usually referred to as `lumps'), and a mathematically rigorous existence theory for strong surface tension (Bond number {β} greater than {1/3}) has recently been given. In this article we present an existence theory for the physically more realistic case {0 < β < 1/3}. A classical variational principle for fully localised solitary waves is reduced to a locally equivalent variational principle featuring a perturbation of the functional associated with the Davey-Stewartson equation. A nontrivial critical point of the reduced functional is found by minimising it over its natural constraint set.

An ignition-temperature model with two free interfaces in premixed flames

NASA Astrophysics Data System (ADS)

Brauner, Claude-Michel; Gordon, Peter V.; Zhang, Wen

2016-11-01

In this paper we consider an ignition-temperature zero-order reaction model of thermo-diffusive combustion. This model describes the dynamics of thick flames, which have recently received considerable attention in the physical and engineering literature. The model admits a unique (up to translations) planar travelling wave solution. This travelling wave solution is quite different from those usually studied in combustion theory. The main qualitative feature of this travelling wave is that it has two interfaces: the ignition interface where the ignition temperature is attained and the trailing interface where the concentration of deficient reactants reaches zero. We give a new mathematical framework for studying the cellular instability of such travelling front solutions. Our approach allows the analysis of a free boundary problem to be converted into the analysis of a boundary value problem having a fully nonlinear system of parabolic equations. The latter is very suitable for both mathematical and numerical analysis. We prove the existence of a critical Lewis number such that the travelling wave solution is stable for values of Lewis number below the critical one and is unstable for Lewis numbers that exceed this critical value. Finally, we discuss the results of numerical simulations of a fully nonlinear system that describes the perturbation dynamics of planar fronts. These simulations reveal, in particular, some very interesting 'two-cell' steady patterns of curved combustion fronts.

Well-posedness, linear perturbations, and mass conservation for the axisymmetric Einstein equations

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

Dain, Sergio; Ortiz, Omar E.; Facultad de Matematica, Astronomia y Fisica, FaMAF, Universidad Nacional de Cordoba, Instituto de Fisica Enrique Gaviola, IFEG, CONICET, Ciudad Universitaria

2010-02-15

For axially symmetric solutions of Einstein equations there exists a gauge which has the remarkable property that the total mass can be written as a conserved, positive definite, integral on the spacelike slices. The mass integral provides a nonlinear control of the variables along the whole evolution. In this gauge, Einstein equations reduce to a coupled hyperbolic-elliptic system which is formally singular at the axis. As a first step in analyzing this system of equations we study linear perturbations on a flat background. We prove that the linear equations reduce to a very simple system of equations which provide, thoughmore » the mass formula, useful insight into the structure of the full system. However, the singular behavior of the coefficients at the axis makes the study of this linear system difficult from the analytical point of view. In order to understand the behavior of the solutions, we study the numerical evolution of them. We provide strong numerical evidence that the system is well-posed and that its solutions have the expected behavior. Finally, this linear system allows us to formulate a model problem which is physically interesting in itself, since it is connected with the linear stability of black hole solutions in axial symmetry. This model can contribute significantly to solve the nonlinear problem and at the same time it appears to be tractable.« less

Modeling and Analysis of Wrinkled Membranes: An Overview

NASA Technical Reports Server (NTRS)

Yang, B.; Ding, H.; Lou, M.; Fang, H.; Broduer, Steve (Technical Monitor)

2001-01-01

Thin-film membranes are basic elements of a variety of space inflatable/deployable structures. Wrinkling degrades the performance and reliability of these membrane structures, and hence has been a topic of continued interest. Wrinkling analysis of membranes for general geometry and arbitrary boundary conditions is quite challenging. The objective of this presentation is two-fold. Firstly, the existing models of wrinkled membranes and related numerical solution methods are reviewed. The important issues to be discussed are the capability of a membrane model to characterize taut, wrinkled and slack states of membranes in a consistent and physically reasonable manner; the ability of a wrinkling analysis method to predict the formation and growth of wrinkled regions, and to determine out-of-plane deformation and wrinkled waves; the convergence of a numerical solution method for wrinkling analysis; and the compatibility of a wrinkling analysis with general-purpose finite element codes. According to this review, several opening issues in modeling and analysis of wrinkled membranes that are to be addressed in future research are summarized, The second objective of this presentation is to discuss a newly developed membrane model of two viable parameters (2-VP model) and associated parametric finite element method (PFEM) for wrinkling analysis are introduced. The innovations and advantages of the proposed membrane model and PFEM-based wrinkling analysis are: (1) Via a unified stress-strain relation; the 2-VP model treat the taut, wrinkled, and slack states of membranes consistently; (2) The PFEM-based wrinkling analysis has guaranteed convergence; (3) The 2-VP model along with PFEM is capable of predicting membrane out-of-plane deformations; and (4) The PFEM can be integrated into any existing finite element code. Preliminary numerical examples are also included in this presentation to demonstrate the 2-VP model and PFEM-based wrinkling analysis approach.

Numerical modeling of consolidation processes in hydraulically deposited soils

NASA Astrophysics Data System (ADS)

Brink, Nicholas Robert

Hydraulically deposited soils are encountered in many common engineering applications including mine tailing and geotextile tube fills, though the consolidation process for such soils is highly nonlinear and requires the use of advanced numerical techniques to provide accurate predictions. Several commercially available finite element codes poses the ability to model soil consolidation, and it was the goal of this research to assess the ability of two of these codes, ABAQUS and PLAXIS, to model the large-strain, two-dimensional consolidation processes which occur in hydraulically deposited soils. A series of one- and two-dimensionally drained rectangular models were first created to assess the limitations of ABAQUS and PLAXIS when modeling consolidation of highly compressible soils. Then, geotextile tube and TSF models were created to represent actual scenarios which might be encountered in engineering practice. Several limitations were discovered, including the existence of a minimum preconsolidation stress below which numerical solutions become unstable.

Semi-analytical solution of flow to a well in an unconfined-fractured aquifer system separated by an aquitard

NASA Astrophysics Data System (ADS)

Sedghi, Mohammad M.; Samani, Nozar; Barry, D. A.

2018-04-01

Semi-analytical solutions are presented for flow to a well in an extensive homogeneous and anisotropic unconfined-fractured aquifer system separated by an aquitard. The pumping well is of infinitesimal radius and screened in either the overlying unconfined aquifer or the underlying fractured aquifer. An existing linearization method was used to determine the watertable drainage. The solution was obtained via Laplace and Hankel transforms, with results calculated by numerical inversion. The main findings are presented in the form of non-dimensional drawdown-time curves, as well as scaled sensitivity-dimensionless time curves. The new solution permits determination of the influence of fractures, matrix blocks and watertable drainage parameters on the aquifer drawdown. The effect of the aquitard on the drawdown response of the overlying unconfined aquifer and the underlying fractured aquifer was also explored. The results permit estimation of the unconfined and fractured aquifer hydraulic parameters via type-curve matching or coupling of the solution with a parameter estimation code. The solution can also be used to determine aquifer hydraulic properties from an optimal pumping test set up and duration.

Finite-Length Diocotron Modes in a Non-neutral Plasma Column

NASA Astrophysics Data System (ADS)

Walsh, Daniel; Dubin, Daniel

2017-10-01

Diocotron modes are 2D distortions of a non-neutral plasma column that propagate azimuthally via E × B drifts. While the infinite-length theory of diocotron modes is well-understood for arbitrary azimuthal mode number l, the finite-length mode frequency is less developed (with some exceptions), and is naturally of relevance to experiments. In this poster, we present an approach to address finite length effects, such as temperature dependence of the mode frequency. We use a bounce-averaged solution to the Vlasov Equation, in which the Vlasov Equation is solved using action-angle variables of the unperturbed Hamiltonian. We write the distribution function as a Fourier series in the bounce-angle variable ψ, keeping only the bounce-averaged term. We demonstrate a numerical solution to this equation for a realistic plasma with a finite Debye Length, compare to the existing l = 1 theory, and discuss possible extensions of the existing theory to l ≠ 1 . Supported by NSF/DOE Partnership Grants PHY1414570 and DESC0002451.

Building Units Design and Scale Chemistry

NASA Astrophysics Data System (ADS)

Férey, Gérard

2000-06-01

The concept of a building unit (BU) is used in two ways: the first is an a posteriori tool for description of structures which can be used to imagine new topologies originating from the description; the second one, restricted to the routes leading to the solid from the solution, starts from the reality of these building units in the solution to design new solids obtained by the tuned precipitation of these BUs with proper counterions. The room temperature and the hydrothermal routes are examined. The existence of BUs with different sizes with close topologies, revealed by numerous examples, leads us to define the notion of "scale chemistry" which concerns the edification of solids with various BUs, either organic, hybrid, or inorganic, and the consequences it has for the corresponding frameworks and the voids they generate. Not only the framework is important, and applications of the existence of large cavities are discussed. The paper ends with a discussion of the new trends which arise from this topological concept.

Preservation solutions for cardiac and pulmonary donor grafts: a review of the current literature

PubMed Central

Latchana, Nicholas; Peck, Joshua R.; Whitson, Bryan

2014-01-01

Hypothermic preservation of donor grafts is imperative to ameliorate ischemia related cellular damage prior to organ transplantation. Numerous solutions are in existence with widespread variability among transplant centers as to a consensus regarding the optimal preservation solution. Here, we present a concise review of pertinent preservation studies involving cardiac and pulmonary allografts in an attempt to minimize the variability among institutions and potentially improve graft and patient survival. A biochemical comparison of common preservation solutions was undertaken with an emphasis on Euro Collins (EC), University of Wisconsin (UW), histidine-tryptophan-ketoglutarate (HTK), Celsior (CEL), Perfadex (PER), Papworth, and Plegisol. An appraisal of the literature ensued containing the aforementioned preservation solutions in the setting of cardiac and pulmonary transplantation. Available evidence supports UW solution as the preservation solution of choice for cardiac transplants with encouraging outcomes relative to notable contenders such as CEL. Despite its success in the setting of cardiac transplantation, its use in pulmonary transplantation remains suboptimal and improved outcomes may be seen with PER. Together, we suggest, based on the literature that the use of UW solution and PER for cardiac and pulmonary transplants, respectively may improve transplant outcomes such as graft and patient survival. PMID:25132982

Existence and instability of steady states for a triangular cross-diffusion system: A computer-assisted proof

NASA Astrophysics Data System (ADS)

Breden, Maxime; Castelli, Roberto

2018-05-01

In this paper, we present and apply a computer-assisted method to study steady states of a triangular cross-diffusion system. Our approach consist in an a posteriori validation procedure, that is based on using a fixed point argument around a numerically computed solution, in the spirit of the Newton-Kantorovich theorem. It allows to prove the existence of various non homogeneous steady states for different parameter values. In some situations, we obtain as many as 13 coexisting steady states. We also apply the a posteriori validation procedure to study the linear stability of the obtained steady states, proving that many of them are in fact unstable.

Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation

NASA Astrophysics Data System (ADS)

Castelli, Roberto; Gameiro, Marcio; Lessard, Jean-Philippe

2018-04-01

In this paper, we develop computer-assisted techniques for the analysis of periodic orbits of ill-posed partial differential equations. As a case study, our proposed method is applied to the Boussinesq equation, which has been investigated extensively because of its role in the theory of shallow water waves. The idea is to use the symmetry of the solutions and a Newton-Kantorovich type argument (the radii polynomial approach) to obtain rigorous proofs of existence of the periodic orbits in a weighted ℓ1 Banach space of space-time Fourier coefficients with exponential decay. We present several computer-assisted proofs of the existence of periodic orbits at different parameter values.

Numerical analysis of the asymptotic two-point boundary value solution for N-body trajectories.

NASA Technical Reports Server (NTRS)

Lancaster, J. E.; Allemann, R. A.

1972-01-01

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical boundary value solution applicable to a broad class of trajectory problems. In addition, the earlier first-order solutions have been extended to second-order to determine if improved accuracy is possible. Comparisons between the asymptotic solution and numerical integration for several lunar and interplanetary trajectories show that the asymptotic solution is generally quite accurate. Also, since no iterations are required, a solution to the boundary value problem is obtained in a fraction of the time required for numerically integrated solutions.

A numerical method for solving systems of linear ordinary differential equations with rapidly oscillating solutions

NASA Technical Reports Server (NTRS)

Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.

1992-01-01

The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.

Dynamics of cholera epidemics with impulsive vaccination and disinfection.

PubMed

Sisodiya, Omprakash Singh; Misra, O P; Dhar, Joydip

2018-04-01

Waterborne diseases have a tremendous influence on human life. The contaminated drinking water causes water-borne disease like cholera. Pulse vaccination is an important and effective strategy for the elimination of infectious diseases. A waterborne disease like cholera can also be controlled by using impulse technique. In this paper, we have proposed a delayed SEIRB epidemic model with impulsive vaccination and disinfection. We have studied the pulse vaccination strategy and sanitation to control the cholera disease. The existence and stability of the disease-free and endemic periodic solution are investigated both analytically and numerically. It is shown that there exists an infection-free periodic solution, using the impulsive dynamical system defined by the stroboscopic map. It is observed that the infection-free periodic solution is globally attractive when the impulse period is less than some critical value. From the analysis of the model, we have obtained a sufficient condition for the permanence of the epidemic with pulse vaccination. The main highlight of this paper is to introduce impulse technique along with latent period into the SEIRB epidemic model to investigate the role of pulse vaccination and disinfection on the dynamics of the cholera epidemics. Copyright © 2018 Elsevier Inc. All rights reserved.

A Parallel Decoding Algorithm for Short Polar Codes Based on Error Checking and Correcting

PubMed Central

Pan, Xiaofei; Pan, Kegang; Ye, Zhan; Gong, Chao

2014-01-01

We propose a parallel decoding algorithm based on error checking and correcting to improve the performance of the short polar codes. In order to enhance the error-correcting capacity of the decoding algorithm, we first derive the error-checking equations generated on the basis of the frozen nodes, and then we introduce the method to check the errors in the input nodes of the decoder by the solutions of these equations. In order to further correct those checked errors, we adopt the method of modifying the probability messages of the error nodes with constant values according to the maximization principle. Due to the existence of multiple solutions of the error-checking equations, we formulate a CRC-aided optimization problem of finding the optimal solution with three different target functions, so as to improve the accuracy of error checking. Besides, in order to increase the throughput of decoding, we use a parallel method based on the decoding tree to calculate probability messages of all the nodes in the decoder. Numerical results show that the proposed decoding algorithm achieves better performance than that of some existing decoding algorithms with the same code length. PMID:25540813

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.

A digital matched filter for reverse time chaos

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

Bailey, J. Phillip, E-mail: mchamilton@auburn.edu; Beal, Aubrey N.; Dean, Robert N.

2016-07-15

The use of reverse time chaos allows the realization of hardware chaotic systems that can operate at speeds equivalent to existing state of the art while requiring significantly less complex circuitry. Matched filter decoding is possible for the reverse time system since it exhibits a closed form solution formed partially by a linear basis pulse. Coefficients have been calculated and are used to realize the matched filter digitally as a finite impulse response filter. Numerical simulations confirm that this correctly implements a matched filter that can be used for detection of the chaotic signal. In addition, the direct form ofmore » the filter has been implemented in hardware description language and demonstrates performance in agreement with numerical results.« less

A new procedure for calculating contact stresses in gear teeth

NASA Technical Reports Server (NTRS)

Somprakit, Paisan; Huston, Ronald L.

1991-01-01

A numerical procedure for evaluating and monitoring contact stresses in meshing gear teeth is discussed. The procedure is intended to extend the range of applicability and to improve the accuracy of gear contact stress analysis. The procedure is based upon fundamental solution from the theory of elasticity. It is an iterative numerical procedure. The method is believed to have distinct advantages over the classical Hertz method, the finite-element method, and over existing approaches with the boundary element method. Unlike many classical contact stress analyses, friction effects and sliding are included. Slipping and sticking in the contact region are studied. Several examples are discussed. The results are in agreement with classical results. Applications are presented for spur gears.

Numerical Simulation of Delamination Growth in Composite Materials

NASA Technical Reports Server (NTRS)

Camanho, P. P.; Davila, C. G.; Ambur, D. R.

2001-01-01

The use of decohesion elements for the simulation of delamination in composite materials is reviewed. The test methods available to measure the interfacial fracture toughness used in the formulation of decohesion elements are described initially. After a brief presentation of the virtual crack closure technique, the technique most widely used to simulate delamination growth, the formulation of interfacial decohesion elements is described. Problems related with decohesion element constitutive equations, mixed-mode crack growth, element numerical integration and solution procedures are discussed. Based on these investigations, it is concluded that the use of interfacial decohesion elements is a promising technique that avoids the need for a pre-existing crack and pre-defined crack paths, and that these elements can be used to simulate both delamination onset and growth.

A fast numerical scheme for causal relativistic hydrodynamics with dissipation

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

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

2011-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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

NASA Technical Reports Server (NTRS)

Atkins, Harold L.; Pampell, Alyssa

2011-01-01

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

Numerical Generation of Dense Plume Fingers in Unsaturated Homogeneous Porous Media

NASA Astrophysics Data System (ADS)

Cremer, C.; Graf, T.

2012-04-01

In nature, the migration of dense plumes typically results in the formation of vertical plume fingers. Flow direction in fingers is downwards, which is counterbalanced by upwards flow of less dense fluid between fingers. In heterogeneous media, heterogeneity itself is known to trigger the formation of fingers. In homogeneous media, however, fingers are also created even if all grains had the same diameter. The reason is that pore-scale heterogeneity leading to different flow velocities also exists in homogeneous media due to two effects: (i) Grains of identical size may randomly arrange differently, e.g. forming tetrahedrons, hexahedrons or octahedrons. Each arrangement creates pores of varying diameter, thus resulting in different average flow velocities. (ii) Random variations of solute concentration lead to varying buoyancy effects, thus also resulting in different velocities. As a continuation of previously made efforts to incorporate pore-scale heterogeneity into fully saturated soil such that dense fingers are realistically generated (Cremer and Graf, EGU Assembly, 2011), the current paper extends the research scope from saturated to unsaturated soil. Perturbation methods are evaluated by numerically re-simulating a laboratory-scale experiment of plume transport in homogeneous unsaturated sand (Simmons et al., Transp. Porous Media, 2002). The following 5 methods are being discussed: (i) homogeneous sand, (ii) initial perturbation of solute concentration, (iii) spatially random, time-constant perturbation of solute source, (iv) spatially and temporally random noise of simulated solute concentration, and (v) random K-field that introduces physically insignificant but numerically significant heterogeneity. Results demonstrate that, as opposed to saturated flow, perturbing the solute source will not result in plume fingering. This is because the location of the perturbed source (domain top) and the location of finger generation (groundwater surface) do not coincide. Alternatively, similar to saturated flow, applying either a random concentration noise (iv) or a random K-field (v) generates realistic plume fingering. Future work will focus on the generation mechanisms of plume finger splitting.

Computational Models of Rock Failure

NASA Astrophysics Data System (ADS)

May, Dave A.; Spiegelman, Marc

2017-04-01

Practitioners in computational geodynamics, as per many other branches of applied science, typically do not analyse the underlying PDE's being solved in order to establish the existence or uniqueness of solutions. Rather, such proofs are left to the mathematicians, and all too frequently these results lag far behind (in time) the applied research being conducted, are often unintelligible to the non-specialist, are buried in journals applied scientists simply do not read, or simply have not been proven. As practitioners, we are by definition pragmatic. Thus, rather than first analysing our PDE's, we first attempt to find approximate solutions by throwing all our computational methods and machinery at the given problem and hoping for the best. Typically this approach leads to a satisfactory outcome. Usually it is only if the numerical solutions "look odd" that we start delving deeper into the math. In this presentation I summarise our findings in relation to using pressure dependent (Drucker-Prager type) flow laws in a simplified model of continental extension in which the material is assumed to be an incompressible, highly viscous fluid. Such assumptions represent the current mainstream adopted in computational studies of mantle and lithosphere deformation within our community. In short, we conclude that for the parameter range of cohesion and friction angle relevant to studying rocks, the incompressibility constraint combined with a Drucker-Prager flow law can result in problems which have no solution. This is proven by a 1D analytic model and convincingly demonstrated by 2D numerical simulations. To date, we do not have a robust "fix" for this fundamental problem. The intent of this submission is to highlight the importance of simple analytic models, highlight some of the dangers / risks of interpreting numerical solutions without understanding the properties of the PDE we solved, and lastly to stimulate discussions to develop an improved computational model of rock failure suitable for geodynamic studies.

Numerical simulations to the nonlinear model of interpersonal relationships with time fractional derivative

NASA Astrophysics Data System (ADS)

Gencoglu, Muharrem Tuncay; Baskonus, Haci Mehmet; Bulut, Hasan

2017-01-01

The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretically implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9. The authors would like to thank the reviewers for their comments that help improve the manuscript.

A Theory of L 1-Dissipative Solvers for Scalar Conservation Laws with Discontinuous Flux

NASA Astrophysics Data System (ADS)

Andreianov, Boris; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik

2011-07-01

We propose a general framework for the study of L 1 contractive semigroups of solutions to conservation laws with discontinuous flux: u_t + mathfrak{f}(x,u)_x=0, qquad mathfrak{f}(x,u)= left\\{begin{array}{ll} f^l(u),& x < 0,\\ f^r(u), & x > 0, right.quadquadquad (CL) where the fluxes f l , f r are mainly assumed to be continuous. Developing the ideas of a number of preceding works ( Baiti and Jenssen in J Differ Equ 140(1):161-185, 1997; Towers in SIAM J Numer Anal 38(2):681-698, 2000; Towers in SIAM J Numer Anal 39(4):1197-1218, 2001; Towers et al. in Skr K Nor Vidensk Selsk 3:1-49, 2003; Adimurthi et al. in J Math Kyoto University 43(1):27-70, 2003; Adimurthi et al. in J Hyperbolic Differ Equ 2(4):783-837, 2005; Audusse and Perthame in Proc Roy Soc Edinburgh A 135(2):253-265, 2005; Garavello et al. in Netw Heterog Media 2:159-179, 2007; Bürger et al. in SIAM J Numer Anal 47:1684-1712, 2009), we claim that the whole admissibility issue is reduced to the selection of a family of "elementary solutions", which are piecewise constant weak solutions of the form c(x)=c^l11_{left\\{{x < 0}right\\}}+c^r11_{left\\{{x > 0}right\\}}. We refer to such a family as a "germ". It is well known that (CL) admits many different L 1 contractive semigroups, some of which reflect different physical applications. We revisit a number of the existing admissibility (or entropy) conditions and identify the germs that underly these conditions. We devote specific attention to the "vanishing viscosity" germ, which is a way of expressing the "Γ-condition" of D iehl (J Hyperbolic Differ Equ 6(1):127-159, 2009). For any given germ, we formulate "germ-based" admissibility conditions in the form of a trace condition on the flux discontinuity line { x = 0} [in the spirit of V ol'pert (Math USSR Sbornik 2(2):225-267, 1967)] and in the form of a family of global entropy inequalities [following K ruzhkov (Math USSR Sbornik 10(2):217-243, 1970) and C arrillo (Arch Ration Mech Anal 147(4):269-361, 1999)]. We characterize those germs that lead to the L 1-contraction property for the associated admissible solutions. Our approach offers a streamlined and unifying perspective on many of the known entropy conditions, making it possible to recover earlier uniqueness results under weaker conditions than before, and to provide new results for other less studied problems. Several strategies for proving the existence of admissible solutions are discussed, and existence results are given for fluxes satisfying some additional conditions. These are based on convergence results either for the vanishing viscosity method (with standard viscosity or with specific viscosities "adapted" to the choice of a germ), or for specific germ-adapted finite volume schemes.

Designing an algorithm to preserve privacy for medical record linkage with error-prone data.

PubMed

Pal, Doyel; Chen, Tingting; Zhong, Sheng; Khethavath, Praveen

2014-01-20

Linking medical records across different medical service providers is important to the enhancement of health care quality and public health surveillance. In records linkage, protecting the patients' privacy is a primary requirement. In real-world health care databases, records may well contain errors due to various reasons such as typos. Linking the error-prone data and preserving data privacy at the same time are very difficult. Existing privacy preserving solutions for this problem are only restricted to textual data. To enable different medical service providers to link their error-prone data in a private way, our aim was to provide a holistic solution by designing and developing a medical record linkage system for medical service providers. To initiate a record linkage, one provider selects one of its collaborators in the Connection Management Module, chooses some attributes of the database to be matched, and establishes the connection with the collaborator after the negotiation. In the Data Matching Module, for error-free data, our solution offered two different choices for cryptographic schemes. For error-prone numerical data, we proposed a newly designed privacy preserving linking algorithm named the Error-Tolerant Linking Algorithm, that allows the error-prone data to be correctly matched if the distance between the two records is below a threshold. We designed and developed a comprehensive and user-friendly software system that provides privacy preserving record linkage functions for medical service providers, which meets the regulation of Health Insurance Portability and Accountability Act. It does not require a third party and it is secure in that neither entity can learn the records in the other's database. Moreover, our novel Error-Tolerant Linking Algorithm implemented in this software can work well with error-prone numerical data. We theoretically proved the correctness and security of our Error-Tolerant Linking Algorithm. We have also fully implemented the software. The experimental results showed that it is reliable and efficient. The design of our software is open so that the existing textual matching methods can be easily integrated into the system. Designing algorithms to enable medical records linkage for error-prone numerical data and protect data privacy at the same time is difficult. Our proposed solution does not need a trusted third party and is secure in that in the linking process, neither entity can learn the records in the other's database.

ANNIT - An Efficient Inversion Algorithm based on Prediction Principles

NASA Astrophysics Data System (ADS)

Růžek, B.; Kolář, P.

2009-04-01

Solution of inverse problems represents meaningful job in geophysics. The amount of data is continuously increasing, methods of modeling are being improved and the computer facilities are also advancing great technical progress. Therefore the development of new and efficient algorithms and computer codes for both forward and inverse modeling is still up to date. ANNIT is contributing to this stream since it is a tool for efficient solution of a set of non-linear equations. Typical geophysical problems are based on parametric approach. The system is characterized by a vector of parameters p, the response of the system is characterized by a vector of data d. The forward problem is usually represented by unique mapping F(p)=d. The inverse problem is much more complex and the inverse mapping p=G(d) is available in an analytical or closed form only exceptionally and generally it may not exist at all. Technically, both forward and inverse mapping F and G are sets of non-linear equations. ANNIT solves such situation as follows: (i) joint subspaces {pD, pM} of original data and model spaces D, M, resp. are searched for, within which the forward mapping F is sufficiently smooth that the inverse mapping G does exist, (ii) numerical approximation of G in subspaces {pD, pM} is found, (iii) candidate solution is predicted by using this numerical approximation. ANNIT is working in an iterative way in cycles. The subspaces {pD, pM} are searched for by generating suitable populations of individuals (models) covering data and model spaces. The approximation of the inverse mapping is made by using three methods: (a) linear regression, (b) Radial Basis Function Network technique, (c) linear prediction (also known as "Kriging"). The ANNIT algorithm has built in also an archive of already evaluated models. Archive models are re-used in a suitable way and thus the number of forward evaluations is minimized. ANNIT is now implemented both in MATLAB and SCILAB. Numerical tests show good performance of the algorithm. Both versions and documentation are available on Internet and anybody can download them. The goal of this presentation is to offer the algorithm and computer codes for anybody interested in the solution to inverse problems.

Flexwall Hydraulic Hose Replacement in the NASA Glenn 10- by 10-Foot Supersonic Propulsion Wind Tunnel

NASA Technical Reports Server (NTRS)

Smith, Larry E.; Roeder, James W.; Linne, Alan A.; Klann, Gary A.

2003-01-01

The space-time conservation-element and solution-element method is employed to numerically study the near-field screech-tone noise of a typical underexpanded circular jet issuing from a sonic nozzle. Both axisymmetric and fully three-dimensional computations are carried out. The self-sustained feedback loop is properly simulated. The computed shock-cell structure, acoustic wave length, screech-tone frequency, and sound-pressure levels are in good agreement with existing experimental results.

Computationally efficient multibody simulations

NASA Technical Reports Server (NTRS)

Ramakrishnan, Jayant; Kumar, Manoj

1994-01-01

Computationally efficient approaches to the solution of the dynamics of multibody systems are presented in this work. The computational efficiency is derived from both the algorithmic and implementational standpoint. Order(n) approaches provide a new formulation of the equations of motion eliminating the assembly and numerical inversion of a system mass matrix as required by conventional algorithms. Computational efficiency is also gained in the implementation phase by the symbolic processing and parallel implementation of these equations. Comparison of this algorithm with existing multibody simulation programs illustrates the increased computational efficiency.

A numerical study on weak-dissipative two-mode perturbed Burgers' and Ostrovsky models: right-left moving waves

NASA Astrophysics Data System (ADS)

Jaradat, Imad; Alquran, Marwan; Ali, Mohammed

2018-04-01

The purpose of this study is threefold. First, it derives newly developed two-mode nonlinear equations, two-mode perturbed Burgers' and two-mode Ostrovsky models. Second, it investigates the values of the nonlinearity and dispersion parameters that support the existence of two right-left (R-L) moving wave solutions to these models. Finally, it provides a graphical analysis of the "two-mode" concept and the impact of its phase velocity on the field function.

A stabilized MFE reduced-order extrapolation model based on POD for the 2D unsteady conduction-convection problem.

PubMed

Xia, Hong; Luo, Zhendong

2017-01-01

In this study, we devote ourselves to establishing a stabilized mixed finite element (MFE) reduced-order extrapolation (SMFEROE) model holding seldom unknowns for the two-dimensional (2D) unsteady conduction-convection problem via the proper orthogonal decomposition (POD) technique, analyzing the existence and uniqueness and the stability as well as the convergence of the SMFEROE solutions and validating the correctness and dependability of the SMFEROE model by means of numerical simulations.

Simulation of ground-water flow and solute transport in the Glen Canyon aquifer, East-Central Utah

USGS Publications Warehouse

Freethey, Geoffrey W.; Stolp, Bernard J.

2010-01-01

The extraction of methane from coal beds in the Ferron coal trend in central Utah started in the mid-1980s. Beginning in 1994, water from the extraction process was pressure injected into the Glen Canyon aquifer. The lateral extent of the aquifer that could be affected by injection is about 7,600 square miles. To address regional-scale effects of injection over a decadal time frame, a conceptual model of ground-water movement and transport of dissolved solids was formulated. A numerical model that incorporates aquifer concepts was then constructed and used to simulate injection.The Glen Canyon aquifer within the study area is conceptualized in two parts—an active area of ground-water flow and solute transport that exists between recharge areas in the San Rafael Swell and Desert, Waterpocket Fold, and Henry Mountains and discharge locations along the Muddy, Dirty Devil, San Rafael, and Green Rivers. An area of little or negligible ground-water flow exists north of Price, Utah, and beneath the Wasatch Plateau. Pressurized injection of coal-bed methane production water occurs in this area where dissolved-solids concentrations can be more than 100,000 milligrams per liter. Injection has the potential to increase hydrologic interaction with the active flow area, where dissolved-solids concentrations are generally less than 3,000 milligrams per liter.Pressurized injection of coal-bed methane production water in 1994 initiated a net addition of flow and mass of solutes into the Glen Canyon aquifer. To better understand the regional scale hydrologic interaction between the two areas of the Glen Canyon aquifer, pressurized injection was numerically simulated. Data constraints precluded development of a fully calibrated simulation; instead, an uncalibrated model was constructed that is a plausible representation of the conceptual flow and solute-transport processes. The amount of injected water over the 36-year simulation period is about 25,000 acre-feet. As a result, simulated water levels in the injection areas increased by 50 feet and dissolved-solids concentrations increased by 100 milligrams per liter or more. These increases are accrued into aquifer storage and do not extend to the rivers during the 36-year simulation period. The amount of change in simulated discharge and solute load to the rivers is less than the resolution accuracy of the numerical simulation and is interpreted as no significant change over the considered time period.

Peculiarities of the electron energy spectrum in the Coulomb field of a superheavy nucleus

NASA Astrophysics Data System (ADS)

Voronov, B. L.; Gitman, D. M.; Levin, A. D.; Ferreira, R.

2016-05-01

We consider the peculiarities of the electron energy spectrum in the Coulomb field of a superheavy nucleus and discuss the long history of an incorrect interpretation of this problem in the case of a pointlike nucleus and its current correct solution. We consider the spectral problem in the case of a regularized Coulomb potential. For some special regularizations, we derive an exact equation for the point spectrum in the energy interval (-m,m) and find some of its solutions numerically. We also derive an exact equation for charges yielding bound states with the energy E = -m; some call them supercritical charges. We show the existence of an infinite number of such charges. Their existence does not mean that the oneparticle relativistic quantum mechanics based on the Dirac Hamiltonian with the Coulomb field of such charges is mathematically inconsistent, although it is physically unacceptable because the spectrum of the Hamiltonian is unbounded from below. The question of constructing a consistent nonperturbative second-quantized theory remains open, and the consequences of the existence of supercritical charges from the standpoint of the possibility of constructing such a theory also remain unclear.

Theory of precipitation effects on dead cylindrical fuels

Treesearch

Michael A. Fosberg

1972-01-01

Numerical and analytical solutions of the Fickian diffusion equation were used to determine the effects of precipitation on dead cylindrical forest fuels. The analytical solution provided a physical framework. The numerical solutions were then used to refine the analytical solution through a similarity argument. The theoretical solutions predicted realistic rates of...

Development and Implementation of a Transport Method for the Transport and Reaction Simulation Engine (TaRSE) based on the Godunov-Mixed Finite Element Method

USGS Publications Warehouse

James, Andrew I.; Jawitz, James W.; Munoz-Carpena, Rafael

2009-01-01

A model to simulate transport of materials in surface water and ground water has been developed to numerically approximate solutions to the advection-dispersion equation. This model, known as the Transport and Reaction Simulation Engine (TaRSE), uses an algorithm that incorporates a time-splitting technique where the advective part of the equation is solved separately from the dispersive part. An explicit finite-volume Godunov method is used to approximate the advective part, while a mixed-finite element technique is used to approximate the dispersive part. The dispersive part uses an implicit discretization, which allows it to run stably with a larger time step than the explicit advective step. The potential exists to develop algorithms that run several advective steps, and then one dispersive step that encompasses the time interval of the advective steps. Because the dispersive step is computationally most expensive, schemes can be implemented that are more computationally efficient than non-time-split algorithms. This technique enables scientists to solve problems with high grid Peclet numbers, such as transport problems with sharp solute fronts, without spurious oscillations in the numerical approximation to the solution and with virtually no artificial diffusion.

On the bistable zone of milling processes

PubMed Central

Dombovari, Zoltan; Stepan, Gabor

2015-01-01

A modal-based model of milling machine tools subjected to time-periodic nonlinear cutting forces is introduced. The model describes the phenomenon of bistability for certain cutting parameters. In engineering, these parameter domains are referred to as unsafe zones, where steady-state milling may switch to chatter for certain perturbations. In mathematical terms, these are the parameter domains where the periodic solution of the corresponding nonlinear, time-periodic delay differential equation is linearly stable, but its domain of attraction is limited due to the existence of an unstable quasi-periodic solution emerging from a secondary Hopf bifurcation. A semi-numerical method is presented to identify the borders of these bistable zones by tracking the motion of the milling tool edges as they might leave the surface of the workpiece during the cutting operation. This requires the tracking of unstable quasi-periodic solutions and the checking of their grazing to a time-periodic switching surface in the infinite-dimensional phase space. As the parameters of the linear structural behaviour of the tool/machine tool system can be obtained by means of standard modal testing, the developed numerical algorithm provides efficient support for the design of milling processes with quick estimates of those parameter domains where chatter can still appear in spite of setting the parameters into linearly stable domains. PMID:26303918

Existing Whole-House Solutions Case Study: Retrofitting a 1960s Split-Level Cold-Climate Home

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

Puttagunta, S.

2015-08-01

National programs such as Home Performance with ENERGY STAR® and numerous other utility air sealing programs have brought awareness to homeowners of the benefits of energy efficiency retrofits. Yet, these programs tend to focus on the low-hanging fruit: air-sealing the thermal envelope and ductwork where accessible, switch to efficient lighting, and low-flow fixtures. At the other end of the spectrum, deep-energy retrofit programs are also being encouraged by various utilities across the country. While deep energy retrofits typically seek 50% energy savings, they are often quite costly and most applicable to gut-rehab projects. A significant potential for lowering energy usagemore » in existing homes lies between the low hanging fruit and deep energy retrofit approaches - retrofits that save approximately 30% in energy over the existing conditions.« less

Lagrangian averaging, nonlinear waves, and shock regularization

NASA Astrophysics Data System (ADS)

Bhat, Harish S.

In this thesis, we explore various models for the flow of a compressible fluid as well as model equations for shock formation, one of the main features of compressible fluid flows. We begin by reviewing the variational structure of compressible fluid mechanics. We derive the barotropic compressible Euler equations from a variational principle in both material and spatial frames. Writing the resulting equations of motion requires certain Lie-algebraic calculations that we carry out in detail for expository purposes. Next, we extend the derivation of the Lagrangian averaged Euler (LAE-alpha) equations to the case of barotropic compressible flows. The derivation in this thesis involves averaging over a tube of trajectories etaepsilon centered around a given Lagrangian flow eta. With this tube framework, the LAE-alpha equations are derived by following a simple procedure: start with a given action, expand via Taylor series in terms of small-scale fluid fluctuations xi, truncate, average, and then model those terms that are nonlinear functions of xi. We then analyze a one-dimensional subcase of the general models derived above. We prove the existence of a large family of traveling wave solutions. Computing the dispersion relation for this model, we find it is nonlinear, implying that the equation is dispersive. We carry out numerical experiments that show that the model possesses smooth, bounded solutions that display interesting pattern formation. Finally, we examine a Hamiltonian partial differential equation (PDE) that regularizes the inviscid Burgers equation without the addition of standard viscosity. Here alpha is a small parameter that controls a nonlinear smoothing term that we have added to the inviscid Burgers equation. We show the existence of a large family of traveling front solutions. We analyze the initial-value problem and prove well-posedness for a certain class of initial data. We prove that in the zero-alpha limit, without any standard viscosity, solutions of the PDE converge strongly to weak solutions of the inviscid Burgers equation. We provide numerical evidence that this limit satisfies an entropy inequality for the inviscid Burgers equation. We demonstrate a Hamiltonian structure for the PDE.

Non-autonomous equations with unpredictable solutions

NASA Astrophysics Data System (ADS)

Akhmet, Marat; Fen, Mehmet Onur

2018-06-01

To make research of chaos more amenable to investigating differential and discrete equations, we introduce the concepts of an unpredictable function and sequence. The topology of uniform convergence on compact sets is applied to define unpredictable functions [1,2]. The unpredictable sequence is defined as a specific unpredictable function on the set of integers. The definitions are convenient to be verified as solutions of differential and discrete equations. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and uniqueness of the unpredictable solution for a delay differential equation are proved as well as for quasilinear discrete systems. As a corollary of the theorem, a similar assertion for a quasilinear ordinary differential equation is formulated. The results are demonstrated numerically, and an application to Hopfield neural networks is provided. In particular, Poincaré chaos near periodic orbits is observed. The completed research contributes to the theory of chaos as well as to the theory of differential and discrete equations, considering unpredictable solutions.

Neural network for nonsmooth pseudoconvex optimization with general convex constraints.

PubMed

Bian, Wei; Ma, Litao; Qin, Sitian; Xue, Xiaoping

2018-05-01

In this paper, a one-layer recurrent neural network is proposed for solving a class of nonsmooth, pseudoconvex optimization problems with general convex constraints. Based on the smoothing method, we construct a new regularization function, which does not depend on any information of the feasible region. Thanks to the special structure of the regularization function, we prove the global existence, uniqueness and "slow solution" character of the state of the proposed neural network. Moreover, the state solution of the proposed network is proved to be convergent to the feasible region in finite time and to the optimal solution set of the related optimization problem subsequently. In particular, the convergence of the state to an exact optimal solution is also considered in this paper. Numerical examples with simulation results are given to show the efficiency and good characteristics of the proposed network. In addition, some preliminary theoretical analysis and application of the proposed network for a wider class of dynamic portfolio optimization are included. Copyright © 2018 Elsevier Ltd. All rights reserved.

Dynamics from a mathematical model of a two-state gas laser

NASA Astrophysics Data System (ADS)

Kleanthous, Antigoni; Hua, Tianshu; Manai, Alexandre; Yawar, Kamran; Van Gorder, Robert A.

2018-05-01

Motivated by recent work in the area, we consider the behavior of solutions to a nonlinear PDE model of a two-state gas laser. We first review the derivation of the two-state gas laser model, before deriving a non-dimensional model given in terms of coupled nonlinear partial differential equations. We then classify the steady states of this system, in order to determine the possible long-time asymptotic solutions to this model, as well as corresponding stability results, showing that the only uniform steady state (the zero motion state) is unstable, while a linear profile in space is stable. We then provide numerical simulations for the full unsteady model. We show for a wide variety of initial conditions that the solutions tend toward the stable linear steady state profiles. We also consider traveling wave solutions, and determine the unique wave speed (in terms of the other model parameters) which allows wave-like solutions to exist. Despite some similarities between the model and the inviscid Burger's equation, the solutions we obtain are much more regular than the solutions to the inviscid Burger's equation, with no evidence of shock formation or loss of regularity.

An analytical solution of groundwater response to tidal fluctuation in a leaky confined aquifer

NASA Astrophysics Data System (ADS)

Jiao, Jiu Jimmy; Tang, Zhonghua

1999-03-01

An analytical solution is derived to investigate the influence of leakage on tidal response in a coastal leaky confined aquifer system. The analytical solution developed here is more general than the traditional solution obtained by Ferris [1951], which can be regarded as a special case of the solution presented in this paper. This solution is based on a conceptual model under the assumption that the groundwater level in the confined aquifer fluctuates in response to sea tide while that of the overlying unconfined aquifer remains constant. This conceptual model is supported by numerous field studies by previous researchers which have demonstrated that the tidal response in an unconfined aquifer may be negligible compared to that in a confined aquifer. The leakage has a significant impact on the tidal behavior of the confined aquifer. Hypothetical studies indicate that both tidal amplitude of groundwater head in the aquifer and the distance over which the aquifer can be disturbed by the sea tide will be considerably reduced because of the existence of leakage. This analytical solution is used to investigate the tidal and piezometer data at the Chek Lap Kok airport, Hong Kong Special Administrative Region, People's Republic of China.

Crank-Nicholson difference scheme for a stochastic parabolic equation with a dependent operator coefficient

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

Ashyralyev, Allaberen; Okur, Ulker

In the present paper, the Crank-Nicolson difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is considered. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, convergence estimates for the solution of difference schemes for the numerical solution of three mixed problems for parabolic equations are obtained. The numerical results are given.

NOTE: Solving the ECG forward problem by means of a meshless finite element method

NASA Astrophysics Data System (ADS)

Li, Z. S.; Zhu, S. A.; He, Bin

2007-07-01

The conventional numerical computational techniques such as the finite element method (FEM) and the boundary element method (BEM) require laborious and time-consuming model meshing. The new meshless FEM only uses the boundary description and the node distribution and no meshing of the model is required. This paper presents the fundamentals and implementation of meshless FEM and the meshless FEM method is adapted to solve the electrocardiography (ECG) forward problem. The method is evaluated on a single-layer torso model, in which the analytical solution exists, and tested in a realistic geometry homogeneous torso model, with satisfactory results being obtained. The present results suggest that the meshless FEM may provide an alternative for ECG forward solutions.

Modelling and simulation of a dynamical system with the Atangana-Baleanu fractional derivative

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.

2018-01-01

In this paper, we model an ecological system consisting of a predator and two preys with the newly derived two-step fractional Adams-Bashforth method via the Atangana-Baleanu derivative in the Caputo sense. We analyze the dynamical system for correct choice of parameter values that are biologically meaningful. The local analysis of the main model is based on the application of qualitative theory for ordinary differential equations. By using the fixed point theorem idea, we establish the existence and uniqueness of the solutions. Convergence results of the new scheme are verified in both space and time. Dynamical wave phenomena of solutions are verified via some numerical results obtained for different values of the fractional index, which have some interesting ecological implications.

1D gasdynamics of wind-blown bubbles: effects of thermal conduction

NASA Astrophysics Data System (ADS)

Zhekov, S. A.; Myasnikov, A. V.

1998-03-01

Gasdynamic properties of the wind-blown bubbles are considered in the framework of the 1D spherically symmetric flow. The model self-consistently takes into account the optically-thin-plasma cooling and the electron thermal conduction. The numerical method used in calculations is described in details. A comparison with the existing self-similar solution is provided. It is shown that the self-similar solution gives a relatively well representation of the hot-bubble interior and could be used for estimations of some of its spectral characteristics. However, it is also shown that the thermal conduction in combination with the cooling may cause additional multiple shocks to appear in the interaction region and the analysis of the nature of these shocks is provided.

A Modified Kirchhoff plate theory for Free Vibration analysis of functionally graded material plates using meshfree method

NASA Astrophysics Data System (ADS)

Nguyen Van Do, Vuong

2018-04-01

In this paper, a modified Kirchhoff theory is presented for free vibration analyses of functionally graded material (FGM) plate based on modified radial point interpolation method (RPIM). The shear deformation effects are taken account into modified theory to ignore the locking phenomenon of thin plates. Due to the proposed refined plate theory, the number of independent unknowns reduces one variable and exists with four degrees of freedom per node. The simulated free vibration results employed by the modified RPIM are compared with the other analytical solutions to verify the effectiveness and the accuracy of the developed mesh-free method. Detail parametric studies of the proposed method are then conducted including the effectiveness of thickness ratio, boundary condition and material inhomogeneity on the sample problems of square plates. Results illustrated that the modified mesh-free RPIM can effectively predict the numerical calculation as compared to the exact solutions. The obtained numerical results are indicated that the proposed method are stable and well accurate prediction to evaluate with other published analyses.

Multiple solutions and numerical analysis to the dynamic and stationary models coupling a delayed energy balance model involving latent heat and discontinuous albedo with a deep ocean.

PubMed

Díaz, J I; Hidalgo, A; Tello, L

2014-10-08

We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscillatory reconstruction and Runge-Kutta total variation diminishing for time integration.

Constrained orbital intercept-evasion

NASA Astrophysics Data System (ADS)

Zatezalo, Aleksandar; Stipanovic, Dusan M.; Mehra, Raman K.; Pham, Khanh

2014-06-01

An effective characterization of intercept-evasion confrontations in various space environments and a derivation of corresponding solutions considering a variety of real-world constraints are daunting theoretical and practical challenges. Current and future space-based platforms have to simultaneously operate as components of satellite formations and/or systems and at the same time, have a capability to evade potential collisions with other maneuver constrained space objects. In this article, we formulate and numerically approximate solutions of a Low Earth Orbit (LEO) intercept-maneuver problem in terms of game-theoretic capture-evasion guaranteed strategies. The space intercept-evasion approach is based on Liapunov methodology that has been successfully implemented in a number of air and ground based multi-player multi-goal game/control applications. The corresponding numerical algorithms are derived using computationally efficient and orbital propagator independent methods that are previously developed for Space Situational Awareness (SSA). This game theoretical but at the same time robust and practical approach is demonstrated on a realistic LEO scenario using existing Two Line Element (TLE) sets and Simplified General Perturbation-4 (SGP-4) propagator.

Exact solutions for discrete breathers in a forced-damped chain.

PubMed

Gendelman, O V

2013-06-01

Exact solutions for symmetric on-site discrete breathers (DBs) are obtained in a forced-damped linear chain with on-site vibro-impact constraints. The damping in the system is caused by inelastic impacts; the forcing functions should satisfy conditions of periodicity and antisymmetry. Global conditions for existence and stability of the DBs are established by a combination of analytic and numeric methods. The DB can lose its stability through either pitchfork, or Neimark-Sacker bifurcations. The pitchfork bifurcation is related to the internal dynamics of each individual oscillator. It is revealed that the coupling can suppress this type of instability. To the contrary, the Neimark-Sacker bifurcation occurs for relatively large values of the coupling, presumably due to closeness of the excitation frequency to a boundary of the propagation zone of the chain. Both bifurcation mechanisms seem to be generic for the considered type of forced-damped lattices. Some unusual phenomena, like nonmonotonous dependence of the stability boundary on the forcing amplitude, are revealed analytically for the initial system and illustrated numerically for small periodic lattices.

Development of an upwind, finite-volume code with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Molvik, Gregory A.

1995-01-01

Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques and of a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data. This report summarizes the research that took place from August 1,1994 to January 1, 1995.

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Yang, Haijian; Sun, Shuyu; Yang, Chao

2017-03-01

Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.

Multiple solutions and numerical analysis to the dynamic and stationary models coupling a delayed energy balance model involving latent heat and discontinuous albedo with a deep ocean

PubMed Central

Díaz, J. I.; Hidalgo, A.; Tello, L.

2014-01-01

We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscillatory reconstruction and Runge–Kutta total variation diminishing for time integration. PMID:25294969

Three-dimensional unsteady lifting surface theory in the subsonic range

NASA Technical Reports Server (NTRS)

Kuessner, H. G.

1985-01-01

The methods of the unsteady lifting surface theory are surveyed. Linearized Euler's equations are simplified by means of a Galileo-Lorentz transformation and a Laplace transformation so that the time and the compressibility of the fluid are limited to two constants. The solutions to this simplified problem are represented as integrals with a differential nucleus; these results in tolerance conditions, for which any exact solution must suffice. It is shown that none of the existing three-dimensional lifting surface theories in subsonic range satisfy these conditions. An oscillating elliptic lifting surface which satisfies the tolerance conditions is calculated through the use of Lame's functions. Numerical examples are calculated for the borderline cases of infinitely stretched elliptic lifting surfaces and of circular lifting surfaces. Out of the harmonic solutions any such temporal changes of the down current are calculated through the use of an inverse Laplace transformation.

Evolution of thick domain walls in de Sitter universe

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

Dolgov, A.D.; Godunov, S.I.; Rudenko, A.S., E-mail: dolgov@fe.infn.it, E-mail: sgodunov@itep.ru, E-mail: a.s.rudenko@inp.nsk.su

We consider thick domain walls in a de Sitter universe following paper by Basu and Vilenkin. However, we are interested not only in stationary solutions found therein, but also investigate the general case of domain wall evolution with time. When the wall thickness parameter, δ{sub 0}, is smaller than H {sup −1}/√2, where H is the Hubble parameter in de Sitter space-time, then the stationary solutions exist, and initial field configurations tend with time to the stationary ones. However, there are no stationary solutions for δ{sub 0} ≥ H {sup −1}/√2. We have calculated numerically the rate of the wallmore » expansion in this case and have found that the width of the wall grows exponentially fast for δ{sub 0} >> H {sup −1}. An explanation for the critical value δ{sub 0} {sub c} = H {sup −1}/√2 is also proposed.« less

Slip effects on MHD flow and heat transfer of ferrofluids over a moving flat plate

NASA Astrophysics Data System (ADS)

Ramli, Norshafira; Ahmad, Syakila; Pop, Ioan

2017-08-01

In this study, the problem of MHD flow and heat transfer of ferrofluids over a moving flat plate with slip effect and uniform heat flux is considered. The governing ordinary differential equations are solved via shooting method. The effect of slip parameter on the dimensionless velocity, temperature, skin friction and Nusselt numbers are numerically studied for the three selected ferroparticles; magnetite (Fe3O4), cobalt ferrite (CoFe2O4) and Mn-Zn ferrite (Mn-ZnFe2O4) with water-based fluid. The results indicate that dual solutions exist for a plate moving towards the origin. It is found that the slip process delays the boundary layer separation. Moreover, the velocity and thermal boundary-layer thicknesses decrease in the first solution while increase with the increase of the value of slip parameters in second solution.

A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.

PubMed

Benhammouda, Brahim; Vazquez-Leal, Hector

2016-01-01

This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.

Reformulation of the covering and quantizer problems as ground states of interacting particles.

PubMed

Torquato, S

2010-11-01

It is known that the sphere-packing problem and the number-variance problem (closely related to an optimization problem in number theory) can be posed as energy minimizations associated with an infinite number of point particles in d-dimensional Euclidean space R(d) interacting via certain repulsive pair potentials. We reformulate the covering and quantizer problems as the determination of the ground states of interacting particles in R(d) that generally involve single-body, two-body, three-body, and higher-body interactions. This is done by linking the covering and quantizer problems to certain optimization problems involving the "void" nearest-neighbor functions that arise in the theory of random media and statistical mechanics. These reformulations, which again exemplify the deep interplay between geometry and physics, allow one now to employ theoretical and numerical optimization techniques to analyze and solve these energy minimization problems. The covering and quantizer problems have relevance in numerous applications, including wireless communication network layouts, the search of high-dimensional data parameter spaces, stereotactic radiation therapy, data compression, digital communications, meshing of space for numerical analysis, and coding and cryptography, among other examples. In the first three space dimensions, the best known solutions of the sphere-packing and number-variance problems (or their "dual" solutions) are directly related to those of the covering and quantizer problems, but such relationships may or may not exist for d≥4 , depending on the peculiarities of the dimensions involved. Our reformulation sheds light on the reasons for these similarities and differences. We also show that disordered saturated sphere packings provide relatively thin (economical) coverings and may yield thinner coverings than the best known lattice coverings in sufficiently large dimensions. In the case of the quantizer problem, we derive improved upper bounds on the quantizer error using sphere-packing solutions, which are generally substantially sharper than an existing upper bound in low to moderately large dimensions. We also demonstrate that disordered saturated sphere packings yield relatively good quantizers. Finally, we remark on possible applications of our results for the detection of gravitational waves.

Reformulation of the covering and quantizer problems as ground states of interacting particles

NASA Astrophysics Data System (ADS)

Torquato, S.

2010-11-01

It is known that the sphere-packing problem and the number-variance problem (closely related to an optimization problem in number theory) can be posed as energy minimizations associated with an infinite number of point particles in d -dimensional Euclidean space Rd interacting via certain repulsive pair potentials. We reformulate the covering and quantizer problems as the determination of the ground states of interacting particles in Rd that generally involve single-body, two-body, three-body, and higher-body interactions. This is done by linking the covering and quantizer problems to certain optimization problems involving the “void” nearest-neighbor functions that arise in the theory of random media and statistical mechanics. These reformulations, which again exemplify the deep interplay between geometry and physics, allow one now to employ theoretical and numerical optimization techniques to analyze and solve these energy minimization problems. The covering and quantizer problems have relevance in numerous applications, including wireless communication network layouts, the search of high-dimensional data parameter spaces, stereotactic radiation therapy, data compression, digital communications, meshing of space for numerical analysis, and coding and cryptography, among other examples. In the first three space dimensions, the best known solutions of the sphere-packing and number-variance problems (or their “dual” solutions) are directly related to those of the covering and quantizer problems, but such relationships may or may not exist for d≥4 , depending on the peculiarities of the dimensions involved. Our reformulation sheds light on the reasons for these similarities and differences. We also show that disordered saturated sphere packings provide relatively thin (economical) coverings and may yield thinner coverings than the best known lattice coverings in sufficiently large dimensions. In the case of the quantizer problem, we derive improved upper bounds on the quantizer error using sphere-packing solutions, which are generally substantially sharper than an existing upper bound in low to moderately large dimensions. We also demonstrate that disordered saturated sphere packings yield relatively good quantizers. Finally, we remark on possible applications of our results for the detection of gravitational waves.

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

NASA Technical Reports Server (NTRS)

Han, Samuel Bang-Moo

1987-01-01

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

Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell. Part 1: Velocity selection

NASA Technical Reports Server (NTRS)

Tanveer, Saleh

1989-01-01

An asymptotic theory is presented for the determination of velocity and linear stability of a steady symmetric bubble in a Hele-Shaw cell for small surface tension. In the first part, the bubble velocity U relative to the fluid velocity at infinity is determined for small surface tension T by determining transcendentally small correction to the asymptotic series solution. It is found that for any relative bubble velocity U in the interval (U(c),2), solutions exist at a countably infinite set of values of T (which has zero as its limit point) corresponding to the different branches of bubble solutions. U(c) decreases monotonically from 2 to 1 as the bubble area increases from 0 to infinity. However, for a bubble of arbitrarily given size, as T approaches 0, solution exists on any given branch with relative bubble velocity U satisfying the relation 2-U = cT to the 2/3 power, where c depends on the branch but is independent of the bubble area. The analytical evidence further suggests that there are no solutions for U greater than 2. These results are in agreement with earlier analytical results for a finger. In Part 2, an analytic theory is presented for the determination of the linear stability of the bubble in the limit of zero surface tension. Only the solution branch corresponding to the largest possible U for given surface tension is found to be stable, while all the others are unstable, in accordance with earlier numerical results.

An efficient and accurate solution methodology for bilevel multi-objective programming problems using a hybrid evolutionary-local-search algorithm.

PubMed

Deb, Kalyanmoy; Sinha, Ankur

2010-01-01

Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes II: Size Effects on Ionic Distributions and Diffusion-Reaction Rates

PubMed Central

Lu, Benzhuo; Zhou, Y.C.

2011-01-01

The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582

Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid.

PubMed

Xiao, Li; Luo, Ray

2017-12-07

We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.

A 2D flood inundation model based on cellular automata approach

NASA Astrophysics Data System (ADS)

Dottori, Francesco; Todini, Ezio

2010-05-01

In the past years, the cellular automata approach has been successfully applied in two-dimensional modelling of flood events. When used in experimental applications, models based on such approach have provided good results, comparable to those obtained with more complex 2D models; moreover, CA models have proven significantly faster and easier to apply than most of existing models, and these features make them a valuable tool for flood analysis especially when dealing with large areas. However, to date the real degree of accuracy of such models has not been demonstrated, since they have been mainly used in experimental applications, while very few comparisons with theoretical solutions have been made. Also, the use of an explicit scheme of solution, which is inherent in cellular automata models, forces them to work only with small time steps, thus reducing model computation speed. The present work describes a cellular automata model based on the continuity and diffusive wave equations. Several model versions based on different solution schemes have been realized and tested in a number of numerical cases, both 1D and 2D, comparing the results with theoretical and numerical solutions. In all cases, the model performed well compared to the reference solutions, and proved to be both stable and accurate. Finally, the version providing the best results in terms of stability was tested in a real flood event and compared with different hydraulic models. Again, the cellular automata model provided very good results, both in term of computational speed and reproduction of the simulated event.

An efficient approach for treating composition-dependent diffusion within organic particles

DOE PAGES

O'Meara, Simon; Topping, David O.; Zaveri, Rahul A.; ...

2017-09-07

Mounting evidence demonstrates that under certain conditions the rate of component partitioning between the gas and particle phase in atmospheric organic aerosol is limited by particle-phase diffusion. To date, however, particle-phase diffusion has not been incorporated into regional atmospheric models. An analytical rather than numerical solution to diffusion through organic particulate matter is desirable because of its comparatively small computational expense in regional models. Current analytical models assume diffusion to be independent of composition and therefore use a constant diffusion coefficient. To realistically model diffusion, however, it should be composition-dependent (e.g. due to the partitioning of components that plasticise, vitrifymore » or solidify). This study assesses the modelling capability of an analytical solution to diffusion corrected to account for composition dependence against a numerical solution. Results show reasonable agreement when the gas-phase saturation ratio of a partitioning component is constant and particle-phase diffusion limits partitioning rate (<10% discrepancy in estimated radius change). However, when the saturation ratio of the partitioning component varies, a generally applicable correction cannot be found, indicating that existing methodologies are incapable of deriving a general solution. Until such time as a general solution is found, caution should be given to sensitivity studies that assume constant diffusivity. Furthermore, the correction was implemented in the polydisperse, multi-process Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) and is used to illustrate how the evolution of number size distribution may be accelerated by condensation of a plasticising component onto viscous organic particles.« less

An efficient approach for treating composition-dependent diffusion within organic particles

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

O'Meara, Simon; Topping, David O.; Zaveri, Rahul A.

Mounting evidence demonstrates that under certain conditions the rate of component partitioning between the gas and particle phase in atmospheric organic aerosol is limited by particle-phase diffusion. To date, however, particle-phase diffusion has not been incorporated into regional atmospheric models. An analytical rather than numerical solution to diffusion through organic particulate matter is desirable because of its comparatively small computational expense in regional models. Current analytical models assume diffusion to be independent of composition and therefore use a constant diffusion coefficient. To realistically model diffusion, however, it should be composition-dependent (e.g. due to the partitioning of components that plasticise, vitrifymore » or solidify). This study assesses the modelling capability of an analytical solution to diffusion corrected to account for composition dependence against a numerical solution. Results show reasonable agreement when the gas-phase saturation ratio of a partitioning component is constant and particle-phase diffusion limits partitioning rate (<10% discrepancy in estimated radius change). However, when the saturation ratio of the partitioning component varies, a generally applicable correction cannot be found, indicating that existing methodologies are incapable of deriving a general solution. Until such time as a general solution is found, caution should be given to sensitivity studies that assume constant diffusivity. Furthermore, the correction was implemented in the polydisperse, multi-process Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) and is used to illustrate how the evolution of number size distribution may be accelerated by condensation of a plasticising component onto viscous organic particles.« less

Black holes in vector-tensor theories

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

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic andmore » quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.« less

Long-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering data

NASA Astrophysics Data System (ADS)

Chang, Chueh-Hsin; Yu, Ching-Hao; Sheu, Tony Wen-Hann

2016-10-01

In this article, we numerically revisit the long-time solution behavior of the Camassa-Holm equation ut - uxxt + 2ux + 3uux = 2uxuxx + uuxxx. The finite difference solution of this integrable equation is sought subject to the newly derived initial condition with Delta-function potential. Our underlying strategy of deriving a numerical phase accurate finite difference scheme in time domain is to reduce the numerical dispersion error through minimization of the derived discrepancy between the numerical and exact modified wavenumbers. Additionally, to achieve the goal of conserving Hamiltonians in the completely integrable equation of current interest, a symplecticity-preserving time-stepping scheme is developed. Based on the solutions computed from the temporally symplecticity-preserving and the spatially wavenumber-preserving schemes, the long-time asymptotic CH solution characters can be accurately depicted in distinct regions of the space-time domain featuring with their own quantitatively very different solution behaviors. We also aim to numerically confirm that in the two transition zones their long-time asymptotics can indeed be described in terms of the theoretically derived Painlevé transcendents. Another attempt of this study is to numerically exhibit a close connection between the presently predicted finite-difference solution and the solution of the Painlevé ordinary differential equation of type II in two different transition zones.

Comparison of NACA 0012 Laminar Flow Solutions: Structured and Unstructured Grid Methods

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Langer, S.

2016-01-01

In this paper we consider the solution of the compressible Navier-Stokes equations for a class of laminar airfoil flows. The principal objective of this paper is to demonstrate that members of this class of laminar flows have steady-state solutions. These laminar airfoil flow cases are often used to evaluate accuracy, stability and convergence of numerical solution algorithms for the Navier-Stokes equations. In recent years, such flows have also been used as test cases for high-order numerical schemes. While generally consistent steady-state solutions have been obtained for these flows using higher order schemes, a number of results have been published with various solutions, including unsteady ones. We demonstrate with two different numerical methods and a range of meshes with a maximum density that exceeds 8 × 106 grid points that steady-state solutions are obtained. Furthermore, numerical evidence is presented that even when solving the equations with an unsteady algorithm, one obtains steady-state solutions.

Influence of distributed delays on the dynamics of a generalized immune system cancerous cells interactions model

NASA Astrophysics Data System (ADS)

Piotrowska, M. J.; Bodnar, M.

2018-01-01

We present a generalisation of the mathematical models describing the interactions between the immune system and tumour cells which takes into account distributed time delays. For the analytical study we do not assume any particular form of the stimulus function describing the immune system reaction to presence of tumour cells but we only postulate its general properties. We analyse basic mathematical properties of the considered model such as existence and uniqueness of the solutions. Next, we discuss the existence of the stationary solutions and analytically investigate their stability depending on the forms of considered probability densities that is: Erlang, triangular and uniform probability densities separated or not from zero. Particular instability results are obtained for a general type of probability densities. Our results are compared with those for the model with discrete delays know from the literature. In addition, for each considered type of probability density, the model is fitted to the experimental data for the mice B-cell lymphoma showing mean square errors at the same comparable level. For estimated sets of parameters we discuss possibility of stabilisation of the tumour dormant steady state. Instability of this steady state results in uncontrolled tumour growth. In order to perform numerical simulation, following the idea of linear chain trick, we derive numerical procedures that allow us to solve systems with considered probability densities using standard algorithm for ordinary differential equations or differential equations with discrete delays.

Quantification of the electrical anisotropy in the pro­cess of numerical modelling for hydrogeological characterization

NASA Astrophysics Data System (ADS)

Gernez, S.; Bouchedda, A.; Gloaguen, E.; Paradis, D.

2017-12-01

In order to understand groundwater flow and contaminant transport in the subsurface, it is important to characterize accurately its permeability. Hydrogeophysics, which involves the use of geophysical data to infer the hydraulic properties of the subsurface, is a relatively new geoscience field that is promising to improve hydrogeological characterization. Amongst existing geophysical methods, Electrical Resistivity Tomography (ERT), that can cover a large continuous underground surface or volume, has been widely applied. The inversed electrical resistivities obtained are related to the permeabilities by different means and the resistivity anisotropy should theoretically be a proxy to the permeability anisotropy. However, the existing hydrogeophysical inversion tools usually do not take into account anisotropy. In this paper, we present an anisotropic forward- and inverse-problem 2.5D finite-differences electrical study, which allows to produce improved anisotropic permeability characterization models. We first detail the theoretical basis of the anisotropic ERT, which introduces a resistivity tensor in place of a scalar, and its numerical implementation. After that, we build a synthetic case presenting a simple but representative geological structure in two horizontal homogeneous and anisotropic beds: the numerical forward modelling shows a difference of less than 1% with the analytical solution; the inverse modelling is able to reproduce the initial structure well, with resistivity values close to the initial synthetic model (see attached figure). We show that by using both surface and single-borehole arrays, we overcome the equivalence principle making sure that a unique solution arises. The latter cannot be obtained when considering the media isotropic as typically assumed with existing inversion tools. Finally, we discuss the consequences of the integration of anisotropy in the data-integrated characterization of the permeability. We show that it has a significant influence on the electrical inversion results and then on the hydrogeological characterization. It suggests that anisotropy should be taken into account in any characterization study when its presence is presumed or known in order to produce a model closer to the true hydraulic state of the ground.

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.

A new extrapolation cascadic multigrid method for three dimensional elliptic boundary value problems

NASA Astrophysics Data System (ADS)

Pan, Kejia; He, Dongdong; Hu, Hongling; Ren, Zhengyong

2017-09-01

In this paper, we develop a new extrapolation cascadic multigrid method, which makes it possible to solve three dimensional elliptic boundary value problems with over 100 million unknowns on a desktop computer in half a minute. First, by combining Richardson extrapolation and quadratic finite element (FE) interpolation for the numerical solutions on two-level of grids (current and previous grids), we provide a quite good initial guess for the iterative solution on the next finer grid, which is a third-order approximation to the FE solution. And the resulting large linear system from the FE discretization is then solved by the Jacobi-preconditioned conjugate gradient (JCG) method with the obtained initial guess. Additionally, instead of performing a fixed number of iterations as used in existing cascadic multigrid methods, a relative residual tolerance is introduced in the JCG solver, which enables us to obtain conveniently the numerical solution with the desired accuracy. Moreover, a simple method based on the midpoint extrapolation formula is proposed to achieve higher-order accuracy on the finest grid cheaply and directly. Test results from four examples including two smooth problems with both constant and variable coefficients, an H3-regular problem as well as an anisotropic problem are reported to show that the proposed method has much better efficiency compared to the classical V-cycle and W-cycle multigrid methods. Finally, we present the reason why our method is highly efficient for solving these elliptic problems.

Stiffness of frictional contact of dissimilar elastic solids

DOE PAGES

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.; ...

2017-12-22

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This study gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the frictionmore » coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations – adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. Finally, the correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.« less

Stiffness of frictional contact of dissimilar elastic solids

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

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This study gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the frictionmore » coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations – adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. Finally, the correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.« less

Stiffness of frictional contact of dissimilar elastic solids

NASA Astrophysics Data System (ADS)

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.; Xu, Haitao; Pharr, George M.

2018-03-01

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This paper gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the friction coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations - adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. The correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.

Spike solutions in Gierer#x2013;Meinhardt model with a time dependent anomaly exponent

NASA Astrophysics Data System (ADS)

Nec, Yana

2018-01-01

Experimental evidence of complex dispersion regimes in natural systems, where the growth of the mean square displacement in time cannot be characterised by a single power, has been accruing for the past two decades. In such processes the exponent γ(t) in ⟨r2⟩ ∼ tγ(t) at times might be approximated by a piecewise constant function, or it can be a continuous function. Variable order differential equations are an emerging mathematical tool with a strong potential to model these systems. However, variable order differential equations are not tractable by the classic differential equations theory. This contribution illustrates how a classic method can be adapted to gain insight into a system of this type. Herein a variable order Gierer-Meinhardt model is posed, a generic reaction- diffusion system of a chemical origin. With a fixed order this system possesses a solution in the form of a constellation of arbitrarily situated localised pulses, when the components' diffusivity ratio is asymptotically small. The pattern was shown to exist subject to multiple step-like transitions between normal diffusion and sub-diffusion, as well as between distinct sub-diffusive regimes. The analytical approximation obtained permits qualitative analysis of the impact thereof. Numerical solution for typical cross-over scenarios revealed such features as earlier equilibration and non-monotonic excursions before attainment of equilibrium. The method is general and allows for an approximate numerical solution with any reasonably behaved γ(t).

Inversion of geophysical potential field data using the finite element method

NASA Astrophysics Data System (ADS)

Lamichhane, Bishnu P.; Gross, Lutz

2017-12-01

The inversion of geophysical potential field data can be formulated as an optimization problem with a constraint in the form of a partial differential equation (PDE). It is common practice, if possible, to provide an analytical solution for the forward problem and to reduce the problem to a finite dimensional optimization problem. In an alternative approach the optimization is applied to the problem and the resulting continuous problem which is defined by a set of coupled PDEs is subsequently solved using a standard PDE discretization method, such as the finite element method (FEM). In this paper, we show that under very mild conditions on the data misfit functional and the forward problem in the three-dimensional space, the continuous optimization problem and its FEM discretization are well-posed including the existence and uniqueness of respective solutions. We provide error estimates for the FEM solution. A main result of the paper is that the FEM spaces used for the forward problem and the Lagrange multiplier need to be identical but can be chosen independently from the FEM space used to represent the unknown physical property. We will demonstrate the convergence of the solution approximations in a numerical example. The second numerical example which investigates the selection of FEM spaces, shows that from the perspective of computational efficiency one should use 2 to 4 times finer mesh for the forward problem in comparison to the mesh of the physical property.

Benchmark Problems of the Geothermal Technologies Office Code Comparison Study

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

White, Mark D.; Podgorney, Robert; Kelkar, Sharad M.

A diverse suite of numerical simulators is currently being applied to predict or understand the performance of enhanced geothermal systems (EGS). To build confidence and identify critical development needs for these analytical tools, the United States Department of Energy, Geothermal Technologies Office has sponsored a Code Comparison Study (GTO-CCS), with participants from universities, industry, and national laboratories. A principal objective for the study was to create a community forum for improvement and verification of numerical simulators for EGS modeling. Teams participating in the study were those representing U.S. national laboratories, universities, and industries, and each team brought unique numerical simulationmore » capabilities to bear on the problems. Two classes of problems were developed during the study, benchmark problems and challenge problems. The benchmark problems were structured to test the ability of the collection of numerical simulators to solve various combinations of coupled thermal, hydrologic, geomechanical, and geochemical processes. This class of problems was strictly defined in terms of properties, driving forces, initial conditions, and boundary conditions. Study participants submitted solutions to problems for which their simulation tools were deemed capable or nearly capable. Some participating codes were originally developed for EGS applications whereas some others were designed for different applications but can simulate processes similar to those in EGS. Solution submissions from both were encouraged. In some cases, participants made small incremental changes to their numerical simulation codes to address specific elements of the problem, and in other cases participants submitted solutions with existing simulation tools, acknowledging the limitations of the code. The challenge problems were based on the enhanced geothermal systems research conducted at Fenton Hill, near Los Alamos, New Mexico, between 1974 and 1995. The problems involved two phases of research, stimulation, development, and circulation in two separate reservoirs. The challenge problems had specific questions to be answered via numerical simulation in three topical areas: 1) reservoir creation/stimulation, 2) reactive and passive transport, and 3) thermal recovery. Whereas the benchmark class of problems were designed to test capabilities for modeling coupled processes under strictly specified conditions, the stated objective for the challenge class of problems was to demonstrate what new understanding of the Fenton Hill experiments could be realized via the application of modern numerical simulation tools by recognized expert practitioners.« less

Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method

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

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-04-01

The phase appearance/disappearance issue presents serious numerical challenges in two-phase flow simulations. Many existing reactor safety analysis codes use different kinds of treatments for the phase appearance/disappearance problem. However, to our best knowledge, there are no fully satisfactory solutions. Additionally, the majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many situations, it is desirable to use high-resolution spatial discretization and fully implicit time integration schemes to reduce numerical errors. In this work, we adapted a high-resolution spatial discretization scheme on staggered grid mesh and fully implicit time integrationmore » methods (such as BDF1 and BDF2) to solve the two-phase flow problems. The discretized nonlinear system was solved by the Jacobian-free Newton Krylov (JFNK) method, which does not require the derivation and implementation of analytical Jacobian matrix. These methods were tested with a few two-phase flow problems with phase appearance/disappearance phenomena considered, such as a linear advection problem, an oscillating manometer problem, and a sedimentation problem. The JFNK method demonstrated extremely robust and stable behaviors in solving the two-phase flow problems with phase appearance/disappearance. No special treatments such as water level tracking or void fraction limiting were used. High-resolution spatial discretization and second- order fully implicit method also demonstrated their capabilities in significantly reducing numerical errors.« less

Modeling flow and solute transport in irrigation furrows

USDA-ARS?s Scientific Manuscript database

This paper presents an internally coupled flow and solute transport model for free-draining irrigation furrows. Furrow hydraulics is simulated with a numerical zero-inertia model and solute transport is computed with a model based on a numerical solution of the cross-section averaged advection-dispe...

Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons

PubMed Central

Wilson, Hugh R.; Cowan, Jack D.

1972-01-01

Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli. The results obtained show simple and multiple hysteresis phenomena and limit cycle activity. The latter is particularly interesting since the frequency of the limit cycle oscillation is found to be a monotonic function of stimulus intensity. Finally, it is proved that the existence of limit cycle dynamics in response to one class of stimuli implies the existence of multiple stable states and hysteresis in response to a different class of stimuli. The relation between these findings and a number of experiments is discussed. PMID:4332108

Dynamics of a Stochastic Predator-Prey Model with Stage Structure for Predator and Holling Type II Functional Response

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed

2018-01-01

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.

Traveling waves for the mass in mass model of granular chains

DOE PAGES

Kevrekidis, Panayotis G.; Stefanov, Atanas G.; Xu, Haitao

2016-06-03

In this work, we consider the mass in mass (or mass with mass) system of granular chains, namely, a granular chain involving additionally an internal (or, respectively, external) resonator. For these chains, we rigorously establish that under suitable “anti-resonance” conditions connecting the mass of the resonator and the speed of the wave, bell-shaped traveling-wave solutions continue to exist in the system, in a way reminiscent of the results proven for the standard granular chain of elastic Hertzian contacts. Finally, we also numerically touch upon settings, where the conditions do not hold, illustrating, in line also with recent experimental work, thatmore » non-monotonic waves bearing non-vanishing tails may exist in the latter case.« less

Dynamics of a Stochastic Predator-Prey Model with Stage Structure for Predator and Holling Type II Functional Response

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed

2018-06-01

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.

Traveling waves for the mass in mass model of granular chains

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

Kevrekidis, Panayotis G.; Stefanov, Atanas G.; Xu, Haitao

In this work, we consider the mass in mass (or mass with mass) system of granular chains, namely, a granular chain involving additionally an internal (or, respectively, external) resonator. For these chains, we rigorously establish that under suitable “anti-resonance” conditions connecting the mass of the resonator and the speed of the wave, bell-shaped traveling-wave solutions continue to exist in the system, in a way reminiscent of the results proven for the standard granular chain of elastic Hertzian contacts. Finally, we also numerically touch upon settings, where the conditions do not hold, illustrating, in line also with recent experimental work, thatmore » non-monotonic waves bearing non-vanishing tails may exist in the latter case.« less

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

Dall-Anese, Emiliano; Simonetto, Andrea

This paper focuses on the design of online algorithms based on prediction-correction steps to track the optimal solution of a time-varying constrained problem. Existing prediction-correction methods have been shown to work well for unconstrained convex problems and for settings where obtaining the inverse of the Hessian of the cost function can be computationally affordable. The prediction-correction algorithm proposed in this paper addresses the limitations of existing methods by tackling constrained problems and by designing a first-order prediction step that relies on the Hessian of the cost function (and do not require the computation of its inverse). Analytical results are establishedmore » to quantify the tracking error. Numerical simulations corroborate the analytical results and showcase performance and benefits of the algorithms.« less

General Potential Theory of Arbitrary Wing Sections

NASA Technical Reports Server (NTRS)

Theodorsen, T.; Garrick, I. E.

1979-01-01

The problem of determining the two dimensional potential flow around wing sections of any shape is examined. The problem is condensed into the compact form of an integral equation capable of yielding numerical solutions by a direct process. An attempt is made to analyze and coordinate the results of earlier studies relating to properties of wing sections. The existing approximate theory of thin wing sections and the Joukowski theory with its numerous generalizations are reduced to special cases of the general theory of arbitrary sections, permitting a clearer perspective of the entire field. The method which permits the determination of the velocity at any point of an arbitrary section and the associated lift and moments is described. The method is also discussed in terms for developing new shapes of preassigned aerodynamical properties.

Dark-bright quadratic solitons with a focusing effective Kerr nonlinearity

NASA Astrophysics Data System (ADS)

Chen, Manna; Ping, Xiaorou; Liang, Guo; Guo, Qi; Lu, Daquan; Hu, Wei

2018-01-01

Dark solitons are traditionally considered to exist in defocusing Kerr nonlinearity media. We investigate dark quadratic solitons with a focusing effective Kerr nonlinearity and a sine-oscillatory nonlocal response. A nonlinear refractive index with a focusing sine-oscillatory response leads to a defocusing effect with a strong degree of nonlocality, which causes the formation of dark solitons. By analyzing the modulational instability, we determine the parameter domain for dark quadratic solitons with a stable background and numerically obtain dark-bright soliton solutions in the form of pairs, which avoid radiative phenomena. Based on a numerical simulation, we find that all dark-bright soliton pairs are unstable after a relatively long propagation distance, and their stabilities are affected by the soliton interval and the degree of nonlocality.

Pattern formation for NO+N H3 on Pt(100): Two-dimensional numerical results

NASA Astrophysics Data System (ADS)

Uecker, Hannes

2005-01-01

The Lombardo-Fink-Imbihl model of the NO+NH3 reaction on a Pt(100) surface consists of seven coupled ordinary differential equations (ODE) and shows stable relaxation oscillations with sharp transitions in the relevant temperature range. Here we study numerically the effect of coupling of these oscillators by surface diffusion in two dimensions. We find different types of patterns, in particular phase clusters and standing waves. In models of related surface reactions such clustered solutions are known to exist only under a global coupling through the gas phase. This global coupling is replaced here by relatively fast diffusion of two variables which are kinetically slaved in the ODE. We also compare our simulations with experimental results and discuss some shortcomings of the model.

Effects of wall suction/blowing on two-dimensional flow past a confined square cylinder.

PubMed

Zhang, Wei; Jiang, Yanqun; Li, Lang; Chen, Guoping

2016-01-01

A numerical simulation is conducted to study the laminar flow past a square cylinder confined in a channel (the ratio of side length of the square to channel width is fixed at 1/4) subjected to a locally uniform blowing/suction speed placed at the top and bottom channel walls. Governing equations with boundary conditions are resolved using a finite volume method in pressure-velocity formulation. The flow patterns relevant to the critical spacing values are investigated. Numerical results show that wall blowing has a stabilizing effect on the flow, and the corresponding critical Reynolds number increases monotonically with increasing blowing velocity. Remarkably, steady asymmetric solutions and hysteretic mode transitions exist in a certain range of parameters (Reynolds number and suction speed) in the case of suction.

Modelling of non-equilibrium flow in the branched pipeline systems

NASA Astrophysics Data System (ADS)

Sumskoi, S. I.; Sverchkov, A. M.; Lisanov, M. V.; Egorov, A. F.

2016-09-01

This article presents a mathematical model and a numerical method for solving the task of water hammer in the branched pipeline system. The task is considered in the onedimensional non-stationary formulation taking into account the realities such as the change in the diameter of the pipeline and its branches. By comparison with the existing analytic solution it has been shown that the proposed method possesses good accuracy. With the help of the developed model and numerical method the task has been solved concerning the transmission of the compression waves complex in the branching pipeline system when several shut down valves operate. It should be noted that the offered model and method may be easily introduced to a number of other tasks, for example, to describe the flow of blood in the vessels.

On non-local energy transfer via zonal flow in the Dimits shift

NASA Astrophysics Data System (ADS)

St-Onge, Denis A.

2017-10-01

The two-dimensional Terry-Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth-Hinton states. This phenomenon persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the flux-averaged potential, results in an nonlinearity that can efficiently transfer energy non-locally to length scales of the order of the sound radius. The size of the shift for the nonlinear system is heuristically calculated and found to be in excellent agreement with numerical solutions. The existence of the Dimits shift for this system is then understood as an ability of the unstable primary modes to efficiently couple to stable modes at smaller scales, and the shift ends when these stable modes eventually destabilize as the density gradient is increased. This non-local mechanism of energy transfer is argued to be generically important even for more physically complete systems.

The dynamics of a harvested predator-prey system with Holling type IV functional response.

PubMed

Liu, Xinxin; Huang, Qingdao

2018-05-31

The paper aims to investigate the dynamical behavior of a predator-prey system with Holling type IV functional response in which both the species are subject to capturing. We mainly consider how the harvesting affects equilibria, stability, limit cycles and bifurcations in this system. We adopt the method of qualitative and quantitative analysis, which is based on the dynamical theory, bifurcation theory and numerical simulation. The boundedness of solutions, the existence and stability of equilibrium points of the system are further studied. Based on the Sotomayor's theorem, the existence of transcritical bifurcation and saddle-node bifurcation are derived. We use the normal form theorem to analyze the Hopf bifurcation. Simulation results show that the first Lyapunov coefficient is negative and a stable limit cycle may bifurcate. Numerical simulations are performed to make analytical studies more complete. This work illustrates that using the harvesting effort as control parameter can change the behaviors of the system, which may be useful for the biological management. Copyright © 2018 Elsevier B.V. All rights reserved.

New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

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

Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil

2016-04-29

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less

Computing the Evans function via solving a linear boundary value ODE

NASA Astrophysics Data System (ADS)

Wahl, Colin; Nguyen, Rose; Ventura, Nathaniel; Barker, Blake; Sandstede, Bjorn

2015-11-01

Determining the stability of traveling wave solutions to partial differential equations can oftentimes be computationally intensive but of great importance to understanding the effects of perturbations on the physical systems (chemical reactions, hydrodynamics, etc.) they model. For waves in one spatial dimension, one may linearize around the wave and form an Evans function - an analytic Wronskian-like function which has zeros that correspond in multiplicity to the eigenvalues of the linearized system. If eigenvalues with a positive real part do not exist, the traveling wave will be stable. Two methods exist for calculating the Evans function numerically: the exterior-product method and the method of continuous orthogonalization. The first is numerically expensive, and the second reformulates the originally linear system as a nonlinear system. We develop a new algorithm for computing the Evans function through appropriate linear boundary-value problems. This algorithm is cheaper than the previous methods, and we prove that it preserves analyticity of the Evans function. We also provide error estimates and implement it on some classical one- and two-dimensional systems, one being the Swift-Hohenberg equation in a channel, to show the advantages.

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

St-Onge, Denis A.

The two-dimensional Terry–Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth–Hinton states. This phenomenon persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the flux-averaged potential, results in anmore » $$\\boldsymbol{E}\\times \\boldsymbol{B}$$ nonlinearity that can efficiently transfer energy non-locally to length scales of the order of the sound radius. The size of the shift for the nonlinear system is heuristically calculated and found to be in excellent agreement with numerical solutions. The existence of the Dimits shift for this system is then understood as an ability of the unstable primary modes to efficiently couple to stable modes at smaller scales, and the shift ends when these stable modes eventually destabilize as the density gradient is increased. This non-local mechanism of energy transfer is argued to be generically important even for more physically complete systems.« less

Effect of multiple slip on a chemically reactive MHD non-Newtonian nanofluid power law fluid flow over a stretching sheet with microorganism

NASA Astrophysics Data System (ADS)

Basir, Mohammad Faisal Mohd; Ismail, Fazreen Amira; Amirsom, Nur Ardiana; Latiff, Nur Amalina Abdul; Ismail, Ahmad Izani Md.

2017-04-01

The effect of multiple slip on a chemically reactive magnetohydrodynamic (MHD) non-Newtonian power law fluid flow over a stretching sheet with microorganism was numerically investigated. The governing partial differential equations were transformed into nonlinear ordinary differential equations using the similarity transformations developed by Lie group analysis. The reduced governing nonlinear ordinary differential equations were then numerically solved using the Runge-Kutta-Fehlberg fourth-fifth order method. Good agreement was found between the present numerical solutions with the existing published results to support the validity and the accuracy of the numerical computations. The influences of the velocity, thermal, mass and microorganism slips, the magnetic field parameter and the chemical reaction parameter on the dimensionless velocity, temperature, nanoparticle volume fraction, microorganism concentration, the distribution of the density of motile microorganisms have been illustrated graphically. The effects of the governing parameters on the physical quantities, namely, the local heat transfer rate, the local mass transfer rate and the local microorganism transfer rate were analyzed and discussed.

Development of a linearized unsteady Euler analysis for turbomachinery blade rows

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Montgomery, Matthew D.; Kousen, Kenneth A.

1995-01-01

A linearized unsteady aerodynamic analysis for axial-flow turbomachinery blading is described in this report. The linearization is based on the Euler equations of fluid motion and is motivated by the need for an efficient aerodynamic analysis that can be used in predicting the aeroelastic and aeroacoustic responses of blade rows. The field equations and surface conditions required for inviscid, nonlinear and linearized, unsteady aerodynamic analyses of three-dimensional flow through a single, blade row operating within a cylindrical duct, are derived. An existing numerical algorithm for determining time-accurate solutions of the nonlinear unsteady flow problem is described, and a numerical model, based upon this nonlinear flow solver, is formulated for the first-harmonic linear unsteady problem. The linearized aerodynamic and numerical models have been implemented into a first-harmonic unsteady flow code, called LINFLUX. At present this code applies only to two-dimensional flows, but an extension to three-dimensions is planned as future work. The three-dimensional aerodynamic and numerical formulations are described in this report. Numerical results for two-dimensional unsteady cascade flows, excited by prescribed blade motions and prescribed aerodynamic disturbances at inlet and exit, are also provided to illustrate the present capabilities of the LINFLUX analysis.

Perturbational blowup solutions to the compressible Euler equations with damping.

PubMed

Cheung, Ka Luen

2016-01-01

The N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions. In this article, we construct two families of exact solutions for the one-dimensional isentropic compressible Euler equations with damping by the perturbational method. The two families of exact solutions found include the cases [Formula: see text] and [Formula: see text], where [Formula: see text] is the adiabatic constant. With analysis of the key ordinary differential equation, we show that the classes of solutions include both blowup type and global existence type when the parameters are suitably chosen. Moreover, in the blowup cases, we show that the singularities are of essential type in the sense that they cannot be smoothed by redefining values at the odd points. The two families of exact solutions obtained in this paper can be useful to study of related numerical methods and algorithms such as the finite difference method, the finite element method and the finite volume method that are applied by scientists to simulate the fluids for applications.

Spectral methods in general relativity and large Randall-Sundrum II black holes

NASA Astrophysics Data System (ADS)

Abdolrahimi, Shohreh; Cattoën, Céline; Page, Don N.; \\\\; Yaghoobpour-Tari, Shima

2013-06-01

Using a novel numerical spectral method, we have found solutions for large static Randall-Sundrum II (RSII) black holes by perturbing a numerical AdS5-CFT4 solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. We used a numerical spectral method independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman for a similar numerical solution. We have compared our black-hole solution to the one Figueras and Wiseman have derived by perturbing their numerical AdS5-CFT4 solution, showing that our solution agrees closely with theirs. We have obtained a closed-form approximation to the metric of the black hole on the brane. We have also deduced the new results that to first order in 1/(-ΛM2), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(-Λ).

On recent advances and future research directions for computational fluid dynamics

NASA Technical Reports Server (NTRS)

Baker, A. J.; Soliman, M. O.; Manhardt, P. D.

1986-01-01

This paper highlights some recent accomplishments regarding CFD numerical algorithm constructions for generation of discrete approximate solutions to classes of Reynolds-averaged Navier-Stokes equations. Following an overview of turbulent closure modeling, and development of appropriate conservation law systems, a Taylor weak-statement semi-discrete approximate solution algorithm is developed. Various forms for completion to the final linear algebra statement are cited, as are a range of candidate numerical linear algebra solution procedures. This development sequence emphasizes the key building blocks of a CFD RNS algorithm, including solution trial and test spaces, integration procedure and added numerical stability mechanisms. A range of numerical results are discussed focusing on key topics guiding future research directions.

Multiresolution representation and numerical algorithms: A brief review

NASA Technical Reports Server (NTRS)

Harten, Amiram

1994-01-01

In this paper we review recent developments in techniques to represent data in terms of its local scale components. These techniques enable us to obtain data compression by eliminating scale-coefficients which are sufficiently small. This capability for data compression can be used to reduce the cost of many numerical solution algorithms by either applying it to the numerical solution operator in order to get an approximate sparse representation, or by applying it to the numerical solution itself in order to reduce the number of quantities that need to be computed.

Constructing exact symmetric informationally complete measurements from numerical solutions

NASA Astrophysics Data System (ADS)

Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne

2018-04-01

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.

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

Zhou, Shenggao, E-mail: sgzhou@suda.edu.cn, E-mail: bli@math.ucsd.edu; Sun, Hui; Cheng, Li-Tien

Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. Wemore » also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the “normal velocity” that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach.« less

Non-Linear Dynamics and Chaotic Motions in Feedback Controlled Elastic System

DTIC Science & Technology

1988-01-01

b &IA m t K] t -NA00 202) 767- NM C DD Form 1473. JUN 86 Previous editions areobsolete S ~is PikkjE AFOSR 84-0051 Final Report P.Holmes. Research ...University, England 5/23/88 CNLS, Los Alamos National Lab, N4 8/23/88 R.Rand. Research Activities January 1. 1988 - September 31, 1988 1. Averaging...unstable if an unbounded solution exists. Although numerous papers have been written since the mid-1960’s on this problem, we have gone far further in

An analysis method for two-dimensional transonic viscous flow

NASA Technical Reports Server (NTRS)

Bavitz, P. C.

1975-01-01

A method for the approximate calculation of transonic flow over airfoils, including shock waves and viscous effects, is described. Numerical solutions are obtained by use of a computer program which is discussed in the appendix. The importance of including the boundary layer in the analysis is clearly demonstrated, as well as the need to improve on existing procedures near the trailing edge. Comparisons between calculations and experimental data are presented for both conventional and supercritical airfoils, emphasis being on the surface pressure distribution, and good agreement is indicated.