Non-Noetherian symmetries for oscillators in classical mechanics and in field theory

NASA Technical Reports Server (NTRS)

Hojman, Sergio A.; Delajara, Jamie; Pena, Leda

1995-01-01

Infinitely many new conservation laws both for free fields as well as for test fields evolving on a given gravitational background are presented. The conserved currents are constructed using the field theoretical counterpart of a recently discovered non-Noetherian symmetry which gives rise to a new way of solving the classical small oscillations problem. Several examples are discussed.

L1-Based Approximations of PDEs and Applications

DTIC Science & Technology

2012-09-05

the analysis of the Navier-Stokes equations. The early versions of artificial vis- cosities being overly dissipative, the interest for these technique ...Guermond, and B. Popov. Stability analysis of explicit en- tropy viscosity methods for non-linear scalar conservation equations. Math. Comp., 2012... methods for solv- ing mathematical models of nonlinear phenomena such as nonlinear conservation laws, surface/image/data reconstruction problems

On the application of subcell resolution to conservation laws with stiff source terms

NASA Technical Reports Server (NTRS)

Chang, Shih-Hung

1989-01-01

LeVeque and Yee recently investigated a one-dimensional scalar conservation law with stiff source terms modeling the reacting flow problems and discovered that for the very stiff case most of the current finite difference methods developed for non-reacting flows would produce wrong solutions when there is a propagating discontinuity. A numerical scheme, essentially nonoscillatory/subcell resolution - characteristic direction (ENO/SRCD), is proposed for solving conservation laws with stiff source terms. This scheme is a modification of Harten's ENO scheme with subcell resolution, ENO/SR. The locations of the discontinuities and the characteristic directions are essential in the design. Strang's time-splitting method is used and time evolutions are done by advancing along the characteristics. Numerical experiment using this scheme shows excellent results on the model problem of LeVeque and Yee. Comparisons of the results of ENO, ENO/SR, and ENO/SRCD are also presented.

A mixed-mode crack analysis of rectilinear anisotropic solids using conservation laws of elasticity

NASA Technical Reports Server (NTRS)

Wang, S. S.; Yau, J. F.; Corten, H. T.

1980-01-01

A very simple and convenient method of analysis for studying two-dimensional mixed-mode crack problems in rectilinear anisotropic solids is presented. The analysis is formulated on the basis of conservation laws of anisotropic elasticity and of fundamental relationships in anisotropic fracture mechanics. The problem is reduced to a system of linear algebraic equations in mixed-mode stress intensity factors. One of the salient features of the present approach is that it can determine directly the mixed-mode stress intensity solutions from the conservation integrals evaluated along a path removed from the crack-tip region without the need of solving the corresponding complex near-field boundary value problem. Several examples with solutions available in the literature are solved to ensure the accuracy of the current analysis. This method is further demonstrated to be superior to other approaches in its numerical simplicity and computational efficiency. Solutions of more complicated and practical engineering problems dealing with the crack emanating from a circular hole in composites are presented also to illustrate the capacity of this method.

A Summary of the Space-Time Conservation Element and Solution Element (CESE) Method

NASA Technical Reports Server (NTRS)

Wang, Xiao-Yen J.

2015-01-01

The space-time Conservation Element and Solution Element (CESE) method for solving conservation laws is examined for its development motivation and design requirements. The characteristics of the resulting scheme are discussed. The discretization of the Euler equations is presented to show readers how to construct a scheme based on the CESE method. The differences and similarities between the CESE method and other traditional methods are discussed. The strengths and weaknesses of the method are also addressed.

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

A note on the accuracy of spectral method applied to nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Wong, Peter S.

1994-01-01

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

Constructing space difference schemes which satisfy a cell entropy inequality

NASA Technical Reports Server (NTRS)

Merriam, Marshal L.

1989-01-01

A numerical methodology for solving convection problems is presented, using finite difference schemes which satisfy the second law of thermodynamics on a cell-by-cell basis in addition to the usual conservation laws. It is shown that satisfaction of a cell entropy inequality is sufficient, in some cases, to guarantee nonlinear stability. Some details are given for several one-dimensional problems, including the quasi-one-dimensional Euler equations applied to flow in a nozzle.

78 FR 56856 - Submission for OMB Review; Comment Request

Federal Register 2010, 2011, 2012, 2013, 2014

2013-09-16

... corporations. The loans and grants fund the development of drinking water, wastewater, and solid waste disposal... communities or areas identify and solve problems relating to community drinking water, wastewater, or solid... Collection: The Food, Conservation and Energy Act of 2008, Public Law 110-234 (Farm Bill) amended Section 306...

A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws

DTIC Science & Technology

2012-09-03

prac- tice to solve these initial value problems. Additionally, the predictor / corrector methods are combined with adaptive stepsize and adaptive ...for implementing a numerical path tracking algorithm is to decide which predictor / corrector method to employ, how large to take the step ∆t, and what...the endgame algorithm . Output: A steady state solution Set ǫ = 1 while ǫ >= ǫend do set the stepsize ∆ǫ by using adaptive stepsize control algorithm

A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Hu, Changqing; Shu, Chi-Wang

1998-01-01

In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.

Numerical simulation of conservation laws

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; To, Wai-Ming

1992-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.

Flowfield computation of entry vehicles

NASA Technical Reports Server (NTRS)

Prabhu, Dinesh K.

1990-01-01

The equations governing the multidimensional flow of a reacting mixture of thermally perfect gasses were derived. The modeling procedures for the various terms of the conservation laws are discussed. A numerical algorithm, based on the finite-volume approach, to solve these conservation equations was developed. The advantages and disadvantages of the present numerical scheme are discussed from the point of view of accuracy, computer time, and memory requirements. A simple one-dimensional model problem was solved to prove the feasibility and accuracy of the algorithm. A computer code implementing the above algorithm was developed and is presently being applied to simple geometries and conditions. Once the code is completely debugged and validated, it will be used to compute the complete unsteady flow field around the Aeroassist Flight Experiment (AFE) body.

A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity

NASA Technical Reports Server (NTRS)

Yau, J. F.; Wang, S. S.; Corten, H. T.

1980-01-01

A simple and convenient method of analysis for studying two-dimensional mixed-mode crack problems is presented. The analysis is formulated on the basis of conservation laws of elasticity and of fundamental relationships in fracture mechanics. The problem is reduced to the determination of mixed-mode stress-intensity factor solutions in terms of conservation integrals involving known auxiliary solutions. One of the salient features of the present analysis is that the stress-intensity solutions can be determined directly by using information extracted in the far field. Several examples with solutions available in the literature are solved to examine the accuracy and other characteristics of the current approach. This method is demonstrated to be superior in its numerical simplicity and computational efficiency to other approaches. Solutions of more complicated and practical engineering fracture problems dealing with the crack emanating from a circular hole are presented also to illustrate the capacity of this method

A conservative implicit finite difference algorithm for the unsteady transonic full potential equation

NASA Technical Reports Server (NTRS)

Steger, J. L.; Caradonna, F. X.

1980-01-01

An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.

Summer Study Program in Geophysical Fluid Dynamics 1989. General Circulation of the Oceans

DTIC Science & Technology

1989-11-01

Description of the Surface Circulation 2.2 A Description of the Interior Circulation 2.3 Formation Sites and Circulation of Deepwater Masses 2.4 Mode...and atmosphere, we have to follow basic laws of physics which lead us to try to solve a series of conservation equations, Mass : Dp*+ P() Du. - , ’ O.j...r~--~)(18) where,= vorticity 0 - 1 Vertically integrated mass conservation gives which leads to T.3) (19) Using the fact that Ro, ;<<I, the lowest

The effects of strain heating in lithospheric stretching models

NASA Technical Reports Server (NTRS)

Stanton, M.; Hodge, D.; Cozzarelli, F.

1985-01-01

The deformation by stretching of a continental type lithosphere has been formulated so that the problem can be solved by a continuum mechanical approach. The deformation, stress state, and temperature distribution are constrained to satisfy the physical laws of conservation of mass, energy, momentum, and an experimentally defined rheological response. The conservation of energy equation including a term of strain energy dissipation is given. The continental lithosphere is assumed to have the rheology of an isotropic, incompressible, nonlinear viscous, two layered solid.

Numerical Simulations of Multidimensional Flows in Presence of either Strong Shocks or Strong Gravitational Fields

NASA Astrophysics Data System (ADS)

Font, J. A.; Ibanez, J. M.; Marti, J. M.

1993-04-01

Some numerical solutions via local characteristic approach have been obtained describing multidimensional flows. These solutions have been used as tests of a two- dimensional code which extends some high-resolution shock-captunng methods, designed recently to solve nonlinear hyperbolic systems of conservation laws. K words: HYDRODYNAMICS - BLACK HOLE - RELATIVITY - SHOCK WAVES

First Principles Modeling of the Performance of a Hydrogen-Peroxide-Driven Chem-E-Car

ERIC Educational Resources Information Center

Farhadi, Maryam; Azadi, Pooya; Zarinpanjeh, Nima

2009-01-01

In this study, performance of a hydrogen-peroxide-driven car has been simulated using basic conservation laws and a few numbers of auxiliary equations. A numerical method was implemented to solve sets of highly non-linear ordinary differential equations. Transient pressure and the corresponding traveled distance for three different car weights are…

Electrodynamics; Problems and solutions

NASA Astrophysics Data System (ADS)

Ilie, Carolina C.; Schrecengost, Zachariah S.

2018-05-01

This book of problems and solutions is a natural continuation of Ilie and Schrecengost's first book Electromagnetism: Problems and Solutions. Aimed towards students who would like to work independently on more electrodynamics problems in order to deepen their understanding and problem-solving skills, this book discusses main concepts and techniques related to Maxwell's equations, conservation laws, electromagnetic waves, potentials and fields, and radiation.

Vocabulary and Experiences to Develop a Center of Mass Model

ERIC Educational Resources Information Center

Kaar, Taylor; Pollack, Linda B.; Lerner, Michael E.; Engels, Robert J.

2017-01-01

The use of systems in many introductory courses is limited and often implicit. Modeling two or more objects as a system and tracking the center of mass of that system is usually not included. Thinking in terms of the center of mass facilitates problem solving while exposing the importance of using conservation laws. We present below three…

BEARCLAW: Boundary Embedded Adaptive Refinement Conservation LAW package

NASA Astrophysics Data System (ADS)

Mitran, Sorin

2011-04-01

The BEARCLAW package is a multidimensional, Eulerian AMR-capable computational code written in Fortran to solve hyperbolic systems for astrophysical applications. It is part of AstroBEAR, a hydrodynamic & magnetohydrodynamic code environment designed for a variety of astrophysical applications which allows simulations in 2, 2.5 (i.e., cylindrical), and 3 dimensions, in either cartesian or curvilinear coordinates.

Non-oscillatory central differencing for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Nessyahu, Haim; Tadmor, Eitan

1988-01-01

Many of the recently developed high resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block for these schemes is the averaging of an appropriate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in order to identify the direction of the wind. Instead, the use of the more robust Lax-Friedrichs (LxF) solver is proposed. The main advantage is simplicity: no Riemann problems are solved and hence field-by-field decompositions are avoided. The main disadvantage is the excessive numerical viscosity typical to the LxF solver. This is compensated for by using high-resolution MUSCL-type interpolants. Numerical experiments show that the quality of results obtained by such convenient central differencing is comparable with those of the upwind schemes.

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

Ghosh, Debojyoti; Constantinescu, Emil M.

The numerical simulation of meso-, convective-, and microscale atmospheric flows requires the solution of the Euler or the Navier-Stokes equations. Nonhydrostatic weather prediction algorithms often solve the equations in terms of derived quantities such as Exner pressure and potential temperature (and are thus not conservative) and/or as perturbations to the hydrostatically balanced equilibrium state. This paper presents a well-balanced, conservative finite difference formulation for the Euler equations with a gravitational source term, where the governing equations are solved as conservation laws for mass, momentum, and energy. Preservation of the hydrostatic balance to machine precision by the discretized equations is essentialmore » because atmospheric phenomena are often small perturbations to this balance. The proposed algorithm uses the weighted essentially nonoscillatory and compact-reconstruction weighted essentially nonoscillatory schemes for spatial discretization that yields high-order accurate solutions for smooth flows and is essentially nonoscillatory across strong gradients; however, the well-balanced formulation may be used with other conservative finite difference methods. The performance of the algorithm is demonstrated on test problems as well as benchmark atmospheric flow problems, and the results are verified with those in the literature.« less

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.

Conceptual problem solving in high school physics

NASA Astrophysics Data System (ADS)

Docktor, Jennifer L.; Strand, Natalie E.; Mestre, José P.; Ross, Brian H.

2015-12-01

Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an instructional approach called Conceptual Problem Solving (CPS) which guides students to identify principles, justify their use, and plan their solution in writing before solving a problem. The CPS approach was implemented by high school physics teachers at three schools for major theorems and conservation laws in mechanics and CPS-taught classes were compared to control classes taught using traditional problem solving methods. Information about the teachers' implementation of the approach was gathered from classroom observations and interviews, and the effectiveness of the approach was evaluated from a series of written assessments. Results indicated that teachers found CPS easy to integrate into their curricula, students engaged in classroom discussions and produced problem solutions of a higher quality than before, and students scored higher on conceptual and problem solving measures.

Criticality in conserved dynamical systems: experimental observation vs. exact properties.

PubMed

Marković, Dimitrije; Gros, Claudius; Schuelein, André

2013-03-01

Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for these routing models and governed by cyclic attractors. We consider two classes of information flow, Markovian routing without memory and vertex routing involving a one-step routing memory. Investigating the respective cycle length distributions for complete graphs, we find log corrections to power-law scaling for the mean cycle length, as a function of the number of vertices, and a sub-polynomial growth for the overall number of cycles. When observing experimentally a real-world dynamical system one normally samples stochastically its phase space. The number and the length of the attractors are then weighted by the size of their respective basins of attraction. This situation is equivalent, for theory studies, to "on the fly" generation of the dynamical transition probabilities. For the case of vertex routing models, we find in this case power law scaling for the weighted average length of attractors, for both conserved routing models. These results show that the critical dynamical systems are generically not scale-invariant but may show power-law scaling when sampled stochastically. It is hence important to distinguish between intrinsic properties of a critical dynamical system and its behavior that one would observe when randomly probing its phase space.

Numerical Solution for Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Warsi, Z. U. A.; Weed, R. A.; Thompson, J. F.

1982-01-01

Carefully selected blend of computational techniques solves complete set of equations for viscous, unsteady, hypersonic flow in general curvilinear coordinates. New algorithm has tested computation of axially directed flow about blunt body having shape similar to that of such practical bodies as wide-body aircraft or artillery shells. Method offers significant computational advantages because of conservation-law form of equations and because it reduces amount of metric data required.

Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

NASA Astrophysics Data System (ADS)

Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

A dimensionally split Cartesian cut cell method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Gokhale, Nandan; Nikiforakis, Nikos; Klein, Rupert

2018-07-01

We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a full description of its three-dimensional implementation in the dimensionally split framework of Klein et al. [1]. The convergence and stability of the method are proved for the one-dimensional linear advection equation, while its multi-dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and Euler equations. When compared to the cut cell flux of Klein et al., it was found that the new flux alleviates the problem of oscillatory boundary solutions produced by the former at higher Courant numbers, and also enables the computation of more accurate solutions near stagnation points. Being dimensionally split, the method is simple to implement and extends readily to multiple dimensions.

Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics

NASA Technical Reports Server (NTRS)

Sutjahjo, Edhi; Chamis, Christos C.

1993-01-01

Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.

A Lagrangian discontinuous Galerkin hydrodynamic method

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

Liu, Xiaodong; Morgan, Nathaniel Ray; Burton, Donald E.

Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for solving the two-dimensional gas dynamic equations on unstructured hybrid meshes. The physical conservation laws for the momentum and total energy are discretized using a DG method based on linear Taylor expansions. Three different approaches are investigated for calculating the density variation over the element. The first approach evolves a Taylor expansion of the specific volume field. The second approach follows certain finite element methods and uses the strong mass conservation to calculate the density field at a location inside the element or on the element surface. The thirdmore » approach evolves a Taylor expansion of the density field. The nodal velocity, and the corresponding forces, are explicitly calculated by solving a multidirectional approximate Riemann problem. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. Results from a suite of test problems are presented to demonstrate the robustness and expected second-order accuracy of this new method.« less

A Lagrangian discontinuous Galerkin hydrodynamic method

DOE PAGES

Liu, Xiaodong; Morgan, Nathaniel Ray; Burton, Donald E.

2017-12-11

Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for solving the two-dimensional gas dynamic equations on unstructured hybrid meshes. The physical conservation laws for the momentum and total energy are discretized using a DG method based on linear Taylor expansions. Three different approaches are investigated for calculating the density variation over the element. The first approach evolves a Taylor expansion of the specific volume field. The second approach follows certain finite element methods and uses the strong mass conservation to calculate the density field at a location inside the element or on the element surface. The thirdmore » approach evolves a Taylor expansion of the density field. The nodal velocity, and the corresponding forces, are explicitly calculated by solving a multidirectional approximate Riemann problem. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. Results from a suite of test problems are presented to demonstrate the robustness and expected second-order accuracy of this new method.« less

A conservative scheme of drift kinetic electrons for gyrokinetic simulation of kinetic-MHD processes in toroidal plasmas

NASA Astrophysics Data System (ADS)

Bao, J.; Liu, D.; Lin, Z.

2017-10-01

A conservative scheme of drift kinetic electrons for gyrokinetic simulations of kinetic-magnetohydrodynamic processes in toroidal plasmas has been formulated and verified. Both vector potential and electron perturbed distribution function are decomposed into adiabatic part with analytic solution and non-adiabatic part solved numerically. The adiabatic parallel electric field is solved directly from the electron adiabatic response, resulting in a high degree of accuracy. The consistency between electrostatic potential and parallel vector potential is enforced by using the electron continuity equation. Since particles are only used to calculate the non-adiabatic response, which is used to calculate the non-adiabatic vector potential through Ohm's law, the conservative scheme minimizes the electron particle noise and mitigates the cancellation problem. Linear dispersion relations of the kinetic Alfvén wave and the collisionless tearing mode in cylindrical geometry have been verified in gyrokinetic toroidal code simulations, which show that the perpendicular grid size can be larger than the electron collisionless skin depth when the mode wavelength is longer than the electron skin depth.

High-Resolution Genuinely Multidimensional Solution of Conservation Laws by the Space-Time Conservation Element and Solution Element Method

NASA Technical Reports Server (NTRS)

Himansu, Ananda; Chang, Sin-Chung; Yu, Sheng-Tao; Wang, Xiao-Yen; Loh, Ching-Yuen; Jorgenson, Philip C. E.

1999-01-01

In this overview paper, we review the basic principles of the method of space-time conservation element and solution element for solving the conservation laws in one and two spatial dimensions. The present method is developed on the basis of local and global flux conservation in a space-time domain, in which space and time are treated in a unified manner. In contrast to the modern upwind schemes, the approach here does not use the Riemann solver and the reconstruction procedure as the building blocks. The drawbacks of the upwind approach, such as the difficulty of rationally extending the 1D scalar approach to systems of equations and particularly to multiple dimensions is here contrasted with the uniformity and ease of generalization of the Conservation Element and Solution Element (CE/SE) 1D scalar schemes to systems of equations and to multiple spatial dimensions. The assured compatibility with the simplest type of unstructured meshes, and the uniquely simple nonreflecting boundary conditions of the present method are also discussed. The present approach has yielded high-resolution shocks, rarefaction waves, acoustic waves, vortices, ZND detonation waves, and shock/acoustic waves/vortices interactions. Moreover, since no directional splitting is employed, numerical resolution of two-dimensional calculations is comparable to that of the one-dimensional calculations. Some sample applications displaying the strengths and broad applicability of the CE/SE method are reviewed.

A conservative finite difference algorithm for the unsteady transonic potential equation in generalized coordinates

NASA Technical Reports Server (NTRS)

Bridgeman, J. O.; Steger, J. L.; Caradonna, F. X.

1982-01-01

An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.

Dissipation-preserving spectral element method for damped seismic wave equations

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai; Wang, Yushun

2017-12-01

This article describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems, which has superior behaviors in long-time stability and dissipation preservation. To reveal the intrinsic dissipative properties of the model equations, we first reformulate the original systems in their equivalent conformal multi-symplectic structures and derive the corresponding conformal symplectic conservation laws. We thereafter separate each system into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed conformal symplectic method. A relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh wave in elastic wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic methods in both the attenuating homogeneous and heterogeneous media.

Non-Darcy flow of water-based carbon nanotubes with nonlinear radiation and heat generation/absorption

NASA Astrophysics Data System (ADS)

Hayat, T.; Ullah, Siraj; Khan, M. Ijaz; Alsaedi, A.; Zaigham Zia, Q. M.

2018-03-01

Here modeling and computations are presented to introduce the novel concept of Darcy-Forchheimer three-dimensional flow of water-based carbon nanotubes with nonlinear thermal radiation and heat generation/absorption. Bidirectional stretching surface induces the flow. Darcy's law is commonly replace by Forchheimer relation. Xue model is implemented for nonliquid transport mechanism. Nonlinear formulation based upon conservation laws of mass, momentum and energy is first modeled and then solved by optimal homotopy analysis technique. Optimal estimations of auxiliary variables are obtained. Importance of influential variables on the velocity and thermal fields is interpreted graphically. Moreover velocity and temperature gradients are discussed and analyzed. Physical interpretation of influential variables is examined.

A model and numerical method for compressible flows with capillary effects

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

Schmidmayer, Kevin, E-mail: kevin.schmidmayer@univ-amu.fr; Petitpas, Fabien, E-mail: fabien.petitpas@univ-amu.fr; Daniel, Eric, E-mail: eric.daniel@univ-amu.fr

2017-04-01

A new model for interface problems with capillary effects in compressible fluids is presented together with a specific numerical method to treat capillary flows and pressure waves propagation. This new multiphase model is in agreement with physical principles of conservation and respects the second law of thermodynamics. A new numerical method is also proposed where the global system of equations is split into several submodels. Each submodel is hyperbolic or weakly hyperbolic and can be solved with an adequate numerical method. This method is tested and validated thanks to comparisons with analytical solutions (Laplace law) and with experimental results onmore » droplet breakup induced by a shock wave.« less

Modeling of shock wave propagation in large amplitude ultrasound.

PubMed

Pinton, Gianmarco F; Trahey, Gregg E

2008-01-01

The Rankine-Hugoniot relation for shock wave propagation describes the shock speed of a nonlinear wave. This paper investigates time-domain numerical methods that solve the nonlinear parabolic wave equation, or the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, and the conditions they require to satisfy the Rankine-Hugoniot relation. Two numerical methods commonly used in hyperbolic conservation laws are adapted to solve the KZK equation: Godunov's method and the monotonic upwind scheme for conservation laws (MUSCL). It is shown that they satisfy the Rankine-Hugoniot relation regardless of attenuation. These two methods are compared with the current implicit solution based method. When the attenuation is small, such as in water, the current method requires a degree of grid refinement that is computationally impractical. All three numerical methods are compared in simulations for lithotripters and high intensity focused ultrasound (HIFU) where the attenuation is small compared to the nonlinearity because much of the propagation occurs in water. The simulations are performed on grid sizes that are consistent with present-day computational resources but are not sufficiently refined for the current method to satisfy the Rankine-Hugoniot condition. It is shown that satisfying the Rankine-Hugoniot conditions has a significant impact on metrics relevant to lithotripsy (such as peak pressures) and HIFU (intensity). Because the Godunov and MUSCL schemes satisfy the Rankine-Hugoniot conditions on coarse grids, they are particularly advantageous for three-dimensional simulations.

On the application of ENO scheme with subcell resolution to conservation laws with stiff source terms

NASA Technical Reports Server (NTRS)

Chang, Shih-Hung

1991-01-01

Two approaches are used to extend the essentially non-oscillatory (ENO) schemes to treat conservation laws with stiff source terms. One approach is the application of the Strang time-splitting method. Here the basic ENO scheme and the Harten modification using subcell resolution (SR), ENO/SR scheme, are extended this way. The other approach is a direct method and a modification of the ENO/SR. Here the technique of ENO reconstruction with subcell resolution is used to locate the discontinuity within a cell and the time evolution is then accomplished by solving the differential equation along characteristics locally and advancing in the characteristic direction. This scheme is denoted ENO/SRCD (subcell resolution - characteristic direction). All the schemes are tested on the equation of LeVeque and Yee (NASA-TM-100075, 1988) modeling reacting flow problems. Numerical results show that these schemes handle this intriguing model problem very well, especially with ENO/SRCD which produces perfect resolution at the discontinuity.

Consistent description of kinetic equation with triangle anomaly

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

Pu Shi; Gao Jianhua; Wang Qun

2011-05-01

We provide a consistent description of the kinetic equation with a triangle anomaly which is compatible with the entropy principle of the second law of thermodynamics and the charge/energy-momentum conservation equations. In general an anomalous source term is necessary to ensure that the equations for the charge and energy-momentum conservation are satisfied and that the correction terms of distribution functions are compatible to these equations. The constraining equations from the entropy principle are derived for the anomaly-induced leading order corrections to the particle distribution functions. The correction terms can be determined for the minimum number of unknown coefficients in onemore » charge and two charge cases by solving the constraining equations.« less

Chen Ning Yang, Weak Interactions, and Parity Violation

Science.gov Websites

absolute law of parity conservation had been violated." 2 "Yang overturned Paul ... Dirac's explained that symmetry laws generate the law of conservation. The law of right-left symmetry contributed to the formulation of the law of conservation of parity in 1924. Eventually, this law of conservation was

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

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

Interface conditions for domain decomposition with radical grid refinement

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1991-01-01

Interface conditions for coupling the domains in a physically motivated domain decomposition method are discussed. The domain decomposition is based on an asymptotic-induced method for the numerical solution of hyperbolic conservation laws with small viscosity. The method consists of multiple stages. The first stage is to obtain a first approximation using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problem via a domain decomposition. The method is derived and justified via singular perturbation techniques.

Nonlinear dynamics and control of a vibrating rectangular plate

NASA Technical Reports Server (NTRS)

Shebalin, J. V.

1983-01-01

The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

A conservation law for virus infection kinetics in vitro.

PubMed

Kakizoe, Yusuke; Morita, Satoru; Nakaoka, Shinji; Takeuchi, Yasuhiro; Sato, Kei; Miura, Tomoyuki; Beauchemin, Catherine A A; Iwami, Shingo

2015-07-07

Conservation laws are among the most important properties of a physical system, but are not commonplace in biology. We derived a conservation law from the basic model for viral infections which consists in a small set of ordinary differential equations. We challenged the conservation law experimentally for the case of a virus infection in a cell culture. We found that the derived, conserved quantity remained almost constant throughout the infection period, implying that the derived conservation law holds in this biological system. We also suggest a potential use for the conservation law in evaluating the accuracy of experimental measurements. Copyright © 2015 Elsevier Ltd. All rights reserved.

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

DOE PAGES

Su, Hongling; Li, Shengtai

2016-02-03

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

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

Su, Hongling; Li, Shengtai

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less

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

Huesemann, Michael H.

It is currently believed that science and technology can provide effective solutions to most, if not all, environmental problems facing western industrial societies. The validity of this optimistic assumption is highly questionable for at least three reasons: First, current mechanistic, reductionist science is inherently incapable of providing the complete and accurate information which is required to successfully address environmental problems. Second, both the conservation of mass principle and the second law of thermodynamics dictate that most remediation technologies - while successful in solving specific pollution problems - cause unavoidable negative environmental impacts elsewhere or in the future. Third, it ismore » intrinsically impossible to design industrial processes that have no negative environmental impacts. This follows not only from the entropy law but also from the fact that any generation of energy is impossible without negative environmental consequences. It can therefore be concluded that science and technology have only very limited potential in solving current and future environmental problems. Consequently, it will be necessary to address the root cause of environmental deterioration, namely the prevailing materialistic values that are the main driving force for both overpopulation and overconsumption. The long-term protection of the environment is therefore not primarily a technical problem but rather a social and moral problem that can only be solved by drastically reducing the strong influence of materialistic values.« less

Code Development of Three-Dimensional General Relativistic Hydrodynamics with AMR (Adaptive-Mesh Refinement) and Results from Special and General Relativistic Hydrodynamics

NASA Astrophysics Data System (ADS)

Dönmez, Orhan

2004-09-01

In this paper, the general procedure to solve the general relativistic hydrodynamical (GRH) equations with adaptive-mesh refinement (AMR) is presented. In order to achieve, the GRH equations are written in the conservation form to exploit their hyperbolic character. The numerical solutions of GRH equations are obtained by high resolution shock Capturing schemes (HRSC), specifically designed to solve nonlinear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. The Marquina fluxes with MUSCL left and right states are used to solve GRH equations. First, different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations are carried out to verify the second-order convergence of the code in one, two and three dimensions. Results from uniform and AMR grid are compared. It is found that adaptive grid does a better job when the number of resolution is increased. Second, the GRH equations are tested using two different test problems which are Geodesic flow and Circular motion of particle In order to do this, the flux part of GRH equations is coupled with source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time.

Surface conservation laws at microscopically diffuse interfaces.

PubMed

Chu, Kevin T; Bazant, Martin Z

2007-11-01

In studies of interfaces with dynamic chemical composition, bulk and interfacial quantities are often coupled via surface conservation laws of excess surface quantities. While this approach is easily justified for microscopically sharp interfaces, its applicability in the context of microscopically diffuse interfaces is less theoretically well-established. Furthermore, surface conservation laws (and interfacial models in general) are often derived phenomenologically rather than systematically. In this article, we first provide a mathematically rigorous justification for surface conservation laws at diffuse interfaces based on an asymptotic analysis of transport processes in the boundary layer and derive general formulae for the surface and normal fluxes that appear in surface conservation laws. Next, we use nonequilibrium thermodynamics to formulate surface conservation laws in terms of chemical potentials and provide a method for systematically deriving the structure of the interfacial layer. Finally, we derive surface conservation laws for a few examples from diffusive and electrochemical transport.

Demonstrations of the Action and Reaction Law and the Energy Conservation Law Using Fine Spherical Plastic Beads

ERIC Educational Resources Information Center

Khumaeni, A.; Tanaka, S.; Kobayashi, A.; Lee, Y. I.; Kurniawan, K. H.; Ishii, K.; Kagawa, K.

2008-01-01

Equipment for demonstrating Newton's third law and the energy conservation law in mechanics have successfully been constructed utilizing fine spherical plastic beads in place of metal ball bearings. To demonstrate Newton's third law, special magnetized Petri dishes were employed as objects, while to examine the energy conservation law, a…

Developing Legal Problem-Solving Skills.

ERIC Educational Resources Information Center

Nathanson, Stephen

1994-01-01

A law professor explains how he came to view legal problem solving as the driving concept in law school curriculum design and draws on personal experience and a survey of students concerning teaching methods in a commercial law course. He outlines six curriculum design principles for teaching legal problem solving. (MSE)

A Note on Weak Solutions of Conservation Laws and Energy/Entropy Conservation

NASA Astrophysics Data System (ADS)

Gwiazda, Piotr; Michálek, Martin; Świerczewska-Gwiazda, Agnieszka

2018-03-01

A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such cases most often related to the second law of thermodynamics. This observation easily generalizes to any symmetrizable system of conservation laws; they are endowed with nontrivial companion conservation laws, which are immediately satisfied by classical solutions. Not surprisingly, weak solutions may fail to satisfy companion laws, which are then often relaxed from equality to inequality and overtake the role of physical admissibility conditions for weak solutions. We want to answer the question: what is a critical regularity of weak solutions to a general system of conservation laws to satisfy an associated companion law as an equality? An archetypal example of such a result was derived for the incompressible Euler system in the context of Onsager's conjecture in the early nineties. This general result can serve as a simple criterion to numerous systems of mathematical physics to prescribe the regularity of solutions needed for an appropriate companion law to be satisfied.

Conservation laws and conserved quantities for (1+1)D linearized Boussinesq equations

NASA Astrophysics Data System (ADS)

Carvalho, Cindy; Harley, Charis

2017-05-01

Conservation laws and physical conserved quantities for the (1+1)D linearized Boussinesq equations at a constant water depth are presented. These equations describe incompressible, inviscid, irrotational fluid flow in the form of a non steady solitary wave. A systematic multiplier approach is used to obtain the conservation laws of the system of third order partial differential equations (PDEs) in dimensional form. Physical conserved quantities are derived by integrating the conservation laws in the direction of wave propagation and imposing decaying boundary conditions in the horizontal direction. One of these is a newly discovered conserved quantity which relates to an energy flux density.

A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

DOE PAGES

Guzik, Stephen M.; Gao, Xinfeng; Owen, Landon D.; ...

2015-12-20

We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Some novel considerations for formulating the semi-discrete system of equations in computational space are combined with detailed mechanisms for accommodating the adapting grids. Furthermore, these considerations ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). The solution in time is advanced with a fourth-order Runge-Kutta method. A series of tests verifies that the expected accuracy is achieved in smooth flows and the solution ofmore » a Mach reflection problem demonstrates the effectiveness of the algorithm in resolving strong discontinuities.« less

Hyperbolic conservation laws and numerical methods

NASA Technical Reports Server (NTRS)

Leveque, Randall J.

1990-01-01

The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.

78 FR 17229 - Notice of Lodging of Proposed Consent Decree Amendment Under the Clean Air Act; the Clean Water...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-03-20

... Act; the Clean Water Act; the Resource Conservation and Recovery Act; the Missouri Air Conservation Law; the Missouri Clean Water Law and the Missouri Hazardous Waste Management Law On March 14, 2013..., the Missouri Air Conservation Law, the Clean Water Act, the Missouri Clean Water Law, the Resource...

Frequency modulation at a moving material interface and a conservation law for wave number. [acoustic wave reflection and transmission

NASA Technical Reports Server (NTRS)

Kleinstein, G. G.; Gunzburger, M. D.

1976-01-01

An integral conservation law for wave numbers is considered. In order to test the validity of the proposed conservation law, a complete solution for the reflection and transmission of an acoustic wave impinging normally on a material interface moving at a constant speed is derived. The agreement between the frequency condition thus deduced from the dynamic equations of motion and the frequency condition derived from the jump condition associated with the integral equation supports the proposed law as a true conservation law. Additional comparisons such as amplitude discontinuities and Snells' law in a moving media further confirm the stated proposition. Results are stated concerning frequency and wave number relations across a shock front as predicted by the proposed conservation law.

Theoretical analysis of shock induced depolarization and current generation in ferroelectrics

NASA Astrophysics Data System (ADS)

Agrawal, Vinamra; Bhattacharya, Kaushik

Ferroelectric generators are used to generate large magnitude current pulse by impacting a polarized ferroelectric material. The impact causes depolarization of the material and at high impact speeds, dielectric breakdown. Depending on the loading conditions and the electromechanical boundary conditions, the current or voltage profiles obtained vary. In this study, we explore the large deformation dynamic response of a ferroelectric material. Using the Maxwell's equations, conservation laws and the second law of thermodynamics, we derive the governing equations for the phase boundary propagation as well as the driving force acting on it. We allow for the phase boundary to contain surface charges which introduces the contribution of curvature of phase boundary in the governing equations and the driving force. This type of analysis accounts for the dielectric breakdown and resulting conduction in the material. Next, we implement the equations derived to solve a one dimensional impact problem on a ferroelectric material under different electrical boundary conditions. The constitutive law is chosen to be piecewise quadratic in polarization and quadratic in the strain. We solve for the current profile generated in short circuit case and for voltage profile in open circuited case. This work was made possible by the financial support of the US Air Force Office of Scientific Research through the Center of Excellence in High Rate Deformation Physics of Heterogeneous Materials (Grant: FA 9550-12-1-0091).

Parallel discontinuous Galerkin FEM for computing hyperbolic conservation law on unstructured grids

NASA Astrophysics Data System (ADS)

Ma, Xinrong; Duan, Zhijian

2018-04-01

High-order resolution Discontinuous Galerkin finite element methods (DGFEM) has been known as a good method for solving Euler equations and Navier-Stokes equations on unstructured grid, but it costs too much computational resources. An efficient parallel algorithm was presented for solving the compressible Euler equations. Moreover, the multigrid strategy based on three-stage three-order TVD Runge-Kutta scheme was used in order to improve the computational efficiency of DGFEM and accelerate the convergence of the solution of unsteady compressible Euler equations. In order to make each processor maintain load balancing, the domain decomposition method was employed. Numerical experiment performed for the inviscid transonic flow fluid problems around NACA0012 airfoil and M6 wing. The results indicated that our parallel algorithm can improve acceleration and efficiency significantly, which is suitable for calculating the complex flow fluid.

Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes

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

Montecinos, Gino I.; Müller, Lucas O.; Toro, Eleuterio F.

2014-06-01

The applicability of ADER finite volume methods to solve hyperbolic balance laws with stiff source terms in the context of well-balanced and non-conservative schemes is extended to solve a one-dimensional blood flow model for viscoelastic vessels, reformulated as a hyperbolic system, via a relaxation time. A criterion for selecting relaxation times is found and an empirical convergence rate assessment is carried out to support this result. The proposed methodology is validated by applying it to a network of viscoelastic vessels for which experimental and numerical results are available. The agreement between the results obtained in the present paper and thosemore » available in the literature is satisfactory. Key features of the present formulation and numerical methodologies, such as accuracy, efficiency and robustness, are fully discussed in the paper.« less

Trouble with the Lorentz law of force: incompatibility with special relativity and momentum conservation.

PubMed

Mansuripur, Masud

2012-05-11

The Lorentz law of force is the fifth pillar of classical electrodynamics, the other four being Maxwell's macroscopic equations. The Lorentz law is the universal expression of the force exerted by electromagnetic fields on a volume containing a distribution of electrical charges and currents. If electric and magnetic dipoles also happen to be present in a material medium, they are traditionally treated by expressing the corresponding polarization and magnetization distributions in terms of bound-charge and bound-current densities, which are subsequently added to free-charge and free-current densities, respectively. In this way, Maxwell's macroscopic equations are reduced to his microscopic equations, and the Lorentz law is expected to provide a precise expression of the electromagnetic force density on material bodies at all points in space and time. This Letter presents incontrovertible theoretical evidence of the incompatibility of the Lorentz law with the fundamental tenets of special relativity. We argue that the Lorentz law must be abandoned in favor of a more general expression of the electromagnetic force density, such as the one discovered by Einstein and Laub in 1908. Not only is the Einstein-Laub formula consistent with special relativity, it also solves the long-standing problem of "hidden momentum" in classical electrodynamics.

Structure-preserving spectral element method in attenuating seismic wave modeling

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai

2016-04-01

This work describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems which has superior behaviors in long-time stability and dissipation preservation. To construct the conformal symplectic method, we first reformulate the damped acoustic wave equation and the elastic wave equations in their equivalent conformal multi-symplectic structures, which naturally reveal the intrinsic properties of the original systems, especially, the dissipation laws. We thereafter separate each structures into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed numerical scheme, which is conformal symplectic and can therefore guarantee the numerical stability and dissipation preservation after a large time modeling. Additionally, a relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh-wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic method in both the attenuating homogeneous and heterogeneous mediums.

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

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

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

Manzini, Gianmarco; Delzanno, Gian Luca; Vencels, Juris

In this study, we present the design and implementation of an L 2-stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations ismore » iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L 2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.« less

A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

DOE PAGES

Manzini, Gianmarco; Delzanno, Gian Luca; Vencels, Juris; ...

2016-04-22

In this study, we present the design and implementation of an L 2-stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations ismore » iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L 2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.« less

Geometry of Conservation Laws for a Class of Parabolic Partial Differential Equations

NASA Astrophysics Data System (ADS)

Clelland, Jeanne Nielsen

1996-08-01

I consider the problem of computing the space of conservation laws for a second-order, parabolic partial differential equation for one function of three independent variables. The PDE is formulated as an exterior differential system {cal I} on a 12 -manifold M, and its conservation laws are identified with the vector space of closed 3-forms in the infinite prolongation of {cal I} modulo the so -called "trivial" conservation laws. I use the tools of exterior differential systems and Cartan's method of equivalence to study the structure of the space of conservation laws. My main result is:. Theorem. Any conservation law for a second-order, parabolic PDE for one function of three independent variables can be represented by a closed 3-form in the differential ideal {cal I} on the original 12-manifold M. I show that if a nontrivial conservation law exists, then {cal I} has a deprolongation to an equivalent system {cal J} on a 7-manifold N, and any conservation law for {cal I} can be expressed as a closed 3-form on N which lies in {cal J}. Furthermore, any such system in the real analytic category is locally equivalent to a system generated by a (parabolic) equation of the formA(u _{xx}u_{yy}-u_sp {xy}{2}) + B_1u_{xx }+2B_2u_{xy} +B_3u_ {yy}+C=0crwhere A, B_{i}, C are functions of x, y, t, u, u_{x}, u _{y}, u_{t}. I compute the space of conservation laws for several examples, and I begin the process of analyzing the general case using Cartan's method of equivalence. I show that the non-linearizable equation u_{t} = {1over2}e ^{-u}(u_{xx}+u_ {yy})has an infinite-dimensional space of conservation laws. This stands in contrast to the two-variable case, for which Bryant and Griffiths showed that any equation whose space of conservation laws has dimension 4 or more is locally equivalent to a linear equation, i.e., is linearizable.

On the wavelet optimized finite difference method

NASA Technical Reports Server (NTRS)

Jameson, Leland

1994-01-01

When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.

A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems

NASA Astrophysics Data System (ADS)

Liu, Hailiang; Wang, Zhongming

2017-01-01

We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for solving time-dependent Poisson-Nernst-Planck systems. Both the semi-discrete and fully discrete DG methods are shown to satisfy the corresponding discrete free energy dissipation law for positive numerical solutions. Positivity of numerical solutions is enforced by an accuracy-preserving limiter in reference to positive cell averages. Numerical examples are presented to demonstrate the high resolution of the numerical algorithm and to illustrate the proven properties of mass conservation, free energy dissipation, as well as the preservation of steady states.

On conservation laws for a generalized Boussinesq equation

NASA Astrophysics Data System (ADS)

Anco, S.; Rosa, M.; Gandarias, M. L.

2017-07-01

In this work, we study a Boussinesq equation with a strong damping term from the point of view of the Lie theory. By using the low order conservation laws we apply the conservation laws multiplier method to the associated potential systems.

7 CFR 1468.3 - Definitions.

Code of Federal Regulations, 2012 CFR

2012-01-01

... to the State or territorial soil conservation district law, or tribal law. The subdivision may be a conservation district, soil conservation district, soil and water conservation district, resource conservation... county or area, in accordance with Sec. 8(b) of the Soil Conservation and Domestic Allotment Act, as...

7 CFR 1468.3 - Definitions.

Code of Federal Regulations, 2014 CFR

2014-01-01

... to the State or territorial soil conservation district law, or tribal law. The subdivision may be a conservation district, soil conservation district, soil and water conservation district, resource conservation... county or area, in accordance with Sec. 8(b) of the Soil Conservation and Domestic Allotment Act, as...

7 CFR 1468.3 - Definitions.

Code of Federal Regulations, 2013 CFR

2013-01-01

... to the State or territorial soil conservation district law, or tribal law. The subdivision may be a conservation district, soil conservation district, soil and water conservation district, resource conservation... county or area, in accordance with Sec. 8(b) of the Soil Conservation and Domestic Allotment Act, as...

Computational Aeroacoustics by the Space-time CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2001-01-01

In recent years, a new numerical methodology for conservation laws-the Space-Time Conservation Element and Solution Element Method (CE/SE), was developed by Dr. Chang of NASA Glenn Research Center and collaborators. In nature, the new method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its rigorous treatment of the fluxes and geometry, it is different from the existing schemes. The CE/SE scheme features: (1) space and time treated on the same footing, the integral equations of conservation laws are solve( for with second order accuracy, (2) high resolution, low dispersion and low dissipation, (3) novel, truly multi-dimensional, simple but effective non-reflecting boundary condition, (4) effortless implementation of computation, no numerical fix or parameter choice is needed, an( (5) robust enough to cover a wide spectrum of compressible flow: from weak linear acoustic waves to strong, discontinuous waves (shocks) appropriate for linear and nonlinear aeroacoustics. Currently, the CE/SE scheme has been developed to such a stage that a 3-13 unstructured CE/SE Navier-Stokes solver is already available. However, in the present paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen as a prototype and is sketched in Section 2. Then applications of the CE/SE scheme to linear, nonlinear aeroacoustics and airframe noise are depicted in Sections 3, 4, and 5 respectively to demonstrate its robustness and capability.

Examination of the relationship between preservice science teachers' scientific reasoning and problem solving skills on basic mechanics

NASA Astrophysics Data System (ADS)

Yuksel, Ibrahim; Ates, Salih

2018-02-01

The purpose of this study is to determine relationship between scientific reasoning and mechanics problem solving skills of students in science education program. Scientific Reasoning Skills Test (SRST) and Basic Mechanics Knowledge Test (BMKT) were applied to 90 second, third and fourth grade students who took Scientific Reasoning Skills course at science teaching program of Gazi Faculty of Education for three successive fall semesters of 2014, 2015 and 2016 academic years. It was found a statistically significant positive (p = 0.038 <0.05) but a low correlation (r = 0.219) between SRST and BMKT. There were no significant relationship among Conservation Laws, Proportional Thinking, Combinational Thinking, Correlational Thinking, Probabilistic Thinking subskills of reasoning and BMKT. There were significant and positive correlation among Hypothetical Thinking and Identifying and Controlling Variables subskills of reasoning and BMKT. The findings of the study were compared with other studies in the field and discussed.

On the conservation laws of Derrida-Lebowitz-Speer-Spohn equation

NASA Astrophysics Data System (ADS)

San, Sait; Yaşar, Emrullah

2015-05-01

In this study, the nonlocal conservation theorem and multiplier approach are performed on the 1 + 1 dimensional Derrida-Lebowitz-Speer-Spohn (DLSS) equation which arises in quantum semi conductor theory. We obtain local conservation laws by using the both methods. Furthermore by utilizing the relationship between conservation laws and Lie point symmetries, the DLSS equation is reduced to third order ordinary differential equation.

Exploiting the hidden symmetry of spinning black holes: conservation laws and numerical tests

NASA Astrophysics Data System (ADS)

Witzany, Vojtěch

2018-01-01

The Kerr black hole is stationary and axisymmetric, which leads to conservation of energy and azimuthal angular momentum along the orbits of free test particles in its vicinity, but also to conservation laws for the evolution of continuum matter fields. However, the Kerr space-time possesses an additional 'hidden symmetry', which exhibits itself in an unexpected conserved quantity along geodesics known as the Carter constant. We investigate the possibility of using this hidden symmetry to obtain conservation laws and other identities that could be used to test astrophysical simulations of the evolution of matter fields near spinning black holes. After deriving such identities, we set up a simple numerical toy model on which we demonstrate how they can detect the violations of evolution equations in a numerical simulation. Even though one of the expressions we derive is in the form of a conservation law, we end up recommending an equivalent but simpler expression that is not in the form of a conservation law for practical implementation.

Misunderstandings of "Law" and "Conservation": A Study of Pupils' Meanings of these Terms.

ERIC Educational Resources Information Center

Boyes, Edward; Stanisstreet, Martin

1990-01-01

Presented is the extent to which pupils of different ages tend to confuse scientific and everyday meanings of "Law" and "Conservation." The concepts of resource economy, environmental concern, and the law of conservation of energy are discussed in terms of potential teaching difficulties. (KR)

Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws

NASA Technical Reports Server (NTRS)

Barth, Timothy; Charrier, Pierre; Mansour, Nagi N. (Technical Monitor)

2001-01-01

We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio

1989-01-01

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1993-01-01

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the 2-D or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating-direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 3 is the Programmer's Reference, and describes the program structure, the FORTRAN variables stored in common blocks, and the details of each subprogram.

General relativistic hydrodynamics with Adaptive-Mesh Refinement (AMR) and modeling of accretion disks

NASA Astrophysics Data System (ADS)

Donmez, Orhan

We present a general procedure to solve the General Relativistic Hydrodynamical (GRH) equations with Adaptive-Mesh Refinement (AMR) and model of an accretion disk around a black hole. To do this, the GRH equations are written in a conservative form to exploit their hyperbolic character. The numerical solutions of the general relativistic hydrodynamic equations is done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. We use Marquina fluxes with MUSCL left and right states to solve GRH equations. First, we carry out different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations to verify the second order convergence of the code in 1D, 2 D and 3D. Second, we solve the GRH equations and use the general relativistic test problems to compare the numerical solutions with analytic ones. In order to this, we couple the flux part of general relativistic hydrodynamic equation with a source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time. The test problems examined include shock tubes, geodesic flows, and circular motion of particle around the black hole. Finally, we apply this code to the accretion disk problems around the black hole using the Schwarzschild metric at the background of the computational domain. We find spiral shocks on the accretion disk. They are observationally expected results. We also examine the star-disk interaction near a massive black hole. We find that when stars are grounded down or a hole is punched on the accretion disk, they create shock waves which destroy the accretion disk.

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

NASA Technical Reports Server (NTRS)

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

1998-01-01

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

Material point method modeling in oil and gas reservoirs

DOEpatents

Vanderheyden, William Brian; Zhang, Duan

2016-06-28

A computer system and method of simulating the behavior of an oil and gas reservoir including changes in the margins of frangible solids. A system of equations including state equations such as momentum, and conservation laws such as mass conservation and volume fraction continuity, are defined and discretized for at least two phases in a modeled volume, one of which corresponds to frangible material. A material point model technique for numerically solving the system of discretized equations, to derive fluid flow at each of a plurality of mesh nodes in the modeled volume, and the velocity of at each of a plurality of particles representing the frangible material in the modeled volume. A time-splitting technique improves the computational efficiency of the simulation while maintaining accuracy on the deformation scale. The method can be applied to derive accurate upscaled model equations for larger volume scale simulations.

Computing Axisymmetric Jet Screech Tones Using Unstructured Grids

NASA Technical Reports Server (NTRS)

Jorgenson, Philip C. E.; Loh, Ching Y.

2002-01-01

The space-time conservation element and solution element (CE/SE) method is used to solve the conservation law form of the compressible axisymmetric Navier-Stokes equations. The equations are time marched to predict the unsteady flow and the near-field screech tone noise issuing from an underexpanded circular jet. The CE/SE method uses an unstructured grid based data structure. The unstructured grids for these calculations are generated based on the method of Delaunay triangulation. The purpose of this paper is to show that an acoustics solution with a feedback loop can be obtained using truly unstructured grid technology. Numerical results are presented for two different nozzle geometries. The first is considered to have a thin nozzle lip and the second has a thick nozzle lip. Comparisons with available experimental data are shown for flows corresponding to several different jet Mach numbers. Generally good agreement is obtained in terms of flow physics, screech tone frequency, and sound pressure level.

Illustrating some implications of the conservation laws in relativistic mechanics

NASA Astrophysics Data System (ADS)

Boyer, Timothy H.

2009-06-01

The conservation laws of nonrelativistic and relativistic systems are reviewed and some simple illustrations are provided for the restrictive nature of the relativistic conservation law involving the center of energy compared to the nonrelativistic conservation law for the center of mass. Extension of the nonrelativistic interaction of particles through a potential to a system that is Lorentz-invariant through order v2/c2 is found to require new velocity- and acceleration-dependent forces that are suggestive of a field theory where the no-interaction theorem of Currie, Jordan, and Sudershan does not hold.

Dark optical, singular solitons and conservation laws to the nonlinear Schrödinger’s equation with spatio-temporal dispersion

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi

2017-05-01

This paper studies the dynamics of solitons to the nonlinear Schrödinger’s equation (NLSE) with spatio-temporal dispersion (STD). The integration algorithm that is employed in this paper is the Riccati-Bernoulli sub-ODE method. This leads to dark and singular soliton solutions that are important in the field of optoelectronics and fiber optics. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. There are four types of nonlinear media studied in this paper. They are Kerr law, power law, parabolic law and dual law. The conservation laws (Cls) for the Kerr law and parabolic law nonlinear media are constructed using the conservation theorem presented by Ibragimov.

A cell-centered Lagrangian finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries

NASA Astrophysics Data System (ADS)

Sambasivan, Shiv Kumar; Shashkov, Mikhail J.; Burton, Donald E.

2013-03-01

A finite volume cell-centered Lagrangian formulation is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor-corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke's law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the J2 von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative Eulerian and Lagrangian hydrocodes in addition to analytical and experimental results are made to validate the current approach.

Particle Number Conserving Approach to the Collective States in a Small Fermi-System

NASA Astrophysics Data System (ADS)

Glick, Jennifer; Zelevinsky, Vladimir

2014-03-01

The standard Bardeen-Cooper-Schrieffer (BCS) description of pairing theory, random phase approximation (RPA) and Hartree-Fock-Bogoliubov (HFB) methods, routinely used in macroscopic many-body physics when the dimension of the Hamiltonian matrix is prohibitively large, include features which are not well suited to describe mesoscopic systems such as nuclei or cold atoms in traps. Two important disadvantages are the non-conservation of exact particle number through the introduction of quasiparticles, and the absence of a non-trivial paired solution in the discrete spectrum with weak pairing. We develop the pairing theory based on the exact particle number conservation, whose first applications to the ground state physics presented in [A. Volya and V. Zelevinsky, in 50 Years of Nuclear BCS, World Scientific, 2012] demonstrated that such an approach avoids well known deficiencies of the standard treatment, especially in the region of weak pairing. Now, we use the method for low-lying collective excitations which in many cases are even more sensitive to conservation laws. We show that the RPA version based on solving the operator equations of motion is reduced to the set of recurrence relations for neighboring systems which precisely conserve the exact particle number. Supported by the NSF grant PHY-1068217.

Research on the supercapacitor support schemes for LVRT of variable-frequency drive in the thermal power plant

NASA Astrophysics Data System (ADS)

Han, Qiguo; Zhu, Kai; Shi, Wenming; Wu, Kuayu; Chen, Kai

2018-02-01

In order to solve the problem of low voltage ride through(LVRT) of the major auxiliary equipment’s variable-frequency drive (VFD) in thermal power plant, the scheme of supercapacitor paralleled in the DC link of VFD is put forward, furthermore, two solutions of direct parallel support and voltage boost parallel support of supercapacitor are proposed. The capacitor values for the relevant motor loads are calculated according to the law of energy conservation, and they are verified by Matlab simulation. At last, a set of test prototype is set up, and the test results prove the feasibility of the proposed schemes.

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

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1993-01-01

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

Equivalence transformations and conservation laws for a generalized variable-coefficient Gardner equation

NASA Astrophysics Data System (ADS)

de la Rosa, R.; Gandarias, M. L.; Bruzón, M. S.

2016-11-01

In this paper we study the generalized variable-coefficient Gardner equations of the form ut + A(t) unux + C(t) u2nux + B(t) uxxx + Q(t) u = 0 . This class broadens out many other equations previously considered: Johnpillai and Khalique (2010), Molati and Ramollo (2012) and Vaneeva et al. (2015). The use of the equivalence group of this class allows us to perform an exhaustive study and a simple and clear formulation of the results. Some conservation laws are derived for the nonlinearly self-adjoint equations by using a general theorem on conservation laws. We also construct conservation laws by applying the multipliers method.

Development and application of discontinuous Galerkin method for the solution of two-dimensional Maxwell equations

NASA Astrophysics Data System (ADS)

Wong, See-Cheuk

We inhabit an environment of electromagnetic (EM) waves. The waves within the EM spectrum---whether light, radio, or microwaves---all obey the same physical laws. A band in the spectrum is designated to the microwave frequencies (30MHz--300GHz), at which radar systems operate. The precise modeling of the scattered EM-ields about a target, as well as the numerical prediction of the radar return is the crux of the computational electromagnetics (CEM) problems. The signature or return from a target observed by radar is commonly provided in the form of radar cross section (RCS). Incidentally, the efforts in the reduction of such return forms the basis of stealth aircraft design. The object of this dissertation is to extend Discontinuous Galerkin (DG) method to solve numerically the Maxwell equations for scatterings from perfect electric conductor (PEC) objects. The governing equations are derived by writing the Maxwell equations in conservation-law form for scattered field quantities. The transverse magnetic (TM) and the transverse electric (TE) waveforms of the Maxwell equations are considered. A finite-element scheme is developed with proper representations for the electric and magnetic fluxes at a cell interface to account for variations in properties, in both space and time. A characteristic sub-path integration process, known as the "Riemann solver" is involved. An explicit Runge-Kutta Discontinuous Galerkin (RKDG) upwind scheme, which is fourth-order accurate in time and second-order in space, is employed to solve the TM and TE equations. Arbitrary cross-sectioned bodies are modeled, around which computational grids using random triangulation are generated. The RKDG method, in its development stage, was constructed and studied for solving hyperbolic conservation equations numerically. It was later extended to multidimensional nonlinear systems of conservation laws. The algorithms are described, including the formulations and treatments to the numerical fluxes, degrees of freedom, boundary conditions, and other implementation issues. The computational solution amounts to a near-field solution in form of contour plot and one extending from the scatterer to a far-field boundary located a few wavelengths away. Near-field to far-field transformation utilizing the Green's function is performed to obtain the bistatic radar cross section information. Results are presented for scatterings from a series of two-dimensional objects, including circular and square cylinders, ogive and NACA airfoils. Also, scatterings from more complex geometries such as cylindrical and rectangular cavitations are simulated. Exact solutions for selected cases are compared to the computational results and demonstrate excellent accuracy and efficiency in the RKDG calculations. In the whole, its ease and flexibility to incorporate the characteristic-based schemes for the flux integrals between cell interfaces, and the compact formulation allowing direct application to the boundary elements without modification are some of the admired features of the DG method.

The Conservation Principles and Kepler's Laws of Planetary Motion

ERIC Educational Resources Information Center

Motz, Lloyd

1975-01-01

Derives Kepler's three laws of planetary motion algebraically from conservation principles without introducing Newton's law of force explicitly. This procedure can be presented to students who have had no more than high school algebra. (Author)

Conservation laws for waves on a string from isometries and conformal isometries of the Minkowski metric

NASA Astrophysics Data System (ADS)

Miller, Brandon; Menon, Balraj

Noether's theorems describe the interplay between variational symmetries (symmetries of the action functional) and local conservation laws admitted by a physical system. In Lagrangian field theories defined on a differentiable manifold  endowed with a metric g, the variational symmetries are intimately tied to the isometries of the metric g. We highlight this connection by relating the variational symmetries of waves on a string to the isometries and conformal isometries of the Minkowski metric. The associated local conservation laws and conserved quantities for this physical system are determined and their physical significance discussed. The geometric nature of these conservation laws are further elucidated by discussing their Poisson bracket formulation in the Hamiltonian framework. This work was partially supported by the UCA Robert Noyce Scholars Program.

18 CFR 1314.4 - Law governing the rights and obligations of TVA and Reserve Banks; law governing the rights of...

Code of Federal Regulations, 2010 CFR

2010-04-01

... 18 Conservation of Power and Water Resources 2 2010-04-01 2010-04-01 false Law governing the rights and obligations of TVA and Reserve Banks; law governing the rights of any Person against TVA and Reserve Banks; law governing other interests. 1314.4 Section 1314.4 Conservation of Power and Water...

Motion of gas in highly rarefied space

NASA Astrophysics Data System (ADS)

Chirkunov, Yu A.

2017-10-01

A model describing a motion of gas in a highly rarefied space received an unlucky number 13 in the list of the basic models of the motion of gas in the three-dimensional space obtained by L.V. Ovsyannikov. For a given initial pressure distribution, a special choice of mass Lagrangian variables leads to the system describing this motion for which the number of independent variables is less by one. Hence, there is a foliation of a highly rarefied gas with respect to pressure. In a strongly rarefied space for each given initial pressure distribution, all gas particles are localized on a two-dimensional surface that moves with time in this space We found some exact solutions of the obtained system that describe the processes taking place inside of the tornado. For this system we found all nontrivial conservation laws of the first order. In addition to the classical conservation laws the system has another conservation law, which generalizes the energy conservation law. With the additional condition we found another one generalized energy conservation law.

Hamiltonian structures for systems of hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Olver, Peter J.; Nutku, Yavuz

1988-07-01

The bi-Hamiltonian structure for a large class of one-dimensional hyberbolic systems of conservation laws in two field variables, including the equations of gas dynamics, shallow water waves, one-dimensional elastic media, and the Born-Infeld equation from nonlinear electrodynamics, is exhibited. For polytropic gas dynamics, these results lead to a quadri-Hamiltonian structure. New higher-order entropy-flux pairs (conservation laws) and higher-order symmetries are exhibited.

Development of a Hands-On Model Embedded with Guided Inquiry Laboratory to Enhance Students' Understanding of Law of Mechanical Energy Conservation

ERIC Educational Resources Information Center

Wangdi, Dumcho; Kanthang, Paisan; Precharattana, Monamorn

2017-01-01

This paper attempts to investigate the understanding of the law of mechanical energy conservation using a guided inquiry approach. A simple hands-on model was constructed and used to demonstrate the law of mechanical energy conservation. A total of 30 grade ten students from one of the middle secondary schools in western Bhutan participated in…

Analysis of self-similar solutions of multidimensional conservation laws

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

Keyfitz, Barbara Lee

2014-02-15

This project focused on analysis of multidimensional conservation laws, specifically on extensions to the study of self-siminar solutions, a project initiated by the PI. In addition, progress was made on an approach to studying conservation laws of very low regularity; in this research, the context was a novel problem in chromatography. Two graduate students in mathematics were supported during the grant period, and have almost completed their thesis research.

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

Cheviakov, Alexei F., E-mail: chevaikov@math.usask.ca

Partial differential equations of the form divN=0, N{sub t}+curl M=0 involving two vector functions in R{sup 3} depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergence-type conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lower-degree (degree two) conservation law in R{sup 4}(t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations,more » it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the Galas-Bogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lower-degree conservation law is further shown to yield curl-type conservation laws and determined potential equations in certain lower-dimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal time-dependent MHD equations in 2+1 dimensions, are presented.« less

A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry

NASA Astrophysics Data System (ADS)

Jaouen, Stéphane

2007-07-01

In many physical applications, one wishes to control the development of multi-dimensional instabilities around a one-dimensional (1D) complex flow. For predicting the growth rates of these perturbations, a general numerical approach is viable which consists in solving simultaneously the one-dimensional equations and their linearized form for three-dimensional perturbations. In Clarisse et al. [J.-M. Clarisse, S. Jaouen, P.-A. Raviart, A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys. 198 (2004) 80-105], a class of Godunov-type schemes for planar-symmetric flows of gas dynamics has been proposed. Pursuing this effort, we extend these results to spherically symmetric flows. A new method to derive the Lagrangian perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian systems, Arch. Rational Mech. Anal. 178 (2005) 327-372] is also described. It leads to many advantages. First of all, many physical problems we are interested in enter this formalism (gas dynamics, two-temperature plasma equations, ideal magnetohydrodynamics, etc.) whatever is the geometry. Secondly, a class of numerical entropic schemes is available for the basic flow [11]. Last, linearizing and devising numerical schemes for the perturbed flow is straightforward. The numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that - due to its simplicity and its low computational cost - the Linear Perturbations Code (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.

25 CFR 12.61 - Can I be paid for information that helps solve a crime?

Code of Federal Regulations, 2011 CFR

2011-04-01

... 25 Indians 1 2011-04-01 2011-04-01 false Can I be paid for information that helps solve a crime? 12.61 Section 12.61 Indians BUREAU OF INDIAN AFFAIRS, DEPARTMENT OF THE INTERIOR LAW AND ORDER INDIAN COUNTRY LAW ENFORCEMENT Support Functions § 12.61 Can I be paid for information that helps solve a crime...

25 CFR 12.61 - Can I be paid for information that helps solve a crime?

Code of Federal Regulations, 2010 CFR

2010-04-01

... 25 Indians 1 2010-04-01 2010-04-01 false Can I be paid for information that helps solve a crime? 12.61 Section 12.61 Indians BUREAU OF INDIAN AFFAIRS, DEPARTMENT OF THE INTERIOR LAW AND ORDER INDIAN COUNTRY LAW ENFORCEMENT Support Functions § 12.61 Can I be paid for information that helps solve a crime...

25 CFR 12.61 - Can I be paid for information that helps solve a crime?

Code of Federal Regulations, 2013 CFR

2013-04-01

... 25 Indians 1 2013-04-01 2013-04-01 false Can I be paid for information that helps solve a crime? 12.61 Section 12.61 Indians BUREAU OF INDIAN AFFAIRS, DEPARTMENT OF THE INTERIOR LAW AND ORDER INDIAN COUNTRY LAW ENFORCEMENT Support Functions § 12.61 Can I be paid for information that helps solve a crime...

25 CFR 12.61 - Can I be paid for information that helps solve a crime?

Code of Federal Regulations, 2012 CFR

2012-04-01

... 25 Indians 1 2012-04-01 2011-04-01 true Can I be paid for information that helps solve a crime? 12.61 Section 12.61 Indians BUREAU OF INDIAN AFFAIRS, DEPARTMENT OF THE INTERIOR LAW AND ORDER INDIAN COUNTRY LAW ENFORCEMENT Support Functions § 12.61 Can I be paid for information that helps solve a crime...

25 CFR 12.61 - Can I be paid for information that helps solve a crime?

Code of Federal Regulations, 2014 CFR

2014-04-01

... 25 Indians 1 2014-04-01 2014-04-01 false Can I be paid for information that helps solve a crime? 12.61 Section 12.61 Indians BUREAU OF INDIAN AFFAIRS, DEPARTMENT OF THE INTERIOR LAW AND ORDER INDIAN COUNTRY LAW ENFORCEMENT Support Functions § 12.61 Can I be paid for information that helps solve a crime...

Scaling and scale invariance of conservation laws in Reynolds transport theorem framework

NASA Astrophysics Data System (ADS)

Haltas, Ismail; Ulusoy, Suleyman

2015-07-01

Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework.

Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation

DOE PAGES

Chen, Zhangxin; Cockburn, Bernardo; Jerome, Joseph W.; ...

1995-01-01

In this paper we introduce a new method for numerically solving the equations of the hydrodynamic model for semiconductor devices in two space dimensions. The method combines a standard mixed finite element method, used to obtain directly an approximation to the electric field, with the so-called Runge-Kutta Discontinuous Galerkin (RKDG) method, originally devised for numerically solving multi-dimensional hyperbolic systems of conservation laws, which is applied here to the convective part of the equations. Numerical simulations showing the performance of the new method are displayed, and the results compared with those obtained by using Essentially Nonoscillatory (ENO) finite difference schemes. Frommore » the perspective of device modeling, these methods are robust, since they are capable of encompassing broad parameter ranges, including those for which shock formation is possible. The simulations presented here are for Gallium Arsenide at room temperature, but we have tested them much more generally with considerable success.« less

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

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

NASA Astrophysics Data System (ADS)

Toth, G.; Keppens, R.; Botchev, M. A.

1998-04-01

We describe and evaluate various implicit and semi-implicit time integration schemes applied to the numerical simulation of hydrodynamical and magnetohydrodynamical problems. The schemes were implemented recently in the software package Versatile Advection Code, which uses modern shock capturing methods to solve systems of conservation laws with optional source terms. The main advantage of implicit solution strategies over explicit time integration is that the restrictive constraint on the allowed time step can be (partially) eliminated, thus the computational cost is reduced. The test problems cover one and two dimensional, steady state and time accurate computations, and the solutions contain discontinuities. For each test, we confront explicit with implicit solution strategies.

Statistical mechanical foundation of the peridynamic nonlocal continuum theory: energy and momentum conservation laws.

PubMed

Lehoucq, R B; Sears, Mark P

2011-09-01

The purpose of this paper is to derive the energy and momentum conservation laws of the peridynamic nonlocal continuum theory using the principles of classical statistical mechanics. The peridynamic laws allow the consideration of discontinuous motion, or deformation, by relying on integral operators. These operators sum forces and power expenditures separated by a finite distance and so represent nonlocal interaction. The integral operators replace the differential divergence operators conventionally used, thereby obviating special treatment at points of discontinuity. The derivation presented employs a general multibody interatomic potential, avoiding the standard assumption of a pairwise decomposition. The integral operators are also expressed in terms of a stress tensor and heat flux vector under the assumption that these fields are differentiable, demonstrating that the classical continuum energy and momentum conservation laws are consequences of the more general peridynamic laws. An important conclusion is that nonlocal interaction is intrinsic to continuum conservation laws when derived using the principles of statistical mechanics.

Statistical conservation law in two- and three-dimensional turbulent flows.

PubMed

Frishman, Anna; Boffetta, Guido; De Lillo, Filippo; Liberzon, Alex

2015-03-01

Particles in turbulence live complicated lives. It is nonetheless sometimes possible to find order in this complexity. It was proposed in Falkovich et al. [Phys. Rev. Lett. 110, 214502 (2013)] that pairs of Lagrangian tracers at small scales, in an incompressible isotropic turbulent flow, have a statistical conservation law. More specifically, in a d-dimensional flow the distance R(t) between two neutrally buoyant particles, raised to the power -d and averaged over velocity realizations, remains at all times equal to the initial, fixed, separation raised to the same power. In this work we present evidence from direct numerical simulations of two- and three-dimensional turbulence for this conservation. In both cases the conservation is lost when particles exit the linear flow regime. In two dimensions we show that, as an extension of the conservation law, an Evans-Cohen-Morriss or Gallavotti-Cohen type fluctuation relation exists. We also analyze data from a 3D laboratory experiment [Liberzon et al., Physica D 241, 208 (2012)], finding that although it probes small scales they are not in the smooth regime. Thus instead of 〈R-3〉, we look for a similar, power-law-in-separation conservation law. We show that the existence of an initially slowly varying function of this form can be predicted but that it does not turn into a conservation law. We suggest that the conservation of 〈R-d〉, demonstrated here, can be used as a check of isotropy, incompressibility, and flow dimensionality in numerical and laboratory experiments that focus on small scales.

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 1 is the Analysis Description, and describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 2 is the User's Guide, and describes the program's general features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This User's Guide describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

An implicit numerical scheme for the simulation of internal viscous flows on unstructured grids

NASA Technical Reports Server (NTRS)

Jorgenson, Philip C. E.; Pletcher, Richard H.

1994-01-01

The Navier-Stokes equations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.

Diffusion Processes Satisfying a Conservation Law Constraint

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2014-03-04

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Diffusion Processes Satisfying a Conservation Law Constraint

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

Bakosi, J.; Ristorcelli, J. R.

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Conservation law of angular momentum in helicity-dependent Raman and Rayleigh scattering

NASA Astrophysics Data System (ADS)

Tatsumi, Yuki; Kaneko, Tomoaki; Saito, Riichiro

2018-05-01

In first-order Raman scattering, helicity of circularly polarized incident light is either conserved or changed depending on the Raman modes. When the helicity of incident light changes in the scattered light, the angular momentum of a photon is transferred to the material. Here, we present the conservation law of pseudoangular momentum in the helicity-dependent Raman scattering for a N -fold (N =1 -4 ,6 ) rotational symmetry of a crystal. Furthermore, the conservation law of electron-phonon interaction is discussed by considering the vibration direction of a phonon that has the same or lower symmetry than the symmetry of the crystal, which is essential to allow the helicity change in Raman scattering in a highly symmetric material, such as graphene. We also discuss the conservation law of pseudoangular momentum in Rayleigh scattering and show that the helicity change is allowed only in the crystal with one- or twofold rotational symmetry.

Divergent conservation laws in hyperbolic thermoelasticity

NASA Astrophysics Data System (ADS)

Murashkin, E. V.; Radayev, Y. N.

2018-05-01

The present study is devoted to the problem of formulation of conservation laws in divergent form for hyperbolic thermoelastic continua. The field formalism is applied to study the problem. A natural density of thermoelastic action and the corresponding variational least action principle are formulated. A special form of the first variation of the action is employed to obtain 4-covariant divergent conservation laws. Differential field equations and constitutive laws are derived from a special form of the first variation of the action integral. The objectivity of constitutive equations is provided by the rotationally invariant forms of the Lagrangian employed.

Numerical Modeling of Saturated Boiling in a Heated Tube

NASA Technical Reports Server (NTRS)

Majumdar, Alok; LeClair, Andre; Hartwig, Jason

2017-01-01

This paper describes a mathematical formulation and numerical solution of boiling in a heated tube. The mathematical formulation involves a discretization of the tube into a flow network consisting of fluid nodes and branches and a thermal network consisting of solid nodes and conductors. In the fluid network, the mass, momentum and energy conservation equations are solved and in the thermal network, the energy conservation equation of solids is solved. A pressure-based, finite-volume formulation has been used to solve the equations in the fluid network. The system of equations is solved by a hybrid numerical scheme which solves the mass and momentum conservation equations by a simultaneous Newton-Raphson method and the energy conservation equation by a successive substitution method. The fluid network and thermal network are coupled through heat transfer between the solid and fluid nodes which is computed by Chen's correlation of saturated boiling heat transfer. The computer model is developed using the Generalized Fluid System Simulation Program and the numerical predictions are compared with test data.

78 FR 20291 - Fisheries of the United States; Billfish Conservation Act of 2012 Implementing Regulations

Federal Register 2010, 2011, 2012, 2013, 2014

2013-04-04

.... 121227743-3275-01] RIN 0648-BC86 Fisheries of the United States; Billfish Conservation Act of 2012... request public comment on potential issues related to the implementation of the Billfish Conservation Act... Conservation Act of 2012 (BCA), Public Law 112-183, 16 U.S.C. 1827a, was signed into law on October 5, 2012...

Computing nonhydrostatic shallow-water flow over steep terrain

USGS Publications Warehouse

Denlinger, R.P.; O'Connell, D. R. H.

2008-01-01

Flood and dambreak hazards are not limited to moderate terrain, yet most shallow-water models assume that flow occurs over gentle slopes. Shallow-water flow over rugged or steep terrain often generates significant nonhydrostatic pressures, violating the assumption of hydrostatic pressure made in most shallow-water codes. In this paper, we adapt a previously published nonhydrostatic granular flow model to simulate shallow-water flow, and we solve conservation equations using a finite volume approach and an Harten, Lax, Van Leer, and Einfeldt approximate Riemann solver that is modified for a sloping bed and transient wetting and drying conditions. To simulate bed friction, we use the law of the wall. We test the model by comparison with an analytical solution and with results of experiments in flumes that have steep (31??) or shallow (0.3??) slopes. The law of the wall provides an accurate prediction of the effect of bed roughness on mean flow velocity over two orders of magnitude of bed roughness. Our nonhydrostatic, law-of-the-wall flow simulation accurately reproduces flume measurements of front propagation speed, flow depth, and bed-shear stress for conditions of large bed roughness. ?? 2008 ASCE.

Nonaltruistic kidney donations in contemporary Jewish law and ethics.

PubMed

Grazi, Richard V; Wolowelsky, Joel B

2003-01-27

In 2000, the Consensus Statement on the Live Organ Donor reported that "direct financial compensation for an organ from a living donor remains controversial and illegal in the United States" and took note of the position of the Transplantation Society that "Organs and tissue should be given without commercial consideration or commercial profit." Christian authorities insist that organ donors must not accrue economic advantage, and "selling" organs deprives the donation of its ethical quality. The writings of major contemporary authorities of Jewish law and ethics whose halakhic positions on bioethical issues are regularly considered by Orthodox, Conservative, and Reform ethicists were reviewed. Their positions on this issue were contrasted with those of various contemporary secular and religious authorities. These Jewish authorities reject the notion that generosity and charity, rather than monetary gain and greed, must serve as the exclusive basis for donation of functioning organs. Although nonaltruistic sale of kidneys may be theoretically ethical, ultimately its ethical status in Jewish ethics and law is inextricably connected to solving a series of pragmatic programs, such as creating a system that ensures that potential vendors and donors are properly informed and not exploited. Lacking such arrangements, ethical nonaltruistic kidney donations remain but a theoretical possibility.

Conservation of wave action. [in discrete oscillating system

NASA Technical Reports Server (NTRS)

Hayes, W. D.

1974-01-01

It is pointed out that two basic principles appear in the theory of wave propagation, including the existence of a phase variable and a law governing the intensity, in terms of a conservation law. The concepts underlying such a conservation law are explored. The waves treated are conservative in the sense that they obey equations derivable from a variational principle applied to a Lagrangian functional. A discrete oscillating system is considered. The approach employed also permits in a natural way the definition of a local action density and flux in problems in which the waves are modal or general.

School, Government, and Energy Interactions.

ERIC Educational Resources Information Center

Canipe, Stephen L.

This document examines three major federal statutes affecting school energy conservation, describes laws and regulations enacted in North Carolina to promote school energy conservation, and touches on possible energy options open to schools. The federal laws discussed are the Energy Policy and Conservation Act of 1975, dealing with the…

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

NASA Technical Reports Server (NTRS)

Tadmor, Eitan

1988-01-01

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

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

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

Tadmor, E.

1988-07-01

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

A Numerical Model for Trickle Bed Reactors

NASA Astrophysics Data System (ADS)

Propp, Richard M.; Colella, Phillip; Crutchfield, William Y.; Day, Marcus S.

2000-12-01

Trickle bed reactors are governed by equations of flow in porous media such as Darcy's law and the conservation of mass. Our numerical method for solving these equations is based on a total-velocity splitting, sequential formulation which leads to an implicit pressure equation and a semi-implicit mass conservation equation. We use high-resolution finite-difference methods to discretize these equations. Our solution scheme extends previous work in modeling porous media flows in two ways. First, we incorporate physical effects due to capillary pressure, a nonlinear inlet boundary condition, spatial porosity variations, and inertial effects on phase mobilities. In particular, capillary forces introduce a parabolic component into the recast evolution equation, and the inertial effects give rise to hyperbolic nonconvexity. Second, we introduce a modification of the slope-limiting algorithm to prevent our numerical method from producing spurious shocks. We present a numerical algorithm for accommodating these difficulties, show the algorithm is second-order accurate, and demonstrate its performance on a number of simplified problems relevant to trickle bed reactor modeling.

Gauge and integrable theories in loop spaces

NASA Astrophysics Data System (ADS)

Ferreira, L. A.; Luchini, G.

2012-05-01

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1+1) dimensions, Chern-Simons theories in (2+1) dimensions, and non-abelian gauge theories in (2+1) and (3+1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3+1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations.

Design of the optical structure of airfield in-pavement LED runway edge lights

NASA Astrophysics Data System (ADS)

Ma, Xiaodan; Yang, Jianhong; Peng, Jun; Li, Lei

2017-02-01

Airfield lighting system is an important aiding system of civil aviation airport that guarantees the taking off, landing, taxiing of airplanes at night, with low visibility, or under other complicated weather conditions. In-pavement LED runway edge lights, with the highest degree of light intensity, are the most important lights for safe civil aviation and are most difficult to design within airfield lighting system. With LED as the source of light and the secondary optical design as the core, in light of basic laws of Fresnel loss and total reflection and the principles of edge-ray etendue conservation and the conservation of energy to design major optical elements as lens, prism of the lamp, the in-pavement LED runway edge lights design successfully solves the designing problem of high-power, high-intensity LED airfield lights with narrow beam angle at closed environment. This success is of great significance for the improvement of LED airfield lighting system in China.

Multi-dimensional computer simulation of MHD combustor hydrodynamics

NASA Astrophysics Data System (ADS)

Berry, G. F.; Chang, S. L.; Lottes, S. A.; Rimkus, W. A.

1991-04-01

Argonne National Laboratory is investigating the nonreacting jet gas mixing patterns in an MHD second stage combustor by using a 2-D multiphase hydrodynamics computer program and a 3-D single phase hydrodynamics computer program. The computer simulations are intended to enhance the understanding of flow and mixing patterns in the combustor, which in turn may lead to improvement of the downstream MHD channel performance. A 2-D steady state computer model, based on mass and momentum conservation laws for multiple gas species, is used to simulate the hydrodynamics of the combustor in which a jet of oxidizer is injected into an unconfined cross stream gas flow. A 3-D code is used to examine the effects of the side walls and the distributed jet flows on the non-reacting jet gas mixing patterns. The code solves the conservation equations of mass, momentum, and energy, and a transport equation of a turbulence parameter and allows permeable surfaces to be specified for any computational cell.

Einstein-like field equations with conserved source and decreasing and Λ term; Their cosmological consequences

NASA Astrophysics Data System (ADS)

Massa, Corrado

1996-03-01

The consequences of a cosmological ∧ term varying asS -2 in a spatially isotropic universe with scale factorS and conserved matter tensor are investigated. One finds a perpetually expanding universe with positive ∧ and gravitational ‘constant’G that increases with time. The ‘hard’ equation of state 3P>U (U mass-energy density,P scalar pressure) applied to the early universe leads to the expansion lawS∝t (t cosmic time) which solves the horizon problem with no need of inflation. Also the flatness problem is resolved without inflation. The model does not affect the well known predictions on the cosmic light elements abundance which come from standard big bang cosmology. In the present, matter dominated universe one findsdG/dt=2∧H/U (H is the Hubble parameter) which is consistent with observations provided ∧<10-57 cm-2. Asymptotically (S→∞) the ∧ term equalsGU/2, in agreement with other studies.

Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes

NASA Astrophysics Data System (ADS)

Zhu, Jun; Zhong, Xinghui; Shu, Chi-Wang; Qiu, Jianxian

2013-09-01

In this paper we generalize a new type of limiters based on the weighted essentially non-oscillatory (WENO) finite volume methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed in [32] for structured meshes, to two-dimensional unstructured triangular meshes. The key idea of such limiters is to use the entire polynomials of the DG solutions from the troubled cell and its immediate neighboring cells, and then apply the classical WENO procedure to form a convex combination of these polynomials based on smoothness indicators and nonlinear weights, with suitable adjustments to guarantee conservation. The main advantage of this new limiter is its simplicity in implementation, especially for the unstructured meshes considered in this paper, as only information from immediate neighbors is needed and the usage of complicated geometric information of the meshes is largely avoided. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good performance of this procedure.

18 CFR 1314.4 - Law governing the rights and obligations of TVA and Reserve Banks; law governing the rights of...

Code of Federal Regulations, 2011 CFR

2011-04-01

... Reserve Banks; law governing other interests. 1314.4 Section 1314.4 Conservation of Power and Water... rights and obligations of TVA and Reserve Banks with respect to: (i) A Book-entry TVA Power Security or... 18 Conservation of Power and Water Resources 2 2011-04-01 2011-04-01 false Law governing the...

Solving multi-objective optimization problems in conservation with the reference point method

PubMed Central

Dujardin, Yann; Chadès, Iadine

2018-01-01

Managing the biodiversity extinction crisis requires wise decision-making processes able to account for the limited resources available. In most decision problems in conservation biology, several conflicting objectives have to be taken into account. Most methods used in conservation either provide suboptimal solutions or use strong assumptions about the decision-maker’s preferences. Our paper reviews some of the existing approaches to solve multi-objective decision problems and presents new multi-objective linear programming formulations of two multi-objective optimization problems in conservation, allowing the use of a reference point approach. Reference point approaches solve multi-objective optimization problems by interactively representing the preferences of the decision-maker with a point in the criteria (objectives) space, called the reference point. We modelled and solved the following two problems in conservation: a dynamic multi-species management problem under uncertainty and a spatial allocation resource management problem. Results show that the reference point method outperforms classic methods while illustrating the use of an interactive methodology for solving combinatorial problems with multiple objectives. The method is general and can be adapted to a wide range of ecological combinatorial problems. PMID:29293650

A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.

PubMed

Pau, George S H; Almgren, Ann S; Bell, John B; Lijewski, Michael J

2009-11-28

In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method.

Hall-Effect Thruster Simulations with 2-D Electron Transport and Hydrodynamic Ions

NASA Technical Reports Server (NTRS)

Mikellides, Ioannis G.; Katz, Ira; Hofer, Richard H.; Goebel, Dan M.

2009-01-01

A computational approach that has been used extensively in the last two decades for Hall thruster simulations is to solve a diffusion equation and energy conservation law for the electrons in a direction that is perpendicular to the magnetic field, and use discrete-particle methods for the heavy species. This "hybrid" approach has allowed for the capture of bulk plasma phenomena inside these thrusters within reasonable computational times. Regions of the thruster with complex magnetic field arrangements (such as those near eroded walls and magnets) and/or reduced Hall parameter (such as those near the anode and the cathode plume) challenge the validity of the quasi-one-dimensional assumption for the electrons. This paper reports on the development of a computer code that solves numerically the 2-D axisymmetric vector form of Ohm's law, with no assumptions regarding the rate of electron transport in the parallel and perpendicular directions. The numerical challenges related to the large disparity of the transport coefficients in the two directions are met by solving the equations in a computational mesh that is aligned with the magnetic field. The fully-2D approach allows for a large physical domain that extends more than five times the thruster channel length in the axial direction, and encompasses the cathode boundary. Ions are treated as an isothermal, cold (relative to the electrons) fluid, accounting for charge-exchange and multiple-ionization collisions in the momentum equations. A first series of simulations of two Hall thrusters, namely the BPT-4000 and a 6-kW laboratory thruster, quantifies the significance of ion diffusion in the anode region and the importance of the extended physical domain on studies related to the impact of the transport coefficients on the electron flow field.

Forward to the Future: Estimating River Discharge with McFLI

NASA Astrophysics Data System (ADS)

Gleason, C. J.; Durand, M. T.; Garambois, P. A.

2016-12-01

The global surface water budget is still poorly understood, and improving our understanding of freshwater budgets requires coordination between in situ observations, models, and remote sensing. The upcoming launch of the NASA/CNES Surface Water and Ocean Topography (SWOT) satellite has generated considerable excitement as a new tool enabling hydrologists to tackle some of the most pressing questions facing their discipline. One question in particular which SWOT seems well suited to answer is river discharge (flow rate) estimation in ungauged basins: SWOT's anticipated measurements of river surface height and area have ushered in a new technique in hydrology- what we are here calling Mass conserved Flow Law Inversions, or McFLI. McFLI algorithms leverage classic hydraulic flow expressions (e.g. Manning's Equation, hydraulic geometry) within mass conserved river reaches to construct a simplified but still underconstrained system of equations to be solved for an unknown discharge. Most existing McFLI techniques have been designed to take advantage of SWOT's measurements and Manning's Equation: SWOT will observe changes in cross sectional area and river surface slope over time, so the McFLI need only solve for baseflow area and Manning's roughness coefficient. Recently published preliminary results have indicated that McFLI can be a viable tool in a global hydrologist's toolbox (discharge errors less than 30% as compared to gauges are possible in most cases). Therefore, we here outline the progress to date for McFLI techniques, and highlight three key areas for future development: 1) Maximize the accuracy and robustness of McFLI by incorporating ancillary data from satellites, models, and in situ observations. 2) Develop new McFLI techniques using novel or underutilized flow laws. 3) Systematically test McFLI to define different inversion classes of rivers with well-defined error budgets based on geography and available data for use in gauged and ungauged basins alike.

Revisiting the Balazs thought experiment in the case of a left-handed material: electromagnetic-pulse-induced displacement of a dispersive, dissipative negative-index slab.

PubMed

Chau, Kenneth J; Lezec, Henri J

2012-04-23

We propose a set of postulates to describe the mechanical interaction between a plane-wave electromagnetic pulse and a dispersive, dissipative slab having a refractive index of arbitrary sign. The postulates include the Abraham electromagnetic momentum density, a generalized Lorentz force law, and a model for absorption-driven mass transfer from the pulse to the medium. These opto-mechanical mechanisms are incorporated into a one-dimensional finite-difference time-domain algorithm that solves Maxwell's equations and calculates the instantaneous force densities exerted by the pulse onto the slab, the momentum-per-unit-area of the pulse and slab, and the trajectories of the slab and system center-of-mass. We show that the postulates are consistent with conservation of global energy, momentum, and center-of-mass velocity at all times, even for cases in which the refractive index of the slab is negative or zero. Consistency between the set of postulates and well-established conservation laws reinforces the Abraham momentum density as the one true electromagnetic momentum density and enables, for the first time, identification of the correct form of the electromagnetic mass density distribution and development of an explicit model for mass transfer due to absorption, for the most general case of a ponderable medium that is both dispersive and dissipative. © 2012 Optical Society of America

The convergence of spectral methods for nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Tadmor, Eitan

1987-01-01

The convergence of the Fourier method for scalar nonlinear conservation laws which exhibit spontaneous shock discontinuities is discussed. Numerical tests indicate that the convergence may (and in fact in some cases must) fail, with or without post-processing of the numerical solution. Instead, a new kind of spectrally accurate vanishing viscosity is introduced to augment the Fourier approximation of such nonlinear conservation laws. Using compensated compactness arguments, it is shown that this spectral viscosity prevents oscillations, and convergence to the unique entropy solution follows.

Identifying all moiety conservation laws in genome-scale metabolic networks.

PubMed

De Martino, Andrea; De Martino, Daniele; Mulet, Roberto; Pagnani, Andrea

2014-01-01

The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell's metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.

Boundary Conditions for Infinite Conservation Laws

NASA Astrophysics Data System (ADS)

Rosenhaus, V.; Bruzón, M. S.; Gandarias, M. L.

2016-12-01

Regular soliton equations (KdV, sine-Gordon, NLS) are known to possess infinite sets of local conservation laws. Some other classes of nonlinear PDE possess infinite-dimensional symmetries parametrized by arbitrary functions of independent or dependent variables; among them are Zabolotskaya-Khokhlov, Kadomtsev-Petviashvili, Davey-Stewartson equations and Born-Infeld equation. Boundary conditions were shown to play an important role for the existence of local conservation laws associated with infinite-dimensional symmetries. In this paper, we analyze boundary conditions for the infinite conserved densities of regular soliton equations: KdV, potential KdV, Sine-Gordon equation, and nonlinear Schrödinger equation, and compare them with boundary conditions for the conserved densities obtained from infinite-dimensional symmetries with arbitrary functions of independent and dependent variables.

18 CFR 375.304 - Delegations to the Chief Administrative Law Judge.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 18 Conservation of Power and Water Resources 1 2011-04-01 2011-04-01 false Delegations to the Chief Administrative Law Judge. 375.304 Section 375.304 Conservation of Power and Water Resources... Law Judge to exercise the power granted to a Presiding Officer by part 385, particularly § 385.504 of...

18 CFR 375.304 - Delegations to the Chief Administrative Law Judge.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 18 Conservation of Power and Water Resources 1 2010-04-01 2010-04-01 false Delegations to the Chief Administrative Law Judge. 375.304 Section 375.304 Conservation of Power and Water Resources... Law Judge to exercise the power granted to a Presiding Officer by part 385, particularly § 385.504 of...

18 CFR 375.304 - Delegations to the Chief Administrative Law Judge.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 18 Conservation of Power and Water Resources 1 2013-04-01 2013-04-01 false Delegations to the Chief Administrative Law Judge. 375.304 Section 375.304 Conservation of Power and Water Resources... Law Judge to exercise the power granted to a Presiding Officer by part 385, particularly § 385.504 of...

18 CFR 375.304 - Delegations to the Chief Administrative Law Judge.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 18 Conservation of Power and Water Resources 1 2014-04-01 2014-04-01 false Delegations to the Chief Administrative Law Judge. 375.304 Section 375.304 Conservation of Power and Water Resources... Law Judge to exercise the power granted to a Presiding Officer by part 385, particularly § 385.504 of...

18 CFR 375.304 - Delegations to the Chief Administrative Law Judge.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 18 Conservation of Power and Water Resources 1 2012-04-01 2012-04-01 false Delegations to the Chief Administrative Law Judge. 375.304 Section 375.304 Conservation of Power and Water Resources... Law Judge to exercise the power granted to a Presiding Officer by part 385, particularly § 385.504 of...

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Some optimal considerations in attitude control systems. [evaluation of value of relative weighting between time and fuel for relay control law

NASA Technical Reports Server (NTRS)

Boland, J. S., III

1973-01-01

The conventional six-engine reaction control jet relay attitude control law with deadband is shown to be a good linear approximation to a weighted time-fuel optimal control law. Techniques for evaluating the value of the relative weighting between time and fuel for a particular relay control law is studied along with techniques to interrelate other parameters for the two control laws. Vehicle attitude control laws employing control moment gyros are then investigated. Steering laws obtained from the expression for the reaction torque of the gyro configuration are compared to a total optimal attitude control law that is derived from optimal linear regulator theory. This total optimal attitude control law has computational disadvantages in the solving of the matrix Riccati equation. Several computational algorithms for solving the matrix Riccati equation are investigated with respect to accuracy, computational storage requirements, and computational speed.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Kumar, Vivek; Raghurama Rao, S. V.

2008-04-01

Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

Nonlocal conservation laws of the constant astigmatism equation

NASA Astrophysics Data System (ADS)

Hlaváč, Adam; Marvan, Michal

2017-03-01

For the constant astigmatism equation, we construct a system of nonlocal conservation laws (an abelian covering) closed under the reciprocal transformations. The corresponding potentials are functionally independent modulo a Wronskian type relation.

Turing patterns in parabolic systems of conservation laws and numerically observed stability of periodic waves

NASA Astrophysics Data System (ADS)

Barker, Blake; Jung, Soyeun; Zumbrun, Kevin

2018-03-01

Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability in conservation laws and (ii) use these conditions to find families of periodic solutions bifurcating from uniform states, numerically continuing these families into the large-amplitude regime. For the examples studied, numerical stability analysis suggests that stable periodic waves can emerge either from supercritical Turing bifurcations or, via secondary bifurcation as amplitude is increased, from subcritical Turing bifurcations. This answers in the affirmative a question of Oh-Zumbrun whether stable periodic solutions of conservation laws can occur. Determination of a full small-amplitude stability diagram - specifically, determination of rigorous Eckhaus-type stability conditions - remains an interesting open problem.

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2000-01-01

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Biological conservation law as an emerging functionality in dynamical neuronal networks.

PubMed

Podobnik, Boris; Jusup, Marko; Tiganj, Zoran; Wang, Wen-Xu; Buldú, Javier M; Stanley, H Eugene

2017-11-07

Scientists strive to understand how functionalities, such as conservation laws, emerge in complex systems. Living complex systems in particular create high-ordered functionalities by pairing up low-ordered complementary processes, e.g., one process to build and the other to correct. We propose a network mechanism that demonstrates how collective statistical laws can emerge at a macro (i.e., whole-network) level even when they do not exist at a unit (i.e., network-node) level. Drawing inspiration from neuroscience, we model a highly stylized dynamical neuronal network in which neurons fire either randomly or in response to the firing of neighboring neurons. A synapse connecting two neighboring neurons strengthens when both of these neurons are excited and weakens otherwise. We demonstrate that during this interplay between the synaptic and neuronal dynamics, when the network is near a critical point, both recurrent spontaneous and stimulated phase transitions enable the phase-dependent processes to replace each other and spontaneously generate a statistical conservation law-the conservation of synaptic strength. This conservation law is an emerging functionality selected by evolution and is thus a form of biological self-organized criticality in which the key dynamical modes are collective.

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

A new stream function formulation for the Euler equations

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Hassan, H. A.

1983-01-01

A new stream function formulation is developed for the solution of Euler's equations in the transonic flow region. The stream function and the density are the dependent variables in this method, while the governing equations for adiabatic flow are the momentum equations which are solved in the strong conservation law form. The application of this method does not require a knowledge of the vorticity. The algorithm is combined with the automatic grid solver (GRAPE) of Steger and Sorenson (1979) in order to study arbitrary geometries. Results of the application of this method are presented for the NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. In addition, detailed comparisons are made with other solutions of the Euler equations.

Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bailey, Harry E.; Beam, Richard M.

1991-01-01

Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.

A simple smoothness indicator for the WENO scheme with adaptive order

NASA Astrophysics Data System (ADS)

Huang, Cong; Chen, Li Li

2018-01-01

The fifth order WENO scheme with adaptive order is competent for solving hyperbolic conservation laws, its reconstruction is a convex combination of a fifth order linear reconstruction and three third order linear reconstructions. Note that, on uniform mesh, the computational cost of smoothness indicator for fifth order linear reconstruction is comparable with the sum of ones for three third order linear reconstructions, thus it is too heavy; on non-uniform mesh, the explicit form of smoothness indicator for fifth order linear reconstruction is difficult to be obtained, and its computational cost is much heavier than the one on uniform mesh. In order to overcome these problems, a simple smoothness indicator for fifth order linear reconstruction is proposed in this paper.

A new adaptively central-upwind sixth-order WENO scheme

NASA Astrophysics Data System (ADS)

Huang, Cong; Chen, Li Li

2018-03-01

In this paper, we propose a new sixth-order WENO scheme for solving one dimensional hyperbolic conservation laws. The new WENO reconstruction has three properties: (1) it is central in smooth region for low dissipation, and is upwind near discontinuities for numerical stability; (2) it is a convex combination of four linear reconstructions, in which one linear reconstruction is sixth order, and the others are third order; (3) its linear weights can be any positive numbers with requirement that their sum equals one. Furthermore, we propose a simple smoothness indicator for the sixth-order linear reconstruction, this smooth indicator not only can distinguish the smooth region and discontinuities exactly, but also can reduce the computational cost, thus it is more efficient than the classical one.

Lattice Boltzmann model for numerical relativity.

PubMed

Ilseven, E; Mendoza, M

2016-02-01

In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.

A Simple Derivation of Kepler's Laws without Solving Differential Equations

ERIC Educational Resources Information Center

Provost, J.-P.; Bracco, C.

2009-01-01

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple…

Eye-Tracking Study of Complexity in Gas Law Problems

ERIC Educational Resources Information Center

Tang, Hui; Pienta, Norbert

2012-01-01

This study, part of a series investigating students' use of online tools to assess problem solving, uses eye-tracking hardware and software to explore the effect of problem difficulty and cognitive processes when students solve gas law word problems. Eye movements are indices of cognition; eye-tracking data typically include the location,…

Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equation

NASA Astrophysics Data System (ADS)

Simbanefayi, Innocent; Khalique, Chaudry Masood

2018-03-01

In this work we study the Korteweg-de Vries-Benjamin-Bona-Mahony (KdV-BBM) equation, which describes the two-way propagation of waves. Using Lie symmetry method together with Jacobi elliptic function expansion and Kudryashov methods we construct its travelling wave solutions. Also, we derive conservation laws of the KdV-BBM equation using the variational derivative approach. In this method, we begin by computing second-order multipliers for the KdV-BBM equation followed by a derivation of the respective conservation laws for each multiplier.

Conservation laws and symmetries of a generalized Kawahara equation

NASA Astrophysics Data System (ADS)

Gandarias, Maria Luz; Rosa, Maria; Recio, Elena; Anco, Stephen

2017-06-01

The generalized Kawahara equation ut = a(t)uxxxxx + b(t)uxxx + c(t) f (u)ux appears in many physical applications. A complete classification of low-order conservation laws and point symmetries is obtained for this equation, which includes as a special case the usual Kawahara equation ut = αuux + βu2ux + γuxxx + μuxxxxx. A general connection between conservation laws and symmetries for the generalized Kawahara equation is derived through the Hamiltonian structure of this equation and its relationship to Noether's theorem using a potential formulation.

Structure of the conversion laws in quantum integrable spin chains with short range interactions

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

Grabowski, M.P.; Mathieu, P.

1995-11-01

The authors present a detailed analysis of the structure of the conservation laws in quantum integrable chains of the XYZ-type and in the Hubbard model. The essential tool for the former class of models is the boost operator, which provides a recursive way of calculating the integrals of motion. With its help, they establish the general form of the XYZ conserved charges in terms of simple polynomials in spin variables and derive recursion relations for the relative coefficients of these polynomials. Although these relations are difficult to solve in general, a subset of the coefficients can be determined. Moreover, formore » two submodels of the XYZ chain, namely the XXX and XY cases, all the charges can be calculated in closed form. Using this approach, the authors rederive the known expressions for the XY charges in a novel way. For the XXX case. a simple description of conserved charges is found in terms of a Catalan tree. This construction is generalized for the su(M) invariant integrable chain. They also investigate the circumstances permitting the existence of a recursive (ladder) operator in general quantum integrable systems. They indicate that a quantum ladder operator can be traced back to the presence of a Hamiltonian mastersymmetry of degree one in the classical continuous version of the model. In this way, quantum chains endowed with a recursive structure can be identified from the properties of their classical relatives. The authors also show that in the quantum continuous limits of the XYZ model, the ladder property of the boost operator disappears. For the Hubbard model they demonstrate the nonexistence of a ladder operator. Nevertheless, the general structure of the conserved charges is indicated, and the expression for the terms linear in the model`s free parameter for all charges is derived in closed form. 62 refs., 4 figs.« less

On the convergence of difference approximations to scalar conservation laws

NASA Technical Reports Server (NTRS)

Osher, Stanley; Tadmor, Eitan

1988-01-01

A unified treatment is given for time-explicit, two-level, second-order-resolution (SOR), total-variation-diminishing (TVD) approximations to scalar conservation laws. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced to obtain results in terms of the latter. The existence of a cell entropy inequality is discussed, and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first-order accurate in general. Convergence for TVD-SOR schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.

On Faraday's law in the presence of extended conductors

NASA Astrophysics Data System (ADS)

Bilbao, Luis

2018-06-01

The use of Faraday's Law of induction for calculating the induced currents in an extended conducting body is discussed. In a general case with arbitrary geometry, the solution to the problem of a moving metal object in the presence of a magnetic field is difficult and implies solving Maxwell's equations in a time-dependent situation. In many cases, including cases with good conductors (but not superconductors) Ampère's Law can be neglected and a simpler solution based solely in Faraday's law can be obtained. The integral form of Faraday's Law along any loop in the conducting body is equivalent to a Kirkhhoff's voltage law of a circuit. Therefore, a numerical solution can be obtained by solving a linear system of equations corresponding to a discrete number of loops in the body.

Energetically consistent collisional gyrokinetics

DOE PAGES

Burby, J. W.; Brizard, A. J.; Qin, H.

2015-10-30

Here, we present a formulation of collisional gyrokinetic theory with exact conservation laws for energy and canonical toroidal momentum. Collisions are accounted for by a nonlinear gyrokinetic Landau operator. Gyroaveraging and linearization do not destroy the operator's conservation properties. Just as in ordinary kinetic theory, the conservation laws for collisional gyrokinetic theory are selected by the limiting collisionless gyrokinetic theory. (C) 2015 AIP Publishing LLC.

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D has been developed to solve the three dimensional, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort has been to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation have been emphasized. The governing equations are solved in generalized non-orthogonal body-fitted coordinates by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. It describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

TESS: A RELATIVISTIC HYDRODYNAMICS CODE ON A MOVING VORONOI MESH

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

Duffell, Paul C.; MacFadyen, Andrew I., E-mail: pcd233@nyu.edu, E-mail: macfadyen@nyu.edu

2011-12-01

We have generalized a method for the numerical solution of hyperbolic systems of equations using a dynamic Voronoi tessellation of the computational domain. The Voronoi tessellation is used to generate moving computational meshes for the solution of multidimensional systems of conservation laws in finite-volume form. The mesh-generating points are free to move with arbitrary velocity, with the choice of zero velocity resulting in an Eulerian formulation. Moving the points at the local fluid velocity makes the formulation effectively Lagrangian. We have written the TESS code to solve the equations of compressible hydrodynamics and magnetohydrodynamics for both relativistic and non-relativistic fluidsmore » on a dynamic Voronoi mesh. When run in Lagrangian mode, TESS is significantly less diffusive than fixed mesh codes and thus preserves contact discontinuities to high precision while also accurately capturing strong shock waves. TESS is written for Cartesian, spherical, and cylindrical coordinates and is modular so that auxiliary physics solvers are readily integrated into the TESS framework and so that this can be readily adapted to solve general systems of equations. We present results from a series of test problems to demonstrate the performance of TESS and to highlight some of the advantages of the dynamic tessellation method for solving challenging problems in astrophysical fluid dynamics.« less

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 2: User's guide

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the User's Guide, and describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Mapping university students' epistemic framing of computational physics using network analysis

NASA Astrophysics Data System (ADS)

Bodin, Madelen

2012-06-01

Solving physics problem in university physics education using a computational approach requires knowledge and skills in several domains, for example, physics, mathematics, programming, and modeling. These competences are in turn related to students’ beliefs about the domains as well as about learning. These knowledge and beliefs components are referred to here as epistemic elements, which together represent the students’ epistemic framing of the situation. The purpose of this study was to investigate university physics students’ epistemic framing when solving and visualizing a physics problem using a particle-spring model system. Students’ epistemic framings are analyzed before and after the task using a network analysis approach on interview transcripts, producing visual representations as epistemic networks. The results show that students change their epistemic framing from a modeling task, with expectancies about learning programming, to a physics task, in which they are challenged to use physics principles and conservation laws in order to troubleshoot and understand their simulations. This implies that the task, even though it is not introducing any new physics, helps the students to develop a more coherent view of the importance of using physics principles in problem solving. The network analysis method used in this study is shown to give intelligible representations of the students’ epistemic framing and is proposed as a useful method of analysis of textual data.

The Earth, the Moon and Conservation of Momentum

ERIC Educational Resources Information Center

Brunt, Marjorie; Brunt, Geoff

2013-01-01

We consider the application of both conservation of momentum and Newton's laws to the Moon in an assumed circular orbit about the Earth. The inadequacy of some texts in applying Newton's laws is considered.

Web-GIS based information management system to Bureau of Law Enforcement for Urban Managementenforcement for urban management

NASA Astrophysics Data System (ADS)

Sun, Hai; Wang, Cheng; Ren, Bo

2007-06-01

Daily works of Law Enforcement Bureau are crucial in the urban management. However, with the development of the city, the information and data which are relative to Law Enforcement Bureau's daily work are increasing and updating. The increasing data result in that some traditional work is limited and inefficient in daily work. Analyzing the demands and obstacles of Law Enforcement Bureau, the paper proposes a new method to solve these problems. A web-GIS based information management system was produced for Bureau of Law Enforcement for Urban Management of Foshan. First part of the paper provides an overview of the system. Second part introduces the architecture of system and data organization. In the third part, the paper describes the design and implement of functional modules detailedly. In the end, this paper is concluded and proposes some strategic recommendations for the further development of the system. This paper focuses on the architecture and implementation of the system, solves the developing issues based on ArcServer, and introduces a new concept to the local government to solve the current problems. Practical application of this system showed that it played very important role in the Law Enforcement Bureau's work.

On the convergence of difference approximations to scalar conservation laws

NASA Technical Reports Server (NTRS)

Osher, S.; Tadmor, E.

1985-01-01

A unified treatment of explicit in time, two level, second order resolution, total variation diminishing, approximations to scalar conservation laws are presented. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced and results in terms of the latter are obtained. The existence of a cell entropy inequality is discussed and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first order accurate in general. Convergence for total variation diminishing-second order resolution schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.

Solutions and conservation laws for a Kaup-Boussinesq system

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Abudiab, Mufid; Khalique, Chaudry Masood

2017-07-01

In this work we study a Kaup-Boussinesq system, which is used in the analysis of long waves in shallow water. Travelling wave solutions are obtained by using direct integration. Secondly, conservation laws are derived by using the multiplier method.

Effects of Ohmic Resistance on Dynamic Characteristics and Impedance of Micro/Nano Cantilever Beam resonators

NASA Astrophysics Data System (ADS)

Rezazadeh, Ghader; Keyvani, Aliasghar; Sadeghi, Morteza H.; Bahrami, Manouchehr

2013-06-01

Effects of Ohmic resistance on MEMS/NEMS vibrating structures that have always been dismissed in some situations may cause important changes in resonance properties and impedance parameters of the MEMS/NEMS based circuits. In this paper it is aimed to present a theoretical model to precisely investigate the problem on a simple cantilever-substrate resonator. In this favor the Ohm's current law and charge conservation law have been merged to find a differential Equation for voltage propagation on the beam and because mostly nano structures are expected as the scope of the problem, modified couple stress theory is used to formulate the dynamic motion of the beam. The two governing equations were coupled and both nonlinear that have been solved simultaneously using a Galerkin based state space formulation. The obtained results that are in exact agreement with previous works show that dynamic pull-in voltage, switching time, and impedance of structure as a MEMS capacitor especially in frequencies higher than natural resonance frequency strongly relay on electrical resistance of the beam and substrate material.

Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates

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

Cheng, Juan, E-mail: cheng_juan@iapcm.ac.cn; Shu, Chi-Wang, E-mail: shu@dam.brown.edu

In applications such as astrophysics and inertial confinement fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simulated by Lagrangian schemes in the two-dimensional cylindrical coordinates. For this type of simulation, a critical issue for the schemes is to keep spherical symmetry in the cylindrical coordinate system if the original physical problem has this symmetry. In the past decades, several Lagrangian schemes with such symmetry property have been developed, but all of them are only first order accurate. In this paper, we develop a second order cell-centered Lagrangian scheme for solving compressible Euler equations in cylindrical coordinates, basedmore » on the control volume discretizations, which is designed to have uniformly second order accuracy and capability to preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid. The scheme maintains several good properties such as conservation for mass, momentum and total energy, and the geometric conservation law. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of accuracy, symmetry, non-oscillation and robustness. The advantage of higher order accuracy is demonstrated in these examples.« less

Discrete conservation properties for shallow water flows using mixed mimetic spectral elements

NASA Astrophysics Data System (ADS)

Lee, D.; Palha, A.; Gerritsma, M.

2018-03-01

A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of calculus with respect to the standard Lagrange basis functions in one dimension. These are used to construct tensor product solution spaces which satisfy the generalized Stokes theorem, as well as the annihilation of the gradient operator by the curl and the curl by the divergence. This allows for the exact conservation of first order moments (mass, vorticity), as well as higher moments (energy, potential enstrophy), subject to the truncation error of the time stepping scheme. The continuity equation is solved in the strong form, such that mass conservation holds point wise, while the momentum equation is solved in the weak form such that vorticity is globally conserved. While mass, vorticity and energy conservation hold for any quadrature rule, potential enstrophy conservation is dependent on exact spatial integration. The method possesses a weak form statement of geostrophic balance due to the compatible nature of the solution spaces and arbitrarily high order spatial error convergence.

Higher-order jump conditions for conservation laws

NASA Astrophysics Data System (ADS)

Oksuzoglu, Hakan

2018-04-01

The hyperbolic conservation laws admit discontinuous solutions where the solution variables can have finite jumps in space and time. The jump conditions for conservation laws are expressed in terms of the speed of the discontinuity and the state variables on both sides. An example from the Gas Dynamics is the Rankine-Hugoniot conditions for the shock speed. Here, we provide an expression for the acceleration of the discontinuity in terms of the state variables and their spatial derivatives on both sides. We derive a jump condition for the shock acceleration. Using this general expression, we show how to obtain explicit shock acceleration formulas for nonlinear hyperbolic conservation laws. We start with the Burgers' equation and check the derived formula with an analytical solution. We next derive formulas for the Shallow Water Equations and the Euler Equations of Gas Dynamics. We will verify our formulas for the Euler Equations using an exact solution for the spherically symmetric blast wave problem. In addition, we discuss the potential use of these formulas for the implementation of shock fitting methods.

The brain and the law.

PubMed Central

Chorvat, Terrence; McCabe, Kevin

2004-01-01

Much has been written about how law as an institution has developed to solve many problems that human societies face. Inherent in all of these explanations are models of how humans make decisions. This article discusses what current neuroscience research tells us about the mechanisms of human decision making of particular relevance to law. This research indicates that humans are both more capable of solving many problems than standard economic models predict, but also limited in ways those models ignore. This article discusses how law is both shaped by our cognitive processes and also shapes them. The article considers some of the implications of this research for improving our understanding of how our current legal regimes operate and how the law can be structured to take advantage of our neural mechanisms to improve social welfare. PMID:15590613

A computational approach for hypersonic nonequilibrium radiation utilizing space partition algorithm and Gauss quadrature

NASA Astrophysics Data System (ADS)

Shang, J. S.; Andrienko, D. A.; Huang, P. G.; Surzhikov, S. T.

2014-06-01

An efficient computational capability for nonequilibrium radiation simulation via the ray tracing technique has been accomplished. The radiative rate equation is iteratively coupled with the aerodynamic conservation laws including nonequilibrium chemical and chemical-physical kinetic models. The spectral properties along tracing rays are determined by a space partition algorithm of the nearest neighbor search process, and the numerical accuracy is further enhanced by a local resolution refinement using the Gauss-Lobatto polynomial. The interdisciplinary governing equations are solved by an implicit delta formulation through the diminishing residual approach. The axisymmetric radiating flow fields over the reentry RAM-CII probe have been simulated and verified with flight data and previous solutions by traditional methods. A computational efficiency gain nearly forty times is realized over that of the existing simulation procedures.

COMMENT Comment on 'Conservation laws of higher order nonlinear PDEs and the variational conservation laws in the class with mixed derivatives'

NASA Astrophysics Data System (ADS)

Sarlet, W.

2010-11-01

In a recent paper (R Narain and A H Kara 2010 J. Phys. A: Math. Theor. 43 085205), the authors claim to be applying Noether's theorem to higher-order partial differential equations and state that in a large class of examples 'the resultant conserved flows display some previously unknown interesting 'divergence properties' owing to the presence of the mixed derivatives' (citation from their abstract). It turns out that what this obscure sentence is meant to say is that the vector whose divergence must be zero (according to Noether's theorem), turns out to have non-zero divergence and subsequently must be modified to obtain a true conservation law. Clearly this cannot be right: we explain in detail the main source of the error.

Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics

NASA Astrophysics Data System (ADS)

Webb, G. M.; Anco, S. C.

2016-02-01

The Lagrangian, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, m i (the Lagrangian mass coordinates) and time t are the independent variables, and in which the Eulerian position of the fluid element {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the Lagrangian map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the Lagrangian map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The Lagrangian is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the Lagrangian energy conservation law with respect to the Lagrangian mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.

A method to stabilize linear systems using eigenvalue gradient information

NASA Technical Reports Server (NTRS)

Wieseman, C. D.

1985-01-01

Formal optimization methods and eigenvalue gradient information are used to develop a stabilizing control law for a closed loop linear system that is initially unstable. The method was originally formulated by using direct, constrained optimization methods with the constraints being the real parts of the eigenvalues. However, because of problems in trying to achieve stabilizing control laws, the problem was reformulated to be solved differently. The method described uses the Davidon-Fletcher-Powell minimization technique to solve an indirect, constrained minimization problem in which the performance index is the Kreisselmeier-Steinhauser function of the real parts of all the eigenvalues. The method is applied successfully to solve two different problems: the determination of a fourth-order control law stabilizes a single-input single-output active flutter suppression system and the determination of a second-order control law for a multi-input multi-output lateral-directional flight control system. Various sets of design variables and initial starting points were chosen to show the robustness of the method.

Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method

NASA Astrophysics Data System (ADS)

Rasin, Alexander G.

2010-06-01

The application of the Gardner method for the generation of conservation laws to all the ABS equations is considered. It is shown that all the necessary information for the application of the Gardner method, namely Bäcklund transformations and initial conservation laws, follows from the multidimensional consistency of ABS equations. We also apply the Gardner method to an asymmetric equation which is not included in the ABS classification. An analog of the Gardner method for the generation of symmetries is developed and applied to the discrete Korteweg-de Vries equation. It can also be applied to all the other ABS equations.

Moisture and Home Energy Conservation: How to Detect, Solve and Avoid Related Problems.

ERIC Educational Resources Information Center

National Center for Appropriate Technology, Butte, MT.

Moisture problems are identified as an important element in home energy conservation programs. A systematic approach to understanding, recognizing, solving, and preventing moisture-related problems is offered in this four-section report. Section I examines the root of moisture problems. Section II discusses symptoms and causes of excess moisture…

Second-order accurate nonoscillatory schemes for scalar conservation laws

NASA Technical Reports Server (NTRS)

Huynh, Hung T.

1989-01-01

Explicit finite difference schemes for the computation of weak solutions of nonlinear scalar conservation laws is presented and analyzed. These schemes are uniformly second-order accurate and nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time.

45 CFR 673.1 - Purpose of regulations.

Code of Federal Regulations, 2014 CFR

2014-10-01

... Welfare Regulations Relating to Public Welfare (Continued) NATIONAL SCIENCE FOUNDATION ANTARCTIC NON... implement the Antarctic Conservation Act of 1978, Public Law 95-541, as amended by the Antarctic Science, Tourism and Conservation Act of 1996, Public Law 104-227, and Article 15 of the Protocol on Environmental...

45 CFR 673.1 - Purpose of regulations.

Code of Federal Regulations, 2012 CFR

2012-10-01

... Welfare Regulations Relating to Public Welfare (Continued) NATIONAL SCIENCE FOUNDATION ANTARCTIC NON... implement the Antarctic Conservation Act of 1978, Public Law 95-541, as amended by the Antarctic Science, Tourism and Conservation Act of 1996, Public Law 104-227, and Article 15 of the Protocol on Environmental...

45 CFR 673.1 - Purpose of regulations.

Code of Federal Regulations, 2011 CFR

2011-10-01

... Welfare Regulations Relating to Public Welfare (Continued) NATIONAL SCIENCE FOUNDATION ANTARCTIC NON... implement the Antarctic Conservation Act of 1978, Public Law 95-541, as amended by the Antarctic Science, Tourism and Conservation Act of 1996, Public Law 104-227, and Article 15 of the Protocol on Environmental...

45 CFR 673.1 - Purpose of regulations.

Code of Federal Regulations, 2013 CFR

2013-10-01

... Welfare Regulations Relating to Public Welfare (Continued) NATIONAL SCIENCE FOUNDATION ANTARCTIC NON... implement the Antarctic Conservation Act of 1978, Public Law 95-541, as amended by the Antarctic Science, Tourism and Conservation Act of 1996, Public Law 104-227, and Article 15 of the Protocol on Environmental...

[Forestry Law and the conservation of natural areas and wildlife].

PubMed

Villacrés, V; Suárez, M; Tafur, V

1996-04-01

The Forest Law of Ecuador consists of 107 articles, whereas its regulations contain 269 articles. They are related to forestry resources, forestry patrimony protection, forests and vegetation, forest production and benefits, the control and mobilization of the forestry resources, research and capacitation, and the forestry industry protection; to natural areas, wild flora and fauna, their patrimony, conservation, and economic support; and to the violation of the law and its judgment.

Biological conservation law as an emerging functionality in dynamical neuronal networks

PubMed Central

Podobnik, Boris; Tiganj, Zoran; Wang, Wen-Xu; Buldú, Javier M.

2017-01-01

Scientists strive to understand how functionalities, such as conservation laws, emerge in complex systems. Living complex systems in particular create high-ordered functionalities by pairing up low-ordered complementary processes, e.g., one process to build and the other to correct. We propose a network mechanism that demonstrates how collective statistical laws can emerge at a macro (i.e., whole-network) level even when they do not exist at a unit (i.e., network-node) level. Drawing inspiration from neuroscience, we model a highly stylized dynamical neuronal network in which neurons fire either randomly or in response to the firing of neighboring neurons. A synapse connecting two neighboring neurons strengthens when both of these neurons are excited and weakens otherwise. We demonstrate that during this interplay between the synaptic and neuronal dynamics, when the network is near a critical point, both recurrent spontaneous and stimulated phase transitions enable the phase-dependent processes to replace each other and spontaneously generate a statistical conservation law—the conservation of synaptic strength. This conservation law is an emerging functionality selected by evolution and is thus a form of biological self-organized criticality in which the key dynamical modes are collective. PMID:29078286

Prospects for reconciling the conflict between economic growth and biodiversity conservation with technological progress.

PubMed

Czech, Brian

2008-12-01

The conflict between economic growth and biodiversity conservation is understood in portions of academia and sometimes acknowledged in political circles. Nevertheless, there is not a unified response. In political and policy circles, the environmental Kuznets curve (EKC) is posited to solve the conflict between economic growth and environmental protection. In academia, however, the EKC has been deemed fallacious in macroeconomic scenarios and largely irrelevant to biodiversity. A more compelling response to the conflict is that it may be resolved with technological progress. Herein I review the conflict between economic growth and biodiversity conservation in the absence of technological progress, explore the prospects for technological progress to reconcile that conflict, and provide linguistic suggestions for describing the relationships among economic growth, technological progress, and biodiversity conservation. The conflict between economic growth and biodiversity conservation is based on the first two laws of thermodynamics and principles of ecology such as trophic levels and competitive exclusion. In this biophysical context, the human economy grows at the competitive exclusion of nonhuman species in the aggregate. Reconciling the conflict via technological progress has not occurred and is infeasible because of the tight linkage between technological progress and economic growth at current levels of technology. Surplus production in existing economic sectors is required for conducting the research and development necessary for bringing new technologies to market. Technological regimes also reflect macroeconomic goals, and if the goal is economic growth, reconciliatory technologies are less likely to be developed. As the economy grows, the loss of biodiversity may be partly mitigated with end-use innovation that increases technical efficiency, but this type of technological progress requires policies that are unlikely if the conflict between economic growth and biodiversity conservation (and other aspects of environmental protection) is not acknowledged.

2×2 systems of conservation laws with L data

NASA Astrophysics Data System (ADS)

Bianchini, Stefano; Colombo, Rinaldo M.; Monti, Francesca

Consider a hyperbolic system of conservation laws with genuinely nonlinear characteristic fields. We extend the classical Glimm-Lax (1970) result [13, Theorem 5.1] proving the existence of solutions for L initial datum, relaxing the assumptions taken therein on the geometry of the shock-rarefaction curves.

Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

1999-01-01

Simplified forms of the space-time discontinuous Galerkin (DG) and discontinuous Galerkin least-squares (DGLS) finite element method are developed and analyzed. The new formulations exploit simplifying properties of entropy endowed conservation law systems while retaining the favorable energy properties associated with symmetric variable formulations.

Translation among Symbolic Representations in Problem-Solving. Revised.

ERIC Educational Resources Information Center

Shavelson, Richard J.; And Others

This study investigated the relationships among the symbolic representation of problems given to students to solve, the mental representations they use to solve the problems, and the accuracy of their solutions. Twenty eleventh-grade science students were asked to think aloud as they solved problems on the ideal gas laws. The problems were…

An Analysis of Kindergarten and First Grade Children's Addition and Subtraction Problem Solving Modeling and Accuracy.

ERIC Educational Resources Information Center

Shores, Jay H.; Underhill, Robert G.

A study was undertaken of the effects of formal education and conservation of numerousness on addition and subtraction problem types. Thirty-six kindergarten and 36 first-grade subjects randomly selected from one area of a school district were administered measures of conservation, problem-solving success, and modeling ability. Following factor…

A True Proteus: A history of energy conservation in German science and culture, 1847-1914

NASA Astrophysics Data System (ADS)

Wegener, F. D. A.

2009-11-01

This thesis follows the career of the law of energy conservation in German science and culture between 1847 and 1914. There is an interesting contrast between the initial reception of Hermann Helmholtz’ 1847 treatise ‘Über die Erhaltung der Kraft’, which was rejected by the editor of the Annalen der Physik, and its later status as a classic of science. ‘Energy’ was the shared concept of the disciplines. It was used by physiologists, physicists, psychologists, sociologists and philosophers. Moreover, the law of energy conservation also made a huge cultural impact. The period around 1900 has justly been called an energetic era. Why did the law of energy conservation become such a universal success? The obvious way to explain this success would be to say: because it is true, and subsequently comment upon its great scientific value. This thesis adopts a different perspective. It adopts Wittgenstein’s definition of meaning as use in language. Consequently, the meaning of the law is only referred to in relation to the way in which it was put to use in communicative practice. From this perspective it is immediately evident that the understanding of the law of energy conservation was subject to considerable change. Helmholtz initially conceptualized the law in terms of atoms and forces; Gustav Kirchhoff and Ernst Mach, rejected atoms and forces as hypothetical entities and they preferred to use the more mundane concept of work instead; Wilhelm Ostwald, finally, thought of energy as an immaterial substance. This thesis meticulously follows the changes in use and understanding to which the law was subject as it penetrated German science and culture. Communication and interests, rather than natural essences, are the central explanatory concepts of the thesis. From 1847 onwards Helmholtz and Du Bois-Reymond actively sought to spread the law of energy conservation among their colleagues and the general public. They told their fellow physiologists, for example, that the law could be invoked as an argument against vitalism. In popular scientific lectures they emphasized the law’s connection to Germany’s industrialization and its ethical value. Thus they partly shaped the reception of the law. But of course, its reception could not be completely controlled. People have interests of their own and they often appropriated the law in unexpected ways. This thesis’ stress on meaning as use, and its use of concepts like interests and appropriation may make it appear as if energy was whatever people wanted it to be. This is a misunderstanding. Obviously, within a specific community, there were limits to what one could reasonably make of energy. But these were social as much as intellectual constraints. More importantly, by the turn of the century, the law of energy conservation had acquired a certain ubiquity in German science and culture. The continuous talk about energy had a persuasive power of its own. Centerum censeo, Du Bois-Reymond said. Ultimately, the law imposed itself on everybody, even those who tried to ignore it.

A kinetic equation with kinetic entropy functions for scalar conservation laws

NASA Technical Reports Server (NTRS)

Perthame, Benoit; Tadmor, Eitan

1990-01-01

A nonlinear kinetic equation is constructed and proved to be well-adapted to describe general multidimensional scalar conservation laws. In particular, it is proved to be well-posed uniformly in epsilon - the microscopic scale. It is also shown that the proposed kinetic equation is equipped with a family of kinetic entropy functions - analogous to Boltzmann's microscopic H-function, such that they recover Krushkov-type entropy inequality on the macroscopic scale. Finally, it is proved by both - BV compactness arguments in the one-dimensional case, that the local density of kinetic particles admits a continuum limit, as it converges strongly with epsilon below 0 to the unique entropy solution of the corresponding conservation law.

Science communication and vernal pool conservation: a study of local decision maker attitudes in a knowledge-action system.

PubMed

McGreavy, Bridie; Webler, Thomas; Calhoun, Aram J K

2012-03-01

In this study, we describe local decision maker attitudes towards vernal pools to inform science communication and enhance vernal pool conservation efforts. We conducted interviews with town planning board and conservation commission members (n = 9) from two towns in the State of Maine in the northeastern United States. We then mailed a questionnaire to a stratified random sample of planning board members in August and September 2007 with a response rate of 48.4% (n = 320). The majority of survey respondents favored the protection and conservation of vernal pools in their towns. Decision makers were familiar with the term "vernal pool" and demonstrated positive attitudes to vernal pools in general. General appreciation and willingness to conserve vernal pools predicted support for the 2006 revisions to the Natural Resource Protection Act regulating Significant Vernal Pools. However, 48% of respondents were unaware of this law and neither prior knowledge of the law nor workshop attendance predicted support for the vernal pool law. Further, concerns about private property rights and development restrictions predicted disagreement with the vernal pool law. We conclude that science communication must rely on specific frames of reference, be sensitive to cultural values, and occur in an iterative system to link knowledge and action in support of vernal pool conservation. Copyright © 2011 Elsevier Ltd. All rights reserved.

Conservation laws of wave action and potential enstrophy for Rossby waves in a stratified atmosphere

NASA Technical Reports Server (NTRS)

Straus, D. M.

1983-01-01

The evolution of wave energy, enstrophy, and wave motion for atmospheric Rossby waves in a variable mean flow are discussed from a theoretical and pedagogic standpoint. In the absence of mean flow gradients, the wave energy density satisfies a local conservation law, with the appropriate flow velocity being the group velocity. In the presence of mean flow variations, wave energy is not conserved, but wave action is, provided the mean flow is independent of longitude. Wave enstrophy is conserved for arbitrary variations of the mean flow. Connections with Eiiassen-Palm flux are also discussed.

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.

2004-01-01

A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. A discussion on the Discontinuous Spectral Difference (SD) Method, locations of the unknowns and flux points and numerical results are also presented.

Conservation laws of wave action and potential enstrophy for Rossby waves in a stratified atmosphere

NASA Technical Reports Server (NTRS)

Straus, D. M.

1983-01-01

The evolution of wave energy, enstrophy, and wave motion for atmospheric Rossby waves in a variable mean flow are discussed from a theoretical and pedagogic standpoint. In the absence of mean flow gradients, the wave energy density satisfies a local conservation law, with the appropriate flow velocity being the group velocity. In the presence of mean flow variations, wave energy is not conserved, but wave action is, provided the mean flow is independent of longitude. Wave enstrophy is conserved for arbitrary variations of the mean flow. Connections with Eliassen-Palm flux are also discussed.

Conservation form of the equations of fluid dynamics in general nonsteady coordinates

NASA Astrophysics Data System (ADS)

Zhang, H.; Camarero, R.; Kahawita, R.

1985-11-01

Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations.

76 FR 70749 - Information Collection Request Sent to the Office of Management and Budget (OMB) for Approval...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-11-15

... the ICR online at http://www.reginfo.gov . Follow the instructions to review Department of the... programs associated with the North American Wetlands Conservation Act (NAWCA), Public Law 101-233, and the Neotropical Migratory Bird Conservation Act (NMBCA), Public Law 106-247. Currently, information that we...

An Historical Note on the Conservation of Mass

ERIC Educational Resources Information Center

Whitaker, Robert D.

1975-01-01

Discusses the fact that although most historians of science attribute the formulation of the law of conservation of matter in chemical reactions to Antoine Lavoisier at the end of the eighteenth century, several earlier researchers had already assumed this law in their work. These researchers include Joseph Black, Henry Cavendish, M. V. Lomonosov,…

Conservation laws in the quantum Hall Liouvillian theory and its generalizations

NASA Astrophysics Data System (ADS)

Moore, Joel

2003-03-01

It is known that the localization length scaling of noninteracting electrons near the quantum Hall plateau transition can be described in a theory of the bosonic density operators, with no reference to the underlying fermions. The resulting ``Liouvillian'' theory has a U(1|1) global supersymmetry as well as a hierarchy of geometric conservation laws related to the noncommutative geometry of the lowest Landau level (LLL). Mean-field and large-N generalizations of the Liouvillian are shown to describe problems of noninteracting bosons (without any obvious pathologies, contrary to recent claims) that enlarge the U(1|1) supersymmetry to U(1|1) × SO(N) or U(1|1) × SU(N). The N>1 generalizations preserve the first two of the hierarchy of geometric conservation laws, leading to logarithmic corrections at order 1/N to the diffusive large-N limit, but do not preserve the remaining conservation laws. The emergence of nontrivial scaling at the plateau transition, in the Liouvillian approach, is shown to depend sensitively on the unusual geometry of Landau levels.

Problem Solving of Newton's Second Law through a System of Total Mass Motion

ERIC Educational Resources Information Center

Abdullah, Helmi

2014-01-01

Nowadays, many researchers discovered various effective strategies in teaching physics, from traditional to modern strategy. However, research on physics problem solving is still inadequate. Physics problem is an integral part of physics learning and requires strategy to solve it. Besides that, problem solving is the best way to convey principle,…

Noether symmetries and stability of ideal gas solutions in Galileon cosmology

NASA Astrophysics Data System (ADS)

Dimakis, N.; Giacomini, Alex; Jamal, Sameerah; Leon, Genly; Paliathanasis, Andronikos

2017-03-01

A class of generalized Galileon cosmological models, which can be described by a pointlike Lagrangian, is considered in order to utilize Noether's theorem to determine conservation laws for the field equations. In the Friedmann-Lemaître-Robertson-Walker universe, the existence of a nontrivial conservation law indicates the integrability of the field equations. Because of the complexity of the latter, we apply the differential invariants approach in order to construct special power-law solutions and study their stability.

The effectiveness of problem-based learning on teaching the first law of thermodynamics

NASA Astrophysics Data System (ADS)

Tatar, Erdal; Oktay, Münir

2011-11-01

Background: Problem-based learning (PBL) is a teaching approach working in cooperation with self-learning and involving research to solve real problems. The first law of thermodynamics states that energy can neither be created nor destroyed, but that energy is conserved. Students had difficulty learning or misconceptions about this law. This study is related to the teaching of the first law of thermodynamics within a PBL environment. Purpose: This study examined the effectiveness of PBL on candidate science teachers' understanding of the first law of thermodynamics and their science process skills. This study also examined their opinions about PBL. Sample: The sample consists of 48 third-grade university students from the Department of Science Education in one of the public universities in Turkey. Design and methods: A one-group pretest-posttest experimental design was used. Data collection tools included the Achievement Test, Science Process Skill Test, Constructivist Learning Environment Survey and an interview with open-ended questions. Paired samples t-test was conducted to examine differences in pre/post tests. Results: The PBL approach has a positive effect on the students' learning abilities and science process skills. The students thought that the PBL environment supports effective and permanent learning, and self-learning planning skills. On the other hand, some students think that the limited time and unfamiliarity of the approach impede learning. Conclusions: The PBL is an active learning approach supporting students in the process of learning. But there are still many practical disadvantages that could reduce the effectiveness of the PBL. To prevent the alienation of the students, simple PBL activities should be applied from the primary school level. In order to overcome time limitations, education researchers should examine short-term and effective PBL activities.

Conservation laws with coinciding smooth solutions but different conserved variables

NASA Astrophysics Data System (ADS)

Colombo, Rinaldo M.; Guerra, Graziano

2018-04-01

Consider two hyperbolic systems of conservation laws in one space dimension with the same eigenvalues and (right) eigenvectors. We prove that solutions to Cauchy problems with the same initial data differ at third order in the total variation of the initial datum. As a first application, relying on the classical Glimm-Lax result (Glimm and Lax in Decay of solutions of systems of nonlinear hyperbolic conservation laws. Memoirs of the American Mathematical Society, No. 101. American Mathematical Society, Providence, 1970), we obtain estimates improving those in Saint-Raymond (Arch Ration Mech Anal 155(3):171-199, 2000) on the distance between solutions to the isentropic and non-isentropic inviscid compressible Euler equations, under general equations of state. Further applications are to the general scalar case, where rather precise estimates are obtained, to an approximation by Di Perna of the p-system and to a traffic model.

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Bart, Timothy J.; Kutler, Paul (Technical Monitor)

1998-01-01

Chapter 1 briefly reviews several related topics associated with the symmetrization of systems of conservation laws and quasi-conservation laws: (1) Basic Entropy Symmetrization Theory; (2) Symmetrization and eigenvector scaling; (3) Symmetrization of the compressible Navier-Stokes equations; and (4) Symmetrization of the quasi-conservative form of the magnetohydrodynamic (MHD) equations. Chapter 2 describes one of the best known tools employed in the study of differential equations, the maximum principle: any function f(x) which satisfies the inequality f(double prime)>0 on the interval [a,b] attains its maximum value at one of the endpoints on the interval. Chapter three examines the upwind finite volume schemes for scalar and system conservation laws. The basic tasks in the upwind finite volume approach have already been presented: reconstruction, flux evaluation, and evolution. By far, the most difficult task in this process is the reconstruction step.

Second- and third-order upwind difference schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Yang, J. Y.

1984-01-01

Second- and third-order two time-level five-point explicit upwind-difference schemes are described for the numerical solution of hyperbolic systems of conservation laws and applied to the Euler equations of inviscid gas dynamics. Nonliner smoothing techniques are used to make the schemes total variation diminishing. In the method both hyperbolicity and conservation properties of the hyperbolic conservation laws are combined in a very natural way by introducing a normalized Jacobian matrix of the hyperbolic system. Entropy satisfying shock transition operators which are consistent with the upwind differencing are locally introduced when transonic shock transition is detected. Schemes thus constructed are suitable for shockcapturing calculations. The stability and the global order of accuracy of the proposed schemes are examined. Numerical experiments for the inviscid Burgers equation and the compressible Euler equations in one and two space dimensions involving various situations of aerodynamic interest are included and compared.

50 CFR 665.2 - Relation to other laws.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 50 Wildlife and Fisheries 9 2010-10-01 2010-10-01 false Relation to other laws. 665.2 Section 665.2 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... other laws. NMFS recognizes that any state law pertaining to vessels registered under the laws of that...

50 CFR 660.2 - Relation to other laws.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 50 Wildlife and Fisheries 9 2010-10-01 2010-10-01 false Relation to other laws. 660.2 Section 660.2 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... other laws. (a) NMFS recognizes that any state law pertaining to vessels registered under the laws of...

Lie symmetries and conservation laws for the time fractional Derrida-Lebowitz-Speer-Spohn equation

NASA Astrophysics Data System (ADS)

Rui, Wenjuan; Zhang, Xiangzhi

2016-05-01

This paper investigates the invariance properties of the time fractional Derrida-Lebowitz-Speer-Spohn (FDLSS) equation with Riemann-Liouville derivative. By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the FDLSS equation. In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.

Free boundary problems in shock reflection/diffraction and related transonic flow problems

PubMed Central

Chen, Gui-Qiang; Feldman, Mikhail

2015-01-01

Shock waves are steep wavefronts that are fundamental in nature, especially in high-speed fluid flows. When a shock hits an obstacle, or a flying body meets a shock, shock reflection/diffraction phenomena occur. In this paper, we show how several long-standing shock reflection/diffraction problems can be formulated as free boundary problems, discuss some recent progress in developing mathematical ideas, approaches and techniques for solving these problems, and present some further open problems in this direction. In particular, these shock problems include von Neumann's problem for shock reflection–diffraction by two-dimensional wedges with concave corner, Lighthill's problem for shock diffraction by two-dimensional wedges with convex corner, and Prandtl-Meyer's problem for supersonic flow impinging onto solid wedges, which are also fundamental in the mathematical theory of multidimensional conservation laws. PMID:26261363

Exact Solutions for Stokes' Flow of a Non-Newtonian Nanofluid Model: A Lie Similarity Approach

NASA Astrophysics Data System (ADS)

Aziz, Taha; Aziz, A.; Khalique, C. M.

2016-07-01

The fully developed time-dependent flow of an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid is investigated. The classical Stokes model is considered in which the flow is generated due to the motion of the plate in its own plane with an impulsive velocity. The Lie symmetry approach is utilised to convert the governing nonlinear partial differential equation into different linear and nonlinear ordinary differential equations. The reduced ordinary differential equations are then solved by using the compatibility and generalised group method. Exact solutions for the model equation are deduced in the form of closed-form exponential functions which are not available in the literature before. In addition, we also derived the conservation laws associated with the governing model. Finally, the physical features of the pertinent parameters are discussed in detail through several graphs.

An iterative Riemann solver for systems of hyperbolic conservation law s, with application to hyperelastic solid mechanics

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

Miller, Gregory H.

2003-08-06

In this paper we present a general iterative method for the solution of the Riemann problem for hyperbolic systems of PDEs. The method is based on the multiple shooting method for free boundary value problems. We demonstrate the method by solving one-dimensional Riemann problems for hyperelastic solid mechanics. Even for conditions representative of routine laboratory conditions and military ballistics, dramatic differences are seen between the exact and approximate Riemann solution. The greatest discrepancy arises from misallocation of energy between compressional and thermal modes by the approximate solver, resulting in nonphysical entropy and temperature estimates. Several pathological conditions arise in commonmore » practice, and modifications to the method to handle these are discussed. These include points where genuine nonlinearity is lost, degeneracies, and eigenvector deficiencies that occur upon melting.« less

MULTISHOCKED,THREE-DIMENSIONAL SUPERSONIC FLOWFIELDS WITH REAL GAS EFFECTS

NASA Technical Reports Server (NTRS)

Kutler, P.

1994-01-01

This program determines the supersonic flowfield surrounding three-dimensional wing-body configurations of a delta wing. It was designed to provide the numerical computation of three dimensional inviscid, flowfields of either perfect or real gases about supersonic or hypersonic airplanes. The governing equations in conservation law form are solved by a finite difference method using a second order noncentered algorithm between the body and the outermost shock wave, which is treated as a sharp discontinuity. Secondary shocks which form between these boundaries are captured automatically. The flowfield between the body and outermost shock is treated in a shock capturing fashion and therefore allows for the correct formation of secondary internal shocks . The program operates in batch mode, is in CDC update format, has been implemented on the CDC 7600, and requires more than 140K (octal) word locations.

Exponential Boundary Observers for Pressurized Water Pipe

NASA Astrophysics Data System (ADS)

Hermine Som, Idellette Judith; Cocquempot, Vincent; Aitouche, Abdel

2015-11-01

This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.

7 CFR 1470.3 - Definitions.

Code of Federal Regulations, 2014 CFR

2014-01-01

..., tribal, or territorial law for the express purpose of developing and carrying out a local soil and water...,” “soil conservation district,” “soil and water conservation district,” “resource conservation district... practices and conservation management systems. It contains detailed information on the conservation of soil...

7 CFR 1470.3 - Definitions.

Code of Federal Regulations, 2013 CFR

2013-01-01

..., tribal, or territorial law for the express purpose of developing and carrying out a local soil and water...,” “soil conservation district,” “soil and water conservation district,” “resource conservation district... practices and conservation management systems. It contains detailed information on the conservation of soil...

7 CFR 1470.3 - Definitions.

Code of Federal Regulations, 2012 CFR

2012-01-01

..., tribal, or territorial law for the express purpose of developing and carrying out a local soil and water...,” “soil conservation district,” “soil and water conservation district,” “resource conservation district... practices and conservation management systems. It contains detailed information on the conservation of soil...

Optimization-based mesh correction with volume and convexity constraints

DOE PAGES

D'Elia, Marta; Ridzal, Denis; Peterson, Kara J.; ...

2016-02-24

In this study, we consider the problem of finding a mesh such that 1) it is the closest, with respect to a suitable metric, to a given source mesh having the same connectivity, and 2) the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh. This volume correction problem arises in important simulation contexts, such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi-Lagrangian transport schemes. In this paper we formulate volume correction as a constrained optimizationmore » problem in which the distance to the source mesh defines an optimization objective, while the prescribed cell volumes, mesh validity and/or cell convexity specify the constraints. We solve this problem numerically using a sequential quadratic programming (SQP) method whose performance scales with the mesh size. To achieve scalable performance we develop a specialized multigrid-based preconditioner for optimality systems that arise in the application of the SQP method to the volume correction problem. Numerical examples illustrate the importance of volume correction, and showcase the accuracy, robustness and scalability of our approach.« less

The Development of Knowledge and Awareness of Environmental Laws and Participation in Environmental Conservation of Probationers

ERIC Educational Resources Information Center

Wanlu, Somchai; Singseewo, Adisak; Suksringarm, Paitool

2015-01-01

This research aimed to develop knowledge and awareness about environmental laws and participation in environmental conservation of probationers in MahaSarakham Province, Thailand. This study was divided into 3 stages. Stage 1: was the development of a training manual and construction of training evaluation instruments which consisted of a…

A (2+1)-dimensional Korteweg-de Vries type equation in water waves: Lie symmetry analysis; multiple exp-function method; conservation laws

NASA Astrophysics Data System (ADS)

Adem, Abdullahi Rashid

2016-05-01

We consider a (2+1)-dimensional Korteweg-de Vries type equation which models the shallow-water waves, surface and internal waves. In the analysis, we use the Lie symmetry method and the multiple exp-function method. Furthermore, conservation laws are computed using the multiplier method.

Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham-Broer-Kaup-Like Equations

NASA Astrophysics Data System (ADS)

Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian

2017-03-01

In this article, a generalised Whitham-Broer-Kaup-Like (WBKL) equations is investigated, which can describe the bidirectional propagation of long waves in shallow water. The equations can be reduced to the dispersive long wave equations, variant Boussinesq equations, Whitham-Broer-Kaup-Like equations, etc. The Lie symmetry analysis method is used to consider the vector fields and optimal system of the equations. The similarity reductions are given on the basic of the optimal system. Furthermore, the power series solutions are derived by using the power series theory. Finally, based on a new theorem of conservation laws, the conservation laws associated with symmetries of this equations are constructed with a detailed derivation.

Upper-Division Students' Difficulties with Ampere's Law

ERIC Educational Resources Information Center

Wallace, Colin S.; Chasteen, Stephanie V.

2010-01-01

This study presents and interprets some conceptual difficulties junior-level physics students experience with Ampere's law. We present both quantitative data, based on students' written responses to conceptual questions, and qualitative data, based on interviews of students solving Ampere's law problems. We find that some students struggle to…

Shock induced phase transitions and current generation in ferroelectric ceramics

NASA Astrophysics Data System (ADS)

Agrawal, Vinamra; Bhattacharya, Kaushik

2017-06-01

Ferroelectric materials are used as ferroelectric generators to obtain pulsed power by subjecting them to a shock loading. The impact induces a phase transition and at high impact speeds, dielectric breakdown. Depending on the loading conditions and the electromechanical boundary conditions, the current or voltage profiles obtained vary. We explore the phenomenon of large deformation dynamic behavior and the associated electro-thermo-mechanical coupling of ferroelectric materials in adiabatic environments. Using conservation laws, Maxwell's equations and second law of thermodynamics, we obtain a set of governing equations for the material and the driving force acting on the propagating phase boundary. We also account for the possibility of surface charges on the phase boundary in case of dielectric breakdown which introduces contribution of curvature of the phase boundary in the equations. Next, the governing equations are used to solve a plate impact problem. The Helmholtz energy of the material is chosen be a combination of piecewise quadratic potential in polarization and thermo-elastic material capable of undergoing phase transformation. We obtain current profiles for short circuit boundary conditions along with strain, particle velocity and temperature maps. US AFOSR through Center of Excellence in High Rate Deformation of Heterogeneous Materials FA 9550-12-1-0091.

Dynamic response of a collidant impacting a low pressure airbag

NASA Astrophysics Data System (ADS)

Dreher, Peter A.

There are many uses of low pressure airbags, both military and commercial. Many of these applications have been hampered by inadequate and inaccurate modeling tools. This dissertation contains the derivation of a four degree-of-freedom system of differential equations from physical laws of mass and energy conservation, force equilibrium, and the Ideal Gas Law. Kinematic equations were derived to model a cylindrical airbag as a single control volume impacted by a parallelepiped collidant. An efficient numerical procedure was devised to solve the simplified system of equations in a manner amenable to discovering design trends. The largest public airbag experiment, both in scale and scope, was designed and built to collect data on low-pressure airbag responses, otherwise unavailable in the literature. The experimental results were compared to computational simulations to validate the simplified numerical model. Experimental response trends are presented that will aid airbag designers. The two objectives of using a low pressure airbag to demonstrate the feasibility to (1) accelerate a munition to 15 feet per second velocity from a bomb bay, and (2) decelerate humans hitting trucks below the human tolerance level of 50 G's, were both met.

Multiphase wavetrains, singular wave interactions and the emergence of the Korteweg–de Vries equation

PubMed Central

Bridges, Thomas J.

2016-01-01

Multiphase wavetrains are multiperiodic travelling waves with a set of distinct wavenumbers and distinct frequencies. In conservative systems, such families are associated with the conservation of wave action or other conservation law. At generic points (where the Jacobian of the wave action flux is non-degenerate), modulation of the wavetrain leads to the dispersionless multiphase conservation of wave action. The main result of this paper is that modulation of the multiphase wavetrain, when the Jacobian of the wave action flux vector is singular, morphs the vector-valued conservation law into the scalar Korteweg–de Vries (KdV) equation. The coefficients in the emergent KdV equation have a geometrical interpretation in terms of projection of the vector components of the conservation law. The theory herein is restricted to two phases to simplify presentation, with extensions to any finite dimension discussed in the concluding remarks. Two applications of the theory are presented: a coupled nonlinear Schrödinger equation and two-layer shallow-water hydrodynamics with a free surface. Both have two-phase solutions where criticality and the properties of the emergent KdV equation can be determined analytically. PMID:28119546

Monitoring Affect States during Effortful Problem Solving Activities

ERIC Educational Resources Information Center

D'Mello, Sidney K.; Lehman, Blair; Person, Natalie

2010-01-01

We explored the affective states that students experienced during effortful problem solving activities. We conducted a study where 41 students solved difficult analytical reasoning problems from the Law School Admission Test. Students viewed videos of their faces and screen captures and judged their emotions from a set of 14 states (basic…

7 CFR 1465.3 - Definitions.

Code of Federal Regulations, 2011 CFR

2011-01-01

... law for the express purpose of developing and carrying out a local soil and water conservation program. Such district or unit of government may be referred to as a “conservation district,” “soil conservation district,” “soil and water conservation district,” “resource conservation district,” “natural resource...

Different realizations of Cooper-Frye sampling with conservation laws

NASA Astrophysics Data System (ADS)

Schwarz, C.; Oliinychenko, D.; Pang, L.-G.; Ryu, S.; Petersen, H.

2018-01-01

Approaches based on viscous hydrodynamics for the hot and dense stage and hadronic transport for the final dilute rescattering stage are successfully applied to the dynamic description of heavy ion reactions at high beam energies. One crucial step in such hybrid approaches is the so-called particlization, which is the transition between the hydrodynamic description and the microscopic degrees of freedom. For this purpose, individual particles are sampled on the Cooper-Frye hypersurface. In this work, four different realizations of the sampling algorithms are compared, with three of them incorporating the global conservation laws of quantum numbers in each event. The algorithms are compared within two types of scenarios: a simple ‘box’ hypersurface consisting of only one static cell and a typical particlization hypersurface for Au+Au collisions at \\sqrt{{s}{NN}}=200 {GeV}. For all algorithms the mean multiplicities (or particle spectra) remain unaffected by global conservation laws in the case of large volumes. In contrast, the fluctuations of the particle numbers are affected considerably. The fluctuations of the newly developed SPREW algorithm based on the exponential weight, and the recently suggested SER algorithm based on ensemble rejection, are smaller than those without conservation laws and agree with the expectation from the canonical ensemble. The previously applied mode sampling algorithm produces dramatically larger fluctuations than expected in the corresponding microcanonical ensemble, and therefore should be avoided in fluctuation studies. This study might be of interest for the investigation of particle fluctuations and correlations, e.g. the suggested signatures for a phase transition or a critical endpoint, in hybrid approaches that are affected by global conservation laws.

The First Law of Elasticity

ERIC Educational Resources Information Center

Girill, T. R.

1972-01-01

The Boyle-Mariotte gas law was formulated in terms of pneumatic springs," subsumed by Hooke under his own stress-strain relation, and generally regarded as a law of elasticity. The subsequent development of Boyle's principle and elasticity provide thought-provoking test cases for Kuhn's notations of paradigm and puzzle solving in physics.…

A Second Law Based Unstructured Finite Volume Procedure for Generalized Flow Simulation

NASA Technical Reports Server (NTRS)

Majumdar, Alok

1998-01-01

An unstructured finite volume procedure has been developed for steady and transient thermo-fluid dynamic analysis of fluid systems and components. The procedure is applicable for a flow network consisting of pipes and various fittings where flow is assumed to be one dimensional. It can also be used to simulate flow in a component by modeling a multi-dimensional flow using the same numerical scheme. The flow domain is discretized into a number of interconnected control volumes located arbitrarily in space. The conservation equations for each control volume account for the transport of mass, momentum and entropy from the neighboring control volumes. In addition, they also include the sources of each conserved variable and time dependent terms. The source term of entropy equation contains entropy generation due to heat transfer and fluid friction. Thermodynamic properties are computed from the equation of state of a real fluid. The system of equations is solved by a hybrid numerical method which is a combination of simultaneous Newton-Raphson and successive substitution schemes. The paper also describes the application and verification of the procedure by comparing its predictions with the analytical and numerical solution of several benchmark problems.

Time-dependent spectral renormalization method

NASA Astrophysics Data System (ADS)

Cole, Justin T.; Musslimani, Ziad H.

2017-11-01

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

A Practical Example Aiding Understanding Momentum in 1D: The Water Gun Experiment

ERIC Educational Resources Information Center

MacLeod, Katarin

2007-01-01

The law of conservation of momentum is one that students often have difficulties understanding. This experiment allows students to use childhood toys to examine and calculate the muzzle velocity of their favourite water gun by using an air track, a spark timer or data logger and the law of conservation of momentum in a one-dimensional case, a…

Helicity and other conservation laws in perfect fluid motion

NASA Astrophysics Data System (ADS)

Serre, Denis

2018-03-01

In this review paper, we discuss helicity from a geometrical point of view and see how it applies to the motion of a perfect fluid. We discuss its relation with the Hamiltonian structure, and then its extension to arbitrary space dimensions. We also comment about the existence of additional conservation laws for the Euler equation, and its unlikely integrability in Liouville's sense.

Iniciativa de ley federal del patrimonio cultural de la nacion (Draft of Federal Law for the Cultural Heritage of the Nation).

ERIC Educational Resources Information Center

Mexico.

This document is an English-language abstract (approximately 1,500 words) of the draft of a law for the preservation of Mexican national heritage, particularly for the protection, conservation, and recuperation of cultural objects. The document consists of twelve chapters and six articles. Chapter 1 declares the protection, conservation,…

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1986-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1989-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Effects of zonal flows on correlation between energy balance and energy conservation associated with nonlinear nonviscous atmospheric dynamics in a thin rotating spherical shell

NASA Astrophysics Data System (ADS)

Ibragimov, Ranis N.

2018-03-01

The nonlinear Euler equations are used to model two-dimensional atmosphere dynamics in a thin rotating spherical shell. The energy balance is deduced on the basis of two classes of functorially independent invariant solutions associated with the model. It it shown that the energy balance is exactly the conservation law for one class of the solutions whereas the second class of invariant solutions provides and asymptotic convergence of the energy balance to the conservation law.

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.

2013-01-01

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schroedinger equations

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

Zhao Dun; Center for Interdisciplinary Studies, Lanzhou University, Lanzhou 730000; Zhang Yujuan

2011-04-15

By constructing nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schroedinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose-Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases of a new integrable model of nonlocal nonautonomous NLS equations. Based on the Lax pairs, the Darboux transformation and conservation laws are explored. It is shown that the local external potentials would break down the classical infinite number of conservation laws. The result indicates that the integrability of the nonautonomous NLSmore » systems may be nontrivial in comparison to the conventional concept of integrability in the canonical case.« less

Lectures series in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Thompson, Kevin W.

1987-01-01

The lecture notes cover the basic principles of computational fluid dynamics (CFD). They are oriented more toward practical applications than theory, and are intended to serve as a unified source for basic material in the CFD field as well as an introduction to more specialized topics in artificial viscosity and boundary conditions. Each chapter in the test is associated with a videotaped lecture. The basic properties of conservation laws, wave equations, and shock waves are described. The duality of the conservation law and wave representations is investigated, and shock waves are examined in some detail. Finite difference techniques are introduced for the solution of wave equations and conservation laws. Stability analysis for finite difference approximations are presented. A consistent description of artificial viscosity methods are provided. Finally, the problem of nonreflecting boundary conditions are treated.

78 FR 41959 - Notice of Permit Modification Received Under the Antarctic Conservation Act of 1978

Federal Register 2010, 2011, 2012, 2013, 2014

2013-07-12

... Conservation Act of 1978 AGENCY: National Science Foundation. ACTION: Notice of permit modification under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National Science Foundation (NSF) is... Conservation Act of 1978. NSF has published regulations under the Antarctic Conservation Act at Title 45 Part...

Metric Theories of Gravity: Perturbations and Conservation Laws

NASA Astrophysics Data System (ADS)

Petrov, Alexander N.; Kopeikin, Sergei M.; Lompay, Robert R.; Tekin, Bayram

2017-04-01

By focusing on the mostly used variational methods, this monograph aspires to give a unified description and comparison of various ways of constructing conserved quantities for perturbations and to study symmetries in general relativity and modified theories of gravity. The main emphasis lies on the field-theoretical covariant formulation of perturbations, the canonical Noether approach and the Belinfante procedure of symmetrisation. The general formalism is applied to build the gauge-invariant cosmological perturbation theory, conserved currents and superpotentials to describe physically important solutions of gravity theories. Meticulous attention is given to the construction of conserved quantities in asymptotically-flat spacetimes as well as in asymptotically constant curvature spacetimes such as the Anti-de Sitter space. Significant part of the book can be used in graduate courses on conservation laws in general relativity.

76 FR 30186 - Proposed Information Collection; Migratory Birds and Wetlands Conservation Grant Programs

Federal Register 2010, 2011, 2012, 2013, 2014

2011-05-24

... 7C] Proposed Information Collection; Migratory Birds and Wetlands Conservation Grant Programs AGENCY...). SUPPLEMENTARY INFORMATION: I. Abstract The Division of Bird Habitat Conservation administers grant programs... Migratory Bird Conservation Act (NMBCA), Public Law 106-247. Currently, information that we collect for...

Convergence of generalized MUSCL schemes

NASA Technical Reports Server (NTRS)

Osher, S.

1984-01-01

Semi-discrete generalizations of the second order extension of Godunov's scheme, known as the MUSCL scheme, are constructed, starting with any three point E scheme. They are used to approximate scalar conservation laws in one space dimension. For convex conservation laws, each member of a wide class is proven to be a convergent approximation to the correct physical solution. Comparison with another class of high resolution convergent schemes is made.

High-resolution schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Harten, A.

1982-01-01

A class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws is presented. These highly nonlinear schemes are obtained by applying a nonoscillatory first order accurae scheme to an appropriately modified flux function. The so derived second order accurate schemes achieve high resolution while preserving the robustness of the original nonoscillatory first order accurate scheme.

LETTER TO THE EDITOR: Bicomplexes and conservation laws in non-Abelian Toda models

NASA Astrophysics Data System (ADS)

Gueuvoghlanian, E. P.

2001-08-01

A bicomplex structure is associated with the Leznov-Saveliev equation of integrable models. The linear problem associated with the zero-curvature condition is derived in terms of the bicomplex linear equation. The explicit example of a non-Abelian conformal affine Toda model is discussed in detail and its conservation laws are derived from the zero-curvature representation of its equation of motion.

Some observations on boundary conditions for numerical conservation laws

NASA Technical Reports Server (NTRS)

Kamowitz, David

1988-01-01

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

Vehicle energy conservation indicating device and process for use

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

Crump, J.M.

A vehicle energy conservation indicating device comprises an integrated instrument cluster functioning basically as a nomographic computing mechanism. The odometer distance traveled indicator computing mechanism is linked with the fuel indicating gauge mechanism such that a three variable equation computing mechanism is obtained. The three variables are distance traveled, quantity of fuel consumed and distance traveled per unit of fuel consumed. Energy conservation is achieved by operating the vehicle under such performance conditions as to produce the highest possible value for distance traveled per unit of fuel consumed. The instrument panel cluster brings the operator's attention to focus upon andmore » continuously stimulated to conserving energy. Furthermore, the vehicle energy conservation indicating device can be adapted for recording these performance variables on tape type print out. The speedometer advises the vehicle operator when he is obeying or breaking the speed laws which are enforced and monitored by the police with specific punishment prescribed for violations of the law. At this time there is no comparable procedure for enforcing vehicle energy conservation. Thus, this direct read out of distance traveled per unit of energy will moderate the operation in an analogous manner similar to subliminal advertising. This device becomes the focal point of the instrument panel along with the speedometer, thereby providing constant motivation to obey both the speed and energy conservation laws.« less

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

NASA Astrophysics Data System (ADS)

de Almeida, Valmor F.

2017-07-01

A phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equation and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.

Numerical Modeling of Flow Distribution in Micro-Fluidics Systems

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Cole, Helen; Chen, C. P.

2005-01-01

This paper describes an application of a general purpose computer program, GFSSP (Generalized Fluid System Simulation Program) for calculating flow distribution in a network of micro-channels. GFSSP employs a finite volume formulation of mass and momentum conservation equations in a network consisting of nodes and branches. Mass conservation equation is solved for pressures at the nodes while the momentum conservation equation is solved at the branches to calculate flowrate. The system of equations describing the fluid network is solved by a numerical method that is a combination of the Newton-Raphson and successive substitution methods. The numerical results have been compared with test data and detailed CFD (computational Fluid Dynamics) calculations. The agreement between test data and predictions is satisfactory. The discrepancies between the predictions and test data can be attributed to the frictional correlation which does not include the effect of surface tension or electro-kinetic effect.

Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations

NASA Technical Reports Server (NTRS)

Osher, Stanley; Sethian, James A.

1987-01-01

New numerical algorithms are devised (PSC algorithms) for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand-sides, by using techniques from the hyperbolic conservation laws. Non-oscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be used also for more general Hamilton-Jacobi-type problems. The algorithms are demonstrated by computing the solution to a variety of surface motion problems.

Quasi-local gravitational angular momentum and centre of mass from generalised Witten equations

NASA Astrophysics Data System (ADS)

Wieland, Wolfgang

2017-03-01

Witten's proof for the positivity of the ADM mass gives a definition of energy in terms of three-surface spinors. In this paper, we give a generalisation for the remaining six Poincaré charges at spacelike infinity, which are the angular momentum and centre of mass. The construction improves on certain three-surface spinor equations introduced by Shaw. We solve these equations asymptotically obtaining the ten Poincaré charges as integrals over the Nester-Witten two-form. We point out that the defining differential equations can be extended to three-surfaces of arbitrary signature and we study them on the entire boundary of a compact four-dimensional region of spacetime. The resulting quasi-local expressions for energy and angular momentum are integrals over a two-dimensional cross-section of the boundary. For any two consecutive such cross-sections, conservation laws are derived that determine the influx (outflow) of matter and gravitational radiation.

Numerical Investigation of a Model Scramjet Combustor Using DDES

NASA Astrophysics Data System (ADS)

Shin, Junsu; Sung, Hong-Gye

2017-04-01

Non-reactive flows moving through a model scramjet were investigated using a delayed detached eddy simulation (DDES), which is a hybrid scheme combining Reynolds averaged Navier-Stokes scheme and a large eddy simulation. The three dimensional Navier-Stokes equations were solved numerically on a structural grid using finite volume methods. An in-house was developed. This code used a monotonic upstream-centered scheme for conservation laws (MUSCL) with an advection upstream splitting method by pressure weight function (AUSMPW+) for space. In addition, a 4th order Runge-Kutta scheme was used with preconditioning for time integration. The geometries and boundary conditions of a scramjet combustor operated by DLR, a German aerospace center, were considered. The profiles of the lower wall pressure and axial velocity obtained from a time-averaged solution were compared with experimental results. Also, the mixing efficiency and total pressure recovery factor were provided in order to inspect the performance of the combustor.

SIAM Conference on Parallel Processing for Scientific Computing, 4th, Chicago, IL, Dec. 11-13, 1989, Proceedings

NASA Technical Reports Server (NTRS)

Dongarra, Jack (Editor); Messina, Paul (Editor); Sorensen, Danny C. (Editor); Voigt, Robert G. (Editor)

1990-01-01

Attention is given to such topics as an evaluation of block algorithm variants in LAPACK and presents a large-grain parallel sparse system solver, a multiprocessor method for the solution of the generalized Eigenvalue problem on an interval, and a parallel QR algorithm for iterative subspace methods on the CM2. A discussion of numerical methods includes the topics of asynchronous numerical solutions of PDEs on parallel computers, parallel homotopy curve tracking on a hypercube, and solving Navier-Stokes equations on the Cedar Multi-Cluster system. A section on differential equations includes a discussion of a six-color procedure for the parallel solution of elliptic systems using the finite quadtree structure, data parallel algorithms for the finite element method, and domain decomposition methods in aerodynamics. Topics dealing with massively parallel computing include hypercube vs. 2-dimensional meshes and massively parallel computation of conservation laws. Performance and tools are also discussed.

Stratification calculations in a heated cryogenic oxygen storage tank at zero gravity

NASA Technical Reports Server (NTRS)

Shuttles, J. T.; Smith, G. L.

1971-01-01

A cylindrical one-dimensional model of the Apollo cyrogenic oxygen storage tank has been developed to study the effect of stratification in the tank. Zero gravity was assumed, and only the thermally induced motions were considered. The governing equations were derived from conservation laws and solved on a digital computer. Realistic thermodynamic and transport properties were used. Calculations were made for a wide range of conditions. The results show the fluid behavior to be dependent on the quantity in the tank or equivalently the bulk fluid temperature. For high quantities (low temperatures) the tank pressure rose rapidly with heat addition, the heater temperature remained low, and significant pressure drop potentials accrued. For low quantities the tank pressure rose more slowly with heat addition and the heater temperature became high. A high degree of stratification resulted for all conditions; however, the stratified region extended appreciably into the tank only for the lowest tank quantity.

77 FR 10997 - Energy Conservation Program: Energy Conservation Standards for Distribution Transformers; Correction

Federal Register 2010, 2011, 2012, 2013, 2014

2012-02-24

... Conservation Program: Energy Conservation Standards for Distribution Transformers; Correction AGENCY: Office of... standards for distribution transformers. It was recently discovered that values in certain tables of the...,'' including distribution transformers. The Energy Policy Act of 1992 (EPACT 1992), Public Law 102-486, amended...

78 FR 28000 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978

Federal Register 2010, 2011, 2012, 2013, 2014

2013-05-13

... Conservation Act of 1978 AGENCY: National Science Foundation. ACTION: Notice of Permit Applications Received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National Science... regulated under the Antarctic Conservation Act of 1978. NSF has published regulations under the Antarctic...

77 FR 67407 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978

Federal Register 2010, 2011, 2012, 2013, 2014

2012-11-09

... Conservation Act of 1978 AGENCY: National Science Foundation. ACTION: Notice of Permit Applications Received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National Science... regulated under the Antarctic Conservation Act of 1978. NSF has published regulations under the Antarctic...

41 CFR 101-25.112 - Energy conservation policy.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 41 Public Contracts and Property Management 2 2011-07-01 2007-07-01 true Energy conservation...-General Policies § 101-25.112 Energy conservation policy. (a) Agency officials responsible for procurement..., which has been established pursuant to Public Law 94-163, Energy Policy and Conservation Act. (b) With...

41 CFR 101-25.112 - Energy conservation policy.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 41 Public Contracts and Property Management 2 2010-07-01 2010-07-01 true Energy conservation...-General Policies § 101-25.112 Energy conservation policy. (a) Agency officials responsible for procurement..., which has been established pursuant to Public Law 94-163, Energy Policy and Conservation Act. (b) With...

41 CFR 101-25.112 - Energy conservation policy.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 41 Public Contracts and Property Management 2 2012-07-01 2012-07-01 false Energy conservation...-General Policies § 101-25.112 Energy conservation policy. (a) Agency officials responsible for procurement..., which has been established pursuant to Public Law 94-163, Energy Policy and Conservation Act. (b) With...

41 CFR 101-25.112 - Energy conservation policy.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 41 Public Contracts and Property Management 2 2014-07-01 2012-07-01 true Energy conservation...-General Policies § 101-25.112 Energy conservation policy. (a) Agency officials responsible for procurement..., which has been established pursuant to Public Law 94-163, Energy Policy and Conservation Act. (b) With...

41 CFR 101-25.112 - Energy conservation policy.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 41 Public Contracts and Property Management 2 2013-07-01 2012-07-01 true Energy conservation...-General Policies § 101-25.112 Energy conservation policy. (a) Agency officials responsible for procurement..., which has been established pursuant to Public Law 94-163, Energy Policy and Conservation Act. (b) With...

Effects of introduction of new resources and fragmentation of existing resources on limiting wealth distribution in asset exchange models

NASA Astrophysics Data System (ADS)

Ali Saif, M.; Gade, Prashant M.

2009-03-01

Pareto law, which states that wealth distribution in societies has a power-law tail, has been the subject of intensive investigations in the statistical physics community. Several models have been employed to explain this behavior. However, most of the agent based models assume the conservation of number of agents and wealth. Both these assumptions are unrealistic. In this paper, we study the limiting wealth distribution when one or both of these assumptions are not valid. Given the universality of the law, we have tried to study the wealth distribution from the asset exchange models point of view. We consider models in which (a) new agents enter the market at a constant rate (b) richer agents fragment with higher probability introducing newer agents in the system (c) both fragmentation and entry of new agents is taking place. While models (a) and (c) do not conserve total wealth or number of agents, model (b) conserves total wealth. All these models lead to a power-law tail in the wealth distribution pointing to the possibility that more generalized asset exchange models could help us to explain the emergence of a power-law tail in wealth distribution.

New Developments in the Method of Space-Time Conservation Element and Solution Element-Applications to Two-Dimensional Time-Marching Problems

NASA Technical Reports Server (NTRS)

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

1994-01-01

A new numerical discretization method for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is motivated by several important physical/numerical considerations and designed to avoid several key limitations of the above traditional methods. As a result of the above considerations, a set of key principles for the design of numerical schemes was put forth in a previous report. These principles were used to construct several numerical schemes that model a 1-D time-dependent convection-diffusion equation. These schemes were then extended to solve the time-dependent Euler and Navier-Stokes equations of a perfect gas. It was shown that the above schemes compared favorably with the traditional schemes in simplicity, generality, and accuracy. In this report, the 2-D versions of the above schemes, except the Navier-Stokes solver, are constructed using the same set of design principles. Their constructions are simplified greatly by the use of a nontraditional space-time mesh. Its use results in the simplest stencil possible, i.e., a tetrahedron in a 3-D space-time with a vertex at the upper time level and other three at the lower time level. Because of the similarity in their design, each of the present 2-D solvers virtually shares with its 1-D counterpart the same fundamental characteristics. Moreover, it is shown that the present Euler solver is capable of generating highly accurate solutions for a famous 2-D shock reflection problem. Specifically, both the incident and the reflected shocks can be resolved by a single data point without the presence of numerical oscillations near the discontinuity.

50 CFR 640.3 - Relation to other laws.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 50 Wildlife and Fisheries 12 2012-10-01 2012-10-01 false Relation to other laws. 640.3 Section 640.3 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... Provisions § 640.3 Relation to other laws. (a) The relation of this part to other laws is set forth in § 600...

50 CFR 648.3 - Relation to other laws.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 50 Wildlife and Fisheries 12 2014-10-01 2014-10-01 false Relation to other laws. 648.3 Section 648.3 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... Relation to other laws. (a) The relation of this part to other laws is set forth in § 600.705. (b) Nothing...

50 CFR 648.3 - Relation to other laws.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 50 Wildlife and Fisheries 12 2012-10-01 2012-10-01 false Relation to other laws. 648.3 Section 648.3 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... Relation to other laws. (a) The relation of this part to other laws is set forth in § 600.705. (b) Nothing...

50 CFR 640.3 - Relation to other laws.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 50 Wildlife and Fisheries 8 2010-10-01 2010-10-01 false Relation to other laws. 640.3 Section 640.3 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... Provisions § 640.3 Relation to other laws. (a) The relation of this part to other laws is set forth in § 600...

50 CFR 660.403 - Relation to other laws.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 50 Wildlife and Fisheries 9 2010-10-01 2010-10-01 false Relation to other laws. 660.403 Section 660.403 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... § 660.403 Relation to other laws. (a) The relation of this part to other laws is set forth in § 600.705...

50 CFR 654.3 - Relation to other laws.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 50 Wildlife and Fisheries 8 2010-10-01 2010-10-01 false Relation to other laws. 654.3 Section 654.3 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... to other laws. (a) The relation of this part to other laws is set forth in § 600.705 of this chapter...

50 CFR 648.3 - Relation to other laws.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 50 Wildlife and Fisheries 8 2010-10-01 2010-10-01 false Relation to other laws. 648.3 Section 648.3 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... Relation to other laws. (a) The relation of this part to other laws is set forth in § 600.705. (b) Nothing...

A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

NASA Astrophysics Data System (ADS)

Bilyeu, David

This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For code development, a one-dimensional solver for the Euler equations was developed. This work is an extension of Chang's work on the fourth-order CESE method for solving a one-dimensional scalar convection equation. A generic formulation for the nth-order CESE method, where n ≥ 4, was derived. Indeed, numerical implementation of the scheme confirmed that the order of convergence was consistent with the order of the scheme. For the two- and three-dimensional solvers, SOLVCON was used as the basic framework for code implementation. A new solver kernel for the fourth-order CESE method has been developed and integrated into the framework provided by SOLVCON. The main part of SOLVCON, which deals with unstructured meshes and parallel computing, remains intact. The SOLVCON code for data transmission between computer nodes for High Performance Computing (HPC). To validate and verify the newly developed high-order CESE algorithms, several one-, two- and three-dimensional simulations where conducted. For the arbitrary order, one-dimensional, CESE solver, three sets of governing equations were selected for simulation: (i) the linear convection equation, (ii) the linear acoustic equations, (iii) the nonlinear Euler equations. All three systems of equations were used to verify the order of convergence through mesh refinement. In addition the Euler equations were used to solve the Shu-Osher and Blastwave problems. These two simulations demonstrated that the new high-order CESE methods can accurately resolve discontinuities in the flow field.For the two-dimensional, fourth-order CESE solver, the Euler equation was employed in four different test cases. The first case was used to verify the order of convergence through mesh refinement. The next three cases demonstrated the ability of the new solver to accurately resolve discontinuities in the flows. This was demonstrated through: (i) the interaction between acoustic waves and an entropy pulse, (ii) supersonic flow over a circular blunt body, (iii) supersonic flow over a guttered wedge. To validate and verify the three-dimensional, fourth-order CESE solver, two different simulations where selected. The first used the linear convection equations to demonstrate fourth-order convergence. The second used the Euler equations to simulate supersonic flow over a spherical body to demonstrate the scheme's ability to accurately resolve shocks. All test cases used are well known benchmark problems and as such, there are multiple sources available to validate the numerical results. Furthermore, the simulations showed that the high-order CESE solver was stable at a CFL number near unity.

The Self-Organization of Insight: Entropy and Power Laws in Problem Solving

ERIC Educational Resources Information Center

Stephen, Damian G.; Dixon, James A.

2008-01-01

Explaining emergent structure remains a challenge for all areas of cognitive science, and problem solving is no exception. The modern study of insight has drawn attention to the issue of emergent cognitive structure in problem solving research. We propose that the explanation of insight is beyond the scope of conventional approaches to cognitive…

On a new class of completely integrable nonlinear wave equations. I. Infinitely many conservation laws

NASA Astrophysics Data System (ADS)

Nutku, Y.

1985-06-01

We point out a class of nonlinear wave equations which admit infinitely many conserved quantities. These equations are characterized by a pair of exact one-forms. The implication that they are closed gives rise to equations, the characteristics and Riemann invariants of which are readily obtained. The construction of the conservation laws requires the solution of a linear second-order equation which can be reduced to canonical form using the Riemann invariants. The hodograph transformation results in a similar linear equation. We discuss also the symplectic structure and Bäcklund transformations associated with these equations.

Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-06-01

In this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK.

Compaction Around a Spherical Inclusion in Partially Molten Rock

NASA Astrophysics Data System (ADS)

Alisic, Laura; Rhebergen, Sander; Rudge, John F.; Katz, Richard F.; Wells, Garth N.

2015-04-01

Conservation laws that describe the behavior of partially molten mantle rock have been established for several decades, but the associated rheology remains poorly understood. Constraints on the rheology may be obtained from recently published torsion experiments involving deformation of partially molten rock around a rigid, spherical inclusion. These experiments give rise to patterns of melt segregation that exhibit the competing effects of pressure shadows around the inclusion and melt-rich bands through the medium. Such patterns provide an opportunity to infer rheological parameters through comparison with models based on the conservation laws and constitutive relations that hypothetically govern the system. To this end, we have developed software tools using the automated code generation package FEniCS to simulate finite strain, two-phase flow around a rigid, spherical inclusion in a three-dimensional configuration that mirrors the laboratory experiments. The equations for compaction and advection-diffusion of a porous medium are solved utilising newly developed matrix preconditioning techniques. Simulations indicate that the evolution of porosity and therefore of melt distribution is predominantly controlled by the non-linear porosity-weakening exponent of the shear viscosity and the poorly known bulk viscosity. In the simulations presented here, we find that the balance of pressure shadows and melt-rich bands observed in experiments only occurs for bulk-to-shear viscosity ratio of less than about five. However, the evolution of porosity in simulations with such low bulk viscosity exceeds physical bounds at unrealistically small strain due to the unchecked, exponential growth of the porosity variations. Processes that limit or balance porosity localization will have to be incorporated in the formulation of the model to produce results that are consistent with the porosity evolution in experiments.

Design and Construction of Multi-Variable Vortex-Ring Bubble Generator for Use in Interactive Exhibit

DTIC Science & Technology

2013-12-01

providing the opportunity to teach complex subjects related to stable and unstable equilibrium, stochastic systems, and conservation laws. The...bubbles through adjustment of three variables. The seal pressure, actuating pressure, and cycle time of the triggering solenoid valve each contribute to...stable and unstable equilibrium, stochastic systems, and conservation laws. The diaphragm valve designed in this thesis provides the centerpiece for

Justification of Shallow-Water Theory

NASA Astrophysics Data System (ADS)

Ostapenko, V. V.

2018-01-01

The basic conservation laws of shallow-water theory are derived from multidimensional mass and momentum integral conservation laws describing the plane-parallel flow of an ideal incompressible fluid above the horizontal bottom. This conclusion is based on the concept of hydrostatic approximation, which generalizes the concept of long-wavelength approximation and is used for justifying the applicability of the shallow-water theory in the simulation of wave flows of fluid with hydraulic bores.

Conservation laws in the quantum Hall Liouvillian theory and its generalizations

NASA Astrophysics Data System (ADS)

Moore, Joel E.

2003-06-01

It is known that the localization length scaling of noninteracting electrons near the quantum Hall plateau transition can be described in a theory of the bosonic density operators, with no reference to the underlying fermions. The resulting "Liouvillian" theory has a U(1|1) global supersymmetry as well as a hierarchy of geometric conservation laws related to the noncommutative geometry of the lowest Landau level (LLL). Approximations to the Liouvillian theory contain quite different physics from standard approximations to the underlying fermionic theory. Mean-field and large- N generalizations of the Liouvillian are shown to describe problems of noninteracting bosons that enlarge the U(1|1) supersymmetry to U(1|1)× SO( N) or U(1|1)× SU( N). These noninteracting bosonic problems are studied numerically for 2⩽ N⩽8 by Monte Carlo simulation and compared to the original N=1 Liouvillian theory. The N>1 generalizations preserve the first two of the hierarchy of geometric conservation laws, leading to logarithmic corrections at order 1/ N to the diffusive large- N limit, but do not preserve the remaining conservation laws. The emergence of nontrivial scaling at the plateau transition, in the Liouvillian approach, is shown to depend sensitively on the unusual geometry of Landau levels.

Conditions for the Validity of Faraday's Law of Induction and Their Experimental Confirmation

ERIC Educational Resources Information Center

Lopez-Ramos, A.; Menendez, J. R.; Pique, C.

2008-01-01

This paper, as its main didactic objective, shows the conditions needed for the validity of Faraday's law of induction. Inadequate comprehension of these conditions has given rise to several paradoxes about the issue; some are analysed and solved in this paper in the light of the theoretical deduction of the induction law. Furthermore, an…

Studying Scientific Discovery by Computer Simulation.

DTIC Science & Technology

1983-03-30

Mendel’s laws of inheritance, the law of Gay- Lussac for gaseous reactions, tile law of Dulong and Petit, the derivation of atomic weights by Avogadro...neceseary mid identify by block number) scientific discovery -ittri sic properties physical laws extensive terms data-driven heuristics intensive...terms theory-driven heuristics conservation laws 20. ABSTRACT (Continue on revere. side It necessary and identify by block number) Scientific discovery

Cosmological constant is a conserved charge

NASA Astrophysics Data System (ADS)

Chernyavsky, Dmitry; Hajian, Kamal

2018-06-01

Cosmological constant can always be considered as the on-shell value of a top form in gravitational theories. The top form is the field strength of a gauge field, and the theory enjoys a gauge symmetry. We show that cosmological constant is the charge of the global part of the gauge symmetry, and is conserved irrespective of the dynamics of the metric and other fields. In addition, we introduce its conjugate chemical potential, and prove the generalized first law of thermodynamics which includes variation of cosmological constant as a conserved charge. We discuss how our new term in the first law is related to the volume–pressure term. In parallel with the seminal Wald entropy, this analysis suggests that pressure can also be considered as a conserved charge.

Anterior cingulate cortex and intuitive bias detection during number conservation.

PubMed

Simon, Grégory; Lubin, Amélie; Houdé, Olivier; De Neys, Wim

2015-01-01

Children's number conservation is often biased by misleading intuitions but the precise nature of these conservation errors is not clear. A key question is whether children detect that their erroneous conservation judgment is unwarranted. The present study reanalyzed available fMRI data to test the implication of the anterior cingulate cortex (ACC) in this detection process. We extracted mean BOLD (Blood Oxygen Level Dependent) signal values in an independently defined ACC region of interest (ROI) during presentation of classic and control number conservation problems. In classic trials, an intuitively cued visuospatial response conflicted with the correct conservation response, whereas this conflict was not present in the control trials. Results showed that ACC activation increased when solving the classic conservation problems. Critically, this increase did not differ between participants who solved the classic problems correctly (i.e., so-called conservers) and incorrectly (i.e., so-called non-conservers). Additional control analyses of inferior and lateral prefrontal ROIs showed that the group of conservers did show stronger activation in the right inferior frontal gyrus and right lateral middle frontal gyrus. In line with recent behavioral findings, these data lend credence to the hypothesis that even non-conserving children detect the biased nature of their judgment. The key difference between conservers and non-conservers seems to lie in a differential recruitment of inferior and lateral prefrontal regions associated with inhibitory control.

Bidirectional Reflectance of a Macroscopically Flat, High-Albedo Particulate Surface: An Efficient Radiative Transfer Solution and Applications to Regoliths

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Zakharova, Nadia T.

1999-01-01

Many remote sensing applications rely on accurate knowledge of the bidirectional reflection function (BRF) of surfaces composed of discrete, randomly positioned scattering particles. Theoretical computations of BRFs for plane-parallel particulate layers are usually reduced to solving the radiative transfer equation (RTE) using one of existing exact or approximate techniques. Since semi-empirical approximate approaches are notorious for their low accuracy, violation of the energy conservation law, and ability to produce unphysical results, the use of numerically exact solutions of RTE has gained justified popularity. For example, the computation of BRFs for macroscopically flat particulate surfaces in many geophysical publications is based on the adding-doubling (AD) and discrete ordinate (DO) methods. A further saving of computer resources can be achieved by using a more efficient technique to solve the plane-parallel RTE than the AD and DO methods. Since many natural particulate surfaces can be well represented by the model of an optically semi-infinite, homogeneous scattering layer, one can find the BRF directly by solving the Ambartsumian's nonlinear integral equation using a simple iterative technique. In this way, the computation of the internal radiation field is avoided and the computer code becomes highly efficient and very accurate and compact. Furthermore, the BRF thus obtained fully obeys the fundamental physical laws of energy conservation and reciprocity. In this paper, we discuss numerical aspects and the computer implementation of this technique, examine the applicability of the Henyey-Greenstein phase function and the sigma-Eddington approximation in BRF and flux calculations, and describe sample applications demonstrating the potential effect of particle shape on the bidirectional reflectance of flat regolith surfaces. Although the effects of packing density and coherent backscattering are currently neglected, they can also be incorporated. The FORTRAN implementation of the technique is available on the World Wide Web, and can be applied to a wide range of remote sensing problems. BRF computations for undulated (macroscopically rough) surfaces are more complicated and often rely on time consuming Monte Carlo procedures. This approach is especially inefficient for optically thick, weakly absorbing media (e.g., snow and desert surfaces at visible wavelengths since a photon may undergo many internal scattering events before it exists the medium or is absorbed. However, undulated surfaces can often be represented as collections of locally flat tilted facets characterized by the BRF found from the traditional plane parallel RTE. In this way the MOnte Carlo procedure could be used only to evaluate the effects of surface shadowing and multiple surface reflections, thereby bypassing the time-consuming ray tracing inside the medium and providing a great savings of CPU time.

Conservation properties of numerical integration methods for systems of ordinary differential equations

NASA Technical Reports Server (NTRS)

Rosenbaum, J. S.

1976-01-01

If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

Hunting, law enforcement, and African primate conservation.

PubMed

N'Goran, Paul K; Boesch, Christophe; Mundry, Roger; N'Goran, Eliezer K; Herbinger, Ilka; Yapi, Fabrice A; Kühl, Hjalmar S

2012-06-01

Primates are regularly hunted for bushmeat in tropical forests, and systematic ecological monitoring can help determine the effect hunting has on these and other hunted species. Monitoring can also be used to inform law enforcement and managers of where hunting is concentrated. We evaluated the effects of law enforcement informed by monitoring data on density and spatial distribution of 8 monkey species in Taï National Park, Côte d'Ivoire. We conducted intensive surveys of monkeys and looked for signs of human activity throughout the park. We also gathered information on the activities of law-enforcement personnel related to hunting and evaluated the relative effects of hunting, forest cover and proximity to rivers, and conservation effort on primate distribution and density. The effects of hunting on monkeys varied among species. Red colobus monkeys (Procolobus badius) were most affected and Campbell's monkeys (Cercopithecus campbelli) were least affected by hunting. Density of monkeys irrespective of species was up to 100 times higher near a research station and tourism site in the southwestern section of the park, where there is little hunting, than in the southeastern part of the park. The results of our monitoring guided law-enforcement patrols toward zones with the most hunting activity. Such systematic coordination of ecological monitoring and law enforcement may be applicable at other sites. ©2012 Society for Conservation Biology.

Methods Used by Pre-Service Nigeria Certificate in Education Teachers in Solving Quantitative Problems in Chemistry

ERIC Educational Resources Information Center

Danjuma, Ibrahim Mohammed

2011-01-01

This paper reports part of the results of research on chemical problem solving behavior of pre-service teachers in Plateau and Northeastern states of Nigeria. Specifically, it examines and describes the methods used by 204 pre-service teachers in solving quantitative problems from four topics in chemistry. Namely, gas laws; electrolysis;…

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

NASA Astrophysics Data System (ADS)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

7 CFR 1465.3 - Definitions.

Code of Federal Regulations, 2012 CFR

2012-01-01

... document that identifies the location and timing of conservation practices that the participant agrees to... Chief of NRCS, United States Department of Agriculture (USDA), or designee. Conservation district means... law for the express purpose of developing and carrying out a local soil and water conservation program...

7 CFR 1465.3 - Definitions.

Code of Federal Regulations, 2013 CFR

2013-01-01

... document that identifies the location and timing of conservation practices that the participant agrees to... Chief of NRCS, United States Department of Agriculture (USDA), or designee. Conservation district means... law for the express purpose of developing and carrying out a local soil and water conservation program...

7 CFR 1465.3 - Definitions.

Code of Federal Regulations, 2014 CFR

2014-01-01

... document that identifies the location and timing of conservation practices that the participant agrees to... Chief of NRCS, United States Department of Agriculture (USDA), or designee. Conservation district means... law for the express purpose of developing and carrying out a local soil and water conservation program...

Lie symmetry analysis, conservation laws and exact solutions of the time-fractional generalized Hirota-Satsuma coupled KdV system

NASA Astrophysics Data System (ADS)

Saberi, Elaheh; Reza Hejazi, S.

2018-02-01

In the present paper, Lie point symmetries of the time-fractional generalized Hirota-Satsuma coupled KdV (HS-cKdV) system based on the Riemann-Liouville derivative are obtained. Using the derived Lie point symmetries, we obtain similarity reductions and conservation laws of the considered system. Finally, some analytic solutions are furnished by means of the invariant subspace method in the Caputo sense.

On the construction and application of implicit factored schemes for conservation laws. [in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Warming, R. F.; Beam, R. M.

1978-01-01

Efficient, noniterative, implicit finite difference algorithms are systematically developed for nonlinear conservation laws including purely hyperbolic systems and mixed hyperbolic parabolic systems. Utilization of a rational fraction or Pade time differencing formulas, yields a direct and natural derivation of an implicit scheme in a delta form. Attention is given to advantages of the delta formation and to various properties of one- and two-dimensional algorithms.

Symmetries and conservation laws of a nonlinear sigma model with gravitino

NASA Astrophysics Data System (ADS)

Jost, Jürgen; Keßler, Enno; Tolksdorf, Jürgen; Wu, Ruijun; Zhu, Miaomiao

2018-06-01

We study the symmetries and invariances of a version of the action functional of the nonlinear sigma model with gravitino, as considered in Jost et al. (2017). The action is invariant under rescaled conformal transformations, super Weyl transformations, and diffeomorphisms. In particular cases the functional possesses a degenerate supersymmetry. The corresponding conservation laws lead to a geometric interpretation of the energy-momentum tensor and supercurrent as holomorphic sections of appropriate bundles.

When Is Momentum Conserved, and What About Car Crashes in Virginia?

NASA Astrophysics Data System (ADS)

Ehrlich, Robert

2005-10-01

Many years ago I consulted on the reconstruction of an automobile accident for an attorney. After writing a report on the accident, I was deposed by the other side's attorney, and my report was challenged. One key calculation in my report made use of the conservation of momentum in the crash, and the attorney notified me that arguments involving conservation of momentum are not recognized by courts in the Commonwealth of Virginia. Apparently the situation today is more mixed, according to an accident reconstructionist I recently spoke with, who noted that about half the judges (the "more open-minded ones") do admit such arguments in court. This real-world experience with a conflict between the laws of physics and the laws of man made me reflect on whether there might be some validity to the disinclination of many judges to acknowledge a law of physics in their courtrooms.

Energy and maximum norm estimates for nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Olsson, Pelle; Oliger, Joseph

1994-01-01

We have devised a technique that makes it possible to obtain energy estimates for initial-boundary value problems for nonlinear conservation laws. The two major tools to achieve the energy estimates are a certain splitting of the flux vector derivative f(u)(sub x), and a structural hypothesis, referred to as a cone condition, on the flux vector f(u). These hypotheses are fulfilled for many equations that occur in practice, such as the Euler equations of gas dynamics. It should be noted that the energy estimates are obtained without any assumptions on the gradient of the solution u. The results extend to weak solutions that are obtained as point wise limits of vanishing viscosity solutions. As a byproduct we obtain explicit expressions for the entropy function and the entropy flux of symmetrizable systems of conservation laws. Under certain circumstances the proposed technique can be applied repeatedly so as to yield estimates in the maximum norm.

A new third order finite volume weighted essentially non-oscillatory scheme on tetrahedral meshes

NASA Astrophysics Data System (ADS)

Zhu, Jun; Qiu, Jianxian

2017-11-01

In this paper a third order finite volume weighted essentially non-oscillatory scheme is designed for solving hyperbolic conservation laws on tetrahedral meshes. Comparing with other finite volume WENO schemes designed on tetrahedral meshes, the crucial advantages of such new WENO scheme are its simplicity and compactness with the application of only six unequal size spatial stencils for reconstructing unequal degree polynomials in the WENO type spatial procedures, and easy choice of the positive linear weights without considering the topology of the meshes. The original innovation of such scheme is to use a quadratic polynomial defined on a big central spatial stencil for obtaining third order numerical approximation at any points inside the target tetrahedral cell in smooth region and switch to at least one of five linear polynomials defined on small biased/central spatial stencils for sustaining sharp shock transitions and keeping essentially non-oscillatory property simultaneously. By performing such new procedures in spatial reconstructions and adopting a third order TVD Runge-Kutta time discretization method for solving the ordinary differential equation (ODE), the new scheme's memory occupancy is decreased and the computing efficiency is increased. So it is suitable for large scale engineering requirements on tetrahedral meshes. Some numerical results are provided to illustrate the good performance of such scheme.

Mass Conservation and Positivity Preservation with Ensemble-type Kalman Filter Algorithms

NASA Technical Reports Server (NTRS)

Janjic, Tijana; McLaughlin, Dennis B.; Cohn, Stephen E.; Verlaan, Martin

2013-01-01

Maintaining conservative physical laws numerically has long been recognized as being important in the development of numerical weather prediction (NWP) models. In the broader context of data assimilation, concerted efforts to maintain conservation laws numerically and to understand the significance of doing so have begun only recently. In order to enforce physically based conservation laws of total mass and positivity in the ensemble Kalman filter, we incorporate constraints to ensure that the filter ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. We show that the analysis steps of ensemble transform Kalman filter (ETKF) algorithm and ensemble Kalman filter algorithm (EnKF) can conserve the mass integral, but do not preserve positivity. Further, if localization is applied or if negative values are simply set to zero, then the total mass is not conserved either. In order to ensure mass conservation, a projection matrix that corrects for localization effects is constructed. In order to maintain both mass conservation and positivity preservation through the analysis step, we construct a data assimilation algorithms based on quadratic programming and ensemble Kalman filtering. Mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate constraints. Some simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. The results show clear improvements in both analyses and forecasts, particularly in the presence of localized features. Behavior of the algorithm is also tested in presence of model error.

Interpreting Recoil for Undergraduate Students

NASA Astrophysics Data System (ADS)

Elsayed, Tarek A.

2012-04-01

The phenomenon of recoil is usually explained to students in the context of Newton's third law. Typically, when a projectile is fired, the recoil of the launch mechanism is interpreted as a reaction to the ejection of the smaller projectile. The same phenomenon is also interpreted in the context of the conservation of linear momentum, which is closely related to Newton's third law. Since the actual microscopic causes of recoil differ from one problem to another, some students (and teachers) may not be satisfied with understanding recoil through the principles of conservation of linear momentum and Newton's third law. For these students, the origin of the recoil motion should be presented in more depth.

Recoverable information and emergent conservation laws in fracton stabilizer codes

NASA Astrophysics Data System (ADS)

Schmitz, A. T.; Ma, Han; Nandkishore, Rahul M.; Parameswaran, S. A.

2018-04-01

We introduce a new quantity that we term recoverable information, defined for stabilizer Hamiltonians. For such models, the recoverable information provides a measure of the topological information as well as a physical interpretation, which is complementary to topological entanglement entropy. We discuss three different ways to calculate the recoverable information and prove their equivalence. To demonstrate its utility, we compute recoverable information for fracton models using all three methods where appropriate. From the recoverable information, we deduce the existence of emergent Z2 Gauss-law-type constraints, which in turn imply emergent Z2 conservation laws for pointlike quasiparticle excitations of an underlying topologically ordered phase.

Data Basin: Expanding Access to Conservation Data, Tools, and People

NASA Astrophysics Data System (ADS)

Comendant, T.; Strittholt, J.; Frost, P.; Ward, B. C.; Bachelet, D. M.; Osborne-Gowey, J.

2009-12-01

Mapping and spatial analysis are a fundamental part of problem solving in conservation science, yet spatial data are widely scattered, difficult to locate, and often unavailable. Valuable time and resources are wasted locating and gaining access to important biological, cultural, and economic datasets, scientific analysis, and experts. As conservation problems become more serious and the demand to solve them grows more urgent, a new way to connect science and practice is needed. To meet this need, an open-access, web tool called Data Basin (www.databasin.org) has been created by the Conservation Biology Institute in partnership with ESRI and the Wilburforce Foundation. Users of Data Basin can gain quick access to datasets, experts, groups, and tools to help solve real-world problems. Individuals and organizations can perform essential tasks such as exploring and downloading from a vast library of conservation datasets, uploading existing datasets, connecting to other external data sources, create groups, and produce customized maps that can be easily shared. Data Basin encourages sharing and publishing, but also provides privacy and security for sensitive information when needed. Users can publish projects within Data Basin to tell more complete and rich stories of discovery and solutions. Projects are an ideal way to publish collections of datasets, maps and other information on the internet to reach wider audiences. Data Basin also houses individual centers that provide direct access to data, maps, and experts focused on specific geographic areas or conservation topics. Current centers being developed include the Boreal Information Centre, the Data Basin Climate Center, and proposed Aquatic and Forest Conservation Centers.

Local conservation laws in spin-\\frac{1}{2} XY chains with open boundary conditions

NASA Astrophysics Data System (ADS)

Fagotti, Maurizio

2016-06-01

We revisit the conserved quantities of the spin-\\frac{1}{2} XY model with open boundary conditions. In the absence of a transverse field, we find new families of local charges and show that half of the seeming conservation laws are conserved only if the number of sites is odd. In even chains the set of noninteracting charges is abelian, like in the periodic case when the number of sites is odd. In odd chains the set is doubled and becomes non-abelian, like in even periodic chains. The dependence of the charges on the parity of the chain’s size undermines the common belief that the thermodynamic limit of diagonal ensembles exists. We consider also the transverse-field Ising chain, where the situation is more ordinary. The generalization to the XY model in a transverse field is not straightforward and we propose a general framework to carry out similar calculations. We conjecture the form of the bulk part of the local charges and discuss the emergence of quasilocal conserved quantities. We provide evidence that in a region of the parameter space there is a reduction of the number of quasilocal conservation laws invariant under chain inversion. As a by-product, we study a class of block-Toeplitz-plus-Hankel operators and identify the conditions that their symbols satisfy in order to commute with a given block-Toeplitz.

INCINERATION OF SOLID WASTE

EPA Science Inventory

The concern over solid waste disposal and dump-site clean-up has resulted in the passage of three major U.S. environmental laws. They are the Resource Conservation and Recovery Act (RCRA) of 1976, Public Law 94-580, the Toxic Substances Control Act (TSCA) of 1976, Public Law 94-4...

Matter Scatter and Energy Anarchy. The Second Law of Thermodynamics is Simply Common Experience.

ERIC Educational Resources Information Center

Ross, Keith A.

1988-01-01

Shows that the second law of thermodynamics is in the common experience of many people and if taught first, before the law of conservation, can result in fewer misconceptions among pupils. Stresses the use of common experiences in teaching. (CW)

The politics of insight

PubMed Central

Salvi, Carola; Cristofori, Irene; Grafman, Jordan; Beeman, Mark

2016-01-01

Previous studies showed that liberals and conservatives differ in cognitive style. Liberals are more flexible, and tolerant of complexity and novelty, whereas conservatives are more rigid, are more resistant to change, and prefer clear answers. We administered a set of compound remote associate problems, a task extensively used to differentiate problem-solving styles (via insight or analysis). Using this task, several researches have proven that self-reports, which differentiate between insight and analytic problem-solving, are reliable and are associated with two different neural circuits. In our research we found that participants self-identifying with distinct political orientations demonstrated differences in problem-solving strategy. Liberals solved significantly more problems via insight instead of in a step-by-step analytic fashion. Our findings extend previous observations that self-identified political orientations reflect differences in cognitive styles. More specifically, we show that type of political orientation is associated with problem-solving strategy. The data converge with previous neurobehavioural and cognitive studies indicating a link between cognitive style and the psychological mechanisms that mediate political beliefs. PMID:26810954

The politics of insight.

PubMed

Salvi, Carola; Cristofori, Irene; Grafman, Jordan; Beeman, Mark

2016-01-01

Previous studies showed that liberals and conservatives differ in cognitive style. Liberals are more flexible, and tolerant of complexity and novelty, whereas conservatives are more rigid, are more resistant to change, and prefer clear answers. We administered a set of compound remote associate problems, a task extensively used to differentiate problem-solving styles (via insight or analysis). Using this task, several researches have proven that self-reports, which differentiate between insight and analytic problem-solving, are reliable and are associated with two different neural circuits. In our research we found that participants self-identifying with distinct political orientations demonstrated differences in problem-solving strategy. Liberals solved significantly more problems via insight instead of in a step-by-step analytic fashion. Our findings extend previous observations that self-identified political orientations reflect differences in cognitive styles. More specifically, we show that type of political orientation is associated with problem-solving strategy. The data converge with previous neurobehavioural and cognitive studies indicating a link between cognitive style and the psychological mechanisms that mediate political beliefs.

Discretely Conservative Finite-Difference Formulations for Nonlinear Conservation Laws in Split Form: Theory and Boundary Conditions

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles

2011-01-01

Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.

Residential energy conservation measures: a penny saved is a penny earned

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

Finklea, E.A.; Treiber, M.P.

The authors are not suggesting that conservation alone will end our dependence on foreign oil. The focus is on basic household energy-conservation measures because they are technically simple, inexpensive, and available compared to more advanced energy-efficiency technologies (e.g., architectural designs and passive solar devices), or to alternative production technologies (e.g., photovoltaics and synthetic fuels). The social, institutional, and economic obstacles to implementing these basic measures are analyzed, and suggestions offered for overcoming these obstacles. During the Carter Administration, Congress enacted four laws to encourage the installation of household energy conservation measures. The laws provide: (1) tax credits for energy conservationmore » expenditures; (2) conservation investment subsidies for low income homeowners; and require: (3) natural gas and electric utilities to implement residential energy conservation programs for their customers; and (4) the federal government to provide loan subsidies for household energy-conservation investments through a conservation bank. The potential effectiveness of these federal programs are analyzed. President Reagan's advisers have indicated that the new administration will place greater emphasis on energy production and less emphasis on conservation. Consequently, the effectiveness of these programs may depend on the priority given them by the Reagan administration.« less

A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes

DOE PAGES

Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; ...

2015-02-24

We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved atmore » the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.« less

Synchronized parameter optimization of the double freeform lenses illumination system used for the CF-LCoS pico-projectors

NASA Astrophysics Data System (ADS)

Chen, Enguo; Liu, Peng; Yu, Feihong

2012-10-01

A novel synchronized optimization method of multiple freeform surfaces is proposed and applied to double lenses illumination system design of CF-LCoS pico-projectors. Based on Snell's law and the energy conservation law, a series of first-order partial differential equations are derived for the multiple freeform surfaces of the initial system. By assigning the light deflection angle to each freeform surface, multiple surfaces can be obtained simultaneously by solving the corresponding equations, meanwhile the restricted angle on CF-LCoS is guaranteed. In order to improve the spatial uniformity, the multi-surfaces are synchronously optimized by using simplex algorithm for an extended LED source. Design example shows that the double lenses based illumination system, which employs a single 2 mm×2 mm LED chip and a CF-LCoS panel with a diagonal of 0.59 inches satisfies the needs of pico-projector. Moreover, analytical result indicates that the design method represents substantial improvement and practical significance over traditional CF-LCoS projection system, which could offer outstanding performance with both portability and low cost. The synchronized optimization design method could not only realize collimating and uniform illumination, but also could be introduced to other specific light conditions.

Steam stripping of the unsaturated zone of contaminated sub-soils: The effect of diffusion/dispersion in the start-up phase

NASA Astrophysics Data System (ADS)

Brouwers, H. J. H.; Gilding, B. H.

2006-02-01

The unsteady process of steam stripping of the unsaturated zone of soils contaminated with volatile organic compounds (VOCs) is addressed. A model is presented. It accounts for the effects of water and contaminants remaining in vapour phase, as well as diffusion and dispersion of contaminants in this phase. The model has two components. The first is a one-dimensional description of the propagation of a steam front in the start-up phase. This is based on Darcy's law and conservation laws of mass and energy. The second component describes the transport of volatile contaminants. Taking the view that non-equilibrium between liquid and vapour phases exists, it accounts for evaporation, transport, and condensation at the front. This leads to a moving-boundary problem. The moving-boundary problem is brought into a fixed domain by a suitable transformation of the governing partial differential equations, and solved numerically. For a broad range of the governing dimensionless numbers, such as the Henry, Merkel and Péclet numbers, computational results are discussed. A mathematical asymptotic analysis supports this discussion. The range of parameter values for which the model is valid is investigated. Diffusion and dispersion are shown to be of qualitative importance, but to have little quantitative effect in the start-up phase.

One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes.

PubMed

Cheviakov, A F; Ganghoffer, J-F

2016-05-01

The framework of incompressible nonlinear hyperelasticity and viscoelasticity is applied to the derivation of one-dimensional models of nonlinear wave propagation in fiber-reinforced elastic solids. Equivalence transformations are used to simplify the resulting wave equations and to reduce the number of parameters. Local conservation laws and global conserved quantities of the models are systematically computed and discussed, along with other related mathematical properties. Sample numerical solutions are presented. The models considered in the paper are appropriate for the mathematical description of certain aspects of the behavior of biological membranes and similar structures. Copyright © 2015 Elsevier Ltd. All rights reserved.

Facilitating Problem Solving in High School Chemistry.

ERIC Educational Resources Information Center

Gabel, Dorothy L.; Sherwood, Robert D.

1983-01-01

Investigated superiority of instructional strategies (factor-label method, proportionality, use of analogies, use of diagrams) in teaching problem-solving related to mole concept, gas laws, stoichiometry, and molarity. Also investigated effectiveness of strategies for students (N=609) with different verbal-visual preferences, proportional…

50 CFR 679.3 - Relation to other laws.

Code of Federal Regulations, 2012 CFR

2012-10-01

....3 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... fishing for groundfish. (1) The conservation and management of groundfish in waters of the territorial sea.... Additional regulations governing the conservation and management of halibut are set forth in subpart E of...

50 CFR 679.3 - Relation to other laws.

Code of Federal Regulations, 2011 CFR

2011-10-01

....3 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... fishing for groundfish. (1) The conservation and management of groundfish in waters of the territorial sea.... Additional regulations governing the conservation and management of halibut are set forth in subpart E of...

ECP (Environmental Conservation Project) Report, No. 5, March 1976. Planning for Energy Conservation.

ERIC Educational Resources Information Center

Environmental Law Inst., Washington, DC.

The culmination of the Environmental Law Institute's Energy Conservation Project will be a series of handbooks addressed to state and local officials, legislators, and interested citizens setting out suggested strategies for conserving energy. This issue of the ECP Report publishes the first of a series of draft chapters from these handbooks - a…

78 FR 54685 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978 (Pub. L. 95-541)

Federal Register 2010, 2011, 2012, 2013, 2014

2013-09-05

... Conservation Act of 1978 (Pub. L. 95-541) AGENCY: National Science Foundation. ACTION: Notice of Permit Applications Received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National... activities regulated under the Antarctic Conservation Act of 1978. NSF has published regulations under the...

76 FR 58049 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978 (Pub. L. 95-541)

Federal Register 2010, 2011, 2012, 2013, 2014

2011-09-19

... Conservation Act of 1978 (Pub. L. 95-541) AGENCY: National Science Foundation. ACTION: Notice of Permit Applications Received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National... activities regulated under the Antarctic Conservation Act of 1978. NSF has published regulations under the...

75 FR 62892 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978 (Pub .L. 95-541)

Federal Register 2010, 2011, 2012, 2013, 2014

2010-10-13

... Conservation Act of 1978 (Pub .L. 95-541) AGENCY: National Science Foundation. ACTION: Notice of Permit Modification Received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National... activities regulated under the Antarctic Conservation Act of 1978. NSF has published regulations under the...

78 FR 52218 - Notice of permit applications received under the Antarctic Conservation Act of 1978 (Pub. L. 95-541)

Federal Register 2010, 2011, 2012, 2013, 2014

2013-08-22

... Conservation Act of 1978 (Pub. L. 95-541) AGENCY: National Science Foundation. ACTION: Notice of permit applications received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National... activities regulated under the Antarctic Conservation Act of 1978. NSF has published regulations under the...

75 FR 62891 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978 (Pub. L. 95-541)

Federal Register 2010, 2011, 2012, 2013, 2014

2010-10-13

... Conservation Act of 1978 (Pub. L. 95-541) AGENCY: National Science Foundation. ACTION: Notice of Permit Applications Received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National... activities regulated under the Antarctic Conservation Act of 1978. NSF has published regulations under the...

76 FR 52354 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978 (Pub. L. 95-541)

Federal Register 2010, 2011, 2012, 2013, 2014

2011-08-22

... Conservation Act of 1978 (Pub. L. 95-541) AGENCY: National Science Foundation. ACTION: Notice of Permit Applications Received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National... activities regulated under the Antarctic Conservation Act of 1978. NSF has published regulations under the...

78 FR 9072 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978 (Pub. L. 95-541)

Federal Register 2010, 2011, 2012, 2013, 2014

2013-02-07

... Conservation Act of 1978 (Pub. L. 95-541) AGENCY: National Science Foundation. ACTION: Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National... activities regulated under the Antarctic Conservation Act of 1978. NSF has published regulations under the...

75 FR 54389 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978 (Pub. L. 95-541)

Federal Register 2010, 2011, 2012, 2013, 2014

2010-09-07

... Conservation Act of 1978 (Pub. L. 95-541) AGENCY: National Science Foundation. ACTION: Notice of Permit Modification Received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National... activities regulated under the Antarctic Conservation Act of 1978. NSF has published regulations under the...

75 FR 25300 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978 (Pub. L. 95-541)

Federal Register 2010, 2011, 2012, 2013, 2014

2010-05-07

... Conservation Act of 1978 (Pub. L. 95-541) AGENCY: National Science Foundation. ACTION: Notice of Permit Applications Received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National... activities regulated under the Antarctic Conservation Act of 1978. NSF has published regulations under the...

76 FR 30397 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978 (Pub. L. 95-541)

Federal Register 2010, 2011, 2012, 2013, 2014

2011-05-25

... Conservation Act of 1978 (Pub. L. 95-541) AGENCY: National Science Foundation. ACTION: Notice of Permit Modification Received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National... activities regulated under the Antarctic Conservation Act of 1978. NSF has published regulations under the...

78 FR 58568 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978 (Pub. L. 95-541)

Federal Register 2010, 2011, 2012, 2013, 2014

2013-09-24

... Conservation Act of 1978 (Pub. L. 95-541) AGENCY: National Science Foundation. ACTION: Notice of Permit Applications Received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National... activities regulated under the Antarctic Conservation Act of 1978. NSF has published regulations under the...

Student's preconception and anxiety when they solve multi representation concepts in Newton laws and it's application

NASA Astrophysics Data System (ADS)

Cari, C.; Suparmi, A.; Handhika, J.

2016-11-01

The purpose of this study was to describe of preconceptions and anxieties students in solving the representation concepts in newton laws and it's application. This research was conducted for junior undergraduate student's in physics department (36 Students) and physics education (31 Students). The method used in this study is a qualitative descriptive. The data was collection using test for multirepresentation concept, questionnaires for anxiety, and interviews. Based on the analysis it can be concluded that (1) the higher is anxiety, the higher is unconsistency (67,16%), (2) the higher is anxiety, the higher is consistency but wrong answer (29,85%), (3) the lower is anxiety, the higher is consistency of right answer (2,98%). Mostly students have understood fewer physics concept in newtons laws.

Structure-preserving operators for thermal-nonequilibrium hydrodynamics

NASA Astrophysics Data System (ADS)

Shiroto, Takashi; Kawai, Soshi; Ohnishi, Naofumi

2018-07-01

Radiation hydrodynamics simulations based on a single fluid two-temperature model may violate the law of energy conservation, because the governing equations are expressed in a nonconservative formulation. In this study, we maintain the important physical requirements by employing a strategy based on the key concept that mathematical structures associated with conservative and nonconservative equations are preserved, even at the discrete level. To this end, we discretize the conservation laws and transform them using exact algebraic operations. The proposed scheme maintains global conservation errors within the round-off level. In addition, a numerical experiment concerning the shock tube problem suggests that the proposed scheme agrees well with the jump conditions at the discontinuities regulated by the Rankine-Hugoniot relationship. The generalized derivation allows us to employ arbitrary central difference, artificial dissipation, and Runge-Kutta methods.

Stabilised finite-element methods for solving the level set equation with mass conservation

NASA Astrophysics Data System (ADS)

Kabirou Touré, Mamadou; Fahsi, Adil; Soulaïmani, Azzeddine

2016-01-01

Finite-element methods are studied for solving moving interface flow problems using the level set approach and a stabilised variational formulation proposed in Touré and Soulaïmani (2012; Touré and Soulaïmani To appear in 2016), coupled with a level set correction method. The level set correction is intended to enhance the mass conservation satisfaction property. The stabilised variational formulation (Touré and Soulaïmani 2012; Touré and Soulaïmani, To appear in 2016) constrains the level set function to remain close to the signed distance function, while the mass conservation is a correction step which enforces the mass balance. The eXtended finite-element method (XFEM) is used to take into account the discontinuities of the properties within an element. XFEM is applied to solve the Navier-Stokes equations for two-phase flows. The numerical methods are numerically evaluated on several test cases such as time-reversed vortex flow, a rigid-body rotation of Zalesak's disc, sloshing flow in a tank, a dam-break over a bed, and a rising bubble subjected to buoyancy. The numerical results show the importance of satisfying global mass conservation to accurately capture the interface position.

Benjamin Banneker and the Law of Sines

ERIC Educational Resources Information Center

Mahoney, John F.

2005-01-01

Benjamin Banneker, a self-taught mathematician, surveyor and astronomer published annual almanacs containing his astronomical observations and predictions. Banneker who also used logarithms to apply the Law of Sines believed that the method used to solve a mathematical problem depends on the tools available.

50 CFR 665.123 - Relation to other laws.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 50 Wildlife and Fisheries 9 2010-10-01 2010-10-01 false Relation to other laws. 665.123 Section 665.123 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... § 665.123 Relation to other laws. To ensure consistency between the management regimes of different...

50 CFR 600.705 - Relation to other laws.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 50 Wildlife and Fisheries 12 2012-10-01 2012-10-01 false Relation to other laws. 600.705 Section 600.705 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... § 600.705 Relation to other laws. (a) General. Persons affected by these regulations should be aware...

50 CFR 600.705 - Relation to other laws.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 50 Wildlife and Fisheries 12 2014-10-01 2014-10-01 false Relation to other laws. 600.705 Section 600.705 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... § 600.705 Relation to other laws. (a) General. Persons affected by these regulations should be aware...

50 CFR 600.705 - Relation to other laws.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 50 Wildlife and Fisheries 12 2013-10-01 2013-10-01 false Relation to other laws. 600.705 Section 600.705 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... § 600.705 Relation to other laws. (a) General. Persons affected by these regulations should be aware...

50 CFR 600.705 - Relation to other laws.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 50 Wildlife and Fisheries 8 2010-10-01 2010-10-01 false Relation to other laws. 600.705 Section 600.705 Wildlife and Fisheries FISHERY CONSERVATION AND MANAGEMENT, NATIONAL OCEANIC AND ATMOSPHERIC... § 600.705 Relation to other laws. (a) General. Persons affected by these regulations should be aware...

Taxonomic and regional uncertainty in species-area relationships and the identification of richness hotspots

PubMed Central

Guilhaumon, François; Gimenez, Olivier; Gaston, Kevin J.; Mouillot, David

2008-01-01

Species-area relationships (SARs) are fundamental to the study of key and high-profile issues in conservation biology and are particularly widely used in establishing the broad patterns of biodiversity that underpin approaches to determining priority areas for biological conservation. Classically, the SAR has been argued in general to conform to a power-law relationship, and this form has been widely assumed in most applications in the field of conservation biology. Here, using nonlinear regressions within an information theoretical model selection framework, we included uncertainty regarding both model selection and parameter estimation in SAR modeling and conducted a global-scale analysis of the form of SARs for vascular plants and major vertebrate groups across 792 terrestrial ecoregions representing almost 97% of Earth's inhabited land. The results revealed a high level of uncertainty in model selection across biomes and taxa, and that the power-law model is clearly the most appropriate in only a minority of cases. Incorporating this uncertainty into a hotspots analysis using multimodel SARs led to the identification of a dramatically different set of global richness hotspots than when the power-law SAR was assumed. Our findings suggest that the results of analyses that assume a power-law model may be at severe odds with real ecological patterns, raising significant concerns for conservation priority-setting schemes and biogeographical studies. PMID:18832179

77 FR 60477 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978

Federal Register 2010, 2011, 2012, 2013, 2014

2012-10-03

... NATIONAL SCIENCE FOUNDATION Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978 AGENCY: National Science Foundation. ACTION: Notice of permit applications received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National Science...

78 FR 60321 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978

Federal Register 2010, 2011, 2012, 2013, 2014

2013-10-01

... NATIONAL SCIENCE FOUNDATION Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978 AGENCY: National Science Foundation. ACTION: Notice of Permit Applications Received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National Science...

77 FR 23766 - Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978

Federal Register 2010, 2011, 2012, 2013, 2014

2012-04-20

... NATIONAL SCIENCE FOUNDATION Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978 AGENCY: National Science Foundation. ACTION: Notice of Permit Applications Received under the Antarctic Conservation Act of 1978, Public Law 95-541. SUMMARY: The National Science...

7 CFR 1469.3 - Definitions.

Code of Federal Regulations, 2013 CFR

2013-01-01

.... Soil quality means resource concerns and/or opportunities related to depletion of soil organic matter..., or Tribal law for the express purpose of developing and carrying out a local soil and water...,” “soil conservation district,” “soil and water conservation district,” “resource conservation district...

7 CFR 1469.3 - Definitions.

Code of Federal Regulations, 2014 CFR

2014-01-01

.... Soil quality means resource concerns and/or opportunities related to depletion of soil organic matter..., or Tribal law for the express purpose of developing and carrying out a local soil and water...,” “soil conservation district,” “soil and water conservation district,” “resource conservation district...

7 CFR 1469.3 - Definitions.

Code of Federal Regulations, 2012 CFR

2012-01-01

.... Soil quality means resource concerns and/or opportunities related to depletion of soil organic matter..., or Tribal law for the express purpose of developing and carrying out a local soil and water...,” “soil conservation district,” “soil and water conservation district,” “resource conservation district...

Tug-of-war model for the two-bandit problem: nonlocally-correlated parallel exploration via resource conservation.

PubMed

Kim, Song-Ju; Aono, Masashi; Hara, Masahiko

2010-07-01

We propose a model - the "tug-of-war (TOW) model" - to conduct unique parallel searches using many nonlocally-correlated search agents. The model is based on the property of a single-celled amoeba, the true slime mold Physarum, which maintains a constant intracellular resource volume while collecting environmental information by concurrently expanding and shrinking its branches. The conservation law entails a "nonlocal correlation" among the branches, i.e., volume increment in one branch is immediately compensated by volume decrement(s) in the other branch(es). This nonlocal correlation was shown to be useful for decision making in the case of a dilemma. The multi-armed bandit problem is to determine the optimal strategy for maximizing the total reward sum with incompatible demands, by either exploiting the rewards obtained using the already collected information or exploring new information for acquiring higher payoffs involving risks. Our model can efficiently manage the "exploration-exploitation dilemma" and exhibits good performances. The average accuracy rate of our model is higher than those of well-known algorithms such as the modified -greedy algorithm and modified softmax algorithm, especially, for solving relatively difficult problems. Moreover, our model flexibly adapts to changing environments, a property essential for living organisms surviving in uncertain environments.

Analysis of Fault Spacing in Thrust-Belt Wedges Using Numerical Modeling

NASA Astrophysics Data System (ADS)

Regensburger, P. V.; Ito, G.

2017-12-01

Numerical modeling is invaluable in studying the mechanical processes governing the evolution of geologic features such as thrust-belt wedges. The mechanisms controlling thrust fault spacing in wedges is not well understood. Our numerical model treats the thrust belt as a visco-elastic-plastic continuum and uses a finite-difference, marker-in-cell method to solve for conservation of mass and momentum. From these conservation laws, stress is calculated and Byerlee's law is used to determine the shear stress required for a fault to form. Each model consists of a layer of crust, initially 3-km-thick, carried on top of a basal décollement, which moves at a constant speed towards a rigid backstop. A series of models were run with varied material properties, focusing on the angle of basal friction at the décollement, the angle of friction within the crust, and the cohesion of the crust. We investigate how these properties affected the spacing between thrusts that have the most time-integrated history of slip and therefore have the greatest effect on the large-scale undulations in surface topography. The surface position of these faults, which extend through most of the crustal layer, are identifiable as local maxima in positive curvature of surface topography. Tracking the temporal evolution of faults, we find that thrust blocks are widest when they first form at the front of the wedge and then they tend to contract over time as more crustal material is carried to the wedge. Within each model, thrust blocks form with similar initial widths, but individual thrust blocks develop differently and may approach an asymptotic width over time. The median of thrust block widths across the whole wedge tends to decrease with time. Median fault spacing shows a positive correlation with both wedge cohesion and internal friction. In contrast, median fault spacing exhibits a negative correlation at small angles of basal friction (<17˚) and a positive correlation with larger angles of basal friction. From these correlations, we will derive scaling laws that can be used to predict fault spacing in thrust-belt wedges.

The role of competing knowledge structures in undermining learning: Newton's second and third laws

NASA Astrophysics Data System (ADS)

Low, David J.; Wilson, Kate F.

2017-01-01

We investigate the development of student understanding of Newton's laws using a pre-instruction test (the Force Concept Inventory), followed by a series of post-instruction tests and interviews. While some students' somewhat naive, pre-existing models of Newton's third law are largely eliminated following a semester of teaching, we find that a particular inconsistent model is highly resilient to, and may even be strengthened by, instruction. If test items contain words that cue students to think of Newton's second law, then students are more likely to apply a "net force" approach to solving problems, even if it is inappropriate to do so. Additional instruction, reinforcing physical concepts in multiple settings and from multiple sources, appears to help students develop a more connected and consistent level of understanding. We recommend explicitly encouraging students to check their work for consistency with physical principles, along with the standard checks for dimensionality and order of magnitude, to encourage reflective and rigorous problem solving.

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

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

de Almeida, Valmor F.

In this work, a phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equationmore » and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.« less

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

DOE PAGES

de Almeida, Valmor F.

2017-04-19

In this work, a phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equationmore » and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.« less

Interference and the Law of Energy Conservation

ERIC Educational Resources Information Center

Drosd, Robert; Minkin, Leonid; Shapovalov, Alexander S.

2014-01-01

Introductory physics textbooks consider interference to be a process of redistribution of energy from the wave sources in the surrounding space resulting in constructive and destructive interferences. As one can expect, the total energy flux is conserved. However, one case of apparent non-conservation energy attracts great attention. Imagine that…

Students' Misunderstandings about the Energy Conservation Principle: A General View to Studies in Literature

ERIC Educational Resources Information Center

Tatar, Erdal; Oktay, Munir

2007-01-01

This paper serves to review previously reported studies on students' misunderstandings about the energy conservation principle (the first law of thermodynamics). Generally, studies in literature highlighted students' misunderstandings about the energy conservation principle stem from preliminaries about energy concept in daily life. Since prior…

Introducing Conservation of Momentum

ERIC Educational Resources Information Center

Brunt, Marjorie; Brunt, Geoff

2013-01-01

The teaching of the principle of conservation of linear momentum is considered (ages 15 + ). From the principle, the momenta of two masses in an isolated system are considered. Sketch graphs of the momenta make Newton's laws appear obvious. Examples using different collision conditions are considered. Conservation of momentum is considered…

76 FR 66089 - Notice of Permit Modification Issued Under the Antarctic Conservation Act of 1978

Federal Register 2010, 2011, 2012, 2013, 2014

2011-10-25

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Federal Register 2010, 2011, 2012, 2013, 2014

2012-10-23

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77 FR 64831 - Notice of Permits Issued Under the Antarctic Conservation Act of 1978

Federal Register 2010, 2011, 2012, 2013, 2014

2012-10-23

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2011-11-01

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Federal Register 2010, 2011, 2012, 2013, 2014

2012-08-21

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Federal Register 2010, 2011, 2012, 2013, 2014

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Federal Register 2010, 2011, 2012, 2013, 2014

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... NATIONAL SCIENCE FOUNDATION Notice of Permits Issued Under the Antarctic Conservation Act of 1978 AGENCY: National Science Foundation. ACTION: Notice of permits issued under the Antarctic Conservation of 1978, Public Law 95-541. SUMMARY: The National Science Foundation (NSF) is required to publish notice...

Conserving Earth's Biodiversity. [CD-ROM and] Instructor's Manual.

ERIC Educational Resources Information Center

2000

This CD-ROM is designed as an interactive learning tool to support teaching in highly interdisciplinary fields such as conservation of biodiversity. Topics introduced in the software include the impact of humans on natural landscapes, threats to biodiversity, methods and theories of conservation biology, environmental laws, and relevant economic…

7 CFR 1467.3 - Definitions.

Code of Federal Regulations, 2011 CFR

2011-01-01

... State by annual tilling of the soil, including tilling by one-trip planters; or sugarcane planted and... or territorial law for the express purpose of developing and carrying out a local soil and water...,” “soil conservation district,” “soil and water conservation district,” “resource conservation district...

Conservation of Mechanical Energy Using Dry Ice Slider-Projectiles

ERIC Educational Resources Information Center

Gales, Jenna; Baker, Blane

2008-01-01

Energy concepts are fundamentally important for describing and analyzing systems ranging from subatomic particles to spiral galaxies. In general, students first encounter such concepts in introductory courses that typically focus on forms of energy, energy transfer, and conservation laws. Within these courses, conservation of mechanical energy is…

HAM2D: 2D Shearing Box Model

NASA Astrophysics Data System (ADS)

Gammie, Charles F.; Guan, Xiaoyue

2012-10-01

HAM solves non-relativistic hyperbolic partial differential equations in conservative form using high-resolution shock-capturing techniques. This version of HAM has been configured to solve the magnetohydrodynamic equations of motion in axisymmetry to evolve a shearing box model.

Mollweide's Formula in Teaching Trigonometry

ERIC Educational Resources Information Center

Karjanto, Natanael

2011-01-01

Trigonometry is one of the topics in mathematics that the students in both high school and pre-undergraduate levels need to learn. Generally, the topic covers trigonometric functions, trigonometric equations, trigonometric identities and solving oblique triangles using the Laws of Sines and Cosines. However, when solving the oblique triangles,…

A priori error estimates for an hp-version of the discontinuous Galerkin method for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Bey, Kim S.; Oden, J. Tinsley

1993-01-01

A priori error estimates are derived for hp-versions of the finite element method for discontinuous Galerkin approximations of a model class of linear, scalar, first-order hyperbolic conservation laws. These estimates are derived in a mesh dependent norm in which the coefficients depend upon both the local mesh size h(sub K) and a number p(sub k) which can be identified with the spectral order of the local approximations over each element.

A practical example aiding understanding momentum in 1D: the water gun experiment

NASA Astrophysics Data System (ADS)

MacLeod, Katarin

2007-09-01

The law of conservation of momentum is one that students often have difficulties understanding. This experiment allows students to use childhood toys to examine and calculate the muzzle velocity of their favourite water gun by using an air track, a spark timer or data logger and the law of conservation of momentum in a one-dimensional case, a modification of the standard ballistic pendulum laboratory experiment (1990 Physics 100 Lab Manual St Francis Xavier University).

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood

2018-03-01

The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

Lenz's law in the kitchen

NASA Astrophysics Data System (ADS)

Dindorf, Wojciech

1999-05-01

A steel blade—a rather vital part of a mixer—has fallen behind a cupboard in my kitchen. The cupboard is heavy and quite permanently mounted between stove and fridge. Hopeless situation! Unless—you are an experimental physicist. This straightforward demonstration helps in appreciating the connection between Lenz's law and the law of conservation of energy.

10 CFR 490.7 - Relationship to other law.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 10 Energy 3 2010-01-01 2010-01-01 false Relationship to other law. 490.7 Section 490.7 Energy DEPARTMENT OF ENERGY ENERGY CONSERVATION ALTERNATIVE FUEL TRANSPORTATION PROGRAM General Provisions § 490.7 Relationship to other law. (a) Nothing in this part shall be construed to require or authorize sale of, or...

Alternative Fuels Data Center: Idle Reduction Laws and Incentives

Science.gov Websites

Conserve Fuel Printable Version Share this resource Send a link to Alternative Fuels Data Center : Idle Reduction Laws and Incentives to someone by E-mail Share Alternative Fuels Data Center: Idle Fuels Data Center: Idle Reduction Laws and Incentives on Digg Find More places to share Alternative

Traveling wave solutions and conservation laws for nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-02-01

In this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire new types of traveling wave solutions for the governing equation. We show that the equation is nonlinear self-adjoint by obtaining suitable substitution. Therefore, we construct conservation laws for the equation using new conservation theorem. The obtained solutions in this work may be used to explain and understand the physical nature of the wave spreads in the most dispersive medium. The constraint condition for the existence of solitons is stated. Some three dimensional figures for some of the acquired results are illustrated.

7 CFR 656.1 - Purpose.

Code of Federal Regulations, 2012 CFR

2012-01-01

... of the Department of Agriculture (Continued) NATURAL RESOURCES CONSERVATION SERVICE, DEPARTMENT OF... ENCOUNTERED IN NRCS-ASSISTED PROGRAMS § 656.1 Purpose. This part prescribes Natural Resources Conservation... laws and appropriate executive orders for administering NRCS programs. ...

7 CFR 656.1 - Purpose.

Code of Federal Regulations, 2014 CFR

2014-01-01

... of the Department of Agriculture (Continued) NATURAL RESOURCES CONSERVATION SERVICE, DEPARTMENT OF... ENCOUNTERED IN NRCS-ASSISTED PROGRAMS § 656.1 Purpose. This part prescribes Natural Resources Conservation... laws and appropriate executive orders for administering NRCS programs. ...

7 CFR 656.1 - Purpose.

Code of Federal Regulations, 2011 CFR

2011-01-01

... of the Department of Agriculture (Continued) NATURAL RESOURCES CONSERVATION SERVICE, DEPARTMENT OF... ENCOUNTERED IN NRCS-ASSISTED PROGRAMS § 656.1 Purpose. This part prescribes Natural Resources Conservation... laws and appropriate executive orders for administering NRCS programs. ...

7 CFR 656.1 - Purpose.

Code of Federal Regulations, 2010 CFR

2010-01-01

... of the Department of Agriculture (Continued) NATURAL RESOURCES CONSERVATION SERVICE, DEPARTMENT OF... ENCOUNTERED IN NRCS-ASSISTED PROGRAMS § 656.1 Purpose. This part prescribes Natural Resources Conservation... laws and appropriate executive orders for administering NRCS programs. ...

7 CFR 656.1 - Purpose.

Code of Federal Regulations, 2013 CFR

2013-01-01

... of the Department of Agriculture (Continued) NATURAL RESOURCES CONSERVATION SERVICE, DEPARTMENT OF... ENCOUNTERED IN NRCS-ASSISTED PROGRAMS § 656.1 Purpose. This part prescribes Natural Resources Conservation... laws and appropriate executive orders for administering NRCS programs. ...

Conservation law for self-paced movements.

PubMed

Huh, Dongsung; Sejnowski, Terrence J

2016-08-02

Optimal control models of biological movements introduce external task factors to specify the pace of movements. Here, we present the dual to the principle of optimality based on a conserved quantity, called "drive," that represents the influence of internal motivation level on movement pace. Optimal control and drive conservation provide equivalent descriptions for the regularities observed within individual movements. For regularities across movements, drive conservation predicts a previously unidentified scaling law between the overall size and speed of various self-paced hand movements in the absence of any external tasks, which we confirmed with psychophysical experiments. Drive can be interpreted as a high-level control variable that sets the overall pace of movements and may be represented in the brain as the tonic levels of neuromodulators that control the level of internal motivation, thus providing insights into how internal states affect biological motor control.

Power law-based local search in spider monkey optimisation for lower order system modelling

NASA Astrophysics Data System (ADS)

Sharma, Ajay; Sharma, Harish; Bhargava, Annapurna; Sharma, Nirmala

2017-01-01

The nature-inspired algorithms (NIAs) have shown efficiency to solve many complex real-world optimisation problems. The efficiency of NIAs is measured by their ability to find adequate results within a reasonable amount of time, rather than an ability to guarantee the optimal solution. This paper presents a solution for lower order system modelling using spider monkey optimisation (SMO) algorithm to obtain a better approximation for lower order systems and reflects almost original higher order system's characteristics. Further, a local search strategy, namely, power law-based local search is incorporated with SMO. The proposed strategy is named as power law-based local search in SMO (PLSMO). The efficiency, accuracy and reliability of the proposed algorithm is tested over 20 well-known benchmark functions. Then, the PLSMO algorithm is applied to solve the lower order system modelling problem.

A new rate law describing microbial respiration.

PubMed

Jin, Qusheng; Bethke, Craig M

2003-04-01

The rate of microbial respiration can be described by a rate law that gives the respiration rate as the product of a rate constant, biomass concentration, and three terms: one describing the kinetics of the electron-donating reaction, one for the kinetics of the electron-accepting reaction, and a thermodynamic term accounting for the energy available in the microbe's environment. The rate law, derived on the basis of chemiosmotic theory and nonlinear thermodynamics, is unique in that it accounts for both forward and reverse fluxes through the electron transport chain. Our analysis demonstrates how a microbe's respiration rate depends on the thermodynamic driving force, i.e., the net difference between the energy available from the environment and energy conserved as ATP. The rate laws commonly applied in microbiology, such as the Monod equation, are specific simplifications of the general law presented. The new rate law is significant because it affords the possibility of extrapolating in a rigorous manner from laboratory experiment to a broad range of natural conditions, including microbial growth where only limited energy is available. The rate law also provides a new explanation of threshold phenomena, which may reflect a thermodynamic equilibrium where the energy released by electron transfer balances that conserved by ADP phosphorylation.

Facilitating Problem Solving in High School Chemistry.

ERIC Educational Resources Information Center

Gabel, Dorothy L.

The major purpose of this study was to determine whether certain types of instructional strategies (factor-label method, use of analogies, use of diagrams, and proportionality) were superior to others in teaching problem solving in four topics (mole concept, gas laws, stoichiometry, and molarity). Also of major interest was whether particular…

Facilitating problem solving in high school chemistry

NASA Astrophysics Data System (ADS)

Gabel, Dorothy L.; Sherwood, Robert D.

The major purpose for conducting this study was to determine whether certain instructional strategies were superior to others in teaching high school chemistry students problem solving. The effectiveness of four instructional strategies for teaching problem solving to students of various proportional reasoning ability, verbal and visual preference, and mathematics anxiety were compared in this aptitude by treatment interaction study. The strategies used were the factor-label method, analogies, diagrams, and proportionality. Six hundred and nine high school students in eight schools were randomly assigned to one of four teaching strategies within each classroom. Students used programmed booklets to study the mole concept, the gas laws, stoichiometry, and molarity. Problem-solving ability was measured by a series of immediate posttests, delayed posttests and the ACS-NSTA Examination in High School Chemistry. Results showed that mathematics anxiety is negatively correlated with science achievement and that problem solving is dependent on students' proportional reasoning ability. The factor-label method was found to be the most desirable method and proportionality the least desirable method for teaching the mole concept. However, the proportionality method was best for teaching the gas laws. Several second-order interactions were found to be significant when mathematics anxiety was one of the aptitudes involved.

Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature

NASA Technical Reports Server (NTRS)

Barth, Timothy; Abgrall, Remi; Biegel, Bryan (Technical Monitor)

2000-01-01

This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.

Modern negligence law: Contribution of the medical cases.

PubMed

Hodgson, John

The law on medical negligence is part of the law of negligence generally. It has played a significant part in developing two key aspects of the law. There are special rules to determine the standard of care expected of experts when advising and solving problems, and medical cases have largely shaped the law. Although cases on causation may arise in any area, several of the key cases happen to be medical ones. They are particularly likely to assist where there are alternative causes, as it is often difficult to distinguish the effects of disease from those of inappropriate treatment.

Rule-governed Approaches to Physics--Newton's Third Law.

ERIC Educational Resources Information Center

Maloney, David P.

1984-01-01

Describes an approach to assessing the use of rules in solving problems related to Newton's third law of motion. Discusses the problems used, method of questioning, scoring of problem sets, and a general overview of the use of the technique in aiding the teacher in dealing with student's conceptual levels. (JM)

The Use of Classroom Discussion at a Law Enforcement Training Academy

ERIC Educational Resources Information Center

Lewis, Cynthia L.

2014-01-01

The ability to solve problems, think critically, and communicate effectively are necessary traits in law enforcement officers (LEOs). Individuals responsible for instructing LEOs must employ adult learning strategies to provide LEOs the opportunity to share ideas, experiences, beliefs, and knowledge. Discussion is one learning strategy that…

Finite Volume Methods: Foundation and Analysis

NASA Technical Reports Server (NTRS)

Barth, Timothy; Ohlberger, Mario

2003-01-01

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Impact of the Illinois Seat Belt Use Law on Accidents, Deaths, and Injuries.

ERIC Educational Resources Information Center

Rock, Steven M.

1992-01-01

The impact of the 1985 Illinois seat belt law is explored using Box-Jenkins Auto-Regressive, Integrated Moving Averages (ARIMA) techniques and monthly accident statistical data from the state department of transportation for January-July 1990. A conservative estimate is that the law provides benefits of $15 million per month in Illinois. (SLD)

Method and Apparatus for Predicting Unsteady Pressure and Flow Rate Distribution in a Fluid Network

NASA Technical Reports Server (NTRS)

Majumdar, Alok K. (Inventor)

2009-01-01

A method and apparatus for analyzing steady state and transient flow in a complex fluid network, modeling phase changes, compressibility, mixture thermodynamics, external body forces such as gravity and centrifugal force and conjugate heat transfer. In some embodiments, a graphical user interface provides for the interactive development of a fluid network simulation having nodes and branches. In some embodiments, mass, energy, and specific conservation equations are solved at the nodes, and momentum conservation equations are solved in the branches. In some embodiments, contained herein are data objects for computing thermodynamic and thermophysical properties for fluids. In some embodiments, the systems of equations describing the fluid network are solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods.

Alternative theoretical method for motion of a sand-filled funnel experiment

NASA Astrophysics Data System (ADS)

Byrd, David; White, Gary

2001-11-01

In "Motion of a Sand-Filled Funnel," Peter Sullivan and Anna McLoon described how to use numerical methods and a Microsoft Excel spreadsheet to predict the motion of a variant of Atwood's machine with variable mass. They wrote for noncalculus-based physics classes, but we solve the same problem using the methods of calculus. Our method highlights the less-familiar but more accurate version of Newton's second law, ∑F =dp/dt. This can help introductory physics students understand a broader definition of Newton's second law and enhance their calculus skills. It also teaches students how to solve a variable-mass problem.

Deterministic and stochastic algorithms for resolving the flow fields in ducts and networks using energy minimization

NASA Astrophysics Data System (ADS)

Sochi, Taha

2016-09-01

Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder-Mead, Quasi-Newton and global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel-Bulkley, Ellis, Ree-Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of computational fluid dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.

Pickup Ion Effect of the Solar Wind Interaction with the Local Interstellar Medium

DOE PAGES

Pogorelov, N. V.; Bedford, M. C.; Kryukov, I. A.; ...

2016-11-22

Pickup ions are created when interstellar neutral atoms resonantly exchange charge with the solar wind (SW) ions, especially in the supersonic part of the wind, where they carry most of the plasma pressure. Here we present numerical simulation results of the 3D heliospheric interface treating pickup ions as a separate proton fluid. To satisfy the fundamental conservation laws, we solve the system of equations describing the flow of the mixture of electrons, thermal protons, and pickup ions. To find the density and pressure of pickup ions behind the termination shock, we employ simple boundary conditions that take into account themore » \\emph{Voyager} observations that showed that the decrease in the kinetic energy of the mixture at the termination shock predominantly contributed to the increase in the pressure of pickup ions. We show that this model adequately describes the flow of the plasma mixture and results in a noticeable decrease in the heliosheath width.« less

Discontinuous Galerkin Approaches for Stokes Flow and Flow in Porous Media

NASA Astrophysics Data System (ADS)

Lehmann, Ragnar; Kaus, Boris; Lukacova, Maria

2014-05-01

Firstly, we present results of a study comparing two different numerical approaches for solving the Stokes equations with strongly varying viscosity: the continuous Galerkin (i.e., FEM) and the discontinuous Galerkin (DG) method. Secondly, we show how the latter method can be extended and applied to flow in porous media governed by Darcy's law. Nonlinearities in the viscosity or other material parameters can lead to discontinuities in the velocity-pressure solution that may not be approximated well with continuous elements. The DG method allows for discontinuities across interior edges of the underlying mesh. Furthermore, depending on the chosen basis functions, it naturally enforces local mass conservation, i.e., in every mesh cell. Computationally, it provides the capability to locally adapt the polynomial degree and needs communication only between directly adjacent mesh cells making it highly flexible and easy to parallelize. The methods are compared for several geophysically relevant benchmarking setups and discussed with respect to speed, accuracy, computational efficiency.

Construction and simulation of a novel continuous traffic flow model

NASA Astrophysics Data System (ADS)

Hwang, Yao-Hsin; Yu, Jui-Ling

2017-12-01

In this paper, we aim to propose a novel mathematical model for traffic flow and apply a newly developed characteristic particle method to solve the associate governing equations. As compared with the existing non-equilibrium higher-order traffic flow models, the present one is put forward to satisfy the following three conditions: Preserve the equilibrium state in the smooth region. Yield an anisotropic propagation of traffic flow information. Expressed with a conservation law form for traffic momentum. These conditions will ensure a more practical simulation in traffic flow physics: The current traffic will not be influenced by the condition in the behind and result in unambiguous condition across a traffic shock. Through analyses of characteristics, stability condition and steady-state solution adherent to the equation system, it is shown that the proposed model actually conform to these conditions. Furthermore, this model can be cast into its characteristic form which, incorporated with the Rankine-Hugoniot relation, is appropriate to be simulated by the characteristic particle method to obtain accurate computational results.

Eulerian and Lagrangian Plasma Jet Modeling for the Plasma Liner Experiment

NASA Astrophysics Data System (ADS)

Hatcher, Richard; Cassibry, Jason; Stanic, Milos; Loverich, John; Hakim, Ammar

2011-10-01

The Plasma Liner Experiment (PLX) aims to demonstrate the feasibility of using spherically-convergent plasma jets to from an imploding plasma liner. Our group has modified two hydrodynamic simulation codes to include radiative loss, tabular equations of state (EOS), and thermal transport. Nautilus, created by TechX Corporation, is a finite-difference Eulerian code which solves the MHD equations formulated as systems of hyperbolic conservation laws. The other is SPHC, a smoothed particle hydrodynamics code produced by Stellingwerf Consulting. Use of the Lagrangian fluid particle approach of SPH is motivated by the ability to accurately track jet interfaces, the plasma vacuum boundary, and mixing of various layers, but Eulerian codes have been in development for much longer and have better shock capturing. We validate these codes against experimental measurements of jet propagation, expansion, and merging of two jets. Precursor jets are observed to form at the jet interface. Conditions that govern evolution of two and more merging jets are explored.

Split Space-Marching Finite-Volume Method for Chemically Reacting Supersonic Flow

NASA Technical Reports Server (NTRS)

Rizzi, Arthur W.; Bailey, Harry E.

1976-01-01

A space-marching finite-volume method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the finite-volume and differential forms of the equations is examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, a representative flow computation is discussed, and some comparisons are made with another method.

Transient regime in second harmonic generation

NASA Astrophysics Data System (ADS)

Szeftel, Jacob; Sandeau, Laure; Sandeau, Nicolas; Delezoide, Camille; Khater, Antoine

2013-09-01

The time growth of the electromagnetic field at the fundamental and double frequencies is studied from the very onset of the second harmonic generation (SHG) process for a set of dipoles lacking a symmetry centre and exhibiting a nonresonant coupling with a classical electromagnetic field. This approach consists first of solving the Schrödinger equation by applying a generalised Rabi rotation to the Hamiltonian describing the light-dipole interaction. This rotation has been devised for the resulting Hamiltonian to show up time-independent for both components of the electromagnetic field at the fundamental frequency and the second harmonic one. Then an energy conservation argument, derived from the Poynting theorem, is introduced to work out an additional relationship between the electromagnetic field and its associated electric polarisation. Finally this analysis yields the full time behaviour of all physical quantities of interest. The calculated results reproduce accurately both the observed spatial oscillations of the SHG intensity (Maker's fringes) and its power law dependence on the intensity of the incoming light at the fundamental frequency.

Physics That Textbook Writers Usually Get Wrong: II. Heat and Energy.

ERIC Educational Resources Information Center

Bauman, Robert P.

1992-01-01

Examines problems that occur with the vocabulary used in physics textbooks related to heat and energy. Discusses the concepts of thermal energy and temperature, conservation of energy laws, and the first law of thermodynamics. (MDH)

7 CFR 631.21 - Compliance with regulatory measures.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 631.21 Agriculture Regulations of the Department of Agriculture (Continued) NATURAL RESOURCES... the implementation and maintenance of the conservation practices in keeping with applicable laws and... others or from any failure to comply with applicable laws or regulations. ...

7 CFR 631.21 - Compliance with regulatory measures.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 631.21 Agriculture Regulations of the Department of Agriculture (Continued) NATURAL RESOURCES... the implementation and maintenance of the conservation practices in keeping with applicable laws and... others or from any failure to comply with applicable laws or regulations. ...

7 CFR 631.21 - Compliance with regulatory measures.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 631.21 Agriculture Regulations of the Department of Agriculture (Continued) NATURAL RESOURCES... the implementation and maintenance of the conservation practices in keeping with applicable laws and... others or from any failure to comply with applicable laws or regulations. ...

7 CFR 631.21 - Compliance with regulatory measures.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 631.21 Agriculture Regulations of the Department of Agriculture (Continued) NATURAL RESOURCES... the implementation and maintenance of the conservation practices in keeping with applicable laws and... others or from any failure to comply with applicable laws or regulations. ...

7 CFR 631.21 - Compliance with regulatory measures.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 631.21 Agriculture Regulations of the Department of Agriculture (Continued) NATURAL RESOURCES... the implementation and maintenance of the conservation practices in keeping with applicable laws and... others or from any failure to comply with applicable laws or regulations. ...

Law School, University of Minnesota, Minneapolis

ERIC Educational Resources Information Center

American School and University, 1977

1977-01-01

The University of Minnesota Law School is a winner in the AS&U 1977 College & University Architectural Competition. The jury commented on the strong recognition of energy conservation and the skillful integration of the building with the existing campus. (Author/MLF)

'Nature Knows No Boundaries': The Role of Nature Conservation in Peacebuilding.

PubMed

Roulin, Alexandre; Abu Rashid, Mansour; Spiegel, Baruch; Charter, Motti; Dreiss, Amélie N; Leshem, Yossi

2017-05-01

Humanity is facing a biodiversity crisis. To solve environmental problems, we bring people from Israel, Jordan, and the Palestinian Authority to the same table. Conservation efforts are beneficial for all communities and facilitate constructive dialog across divides in conflict zones. This pleads for the integration of nature conservation into peacebuilding interventions. Copyright © 2017 Elsevier Ltd. All rights reserved.

Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru

2018-04-01

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

Addressing Students' Difficulties with Faraday's Law: A Guided Problem Solving Approach

ERIC Educational Resources Information Center

Zuza, Kristina; Almudí, José-Manuel; Leniz, Ane; Guisasola, Jenaro

2014-01-01

In traditional teaching, the fundamental concepts of electromagnetic induction are usually quickly analyzed, spending most of the time solving problems in a more or less rote manner. However, physics education research has shown that the fundamental concepts of the electromagnetic induction theory are barely understood by students. This article…

On the Prevention of Juvenile Crime

ERIC Educational Resources Information Center

Lelekov, V. A.; Kosheleva, E. V.

2008-01-01

Crimes committed by juveniles are among the most urgent social problems. Juvenile crime is as prevalent as crime itself is, and it has not been solved completely in any society and cannot be solved through law enforcement measures alone. In this article, the authors discuss the dynamics and structure of juvenile crime in Russia and present data…

Comparison of Numerical Approaches to a Steady-State Landscape Equation

NASA Astrophysics Data System (ADS)

Bachman, S.; Peckham, S.

2008-12-01

A mathematical model of an idealized fluvial landscape has been developed, in which a land surface will evolve to preserve dendritic channel networks as the surface is lowered. The physical basis for this model stems from the equations for conservation of mass for water and sediment. These equations relate the divergence of the 2D vector fields showing the unit-width discharge of water and sediment to the excess rainrate and tectonic uplift on the land surface. The 2D flow direction is taken to be opposite to the water- surface gradient vector. These notions are combined with a generalized Manning-type flow resistance formula and a generalized sediment transport law to give a closed mathematical system that can, in principle, be solved for all variables of interest: discharge of water and sediment, land surface height, vertically- averaged flow velocity, water depth, and shear stress. The hydraulic geometry equations (Leopold et. al, 1964, 1995) are used to incorporate width, depth, velocity, and slope of river channels as powers of the mean-annual river discharge. Combined, they give the unit- width discharge of the stream as a power, γ, of the water surface slope. The simplified steady-state model takes into account three components among those listed above: conservation of mass for water, flow opposite the gradient, and a slope-discharge exponent γ = -1 to reflect mature drainage networks. The mathematical representation of this model appears as a second-order hyperbolic partial differential equation (PDE) where the diffusivity is inversely proportional to the square of the local surface slope. The highly nonlinear nature of this PDE has made it very difficult to solve both analytically and numerically. We present simplistic analytic solutions to this equation which are used to test the validity of the numerical algorithms. We also present three such numerical approaches which have been used in solving the differential equation. The first is based on a nonlinear diffusion filtering technique (Welk et. al, 2007) that has been applied successfully in the context of image processing. The second uses a Ritz finite element approach to the Euler-Lagrange formulation of the PDE in which an eighth degree polynomial is solved whose coefficients are locally dependent on slope and elevation. Lastly, we show a variant to the diffusion filtering approach in which a single-stage Runge-Kutta method is used to iterate a time-derivative to steady- state. The relative merits and drawbacks of these approaches are discussed, as well as stability and consistency requirements.

Systems of conservation laws with third-order Hamiltonian structures

NASA Astrophysics Data System (ADS)

Ferapontov, Evgeny V.; Pavlov, Maxim V.; Vitolo, Raffaele F.

2018-06-01

We investigate n-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences of lines in P^{n+2} satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space W of dimension n+2, classify n-tuples of skew-symmetric 2-forms A^{α } \\in Λ^2(W) such that φ _{β γ }A^{β }\\wedge A^{γ }=0, for some non-degenerate symmetric φ.

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

NASA Astrophysics Data System (ADS)

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

2005-01-01

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

Carl Neumann versus Rudolf Clausius on the propagation of electrodynamic potentials

NASA Astrophysics Data System (ADS)

Archibald, Thomas

1986-09-01

In the late 1860's, German electromagnetic theorists employing W. Weber's velocity-dependent force law were forced to confront the issue of energy conservation. One attempt to formulate a conservation law for such forces was due to Carl Neumann, who introduced a model employing retarded potentials in 1868. Rudolf Clausius quickly pointed out certain problems with the physical interpretation of Neumann's mathematical formalism. The debate between the two men continued until the 1880's and illustrates the strictures facing mathematical approaches to physical problems during this prerelativistic, pre-Maxwellian period.

High order filtering methods for approximating hyperbolic systems of conservation laws

NASA Technical Reports Server (NTRS)

Lafon, F.; Osher, S.

1991-01-01

The essentially nonoscillatory (ENO) schemes, while potentially useful in the computation of discontinuous solutions of hyperbolic conservation-law systems, are computationally costly relative to simple central-difference methods. A filtering technique is presented which employs central differencing of arbitrarily high-order accuracy except where a local test detects the presence of spurious oscillations and calls upon the full ENO apparatus to remove them. A factor-of-three speedup is thus obtained over the full-ENO method for a wide range of problems, with high-order accuracy in regions of smooth flow.

Simulations of relativistic quantum plasmas using real-time lattice scalar QED

NASA Astrophysics Data System (ADS)

Shi, Yuan; Xiao, Jianyuan; Qin, Hong; Fisch, Nathaniel J.

2018-05-01

Real-time lattice quantum electrodynamics (QED) provides a unique tool for simulating plasmas in the strong-field regime, where collective plasma scales are not well separated from relativistic-quantum scales. As a toy model, we study scalar QED, which describes self-consistent interactions between charged bosons and electromagnetic fields. To solve this model on a computer, we first discretize the scalar-QED action on a lattice, in a way that respects geometric structures of exterior calculus and U(1)-gauge symmetry. The lattice scalar QED can then be solved, in the classical-statistics regime, by advancing an ensemble of statistically equivalent initial conditions in time, using classical field equations obtained by extremizing the discrete action. To demonstrate the capability of our numerical scheme, we apply it to two example problems. The first example is the propagation of linear waves, where we recover analytic wave dispersion relations using numerical spectrum. The second example is an intense laser interacting with a one-dimensional plasma slab, where we demonstrate natural transition from wakefield acceleration to pair production when the wave amplitude exceeds the Schwinger threshold. Our real-time lattice scheme is fully explicit and respects local conservation laws, making it reliable for long-time dynamics. The algorithm is readily parallelized using domain decomposition, and the ensemble may be computed using quantum parallelism in the future.

Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

NASA Astrophysics Data System (ADS)

Liang, Hong; Xu, Jiangrong; Chen, Jiangxing; Wang, Huili; Chai, Zhenhua; Shi, Baochang

2018-03-01

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.

Wave propagation through an inhomogeneous slab sandwiched by the piezoelectric and the piezomagnetic half spaces.

PubMed

Jiao, Fengyu; Wei, Peijun; Li, Li

2017-01-01

Wave propagation through a gradient slab sandwiched by the piezoelectric and the piezomagnetic half spaces are studied in this paper. First, the secular equations in the transverse isotropic piezoelectric/piezomagnetic half spaces are derived from the general dynamic equation. Then, the state vectors at piezoelectric and piezomagnetic half spaces are related to the amplitudes of various possible waves. The state transfer equation of the functionally graded slab is derived from the equations of motion by the reduction of order, and the transfer matrix of the functionally gradient slab is obtained by solving the state transfer equation with the spatial-varying coefficient. Finally, the continuous interface conditions are used to lead to the resultant algebraic equations. The algebraic equations are solved to obtain the amplitude ratios of various waves which are further used to obtain the energy reflection and transmission coefficients of various waves. The numerical results are shown graphically and are validated by the energy conservation law. Based on the numerical results on the fives of gradient profiles, the influences of the graded slab on the wave propagation are discussed. It is found that the reflection and transmission coefficients are obviously dependent upon the gradient profile. The various surface waves are more sensitive to the gradient profile than the bulk waves. Copyright © 2016 Elsevier B.V. All rights reserved.

National Energy Conservation Policy Act. Public Law 95-619, 95th Congress.

ERIC Educational Resources Information Center

Congress of the U.S., Washington, DC.

This publication is the National Energy Conservation Policy Act (P.L. 95-619). The purposes of this act are to provide for the regulation of interstate commerce, to reduce the growth in demand for energy in the United States, and to conserve nonrenewable energy resources produced in this nation and elsewhere, without inhibiting beneficial economic…

Conservative discretization of the Landau collision integral

DOE PAGES

Hirvijoki, E.; Adams, M. F.

2017-03-28

Here we describe a density, momentum-, and energy-conserving discretization of the nonlinear Landau collision integral. The method is suitable for both the finite-element and discontinuous Galerkin methods and does not require structured meshes. The conservation laws for the discretization are proven algebraically and demonstrated numerically for an axially symmetric nonlinear relaxation problem using a finite-element implementation.

A review of conservation legislation in Nepal: Past progress and future needs

NASA Astrophysics Data System (ADS)

Heinen, Joel T.; Kattel, Bijaya

1992-11-01

Nepal is considered a leader among developing nations with regard to conservation legislation and programs; it was among the first Asian nations to develop national conservation legislation, sign CITES, and develop a national conservation strategy. We review the history of modern conservation law in Nepal from the Rana period (early 1950s) to the present. The early legislation focused mainly on strict preservation of areas and species; this phase culminated in the National Parks and Wildlife Conservation Act of 1973. Subsequent legislation has evolved more in the direction of an integrated, holistic approach to conservation and is beginning to incorporate the participation of local people; subsequent amendments to the 1973 act allowed greater rights to rural villagers, and the designation of conservation areas in addition to the more strictly defined protected areas (national parks, wildlife reserves, etc.). Our review of conservation legislation suggests that Nepal has had many successes to date; the country has a protected area system covering over 10% of its land area, and many target species are recovering in parks and reserves. There are also some causes of concern, including staff shortages, financial constraints within the Department of National Parks and Wildlife Conservation, and the fact that there is little legal infrastructure outside of protected areas to enforce conservation laws; further, some aspects of hunting regulations are in need of revision. Primary needs include a comprehensive review of these policies and a nationalized strategy to ameliorate the shortcomings.

Testing Theoretical Models of Magnetic Damping Using an Air Track

ERIC Educational Resources Information Center

Vidaurre, Ana; Riera, Jaime; Monsoriu, Juan A.; Gimenez, Marcos H.

2008-01-01

Magnetic braking is a long-established application of Lenz's law. A rigorous analysis of the laws governing this problem involves solving Maxwell's equations in a time-dependent situation. Approximate models have been developed to describe different experimental results related to this phenomenon. In this paper we present a new method for the…

School-Based Partnerships: A Problem-Solving Strategy. COPS Innovations

ERIC Educational Resources Information Center

Uchida, Craig D.; Solomon, Shellie; Katz, Charles M.; Pappas, Cynthia E.

2006-01-01

The Community Oriented Policing Services (COPS) Office funded the School-Based Partnerships (SBP) grant program for the purpose of partnering law enforcement agencies with schools to address crime and disorder problems in and around middle and high schools. In Fiscal Years 1998 and 1999, the COPS Office awarded 275 law enforcement agencies more…

Learning and Learning-to-Learn by Doing: Simulating Corporate Practice in Law School.

ERIC Educational Resources Information Center

Okamoto, Karl S.

1995-01-01

A law school course in advanced corporate legal practice is described. The course, a series of simulated lawyering tasks centered on a hypothetical leveraged buyout transaction, is designed to go beyond basic legal analysis to develop professional expertise in legal problem solving. The course description includes goals, syllabus design,…

Consequences of Symmetries on the Analysis and Construction of Turbulence Models

NASA Astrophysics Data System (ADS)

Razafindralandy, Dina; Hamdouni, Aziz

2006-05-01

Since they represent fundamental physical properties in turbulence (conservation laws, wall laws, Kolmogorov energy spectrum, ...), symmetries are used to analyse common turbulence models. A class of symmetry preserving turbulence models is proposed. This class is refined such that the models respect the second law of thermodynamics. Finally, an example of model belonging to the class is numerically tested.

A mass-conserving multiphase lattice Boltzmann model for simulation of multiphase flows

NASA Astrophysics Data System (ADS)

Niu, Xiao-Dong; Li, You; Ma, Yi-Ren; Chen, Mu-Feng; Li, Xiang; Li, Qiao-Zhong

2018-01-01

In this study, a mass-conserving multiphase lattice Boltzmann (LB) model is proposed for simulating the multiphase flows. The proposed model developed in the present study is to improve the model of Shao et al. ["Free-energy-based lattice Boltzmann model for simulation of multiphase flows with density contrast," Phys. Rev. E 89, 033309 (2014)] by introducing a mass correction term in the lattice Boltzmann model for the interface. The model of Shao et al. [(the improved Zheng-Shu-Chew (Z-S-C model)] correctly considers the effect of the local density variation in momentum equation and has an obvious improvement over the Zheng-Shu-Chew (Z-S-C) model ["A lattice Boltzmann model for multiphase flows with large density ratio," J. Comput. Phys. 218(1), 353-371 (2006)] in terms of solution accuracy. However, due to the physical diffusion and numerical dissipation, the total mass of each fluid phase cannot be conserved correctly. To solve this problem, a mass correction term, which is similar to the one proposed by Wang et al. ["A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio," J. Comput. Phys. 290, 336-351 (2015)], is introduced into the lattice Boltzmann equation for the interface to compensate the mass losses or offset the mass increase. Meanwhile, to implement the wetting boundary condition and the contact angle, a geometric formulation and a local force are incorporated into the present mass-conserving LB model. The proposed model is validated by verifying the Laplace law, simulating both one and two aligned droplets splashing onto a liquid film, droplets standing on an ideal wall, droplets with different wettability splashing onto smooth wax, and bubbles rising under buoyancy. Numerical results show that the proposed model can correctly simulate multiphase flows. It was found that the mass is well-conserved in all cases considered by the model developed in the present study. The developed model has been found to perform better than the improved Z-S-C model in this aspect.

A New Rate Law Describing Microbial Respiration

PubMed Central

Jin, Qusheng; Bethke, Craig M.

2003-01-01

The rate of microbial respiration can be described by a rate law that gives the respiration rate as the product of a rate constant, biomass concentration, and three terms: one describing the kinetics of the electron-donating reaction, one for the kinetics of the electron-accepting reaction, and a thermodynamic term accounting for the energy available in the microbe's environment. The rate law, derived on the basis of chemiosmotic theory and nonlinear thermodynamics, is unique in that it accounts for both forward and reverse fluxes through the electron transport chain. Our analysis demonstrates how a microbe's respiration rate depends on the thermodynamic driving force, i.e., the net difference between the energy available from the environment and energy conserved as ATP. The rate laws commonly applied in microbiology, such as the Monod equation, are specific simplifications of the general law presented. The new rate law is significant because it affords the possibility of extrapolating in a rigorous manner from laboratory experiment to a broad range of natural conditions, including microbial growth where only limited energy is available. The rate law also provides a new explanation of threshold phenomena, which may reflect a thermodynamic equilibrium where the energy released by electron transfer balances that conserved by ADP phosphorylation. PMID:12676718

Conceptual Versus Algorithmic Problem-solving: Focusing on Problems Dealing with Conservation of Matter in Chemistry

NASA Astrophysics Data System (ADS)

Salta, Katerina; Tzougraki, Chryssa

2011-08-01

The students' performance in various types of problems dealing with the conservation of matter during chemical reactions has been investigated at different levels of schooling. The participants were 499 ninth grade (ages 14, 15 years) and 624 eleventh grade (ages 16, 17 years) Greek students. Data was collected using a written questionnaire concerning basic chemical concepts. Results of statistical factor and correlation analysis confirmed the classification of the problems used in three types: "algorithmic-type", "particulate-type", and "conceptual-type". All the students had a far better performance in "particulate-type" problems than in the others. Although students' ability in solving "algorithmic-type" problem increases as their school experience in chemistry progresses, their ability in solving "conceptual-type" problems decreases. Students' achievement in chemistry was measured by a Chemical Concepts Test (CCT) containing 57 questions of various forms. High-achievement students scored higher both on "algorithmic-type" and "particulate-type" problems than low achievers with the greatest difference observed in solving "algorithmic-type" problems. It is concluded that competence in "particulate-type" and "algorithmic-type" problem solving may be independent of competence in solving "conceptual-type" ones. Furthermore, it was found that students' misconceptions concerning chemical reactions and equivalence between mass and energy are impediments to their problem solving abilities. Finally, based on the findings, few suggestions concerning teaching practices are discussed.

Stochastic Mixing Model with Power Law Decay of Variance

NASA Technical Reports Server (NTRS)

Fedotov, S.; Ihme, M.; Pitsch, H.

2003-01-01

Here we present a simple stochastic mixing model based on the law of large numbers (LLN). The reason why the LLN is involved in our formulation of the mixing problem is that the random conserved scalar c = c(t,x(t)) appears to behave as a sample mean. It converges to the mean value mu, while the variance sigma(sup 2)(sub c) (t) decays approximately as t(exp -1). Since the variance of the scalar decays faster than a sample mean (typically is greater than unity), we will introduce some non-linear modifications into the corresponding pdf-equation. The main idea is to develop a robust model which is independent from restrictive assumptions about the shape of the pdf. The remainder of this paper is organized as follows. In Section 2 we derive the integral equation from a stochastic difference equation describing the evolution of the pdf of a passive scalar in time. The stochastic difference equation introduces an exchange rate gamma(sub n) which we model in a first step as a deterministic function. In a second step, we generalize gamma(sub n) as a stochastic variable taking fluctuations in the inhomogeneous environment into account. In Section 3 we solve the non-linear integral equation numerically and analyze the influence of the different parameters on the decay rate. The paper finishes with a conclusion.

Implementation of a hybrid particle code with a PIC description in r–z and a gridless description in ϕ into OSIRIS

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

Davidson, A., E-mail: davidsoa@physics.ucla.edu; Tableman, A., E-mail: Tableman@physics.ucla.edu; An, W., E-mail: anweiming@ucla.edu

2015-01-15

For many plasma physics problems, three-dimensional and kinetic effects are very important. However, such simulations are very computationally intensive. Fortunately, there is a class of problems for which there is nearly azimuthal symmetry and the dominant three-dimensional physics is captured by the inclusion of only a few azimuthal harmonics. Recently, it was proposed [1] to model one such problem, laser wakefield acceleration, by expanding the fields and currents in azimuthal harmonics and truncating the expansion. The complex amplitudes of the fundamental and first harmonic for the fields were solved on an r–z grid and a procedure for calculating the complexmore » current amplitudes for each particle based on its motion in Cartesian geometry was presented using a Marder's correction to maintain the validity of Gauss's law. In this paper, we describe an implementation of this algorithm into OSIRIS using a rigorous charge conserving current deposition method to maintain the validity of Gauss's law. We show that this algorithm is a hybrid method which uses a particles-in-cell description in r–z and a gridless description in ϕ. We include the ability to keep an arbitrary number of harmonics and higher order particle shapes. Examples for laser wakefield acceleration, plasma wakefield acceleration, and beam loading are also presented and directions for future work are discussed.« less

International and European law on protected areas and climate change: need for adaptation or implementation?

PubMed

Cliquet, A

2014-10-01

The protection and management of protected areas must be adapted to the effects of climate change. An important question is if the law on protected areas is capable of dealing with the required changes. In general, both international nature conventions and European Union nature conservation law do not contain any specific provisions on climate change and protected areas. Attention has been paid to this link in non-binding decisions and policy documents. In order to adapt the law to increased dynamics from climate change, more flexibility is needed. This flexibility should not be understood as "legal" flexibility, in the sense of the weakening nature conservation provisions. Scientific uncertainties on the effects of climate change might conflict with the need for legal certainties. In order to adapt to the effects of climate change, the two crucial elements are the strengthening of core protected areas and connectivity between the core areas. At the international level, both elements can be found in non-binding documents. International law enables the required adaptation; however, it often lacks concrete obligations. A stronger legal framework can be found at the level of the European Union. The Birds and Habitats Directives contain sufficient tools to deal with the effects of climate change. The Directives have been insufficiently implemented so far. Especially the central goals of reaching a favorable conservation status and connectivity measures need to be addressed much more in the future.

WATER CONSERVATION: LOCAL SOLUTIONS TO A GLOBAL PROBLEM

EPA Science Inventory

Water conservation issues are discussed. Local solutions to a global problem include changing old habits relating to the usage and abuse of water resources. While the suggested behavioral changes may not solve the world's pending water crisis, they may ease the impact of the l...

A Novel Blast-mitigation Concept for Light Tactical Vehicles

DTIC Science & Technology

2013-01-01

analysis which utilizes the mass and energy (but not linear momentum ) conservation equations is provided. It should be noted that the identical final...results could be obtained using an analogous analysis which combines the mass and the linear momentum conservation equations. For a calorically...governing mass, linear momentum and energy conservation and heat conduction equations are solved within ABAQUS/ Explicit with a second-order accurate

40 CFR 256.30 - Requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... law from entering into long-term contracts for the supply of solid waste to resource recovery... AND IMPLEMENTATION OF STATE SOLID WASTE MANAGEMENT PLANS Resource Conservation and Resource Recovery... resource conservation and recovery, the State plan shall provide for a policy and strategy for...

40 CFR 256.30 - Requirements.

Code of Federal Regulations, 2010 CFR

2010-07-01

... law from entering into long-term contracts for the supply of solid waste to resource recovery... AND IMPLEMENTATION OF STATE SOLID WASTE MANAGEMENT PLANS Resource Conservation and Resource Recovery... resource conservation and recovery, the State plan shall provide for a policy and strategy for...

40 CFR 256.30 - Requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... law from entering into long-term contracts for the supply of solid waste to resource recovery... AND IMPLEMENTATION OF STATE SOLID WASTE MANAGEMENT PLANS Resource Conservation and Resource Recovery... resource conservation and recovery, the State plan shall provide for a policy and strategy for...

40 CFR 256.30 - Requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... law from entering into long-term contracts for the supply of solid waste to resource recovery... AND IMPLEMENTATION OF STATE SOLID WASTE MANAGEMENT PLANS Resource Conservation and Resource Recovery... resource conservation and recovery, the State plan shall provide for a policy and strategy for...

40 CFR 256.30 - Requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... law from entering into long-term contracts for the supply of solid waste to resource recovery... AND IMPLEMENTATION OF STATE SOLID WASTE MANAGEMENT PLANS Resource Conservation and Resource Recovery... resource conservation and recovery, the State plan shall provide for a policy and strategy for...

Conservation Laws in Weak Interactions

DOE R&D Accomplishments Database

Lee, T. D.

1957-03-01

Notes are presented on four lectures given at Harvard University in March 1957 on elementary particle physics, the theta-tau problem, validity of parity conservation, tests for invariance under P, C, and T, and the two-component theory of the neutrino. (W.D.M.)

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Bey, Kim S.

1994-01-01

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

Thermodynamics of third-order Lovelock-AdS black holes in the presence of Born-Infeld type nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Hendi, S. H.; Dehghani, A.

2015-03-01

In this paper, we obtain topological black hole solutions of third-order Lovelock gravity coupled with two classes of Born-Infeld-type nonlinear electrodynamics with anti-de Sitter asymptotic structure. We investigate geometric and thermodynamics properties of the solutions and obtain conserved quantities of the black holes. We examine the first law of thermodynamics and find that the conserved and thermodynamic quantities of the black hole solutions satisfy the first law of thermodynamics. Finally, we calculate the heat capacity and determinant of the Hessian matrix to evaluate thermal stability in both canonical and grand canonical ensembles. Moreover, we consider the extended phase space thermodynamics to obtain a generalized first law of thermodynamics as well as the extended Smarr formula.

Regularized Chapman-Enskog expansion for scalar conservation laws

NASA Technical Reports Server (NTRS)

Schochet, Steven; Tadmor, Eitan

1990-01-01

Rosenau has recently proposed a regularized version of the Chapman-Enskog expansion of hydrodynamics. This regularized expansion resembles the usual Navier-Stokes viscosity terms at law wave-numbers, but unlike the latter, it has the advantage of being a bounded macroscopic approximation to the linearized collision operator. The behavior of Rosenau regularization of the Chapman-Enskog expansion (RCE) is studied in the context of scalar conservation laws. It is shown that thie RCE model retains the essential properties of the usual viscosity approximation, e.g., existence of traveling waves, monotonicity, upper-Lipschitz continuity..., and at the same time, it sharpens the standard viscous shock layers. It is proved that the regularized RCE approximation converges to the underlying inviscid entropy solution as its mean-free-path epsilon approaches 0, and the convergence rate is estimated.

Uzawa algorithm to solve elastic and elastic-plastic fretting wear problems within the bipotential framework

NASA Astrophysics Data System (ADS)

Ning, Po; Feng, Zhi-Qiang; Quintero, Juan Antonio Rojas; Zhou, Yang-Jing; Peng, Lei

2018-03-01

This paper deals with elastic and elastic-plastic fretting problems. The wear gap is taken into account along with the initial contact distance to obtain the Signorini conditions. Both the Signorini conditions and the Coulomb friction laws are written in a compact form. Within the bipotential framework, an augmented Lagrangian method is applied to calculate the contact forces. The Archard wear law is then used to calculate the wear gap at the contact surface. The local fretting problems are solved via the Uzawa algorithm. Numerical examples are performed to show the efficiency and accuracy of the proposed approach. The influence of plasticity has been discussed.

Mathematical modeling of impact of two metal plates using two-fluid approach

NASA Astrophysics Data System (ADS)

Utkin, P. S.; Fortova, S. V.

2018-01-01

The paper is devoted to the development of the two-fluid mathematical model and the computational algorithm for the modeling of two metal plates impact. In one-dimensional case the governing system of equations comprises seven equations: three conservation laws for each fluid and transfer equation for the volume fraction of one of the fluids. Both fluids are considered to be compressible and equilibrium on velocities. Pressures equilibrium is used as fluids interface condition. The system has hyperbolic type but could not be written in the conservative form because of nozzling terms in the right-hand side of the equations. The algorithm is based on the Harten-Lax-van Leer numerical flux function. The robust computation in the presence of the interface boundary is carried out due to the special pressure relaxation procedure. The problem is solved using stiffened gas equations of state for each fluid. The parameters in the equations of state are calibrated using the results of computations using wide-range equations of state for the metals. In simulations of metal plates impact we get two shocks after the initial impact that propagate to the free surfaces of the samples. The characteristics of shock waves are close (maximum relative error in characteristics of shocks is not greater than 7%) to the data from the wide-range equations of states computations.

SPH non-Newtonian Model for Ice Sheet and Ice Shelf Dynamics

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

Tartakovsky, Alexandre M.; Pan, Wenxiao; Monaghan, Joseph J.

2012-07-07

We propose a new three-dimensional smoothed particle hydrodynamics (SPH) non-Newtonian model to study coupled ice sheet and ice shelf dynamics. Most existing ice sheet numerical models use a grid-based Eulerian approach, and are usually restricted to shallow ice sheet and ice shelf approximations of the momentum conservation equation. SPH, a fully Lagrangian particle method, solves the full momentum conservation equation. SPH method also allows modeling of free-surface flows, large material deformation, and material fragmentation without employing complex front-tracking schemes, and does not require re-meshing. As a result, SPH codes are highly scalable. Numerical accuracy of the proposed SPH model ismore » first verified by simulating a plane shear flow with a free surface and the propagation of a blob of ice along a horizontal surface. Next, the SPH model is used to investigate the grounding line dynamics of ice sheet/shelf. The steady position of the grounding line, obtained from our SPH simulations, is in good agreement with laboratory observations for a wide range of bedrock slopes, ice-to-fluid density ratios, and flux. We examine the effect of non-Newtonian behavior of ice on the grounding line dynamics. The non-Newtonian constitutive model is based on Glen's law for a creeping flow of a polycrystalline ice. Finally, we investigate the effect of a bedrock geometry on a steady-state position of the grounding line.« less

Issues and challenges of mangrove conservation in the Anthropocene - Desafios de la conservacion del mangle en el Antropoceno

Treesearch

Ariel. E. Lugo; Ernesto Medina; Kathleen McGinley

2014-01-01

This essay addresses the conservation issues facing mangroves in the Anthropocene, defined as the era of human domination over the world. We review the laws, policies, international agreements, and local actions that address the conservation of mangrove forests in the Neotropics and relate them to the Anthropocene. Collaboration between governments, non-governmental...

Advances in Energy Conservation of China Steel Industry

PubMed Central

Sun, Wenqiang; Cai, Jiuju; Ye, Zhu

2013-01-01

The course, technical progresses, and achievements of energy conservation of China steel industry (CSI) during 1980–2010 were summarized. Then, the paper adopted e-p method to analyze the variation law and influencing factors of energy consumptions of large- and medium-scale steel plants within different stages. It is pointed out that energy consumption per ton of crude steel has been almost one half lower in these thirty years, with 60% as direct energy conservation owing to the change of process energy consumption and 40% as indirect energy conservation attributed to the adjustment of production structure. Next, the latest research progress of some key common technologies in CSI was introduced. Also, the downtrend of energy consumption per ton of crude steel and the potential energy conservation for CSI during 2011–2025 were forecasted. Finally, it is indicated that the key topic of the next 15 years' research on the energy conservation of CSI is the synergistic operation of material flow and energy flow. It could be achieved by the comprehensive study on energy flow network optimization, such as production, allocation, utilization, recovery, reuse, and resource, according to the energy quantity, quality, and user demand following the first and second laws of thermodynamics. PMID:23533344

Advances in energy conservation of China steel industry.

PubMed

Sun, Wenqiang; Cai, Jiuju; Ye, Zhu

2013-01-01

The course, technical progresses, and achievements of energy conservation of China steel industry (CSI) during 1980-2010 were summarized. Then, the paper adopted e-p method to analyze the variation law and influencing factors of energy consumptions of large- and medium-scale steel plants within different stages. It is pointed out that energy consumption per ton of crude steel has been almost one half lower in these thirty years, with 60% as direct energy conservation owing to the change of process energy consumption and 40% as indirect energy conservation attributed to the adjustment of production structure. Next, the latest research progress of some key common technologies in CSI was introduced. Also, the downtrend of energy consumption per ton of crude steel and the potential energy conservation for CSI during 2011-2025 were forecasted. Finally, it is indicated that the key topic of the next 15 years' research on the energy conservation of CSI is the synergistic operation of material flow and energy flow. It could be achieved by the comprehensive study on energy flow network optimization, such as production, allocation, utilization, recovery, reuse, and resource, according to the energy quantity, quality, and user demand following the first and second laws of thermodynamics.

Varying Use of Conceptual Metaphors across Levels of Expertise in Thermodynamics

ERIC Educational Resources Information Center

Jeppsson, Fredrik; Haglund, Jesper; Amin, Tamer G.

2015-01-01

Many studies have previously focused on how people with different levels of expertise solve physics problems. In early work, focus was on characterising differences between experts and novices and a key finding was the central role that propositionally expressed principles and laws play in expert, but not novice, problem-solving. A more recent…

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohammed A.

2014-09-01

In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach

Circulation-based Modeling of Gravity Currents

NASA Astrophysics Data System (ADS)

Meiburg, E. H.; Borden, Z.

2013-05-01

Atmospheric and oceanic flows driven by predominantly horizontal density differences, such as sea breezes, thunderstorm outflows, powder snow avalanches, and turbidity currents, are frequently modeled as gravity currents. Efforts to develop simplified models of such currents date back to von Karman (1940), who considered a two-dimensional gravity current in an inviscid, irrotational and infinitely deep ambient. Benjamin (1968) presented an alternative model, focusing on the inviscid, irrotational flow past a gravity current in a finite-depth channel. More recently, Shin et al. (2004) proposed a model for gravity currents generated by partial-depth lock releases, considering a control volume that encompasses both fronts. All of the above models, in addition to the conservation of mass and horizontal momentum, invoke Bernoulli's law along some specific streamline in the flow field, in order to obtain a closed system of equations that can be solved for the front velocity as function of the current height. More recent computational investigations based on the Navier-Stokes equations, on the other hand, reproduce the dynamics of gravity currents based on the conservation of mass and momentum alone. We propose that it should therefore be possible to formulate a fundamental gravity current model without invoking Bernoulli's law. The talk will show that the front velocity of gravity currents can indeed be predicted as a function of their height from mass and momentum considerations alone, by considering the evolution of interfacial vorticity. This approach does not require information on the pressure field and therefore avoids the need for an energy closure argument such as those invoked by the earlier models. Predictions by the new theory are shown to be in close agreement with direct numerical simulation results. References Von Karman, T. 1940 The engineer grapples with nonlinear problems, Bull. Am. Math Soc. 46, 615-683. Benjamin, T.B. 1968 Gravity currents and related phenomena, J. Fluid Mech. 31, 209-248. Shin, J.O., Dalziel, S.B. and Linden, P.F. 2004 Gravity currents produced by lock exchange, J. Fluid Mech. 521, 1-34.

Correction to the Beer-Lambert-Bouguer law for optical absorption.

PubMed

Abitan, Haim; Bohr, Henrik; Buchhave, Preben

2008-10-10

The Beer-Lambert-Bouguer absorption law, known as Beer's law for absorption in an optical medium, is precise only at power densities lower than a few kW. At higher power densities this law fails because it neglects the processes of stimulated emission and spontaneous emission. In previous models that considered those processes, an analytical expression for the absorption law could not be obtained. We show here that by utilizing the Lambert W-function, the two-level energy rate equation model is solved analytically, and this leads into a general absorption law that is exact because it accounts for absorption as well as stimulated and spontaneous emission. The general absorption law reduces to Beer's law at low power densities. A criterion for its application is given along with experimental examples. (c) 2008 Optical Society of America

Investigating the Effect of Complexity Factors in Gas Law Problems

ERIC Educational Resources Information Center

Schuttlefield, Jennifer D.; Kirk, John; Pienta, Norbert J.; Tang, Hui

2012-01-01

Undergraduate students were asked to complete gas law questions using a Web-based tool as a first step in our understanding of the role of cognitive load in chemistry word questions and in helping us assess student problem-solving. Each question contained five different complexity factors, which were randomly assigned by the tool so that a…

Experimentally Building a Qualitative Understanding of Newton's Second Law

ERIC Educational Resources Information Center

Gates, Joshua

2014-01-01

Newton's second law is one of the cornerstones of the introductory physics curriculum, but it can still trouble a large number of students well after its introduction, hobbling their ability to apply the concept to problem solving and to related concepts, such as momentum, circular motion, and orbits. While there are several possibilities for…

The Cycle of Special Education Policy: Implications for Policy Research.

ERIC Educational Resources Information Center

Intriligator, Barbara A.

Although Public Law 94-142 (Education for All Handicapped Children Act) raised public awareness of the civil rights of the handicapped, the policy problems that it was intended to solve included more than civil rights issues. In particular, the law did not provide for modifications of its policies in improving public education opportunities for…

7 CFR 633.2 - Definitions.

Code of Federal Regulations, 2010 CFR

2010-01-01

... organized pursuant to applicable State law to promote and undertake actions for the conservation of soil... the United States Department of Agriculture, formerly called the Soil Conservation Service. Operator... and improvement of water quality; (3) Attenuation of water flows due to flooding; (4) The recharge of...

7 CFR 633.2 - Definitions.

Code of Federal Regulations, 2011 CFR

2011-01-01

... organized pursuant to applicable State law to promote and undertake actions for the conservation of soil... the United States Department of Agriculture, formerly called the Soil Conservation Service. Operator... and improvement of water quality; (3) Attenuation of water flows due to flooding; (4) The recharge of...

MHD mixed convection analysis of non-Newtonian power law fluid in an open channel with round cavity

NASA Astrophysics Data System (ADS)

Bose, Pritom; Rakib, Tawfiqur; Das, Sourav; Rabbi, Khan Md.; Mojumder, Satyajit

2017-06-01

In this study, magneto-hydrodynamic (MHD) mixed convection flow through a channel with a round cavity at bottom wall using non-Newtonian power law fluid is analysed numerically. The cavity is kept at uniformly high temperature whereas rest of the bottom wall is insulated and top wall of the channel is maintained at a temperature lower than cavity temperature. Grid independency test and code validation are performed to justify the computational accuracy before solving the present problem. Galerkin weighted residual method is appointed to solve the continuity, momentum and energy equations. The problem is solved for wide range of pertinent parameters like Rayleigh number (Ra= 103 - 105), Hartmann number (Ha= 0 - 60) and power law index (n= 0.5 - 1.5) at constant Richardson number Ri= 1.0. The flow and thermal field have been thoroughly discussed through streamline and isothermal lines respectively. The heat transfer performance of the given study is illustrated by average Nusselt number plots. Result of this investigation indicates that heat transfer is highest for dilatant fluids at this configuration and they perform better (47% more heat transfer) in absence of magnetic field. The retardation of heat transfer is offset by shear thickening nature of non-Newtonian fluid.

Introducing Environmental Law in the Undergraduate Curriculum.

ERIC Educational Resources Information Center

Centner, Terence J.; Geyer, L. Leon

1993-01-01

Discusses the development of an undergraduate environmental law course. Initial considerations in course development include the instruction unit, student needs, choice of instructor, and text. Presents materials covered under categories of pollution prevention, conservation and sustainable systems, land use and local government, and cleanup and…

Learning Physics in a Water Park

ERIC Educational Resources Information Center

Cabeza, Cecilia; Rubido, Nicolás; Martí, Arturo C.

2014-01-01

Entertaining and educational experiments that can be conducted in a water park, illustrating physics concepts, principles and fundamental laws, are described. These experiments are suitable for students ranging from senior secondary school to junior university level. Newton's laws of motion, Bernoulli's equation, based on the conservation of…

Application of Hamilton's Law of Varying Action

NASA Technical Reports Server (NTRS)

Bailey, C. D.

1973-01-01

The application of Hamilton's Law to the direct solution of nonstationary as well as stationary problems in mechanics of solids is discussed. Solutions are demonstrated for conservative and monconservative, stationary and/or nonstationary particle motion. Mathematical models are developed to establish the relationships of the parameters.

Test of Von Baer's law of the conservation of early development.

PubMed

Poe, Steven

2006-11-01

One of the oldest and most pervasive ideas in comparative embryology is the perceived evolutionary conservation of early ontogeny relative to late ontogeny. Karl Von Baer first noted the similarity of early ontogeny across taxa, and Ernst Haeckel and Charles Darwin gave evolutionary interpretation to this phenomenon. In spite of a resurgence of interest in comparative embryology and the development of mechanistic explanations for Von Baer's law, the pattern itself has been largely untested. Here, I use statistical phylogenetic approaches to show that Von Baer's law is an unnecessarily complex explanation of the patterns of ontogenetic timing in several clades of vertebrates. Von Baer's law suggests a positive correlation between ontogenetic time and amount of evolutionary change. I compare ranked position in ontogeny to frequency of evolutionary change in rank for developmental events and find that these measures are not correlated, thus failing to support Von Baer's model. An alternative model that postulates that small changes in ontogenetic rank are evolutionarily easier than large changes is tentatively supported.

Definition of (so MIScalled) ''Complexity'' as UTTER-SIMPLICITY!!! Versus Deviations From it as Complicatedness-Measure

NASA Astrophysics Data System (ADS)

Young, F.; Siegel, Edward Carl-Ludwig

2011-03-01

(so MIScalled) "complexity" with INHERENT BOTH SCALE-Invariance Symmetry-RESTORING, AND 1 / w (1.000..) "pink" Zipf-law Archimedes-HYPERBOLICITY INEVITABILITY power-spectrum power-law decay algebraicity. Their CONNECTION is via simple-calculus SCALE-Invariance Symmetry-RESTORING logarithm-function derivative: (d/ d ω) ln(ω) = 1 / ω , i.e. (d/ d ω) [SCALE-Invariance Symmetry-RESTORING](ω) = 1/ ω . Via Noether-theorem continuous-symmetries relation to conservation-laws: (d/ d ω) [inter-scale 4-current 4-div-ergence} = 0](ω) = 1 / ω . Hence (so MIScalled) "complexity" is information inter-scale conservation, in agreement with Anderson-Mandell [Fractals of Brain/Mind, G. Stamov ed.(1994)] experimental-psychology!!!], i.e. (so MIScalled) "complexity" is UTTER-SIMPLICITY!!! Versus COMPLICATEDNESS either PLUS (Additive) VS. TIMES (Multiplicative) COMPLICATIONS of various system-specifics. COMPLICATEDNESS-MEASURE DEVIATIONS FROM complexity's UTTER-SIMPLICITY!!!: EITHER [SCALE-Invariance Symmetry-BREAKING] MINUS [SCALE-Invariance Symmetry-RESTORING] via power-spectrum power-law algebraicity decays DIFFERENCES: ["red"-Pareto] MINUS ["pink"-Zipf Archimedes-HYPERBOLICITY INEVITABILITY]!!!

Feedback Implementation of Zermelo's Optimal Control by Sugeno Approximation

NASA Technical Reports Server (NTRS)

Clifton, C.; Homaifax, A.; Bikdash, M.

1997-01-01

This paper proposes an approach to implement optimal control laws of nonlinear systems in real time. Our methodology does not require solving two-point boundary value problems online and may not require it off-line either. The optimal control law is learned using the original Sugeno controller (OSC) from a family of optimal trajectories. We compare the trajectories generated by the OSC and the trajectories yielded by the optimal feedback control law when applied to Zermelo's ship steering problem.

Codes of professional responsibility for lawyers: ethics or law?

PubMed

Lawry, R P

1984-01-01

The American Bar Association has three times in this century produced a code of ethics for lawyers. The movement has clearly been from a general, hortatory format to one of a statement of principles of law. In the ABA's latest effort, the problems of client confidentiality loom as the most serious and most difficult to solve. The question of ethics versus law weighs heavily in this context, and the ABA's latest resolutions of the confidentiality problems are found to be unsatisfactory.