WorldWideScience

Sample records for releases principles equations

  1. Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation

    Institute of Scientific and Technical Information of China (English)

    LIU Yan-hong; ZHANG Hui-ming

    2007-01-01

    Combining the symplectic variations theory, the homogeneous control equation and isoparametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isoparametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which are often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.

  2. Kelvin principle for a class of singular equations

    Directory of Open Access Journals (Sweden)

    Abdullah Altin

    1989-01-01

    Full Text Available The classical Kelvin principle concerns invariance of solutions of the Laplace equation with respect to inversion in a sphere. By employing a hyperbolic-polar coordinate system, the principle is extended to cover a class of singular equations, which include the ultrahyperbolic equation.

  3. Operator constraint principle for simplifying atmospheric dynamical equations

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Based on the qualitative theory of atmospheric dynamical equations, a new method for simplifying equations, the operator constraint principle, is presented. The general rule of the method and its mathematical strictness are discussed. Moreover, the way that how to use the method to simplify equations rationally and how to get the simplified equations with harmonious and consistent dynamics is given.

  4. Variational principle and dynamical equations of discrete nonconservative holonomic systems

    Institute of Scientific and Technical Information of China (English)

    Liu Rong-Wan; Zhang Hong-Bin; Chen Li-Qun

    2006-01-01

    By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations including Euler-Lagrange equations and Hamilton's canonical equations of the discrete nonconservative holonomic systems are derived on a discrete variational principle. Some illustrative examples are also given.

  5. Rastall's gravity equations and Mach's Principle

    CERN Document Server

    Majernik, V; Majernik, Vladimir; Richterek, Lukas

    2006-01-01

    Rastall generalized Einstein's field equations relaxing the Einstein's assumption that the covariant divergence of the energy-momentum tensor should vanish. His field equations contain a free parameter alpha and in an empty space, i.e. if T_{\\mu\

  6. Principles and practice of structural equation modeling

    CERN Document Server

    Kline, Rex B

    2015-01-01

    Emphasizing concepts and rationale over mathematical minutiae, this is the most widely used, complete, and accessible structural equation modeling (SEM) text. Continuing the tradition of using real data examples from a variety of disciplines, the significantly revised fourth edition incorporates recent developments such as Pearl's graphing theory and the structural causal model (SCM), measurement invariance, and more. Readers gain a comprehensive understanding of all phases of SEM, from data collection and screening to the interpretation and reporting of the results. Learning is enhanced by ex

  7. Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation

    Directory of Open Access Journals (Sweden)

    Petr Stehlík

    2015-01-01

    Full Text Available We study reaction-diffusion equations with a general reaction function f on one-dimensional lattices with continuous or discrete time ux′  (or  Δtux=k(ux-1-2ux+ux+1+f(ux, x∈Z. We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity.

  8. A Matter of Principle: The Principles of Quantum Theory, Dirac's Equation, and Quantum Information

    CERN Document Server

    Plotnitsky, Arkady

    2015-01-01

    This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be be addressed as well in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac's work, which, in particular Dirac's derivation of his relativistic equation for the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall, however, also consider Heisenberg's derivation of quantum mechanics, which inspired Dirac. I argue that Heisenberg's and Dirac's work alike was guided by their adherence to and confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by G. M. D' Ariano and his coworkers on the principles of quantum information theory, which extends quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac's equation from these principles alone...

  9. Onsager's-principle-consistent 13-moment transport equations.

    Science.gov (United States)

    Singh, Narendra; Agrawal, Amit

    2016-06-01

    A new set of generalized transport equations is derived for higher-order moments which are generated in evolution equation for stress tensor and heat flux vector in 13-moment equations. The closure we employ satisfies Onsager's symmetry principle. In the derivation, we do not employ a phase density function based on Hermite polynomial series in terms of higher-order moments, unlike Grad's approach. The distribution function is rather chosen to satisfy collision invariance, and H-theorem and capture relatively strong deviations from equilibrium. The phase density function satisfies the linearized Boltzmann equation and provides the correct value of the Prandtl number for monatomic gas. The derived equations are compared with Grad's 13-moments equations for gas modeled as Maxwellian molecule. The merits of the proposed equations against Grad's and R13 equations are discussed. In particular, it is noted that the proposed equations contain higher-order terms compared to these equations but require a fewer number of boundary conditions as compared to the R13 equations. The Knudsen number envelope which can be covered to describe flows with these equations is therefore expected to be larger as compared to the earlier equations.

  10. Variational Principles for Constrained Electromagnetic Field and Papapetrou Equation

    CERN Document Server

    Muminov, A T

    2007-01-01

    In our previous article [4] an approach to derive Papapetrou equations for constrained electromagnetic field was demonstrated by use of field variational principles. The aim of current work is to present more universal technique of deduction of the equations which could be applied to another types of non-scalar fields. It is based on Noether theorem formulated in terms of Cartan' formalism of orthonormal frames. Under infinitesimal coordinate transformation the one leads to equation which includes volume force of spin-gravitational interaction. Papapetrou equation for vector of propagation of the wave is derived on base of the equation. Such manner of deduction allows to formulate more accurately the constraints and clarify equations for the potential and for spin.

  11. Comparison principle for parabolic equations in the Heisenberg group

    Directory of Open Access Journals (Sweden)

    Thomas Bieske

    2005-09-01

    Full Text Available We define two notions of viscosity solutions to parabolic equations in the Heisenberg group, depending on whether the test functions concern only the past or both the past and the future. We then exploit the Heisenberg geometry to prove a comparison principle for a class of parabolic equations and show the sufficiency of considering the test functions that concern only the past.

  12. MAXIMUM PRINCIPLES FOR SECOND-ORDER PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Antonio Vitolo

    2004-01-01

    This paper is the parabolic counterpart of previous ones about elliptic operators in unbounded domains. Maximum principles for second-order linear parabolic equations are established showing a variant of the ABP-Krylov-Tso estimate, based lower bound for super-solutions due to Krylov and Safonov. The results imply the uniqueness for the Cauchy-Dirichlet problem in a large class of infinite cylindrical and non-cylindrical domains.

  13. Viscous Regularization of the Euler Equations and Entropy Principles

    KAUST Repository

    Guermond, Jean-Luc

    2014-03-11

    This paper investigates a general class of viscous regularizations of the compressible Euler equations. A unique regularization is identified that is compatible with all the generalized entropies, à la [Harten et al., SIAM J. Numer. Anal., 35 (1998), pp. 2117-2127], and satisfies the minimum entropy principle. A connection with a recently proposed phenomenological model by [H. Brenner, Phys. A, 370 (2006), pp. 190-224] is made. © 2014 Society for Industrial and Applied Mathematics.

  14. Computational uncertainty principle in nonlinear ordinary differential equations

    Institute of Scientific and Technical Information of China (English)

    LI; Jianping

    2001-01-01

    [1]Li Jianping, Zeng Qingcun, Chou Jifan, Computational Uncertainty Principle in Nonlinear Ordinary Differential Equations I. Numerical Results, Science in China, Ser. E, 2000, 43(5): 449[2]Henrici, P., Discrete Variable Methods in Ordinary Differential Equations, New York: John Wiley, 1962, 1; 187.[3]Henrici, P., Error Propagation for Difference Methods, New York: John Whiley, 1963.[4]Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations, Englewood Cliffs, NJ: Prentice-Hall, 1971, 1; 72.[5]Hairer, E., Nrsett, S. P., Wanner, G., Solving Ordinary Differential Equations I. Nonstiff Problems, 2nd ed., Berlin-Heidelberg-New York: Springer-Verlag, 1993, 130.[6]Stoer, J., Bulirsch, R., Introduction to Numerical Analysis, 2nd ed., Vol. 1, Berlin-Heidelberg-New York: Springer-Verlag (reprinted in China by Beijing Wold Publishing Corporation), 1998, 428.[7]Li Qingyang, Numerical Methods in Ordinary Differential Equations (Stiff Problems and Boundary Value Problems), in Chinese Beijing: Higher Education Press, 1991, 1.[8]Li Ronghua, Weng Guochen, Numerical Methods in Differential Equations (in Chinese), 3rd ed., Beijing: Higher Education Press, 1996, 1.[9]Dahlquist, G., Convergence and stability in the numerical integration of ordinary differential equations, Math. Scandinavica, 1956, 4: 33.[10]Dahlquist, G., 33 years of numerical instability, Part I, BIT, 1985, 25: 188.[11]Heisenberg, W., The Physical Principles of Quantum Theory, Chicago: University of Chicago Press, 1930.[12]McMurry, S. M., Quantum Mechanics, London: Addison-Wesley Longman Ltd (reprined in China by Beijing World Publishing Corporation), 1998.

  15. Dual Variational Principles for 3-D Navier-Stokes Equations

    Science.gov (United States)

    Liu, G. L.

    Just recently the exact variational principles (VP) of the full 3-D Navier-Stokes equations of viscous flow have been successfully established for the first time by the present author by means of a systematic reversed deduction method via the undetermined function. As a continuation and further development of that - a pair of new dual (reciprocal)VP is generated herein by means of the Friedrichs involutory transformation. These VP have the advantage over the previous ones that they possess apparent physical meaning of energy, providing a new rigorous theoretical basis for the finite element analysis of 3-D viscous flow.

  16. The Equator Principles, Project Finance and the Challenge of Social and Environmental Responsibility

    National Research Council Canada - National Science Library

    Andrew, Jane

    2007-01-01

    The Equator Principles, launched in 2003 and revamped in 2006, are a set of voluntary principles designed to help private lenders make socially and environmentally responsible project financing decisions...

  17. Computational uncertainty principle in nonlinear ordinary differential equations

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    The error propagation for general numerical method in ordinarydifferential equations ODEs is studied. Three kinds of convergence, theoretical, numerical and actual convergences, are presented. The various components of round-off error occurring in floating-point computation are fully detailed. By introducing a new kind of recurrent inequality, the classical error bounds for linear multistep methods are essentially improved, and joining probabilistic theory the “normal” growth of accumulated round-off error is derived. Moreover, a unified estimate for the total error of general method is given. On the basis of these results, we rationally interpret the various phenomena found in the numerical experiments in part I of this paper and derive two universal relations which are independent of types of ODEs, initial values and numerical schemes and are consistent with the numerical results. Furthermore, we give the explicitly mathematical expression of the computational uncertainty principle and expound the intrinsic relation between two uncertainties which result from the inaccuracies of numerical method and calculating machine.

  18. Generalized Variational Principle for Long Water-Wave Equation by He's Semi-Inverse Method

    Directory of Open Access Journals (Sweden)

    Weimin Zhang

    2009-01-01

    Full Text Available Variational principles for nonlinear partial differential equations have come to play an important role in mathematics and physics. However, it is well known that not every nonlinear partial differential equation admits a variational formula. In this paper, He's semi-inverse method is used to construct a family of variational principles for the long water-wave problem.

  19. A comparison principle for singular parabolic equations in the Heisenberg group

    Directory of Open Access Journals (Sweden)

    Pablo Ochoa

    2015-04-01

    Full Text Available In this work, we prove a comparison principle for singular parabolic equations with boundary conditions in the context of the Heisenberg group. In particular, this result applies to interesting equations, such as the parabolic infinite Laplacian, the mean curvature flow equation and more general homogeneous diffusions.

  20. A Fast Melting Release Method in Free-Fall Equivalence Principle Test

    Institute of Scientific and Technical Information of China (English)

    WU Zi-Gang; WANG Dian-Hong; LUO Jun; ZHOU Ze-Bing; NIE Yu-Xin; ZHANG Yuan-Zhong

    2001-01-01

    A fast melting release method for the free-fallequivalence principle test using laser interferometry is discussed. The primary experiment result shows that the uncertainty of the differential release time could be controlled at the level of 1 ms by this release system, which satisfies the requirement of the expected experimental precision.

  1. Comparison principle and stability criteria for stochastic differential delay equations with Markovian switching

    Institute of Scientific and Technical Information of China (English)

    罗交晚; 邹捷中; 侯振挺

    2003-01-01

    In the present paper we first obtain the comparison principle for the nonlinear stochastic differentialdelay equations with Markovian switching. Later, using this comparison principle, we obtain some stabilitycriteria, including stability in probability, asymptotic stability in probability, stability in the pth mean, asymptoticstability in the pth mean and the pth moment exponential stability of such equations. Finally, an example isgiven to illustrate the effectiveness of our results.

  2. Variational principles for the guiding-center Vlasov-Maxwell equations

    CERN Document Server

    Brizard, A J

    2016-01-01

    The Lagrange, Euler, and Euler-Poincar\\'{e} variational principles for the guiding-center Vlasov-Maxwell equations are presented. Each variational principle presents a different approach to deriving guiding-center polarization and magnetization effects into the guiding-center Maxwell equations. The conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guiding-center stress tensor is now shown to be explicitly symmetric.

  3. Social accountability and the finance sector: the case of Equator Principles (EP) institutionalisation

    NARCIS (Netherlands)

    O'Sullivan, N.A.

    2010-01-01

    In June 2003, the Equator Principles (EP) were launched by ten international commercial banks. The EP were designed as a set of voluntary environmental and social risk management guidelines for project finance. Whilst lauded as a revolutionary initiative by the financial sector, the Principles were

  4. Social accountability and the finance sector: the case of Equator Principles (EP) institutionalisation

    NARCIS (Netherlands)

    O'Sullivan, N.A.

    2010-01-01

    In June 2003, the Equator Principles (EP) were launched by ten international commercial banks. The EP were designed as a set of voluntary environmental and social risk management guidelines for project finance. Whilst lauded as a revolutionary initiative by the financial sector, the Principles were

  5. Comparison principles for viscosity solutions of elliptic equations via fuzzy sum rule

    Science.gov (United States)

    Luo, Yousong; Eberhard, Andrew

    2005-07-01

    A comparison principle for viscosity sub- and super-solutions of second order elliptic partial differential equations is derived using the "fuzzy sum rule" of non-smooth calculus. This method allows us to weaken the assumptions made on the function F when the equation F(x,u,=u,=2u)=0 is under consideration.

  6. Invariance principle and model reduction for the Fokker-Planck equation

    Science.gov (United States)

    Karlin, I. V.

    2016-11-01

    The principle of dynamic invariance is applied to obtain closed moment equations from the Fokker-Planck kinetic equation. The analysis is carried out to explicit formulae for computation of the lowest eigenvalue and of the corresponding eigenfunction for arbitrary potentials. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

  7. The first and second monotone integral principles for fundamental solutions of uniformly elliptic equations

    CERN Document Server

    Xiao, Jie

    2009-01-01

    Two optimal monotone integral principles (equivalently for the Laplacian, two sharp iso-weighted-volume inequalities) are established through extending the first and second integral bounds of H. Weinberger for the Green functions (i.e., fundamental solutions) of uniformly elliptic equations in terms of the layer-cake formula, a one-dimensional monotone integral principle, and the isoperimetric and Jenson's inequalities with sharp constants. Surprisingly, a special setting of the first principle can be used to not only verify the low-dimensional P\\'olya conjecture for the principal eigenvalue of the Laplacian but also to characterize the geometry of the Nash inequality for a strong uniform elliptic equation.

  8. Deriving the Hamilton equations of motion for a nonconservative system using a variational principle

    Science.gov (United States)

    Tveter, Frank Thomas

    1998-03-01

    The classical derivation of the canonical transformation theory [H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, 1981)] is based on Hamilton's principle which is only valid for conservative systems. This paper avoids this principle by using an approach that is basically reversed compared to the classical derivation. The Lagrange equations of motion are formulated in the undefined and general variable set {Q,P}, and the general Hamilton equations of motion are derived from the Lagrange equations by using a variational principle. The undefined general variables {Q,P} are defined through a transformation to a special (defined) variable set {q,p}. The transformation equations connecting the two sets are derived by using the invariants property of the value of the Lagrangian. This approach results in a more general interpretation of the generator function.

  9. Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations

    Directory of Open Access Journals (Sweden)

    Domoshnitsky Alexander

    2009-01-01

    Full Text Available We obtain the maximum principles for the first-order neutral functional differential equation where , and are linear continuous operators, and are positive operators, is the space of continuous functions, and is the space of essentially bounded functions defined on . New tests on positivity of the Cauchy function and its derivative are proposed. Results on existence and uniqueness of solutions for various boundary value problems are obtained on the basis of the maximum principles.

  10. An Averaging Principle for Stochastic Differential Delay Equations with Fractional Brownian Motion

    Directory of Open Access Journals (Sweden)

    Yong Xu

    2014-01-01

    Full Text Available An averaging principle for a class of stochastic differential delay equations (SDDEs driven by fractional Brownian motion (fBm with Hurst parameter in (1/2,1 is considered, where stochastic integration is convolved as the path integrals. The solutions to the original SDDEs can be approximated by solutions to the corresponding averaged SDDEs in the sense of both convergence in mean square and in probability, respectively. Two examples are carried out to illustrate the proposed averaging principle.

  11. A maximum principle for forward-backward stochastic Volterra integral equations and applications in finance

    CERN Document Server

    Wang, Tianxiao

    2010-01-01

    This paper formulates and studies a stochastic maximum principle for forward-backward stochastic Volterra integral equations (FBSVIEs in short), while the control area is assumed to be convex. Then a linear quadratic (LQ in short) problem for backward stochastic Volterra integral equations (BSVIEs in short) is present to illustrate the aforementioned optimal control problem. Motivated by the technical skills in solving above problem, a more convenient and briefer method for the unique solvability of M-solution for BSVIEs is proposed. At last, we will investigate a risk minimization problem by means of the maximum principle for FBSVIEs. Closed-form optimal portfolio is obtained in some special cases.

  12. Hydrodynamic equations for electrons in graphene obtained from the maximum entropy principle

    Energy Technology Data Exchange (ETDEWEB)

    Barletti, Luigi, E-mail: luigi.barletti@unifi.it [Dipartimento di Matematica e Informatica “Ulisse Dini”, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134 Firenze (Italy)

    2014-08-15

    The maximum entropy principle is applied to the formal derivation of isothermal, Euler-like equations for semiclassical fermions (electrons and holes) in graphene. After proving general mathematical properties of the equations so obtained, their asymptotic form corresponding to significant physical regimes is investigated. In particular, the diffusive regime, the Maxwell-Boltzmann regime (high temperature), the collimation regime and the degenerate gas limit (vanishing temperature) are considered.

  13. Variational principles for some nonlinear partial differential equations with variable coefficients

    Energy Technology Data Exchange (ETDEWEB)

    He Jihuan E-mail: jhhe@dhu.edu.cn

    2004-03-01

    Variational principles for generalized Korteweg-de Vries equation and nonlinear Schroedinger's equation are obtained by the semi-inverse method. The most interesting features of the proposed method are its extreme simplicity and concise forms of variational functionals for a wide range of nonlinear problems. Comparison with the results obtained by the Noether's theorem is made, revealing the present theorem is a straightforward and attracting mathematical tool.

  14. (ANTI)PETER Principle - Discrete (INVERSE) Logistic Equation with Imprecisely Estimated and Stimulated Carrying Capacity

    CERN Document Server

    Pankovic, V; Glavatovic, R

    2009-01-01

    In this work we consider the Peter principle and anti-Peter principle as the discrete logistic and discrete inverse logistic equation. Especially we discuss imprecisely estimated (by hierarchical control mechanism) carrying capacity, i.e. boundary (in)competence level of a hierarchy member. It implies that Peter principle holds two sub-principles. In the first one objective boundary competence level is increased for estimation error. In the second one objective boundary competence level is decreased for estimation error. Similarly, anti-Peter principle holds two sub-principles too. All this implies that paradoxical situations that follow from Peter and anti-Peter principle can be simply removed by decrease of the error of hierarchical (social) control. Also we discuss cases by Peter principle when error of the boundary competence level by estimation grows up. (Then, in fact, there is no estimation error but stimulation of the boundary level by control mechanism.) By first Peter sub-principle it implies anarch...

  15. Reflection principle for classical solutions of the homogeneous real Monge–Ampère equation

    Directory of Open Access Journals (Sweden)

    Mika Koskenoja

    2015-12-01

    Full Text Available We consider reflection principle for classical solutions of the homogeneous real Monge–Ampère equation. We show that both the odd and the even reflected functions satisfy the Monge–Ampère equation if the second-order partial derivatives have continuous limits on the reflection boundary. In addition to sufficient conditions, we give some necessary conditions. Before stating the main results, we present elementary formulas for the reflected functions and study their differentiability properties across the reflection boundary. As an important special case, we finally consider extension of polynomials satisfying the homogeneous Monge–Ampère equation.

  16. MAXIMUM PRINCIPLES OF NONHOMOGENEOUS SUBELLIPTIC P-LAPLACE EQUATIONS AND APPLICATIONS

    Institute of Scientific and Technical Information of China (English)

    Liu Haifeng; Niu Pengcheng

    2006-01-01

    Maximum principles for weak solutions of nonhomogeneous subelliptic p-Laplace equations related to smooth vector fields {Xj} satisfying the H(o)rmander condition are proved by the choice of suitable test functions and the adaption of the classical Moser iteration method. Some applications are given in this paper.

  17. Variational Principles and Conservation. Laws in the Derivation of Radiation Boundary Conditions for Wave Equations

    NARCIS (Netherlands)

    Daalen, van Edwin F.G.; Broeze, Jan; Groesen, van Embrecht

    1992-01-01

    Radiation boundary conditions are derived for partial differential equations which describe wave phenomena. Assuming the evolution of the system to be governed by a Lagrangian variational principle, boundary conditions are obtained with Noether's theorem from the requirement that they transmit some

  18. Construction of Interval Wavelet Based on Restricted Variational Principle and Its Application for Solving Differential Equations

    Directory of Open Access Journals (Sweden)

    Qin Ma

    2008-05-01

    Full Text Available Based on restricted variational principle, a novel method for interval wavelet construction is proposed. For the excellent local property of quasi-Shannon wavelet, its interval wavelet is constructed, and then applied to solve ordinary differential equations. Parameter choices for the interval wavelet method are discussed and its numerical performance is demonstrated.

  19. MODIFIED H-R MIXED VARIATIONAL PRINCIPLE FOR MAGNETOELECTROELASTIC BODIES AND STATE-VECTOR EQUATION

    Institute of Scientific and Technical Information of China (English)

    QING Guang-hui; QIU Jia-jun; LIU Yan-hong

    2005-01-01

    Based upon the Hellinger-Reissner (H-R) mixed variational principle for three-dimensional elastic bodies, the modified H-R mixed variational theorem for magnetoelectroelastic bodies was established. The state-vector equation of magnetoelectroelastic plates was derived from the proposed theorem by performing the variational operations. To lay a theoretical basis of the semi-analytical solution applied with the magnetoelectroelastic plates, the state-vector equation for the discrete element in plane was proposed through the use of the proposed principle. Finally, it is pointed out that the modified H-R mixed variational principle for pure elastic, single piezoelectric or single piezomagnetic bodies are the special cases of the present variational theorem.

  20. Nonlinear Schrödinger equation from generalized exact uncertainty principle

    Science.gov (United States)

    Rudnicki, Łukasz

    2016-09-01

    Inspired by the generalized uncertainty principle, which adds gravitational effects to the standard description of quantum uncertainty, we extend the exact uncertainty principle approach by Hall and Reginatto (2002 J. Phys. A: Math. Gen. 35 3289), and obtain a (quasi)nonlinear Schrödinger equation. This quantum evolution equation of unusual form, enjoys several desired properties like separation of non-interacting subsystems or plane-wave solutions for free particles. Starting with the harmonic oscillator example, we show that every solution of this equation respects the gravitationally induced minimal position uncertainty proportional to the Planck length. Quite surprisingly, our result successfully merges the core of classical physics with non-relativistic quantum mechanics in its extremal form. We predict that the commonly accepted phenomenon, namely a modification of a free-particle dispersion relation due to quantum gravity might not occur in reality.

  1. First-principle Calculations of Equation of State for Metals at High Energy Density

    Science.gov (United States)

    Minakov, Dmitry; Levashov, Pavel; Khishchenko, Konstantin

    2012-02-01

    In this work, we present quantum molecular dynamics calculations of the shock Hugoniots of solid and porous samples as well as release isentropes and isentropic sound velocity behind the shock front for aluminum. Also we perform similar calculations for nickel and iron. We use the VASP code with ultrasoft and PAW pseudopotentials and GGA exchange-correlation functional. Up to 512 particles have been used in calculations. To calculate Hugoniots we solve the Hugoniot equation numerically. To obtain release isentropes, we use Zel'dovich's approach and integrate an ordinary differential equation for the temperature thus restoring all thermodynamic parameters. Isentropic sound velocity is calculated by differentiation of pressure along isentropes. The results of our calculations are in good agreement with experimental data at densities both higher and lower than the normal one. Thus, quantum molecular dynamics results can be effectively used for verification or calibration of semiempirical equations of state under conditions of lack of experimental information at high energy densities.

  2. The Stampacchia maximum principle for stochastic partial differential equations and applications

    Science.gov (United States)

    Chekroun, Mickaël D.; Park, Eunhee; Temam, Roger

    2016-02-01

    Stochastic partial differential equations (SPDEs) are considered, linear and nonlinear, for which we establish comparison theorems for the solutions, or positivity results a.e., and a.s., for suitable data. Comparison theorems for SPDEs are available in the literature. The originality of our approach is that it is based on the use of truncations, following the Stampacchia approach to maximum principle. We believe that our method, which does not rely too much on probability considerations, is simpler than the existing approaches and to a certain extent, more directly applicable to concrete situations. Among the applications, boundedness results and positivity results are respectively proved for the solutions of a stochastic Boussinesq temperature equation, and of reaction-diffusion equations perturbed by a non-Lipschitz nonlinear noise. Stabilization results to a Chafee-Infante equation perturbed by a nonlinear noise are also derived.

  3. First-principles prediction of the equation of state for TcC with rocksalt structure

    Science.gov (United States)

    Sun, Xiao-Wei; Chu, Yan-Dong; Liu, Zi-Jiang; Song, Ting; Tian, Jun-Hong; Wei, Xiao-Ping

    2014-10-01

    The equation of state of TcC with rocksalt structure is investigated by means of first-principles density functional theory calculations combined with the quasi-harmonic Debye model in which the phononic effects are considered. Particular attention is paid to the predictions of the compressibility, the isothermal bulk modulus and its first pressure derivative which play a central role in the formulation of approximate equations of state for the first time. The properties of TcC with rocksalt structure are summarized in the pressure range of 0-80 GPa and the temperature up to 2500 K.

  4. Foundations of Quantum Mechanics: Derivation of a dissipative Schrödinger equation from first principles

    Energy Technology Data Exchange (ETDEWEB)

    Gonçalves, L.A.; Olavo, L.S.F., E-mail: olavolsf@gmail.com

    2017-05-15

    Dissipation in Quantum Mechanics took some time to become a robust field of investigation after the birth of the field. The main issue hindering developments in the field is that the Quantization process was always tightly connected to the Hamiltonian formulation of Classical Mechanics. In this paper we present a quantization process that does not depend upon the Hamiltonian formulation of Classical Mechanics (although still departs from Classical Mechanics) and thus overcome the problem of finding, from first principles, a completely general Schrödinger equation encompassing dissipation. This generalized process of quantization is shown to be nothing but an extension of a more restricted version that is shown to produce the Schrödinger equation for Hamiltonian systems from first principles (even for Hamiltonian velocity dependent potential). - Highlights: • A Quantization process independent of the Hamiltonian formulation of quantum Mechanics is proposed. • This quantization method is applied to dissipative or absorptive systems. • A Dissipative Schrödinger equation is derived from first principles.

  5. Variational principles and governing equations in nano-dielectrics with the flexoelectric effect

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    The flexoelectric effect is very strong and coupled with large strain gradients for nanoscale dielectrics. At the nanoscale, the electrostatic force cannot be ignored. In this paper, we have established the electric enthalpy variational principle for nanosized dielectrics with the strain gradient and the polarization gradient effect, as well as the effect of the electrostatic force. The complete governing equations, which include the effect of the electrostatic force, are derived from this variational principle, and based on the principle the generalized electrostatic stress is obtained, the generalized electrostatic stress contains the Maxwell stress corresponding to the polarization and strain, and stress related to the polarization gradient and strain gradient. This work provides the basis for the analysis and computations for the electromechanical problems in nanosized dielectric materials.

  6. Poisson Bracket for Fermion Fields: Correspondence Principle, Second Class Constraints and Hamilton-Jacobi equation

    CERN Document Server

    Leclerc, M

    2012-01-01

    We introduce a symmetric Poisson bracket that allows us to describe anticommuting fields on a classical level in the same way as commuting fields, without the use of Grassmann variables. By means of a simple example, we show how the Dirac bracket for the elimination of the second class constraints can be introduced, how the classical Hamiltonian equations can be derived and how quantization can be achieved through a direct correspondence principle. Finally, we show that the semiclassical limit of the corresponding Schroedinger equation leads back to the Hamilton-Jacobi equation of the classical theory. Summarizing, it is shown that the relations between classical and quantum theory are valid for fermionic fields in exactly the same way as in the bosonic case, and that there is no need to introduce anticommuting variables on a classical level.

  7. Gaia Data Release 1. Principles of the photometric calibration of the G band

    Science.gov (United States)

    Carrasco, J. M.; Evans, D. W.; Montegriffo, P.; Jordi, C.; van Leeuwen, F.; Riello, M.; Voss, H.; De Angeli, F.; Busso, G.; Fabricius, C.; Cacciari, C.; Weiler, M.; Pancino, E.; Brown, A. G. A.; Holland, G.; Burgess, P.; Osborne, P.; Altavilla, G.; Gebran, M.; Ragaini, S.; Galleti, S.; Cocozza, G.; Marinoni, S.; Bellazzini, M.; Bragaglia, A.; Federici, L.; Balaguer-Núñez, L.

    2016-11-01

    Context. Gaia is an ESA cornerstone mission launched on 19 December 2013 aiming to obtain the most complete and precise 3D map of our Galaxy by observing more than one billion sources. This paper is part of a series of documents explaining the data processing and its results for Gaia Data Release 1, focussing on the G band photometry. Aims: This paper describes the calibration model of the Gaia photometric passband for Gaia Data Release 1. Methods: The overall principle of splitting the process into internal and external calibrations is outlined. In the internal calibration, a self-consistent photometric system is generated. Then, the external calibration provides the link to the absolute photometric flux scales. Results: The Gaia photometric calibration pipeline explained here was applied to the first data release with good results. Details are given of the various calibration elements including the mathematical formulation of the models used and of the extraction and preparation of the required input parameters (e.g. colour terms). The external calibration in this first release provides the absolute zero point and photometric transformations from the Gaia G passband to other common photometric systems. Conclusions: This paper describes the photometric calibration implemented for the first Gaia data release and the instrumental effects taken into account. For this first release no aperture losses, radiation damage, and other second-order effects have not yet been implemented in the calibration.

  8. Gaia data release 1: Principles of the photometric calibration of the G band

    CERN Document Server

    Carrasco, J M; Montegriffo, P; Jordi, C; van Leeuwen, F; Riello, M; Voss, H; De Angeli, F; Busso, G; Fabricius, C; Cacciari, C; Weiler, M; Pancino, E; Brown, A G A; Holland, G; Burgess, P; Osborne, P; Altavilla, G; Gebran, M; Ragaini, S; Galleti, S; Cocozza, G; Marinoni, S; Bellazzini, M; Bragaglia, A; Federici, L; Balaguer-Núñez, L

    2016-01-01

    Context. Gaia is an ESA cornerstone mission launched on 19 December 2013 aiming to obtain the most complete and precise 3D map of our Galaxy by observing more than one billion sources. This paper is part of a series of documents explaining the data processing and its results for Gaia Data Release 1, focussing on the G band photometry. Aims. This paper describes the calibration model of the Gaia photometric passband for Gaia Data Release 1. Methods. The overall principle of splitting the process into internal and external calibrations is outlined. In the internal calibration, a self-consistent photometric system is generated. Then, the external calibration provides the link to the absolute photometric flux scales. Results. The Gaia photometric calibration pipeline explained here was applied to the first data release with good results. Details are given of the various calibration elements including the mathematical formulation of the models used and of the extraction and preparation of the required input parame...

  9. The Quark-Gluon Plasma Equation of State and the Generalized Uncertainty Principle

    Directory of Open Access Journals (Sweden)

    L. I. Abou-Salem

    2015-01-01

    Full Text Available The quark-gluon plasma (QGP equation of state within a minimal length scenario or Generalized Uncertainty Principle (GUP is studied. The Generalized Uncertainty Principle is implemented on deriving the thermodynamics of ideal QGP at a vanishing chemical potential. We find a significant effect for the GUP term. The main features of QCD lattice results were quantitatively achieved in case of nf=0, nf=2, and nf=2+1 flavors for the energy density, the pressure, and the interaction measure. The exciting point is the large value of bag pressure especially in case of nf=2+1 flavor which reflects the strong correlation between quarks in this bag which is already expected. One can notice that the asymptotic behavior which is characterized by Stephan-Boltzmann limit would be satisfied.

  10. Comment on ``Modified photon equation of motion as a test for the principle of equivalence''

    Science.gov (United States)

    Nityananda, Rajaram

    1992-07-01

    In a recent paper, a modification of the geodesic equation was proposed for spinning photons containing a spin-curvature coupling term. The difference in arrival times of opposite circular polarizations starting simultaneously from a source was computed, obtaining a result linear in the coupling parameter. It is pointed out here that this linear term violates causality and, more generally, Fermat's principle, implying calculational errors. Even if these are corrected, there is a violation of covariance in the way the photon spin was introduced. Rectifying this makes the effect computed vanish entirely.

  11. A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations

    KAUST Repository

    Guermond, Jean-Luc

    2014-01-01

    © 2014 Society for Industrial and Applied Mathematics. This paper proposes an explicit, (at least) second-order, maximum principle satisfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Comput. Methods Appl. Mech. Engrg., 272 (2014), pp. 198-213], a high-order entropy viscosity method, and the Boris-Book-Zalesak flux correction technique. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The formal second-order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems.

  12. A maximum-principle preserving finite element method for scalar conservation equations

    KAUST Repository

    Guermond, Jean-Luc

    2014-04-01

    This paper introduces a first-order viscosity method for the explicit approximation of scalar conservation equations with Lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension. Provided the lumped mass matrix is positive definite, the method is shown to satisfy the local maximum principle under a usual CFL condition. The method is independent of the cell type; for instance, the mesh can be a combination of tetrahedra, hexahedra, and prisms in three space dimensions. © 2014 Elsevier B.V.

  13. A New Monotone Iteration Principle in the Theory of Nonlinear Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Bapurao C. Dhage

    2015-08-01

    Full Text Available In this paper the author proves the algorithms for the existence as well as approximations of the solutions for the initial value problems of nonlinear fractional differential equations using the operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid fixed point theorems of Dhage (2014 in a partially ordered normed linear space and the existence and approximations of the solutions of the considered nonlinear fractional differential equations are obtained under weak mixed partial continuity and partial Lipschitz conditions. Our hypotheses and existence and approximation results are also well illustrated by some numerical examples.

  14. A New Monotone Iteration Principle in the Theory of Nonlinear Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Bapurao C. Dhage

    2015-08-01

    Full Text Available In this paper the author proves the algorithms for the existence as well as approximations of the solutions for the initial value problems of nonlinear fractional differential equations using the operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid fixed point theorems of Dhage (2014 in a partially ordered normed linear space and the existence and approximations of the solutions of the considered nonlinear fractional differential equations are obtained under weak mixed partial continuity and partial Lipschitz conditions. Our hypotheses and existence and approximation results are also well illustrated by some numerical examples.

  15. Comparison of Seven Kinetic Equations for K Release and Application of Kinetic Parameters

    Institute of Scientific and Technical Information of China (English)

    L(U) Xiao-Nan; XU Jian-Ming; MA Wan-Zhu; LU Yun-Fu

    2007-01-01

    Corn field experiments with two treatments, NP and NPK, where N in the form of urea, P in the form of calcium phosphate, and K in the form of KC1 were applied at rates of 187.5, 33.3, and 125 kg ha-1, respectively, on soils derived from Quaternary red clay were conducted in the hilly red soil region of Zhejiang Province, China. Plant grains and stalks were collected for determination of K content. Seven equations were used to describe the kinetics of K release from surface soil samples taken before the corn experiments under electric field strengths of 44.4 and 88.8 V cm-1 by means of electro-ultrafiltration (EUF) and to determine if their parameters had a practical application. The second-order and Elovich equations excellently described K release; the first-order, power function, and parabolic diffusion equations also described K release well; but the zero-order and exponential equations were not so good at reflecting K release. Five reference standards from the field experiments, including relative grain yield (yield of the NP treatment/yield of the NPK treatment), relative dry matter yield (dry matter of the NP treatment/dry matter of the NPK treatment), quantity of K uptake in the NP treatment (no K application), soil exchangeable K, and soil HNO3-soluble K, were used to test the effectiveness of equation parameters obtained from the slope or intercept of these equations. Correlations of the ymax (the maximum desorbable quantity of K) in the second-order equation and the constant b in the first-order and E lovich equations to all five reference standards were highly significant (P ≤ 0.01). The constant a in the power function equation was highly significant (P ≤ 0.01) for four of the five reference standards with the fifth being significant (P ≤ 0.05). The constant b in the parabolic equation was also significantly correlated (P ≤ 0.05) to the relative grain yield and soil HNO3-solublc K. These suggested that all of these parameters could be used to

  16. Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications

    Directory of Open Access Journals (Sweden)

    Jiang Zhu

    2014-01-01

    Full Text Available Some delta-nabla type maximum principles for second-order dynamic equations on time scales are proved. By using these maximum principles, the uniqueness theorems of the solutions, the approximation theorems of the solutions, the existence theorem, and construction techniques of the lower and upper solutions for second-order linear and nonlinear initial value problems and boundary value problems on time scales are proved, the oscillation of second-order mixed delat-nabla differential equations is discussed and, some maximum principles for second order mixed forward and backward difference dynamic system are proved.

  17. A Dynamical Principle For 3D-4D Interlinkage In Salpeter-like Equations

    CERN Document Server

    Mitra, A N

    2001-01-01

    The half-century old Markov-Yukawa Transversality Principle ($MYTP$) which provides a theoretical rationale for the covariant instantaneous approximation ($CIA$) that underlies all Salpeter- like equations, is generalized to a Covariant null-plane Ansatz ($CNPA$). A common characteristic of both formulations is an exact 3D-4D interlinkage of BS amplitudes which provides for a two-tier description, the 3D form for spectroscopy, and the 4D form for transition amplitudes as 4D loop integrals. Some basic applications of $MYTP$ on the covariant null plane (quark mass function, vacuum condensates, and decay constants) are given on the lines of earlier applications of the same under Covariant Instantaneity to such processes. PACS: 03.65.-w ; 03.65.Co ; 11.10.Qr ; 11.10.St Keywords: Markov-Yukawa Transversality Principle ($MYTP$); Salpeter-like eqs; Cov Instantaneity Ansatz ($CIA$); Cov null-plane Ansatz ($CNPA$); 3D-4D interlinkage; Vertex function; 4D loops

  18. First-principles calculation method for electron transport based on the grid Lippmann-Schwinger equation.

    Science.gov (United States)

    Egami, Yoshiyuki; Iwase, Shigeru; Tsukamoto, Shigeru; Ono, Tomoya; Hirose, Kikuji

    2015-09-01

    We develop a first-principles electron-transport simulator based on the Lippmann-Schwinger (LS) equation within the framework of the real-space finite-difference scheme. In our fully real-space-based LS (grid LS) method, the ratio expression technique for the scattering wave functions and the Green's function elements of the reference system is employed to avoid numerical collapse. Furthermore, we present analytical expressions and/or prominent calculation procedures for the retarded Green's function, which are utilized in the grid LS approach. In order to demonstrate the performance of the grid LS method, we simulate the electron-transport properties of the semiconductor-oxide interfaces sandwiched between semi-infinite jellium electrodes. The results confirm that the leakage current through the (001)Si-SiO_{2} model becomes much larger when the dangling-bond state is induced by a defect in the oxygen layer, while that through the (001)Ge-GeO_{2} model is insensitive to the dangling bond state.

  19. First-principles Equations of State and Shock Hugoniots of First- and Second-Row Plasmas

    Science.gov (United States)

    Driver, Kevin; Soubiran, Francois; Zhang, Shuai; Militzer, Burkhard

    A first-principles methodology for studying high energy density physics and warm dense matter is important for the stewardship of plasma science and guiding inertial confinement fusion experiments. In order to address this challenge, we have been developing the capability of path integral Monte Carlo (PIMC) for studying dense plasmas comprised of increasingly heavy elements, including nitrogen, oxygen, and neon. In recent work, we have extended PIMC methodology beyond the free-particle node approximation by implementing localized nodal surfaces capable of describing bound plasma states in second-row elements, such as silicon. We combine results from PIMC with results from density functional theory molecular dynamics (DFT-MD) calculations to produce a coherent equation of state that bridges the entire WDM regime. Analysis of pair-correlation functions and the electronic density of states reveals an evolving plasma structure and ionization process that is driven by temperature and pressure. We also compute shock Hugoniot curves for a wide range of initial densities, which generally reveal an increase in compression as the second and first shells are ionized. This work is funded by the NSF/DOE Partnership in Basic Plasma Science and Engineering (DE-SC0010517).

  20. Computational uncertainty principle in nonlinear ordinary differential equations--Numerical results

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    In a majority of cases of long-time numerical integration for initial-value problems, round-off error has received little attention. Using twenty-nine numerical methods, the influence of round-off error on numerical solutions is generally studied through a large number of numerical experiments. Here we find that there exists a strong dependence on machine precision (which is a new kind of dependence different from the sensitive dependence on initial conditions), maximally effective computation time (MECT) and optimal stepsize (OS) in solving nonlinear ordinary differential equations (ODEs) in finite machine precision. And an optimal searching method for evaluating MECT and OS under finite machine precision is presented. The relationships between MECT, OS, the order of numerical method and machine precision are found. Numerical results show that round-off error plays a significant role in the above phenomena. Moreover, we find two universal relations which are independent of the types of ODEs, initial values and numerical schemes. Based on the results of numerical experiments, we present a computational uncertainty principle, which is a great challenge to the reliability of long-time numerical integration for nonlinear ODEs.

  1. Unification of the Two-Parameter Equation of State and the Principle of Corresponding States

    DEFF Research Database (Denmark)

    Mollerup, Jørgen

    1998-01-01

    A two-parameter equation of state is a two-parameter corresponding states model. A two-parameter corresponding states model is composed of two scale factor correlations and a reference fluid equation of state. In a two-parameter equation of state the reference equation of state is the two......-parameter equation of state itself. If we retain the scale factor correlations derived from a two-parameter equation of state, but replace the two-parameter equation of state with a more accurate pure component equation of state for the reference fluid, we can improve the existing models of equilibrium properties...... without refitting any model parameters, and without imposing other restrictions as regards to species and mixing rules as already imposed by the two-parameter equation of state. The theory and procedure is outlined in the paper....

  2. On the transparent conducting oxide Al doped ZnO: First Principles and Boltzmann equations study

    Energy Technology Data Exchange (ETDEWEB)

    Slassi, A. [Institute of Nanomaterials and Nanotechnology, MAScIR, Rabat (Morocco); LMPHE (URAC 12), Faculté des Sciences, Université Mohammed V-Agdal, Rabat (Morocco); Naji, S. [LMPHE (URAC 12), Faculté des Sciences, Université Mohammed V-Agdal, Rabat (Morocco); Department of Physics, Faculty of Science, Ibb University, Ibb (Yemen); Benyoussef, A. [Institute of Nanomaterials and Nanotechnology, MAScIR, Rabat (Morocco); LMPHE (URAC 12), Faculté des Sciences, Université Mohammed V-Agdal, Rabat (Morocco); Hamedoun, M., E-mail: hamedoun@hotmail.com [Institute of Nanomaterials and Nanotechnology, MAScIR, Rabat (Morocco); El Kenz, A. [LMPHE (URAC 12), Faculté des Sciences, Université Mohammed V-Agdal, Rabat (Morocco)

    2014-08-25

    Highlights: • The incorporation of Al in ZnO increases the optical band edge absorption. • Incorporated Al creates shallow donor states of Al-3s around Fermi level. • Transmittance decreases in the visible and IR regions, while it increases in the UV region. • Electrical conductivity increases and reaches almost the saturation for high concentration of Al. - Abstract: We report, in this work, a theoretical study on the electronic, optical and electrical properties of pure and Al doped ZnO with different concentrations. In fact, we investigate these properties using both First Principles calculations within TB-mBJ approximation and Boltzmann equations under the constant relaxation time approximation for charge carriers. It is found out that, the calculated lattice parameters and the optical band gap of pure ZnO are close to the experimental values and in a good agreement with the other theoretical studies. It is also observed that, the incorporations of Al in ZnO increase the optical band edge absorption which leads to a blue shift and no deep impurities levels are induced in the band gap as well. More precisely, these incorporations create shallow donor states around Fermi level in the conduction band minimum from mainly Al-3s orbital. Beside this, it is found that, the transmittance is decreased in the visible and IR regions, while it is significantly improved in UV region. Finally, our calculations show that the electrical conductivity is enhanced as a result of Al doping and it reaches almost the saturation for high concentration of Al. These features make Al doped ZnO a transparent conducting electrode for optoelectronic device applications.

  3. Process optimization of a novel immediate release film coating system using QbD principles.

    Science.gov (United States)

    Teckoe, Jason; Mascaro, Tracey; Farrell, Thomas P; Rajabi-Siahboomi, Ali R

    2013-06-01

    This work describes a quality-by-design (QbD) approach to determine the optimal coating process conditions and robust process operating space for an immediate release aqueous film coating system (Opadry® 200). Critical quality attributes (CQAs) or associated performance indicators of the coated tablets were measured while coating process parameters such as percent solids of the coating dispersion, coating spray rate, inlet air temperature, airflow rate and pan speed were varied, using a design of experiment protocol. The optimized process parameters were then confirmed by independent coating trials. Disintegration time of coated tablets was not affected by the coating process conditions used in this study, while tablet appearance, as determined by measurement of tablet color, coating defects and gloss was determined to be a CQA. Tablet gloss increased when low spray rate and low percent solids were used, as well as with increased coating pan speed. The study used QbD principles and experimental design models to provide a basis to identify ranges of coating process conditions which afford acceptable product quality. High productivity, color uniformity, and very low defect levels were obtained with Opadry 200 even when using a broad range of coating process conditions.

  4. A Microscopic Convexity Principle for Spacetime Convex Solutions of Fully Nonlinear Parabolic Equations

    Institute of Scientific and Technical Information of China (English)

    Chuan Qiang CHEN; Bo Wen HU

    2013-01-01

    We study microscopic spacetime convexity properties of fully nonlinear parabolic partial differential equations.Under certain general structure condition,we establish a constant rank theorem for the spacetime convex solutions of fully nonlinear parabolic equations.At last,we consider the parabolic convexity of solutions to parabolic equations and the convexity of the spacetime second fundamental form of geometric flows.

  5. Comparison principles for integro-differential equations with L{\\'e}vy operators - the case of spacial depending jumps -

    CERN Document Server

    Arisawa, M

    2010-01-01

    A comparison principle for the integro-differential equation with the L{\\'e}vy operator corresponding to the spacial depending jump process is presented in this paper. The jump $\\beta(x,z)$ at a point $x$ and the L{\\'e}vy measure $dq(z)$ satisfy conditions given independently for each of them, which is a major difference from other works. Moreover, a useful form of the viscosity solution is presented, which is equivalent to more "classical" definitions, and is used to prove the comparison principle easily.

  6. Maximum Principles for P1-Conforming Finite Element Approximations of Quasi-Linear Second Order Elliptic Equations

    CERN Document Server

    Wang, Junping

    2011-01-01

    This paper derives some maximum principles for P1-conforming finite element approximations of quasi-linear second order elliptic equations. The results are extensions of the classical maximum principles in the theory of partial differential equations to finite element methods. The mathematical tools are also extensions of the variational approach that was used in classical PDE theories. The maximum principles for finite element approximations are valid with some geometric conditions that are applied to the angles of each element. For the general quasi-linear elliptic equation, each triangle or tetrahedron needs to be $O(h^\\alpha)$-acute in the sense that each angle $\\alpha_{ij}$ (for triangle) or interior dihedral angle $\\alpha_{ij}$ (for tetrahedron) must satisfy $\\alpha_{ij}\\le \\pi/2-\\gamma h^\\alpha$ for some $\\alpha\\ge 0$ and $\\gamma>0$. For the Poisson problem where the differential operator is given by Laplacian, the angle requirement is the same as the classical one: either all the triangles are non-obt...

  7. Basic Principles and Practical Applications of the Cahn–Hilliard Equation

    Directory of Open Access Journals (Sweden)

    Junseok Kim

    2016-01-01

    Full Text Available The celebrated Cahn–Hilliard (CH equation was proposed to model the process of phase separation in binary alloys by Cahn and Hilliard. Since then the equation has been extended to a variety of chemical, physical, biological, and other engineering fields such as spinodal decomposition, diblock copolymer, image inpainting, multiphase fluid flows, microstructures with elastic inhomogeneity, tumor growth simulation, and topology optimization. Therefore, it is important to understand the basic mechanism of the CH equation in each modeling type. In this paper, we review the applications of the CH equation and describe the basic mechanism of each modeling type with helpful references and computational simulation results.

  8. Dynamical Fractal 3-Space and the Generalised Schördinger Equation: Equivalence Principle and Vorticity Effects

    Directory of Open Access Journals (Sweden)

    Cahill R. T.

    2006-01-01

    Full Text Available The new dynamical “quantum foam” theory of 3-space is described at the classical level by a velocity field. This has been repeatedly detected and for which the dynamical equations are now established. These equations predict 3-space “gravitational wave” effects, and these have been observed, and the 1991 DeWitte data is analysed to reveal the fractal structure of these “gravitational waves”. This velocity field describes the differential motion of 3-space, and the various equations of physics must be generalised to incorporate this 3-space dynamics. Here a new generalised Schrödinger equation is given and analysed. It is shown that from this equation the equivalence principle may be derived as a quantum effect, and that as well this generalised Schrödinger equation determines the effects of vorticity of the 3-space flow, or “frame-dragging”, on matter, and which is being studied by the Gravity Probe B (GP-B satellite gyroscope experiment.

  9. equations

    Directory of Open Access Journals (Sweden)

    Xinzhi Liu

    1998-01-01

    Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.

  10. A first-principles derivation of York scaling and the Lichnerowicz-York equation

    CERN Document Server

    Anderson, E; Foster, B Z; Kelleher, B; O'Murchadha, N; Anderson, Edward; Barbour, Julian; Foster, Brendan Z.; Kelleher, Bryan; Murchadha, Niall O'

    2004-01-01

    The only efficient and robust method of generating consistent initial data in general relativity is the conformal technique initiated by Lichnerowicz and perfected by York. In the spatially compact case, the complete scheme consists of the Arnowitt-Deser-Misner (ADM) Hamiltonian and momentum constraints, the ADM Euler-Lagrange equations, York's constant-mean-curvature (CMC) condition, and a lapse-fixing equation (LFE) that ensures propagation of the CMC condition by the Euler-Lagrange equations. The Hamiltonian constraint is rewritten as the Lichnerowicz-York equation for the conformal factor (psi) of the physical metric (psi)^4(g_{ij}) given an initial unphysical 3-metric (g_{ij}). The CMC condition and LFE introduce a distinguished foliation (definition of simultaneity) on spacetime, and separate scaling laws for the canonical momenta and their trace are used. In this article, we derive all these features in a single package by seeking a gauge theory of geometrodynamics (evolving 3-geometries) invariant und...

  11. Variational principle and a perturbative solution of non-linear string equations in curved space

    CERN Document Server

    Roshchupkin, S N

    1999-01-01

    String dynamics in a curved space-time is studied on the basis of an action functional including a small parameter of rescaled tension constant. A rescaled slow worldsheet time $T=\\epsilon\\tau$ is introduced, and general covariant non-linear string equation are derived. It is shown that in the first order of an $\\epsilon $-expansion these equations are reduced to the known equation for geodesic derivation but complemented by a string oscillatory term. These equations are solved for the de Sitter and Friedmann -Robertson-Walker spaces. The primary string constraints are found to be split into a chain of perturbative constraints and their conservation and consistency are proved. It is established that in the proposed realization of the perturbative approach the string dynamics in the de Sitter space is stable for a large Hubble constant $H

  12. Lagrange Multipliers, Adjoint Equations, the Pontryagin Maximum Principle and Heuristic Proofs

    Science.gov (United States)

    Ollerton, Richard L.

    2013-01-01

    Deeper understanding of important mathematical concepts by students may be promoted through the (initial) use of heuristic proofs, especially when the concepts are also related back to previously encountered mathematical ideas or tools. The approach is illustrated by use of the Pontryagin maximum principle which is then illuminated by reference to…

  13. Application of the comparison principle to analysis of nonlinear systems. [using Lipschitz condition and differential equations

    Science.gov (United States)

    Gunderson, R. W.

    1975-01-01

    A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.

  14. A First-Principles Multi-phase Equation of State of Carbon under Extreme Conditions

    Energy Technology Data Exchange (ETDEWEB)

    Correa, A A; Benedict, X L; Young, D A; Schwegler, E; Bonev, S A

    2008-02-01

    We describe the construction of a multi-phase equation of state for carbon at extreme pressures based on ab initio electronic structure calculations of two solid phases (diamond and BC8) and the liquid. Solid-phase free energies are built from knowledge of the cold curves and phonon calculations, together with direct ab initio molecular dynamics calculations of the equation of state, which are used to extract anharmonic corrections to the phonon free energy. The liquid free energy is constructed based on results from molecular dynamics calculations and constraints determined from previously calculated melting curves, assuming a simple solid-like free energy model. The resulting equation of state is extended to extreme densities and temperatures with a Thomas Fermi-based free energy model. Comparisons to available experimental results are discussed.

  15. Comment on Modified photon equation of motion as a test for the principle of equivalence''

    Energy Technology Data Exchange (ETDEWEB)

    Nityananda, R. (Raman Research Institute, Bangalore 560 080 (India))

    1992-07-15

    In a recent paper, a modification of the geodesic equation was proposed for spinning photons containing a spin-curvature coupling term. The difference in arrival times of opposite circular polarizations starting simultaneously from a source was computed, obtaining a result linear in the coupling parameter. It is pointed out here that this linear term violates causality and, more generally, Fermat's principle, implying calculational errors. Even if these are corrected, there is a violation of covariance in the way the photon spin was introduced. Rectifying this makes the effect computed vanish entirely.

  16. Phase stability, electronic structure and equation of state of cubic TcN from first-principles calculations

    Energy Technology Data Exchange (ETDEWEB)

    Song, T., E-mail: songting_lzjtu@yeah.net [School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070 (China); School of Material Science and Engineering, Lanzhou University of Technology, Lanzhou 730050 (China); Ma, Q. [School of Material Science and Engineering, Lanzhou University of Technology, Lanzhou 730050 (China); Sun, X.W., E-mail: xsun@carnegiescience.edu [School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070 (China); Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20015 (United States); Liu, Z.J., E-mail: liuzj_lzcu@163.com [School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070 (China); Department of Physics, Lanzhou City University, Lanzhou 730070 (China); Fu, Z.J. [School of Electrical and Electronic Engineering, Chongqing University of Arts and Sciences, Chongqing 402160 (China); Wei, X.P.; Wang, T.; Tian, J.H. [School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070 (China)

    2016-09-07

    The phase transition, electronic band structure, and equation of state (EOS) of cubic TcN are investigated by first-principles pseudopotential method based on density-functional theory. The calculated enthalpies show that TcN has a transformation between zincblende and rocksalt phases and the pressure determined by the relative enthalpy is 32 GPa. The calculated band structure indicates the metallic feature and it might make cubic TcN a better candidate for hard materials. Particular attention is paid to the predictions of volume, bulk modulus and its pressure derivative which play a central role in the formulation of approximate EOSs using the quasi-harmonic Debye model. - Highlights: • The phase transition pressure and electronic band structure for cubic TcN are determined. • Particular attention is paid to investigate the equation of state parameters for cubic TcN. • The thermodynamic properties up to 80 GPa and 3000 K are successfully predicted.

  17. Stakeholder perspectives on a financial sector legitimation process: the case of NGOs and the Equator Principles

    NARCIS (Netherlands)

    O'Sullivan, N.; O'Dwyer, B.

    2009-01-01

    Purpose - The purpose of this paper is to present an in-depth, context rich, and stakeholder-focused perspective on the legitimation dynamics surrounding the initiation and evolution of one of the key financial sector environmental and social responsibility initiatives in recent years, the Equator P

  18. Discrete Nonlinear Schrodinger Equation, Solitons and Organizing Principles for Protein Folding

    CERN Document Server

    Molkenthin, Nora; Niemi, Antti J

    2010-01-01

    We introduce a novel generalization of the discrete nonlinear Schr\\"odinger equation. It supports solitons that describe how proteins fold. As an example we scrutinize the villin headpiece HP35, an archetypal protein for testing both experimental and theoretical approaches to protein folding. Using explicit soliton profiles we construct its carbon backbone with an unprecedented accuracy.

  19. Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

    Institute of Scientific and Technical Information of China (English)

    Servet Kutukcu; Adnan Tuna; Atakan T. Yakut

    2007-01-01

    Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.

  20. Stable discretization of the Boltzmann equation based on spherical harmonics, box integration, and a maximum entropy dissipation principle

    Science.gov (United States)

    Jungemann, C.; Pham, A. T.; Meinerzhagen, B.; Ringhofer, C.; Bollhöfer, M.

    2006-07-01

    The Boltzmann equation for transport in semiconductors is projected onto spherical harmonics in such a way that the resultant balance equations for the coefficients of the distribution function times the generalized density of states can be discretized over energy and real spaces by box integration. This ensures exact current continuity for the discrete equations. Spurious oscillations of the distribution function are suppressed by stabilization based on a maximum entropy dissipation principle avoiding the H transformation. The derived formulation can be used on arbitrary grids as long as box integration is possible. The approach works not only with analytical bands but also with full band structures in the case of holes. Results are presented for holes in bulk silicon based on a full band structure and electrons in a Si NPN bipolar junction transistor. The convergence of the spherical harmonics expansion is shown for a device, and it is found that the quasiballistic transport in nanoscale devices requires an expansion of considerably higher order than the usual first one. The stability of the discretization is demonstrated for a range of grid spacings in the real space and bias points which produce huge gradients in the electron density and electric field. It is shown that the resultant large linear system of equations can be solved in a memory efficient way by the numerically robust package ILUPACK.

  1. Process Optimization of a Novel Immediate Release Film Coating System using QbD Principles

    National Research Council Canada - National Science Library

    Teckoe, Jason; Mascaro, Tracey; Farrell, Thomas P; Rajabi-Siahboomi, Ali R

    2013-01-01

    This work describes a quality-by-design (QbD) approach to determine the optimal coating process conditions and robust process operating space for an immediate release aqueous film coating system (Opadry® 200...

  2. The c equivalence principle and the correct form of writing Maxwell's equations

    CERN Document Server

    Heras, Jose A

    2010-01-01

    It is well-known that the speed $c_u=1/\\sqrt{\\epsilon_0\\mu_0}$ is obtained in the process of defining SI units via action-at-a-distance forces, like the force between two static charges and the force between two long and parallel currents. The speed $c_u$ is then physically different from the observed speed of propagation $c$ associated with electromagnetic waves in vacuum. However, repeated experiments have led to the numerical equality $c_u=c,$ which we have called the $c$ equivalence principle. In this paper we point out that $\

  3. Thermoelectric coefficients of n -doped silicon from first principles via the solution of the Boltzmann transport equation

    Science.gov (United States)

    Fiorentini, Mattia; Bonini, Nicola

    2016-08-01

    We present a first-principles computational approach to calculate thermoelectric transport coefficients via the exact solution of the linearized Boltzmann transport equation, also including the effect of nonequilibrium phonon populations induced by a temperature gradient. We use density functional theory and density functional perturbation theory for an accurate description of the electronic and vibrational properties of a system, including electron-phonon interactions; carriers' scattering rates are computed using standard perturbation theory. We exploit Wannier interpolation (both for electronic bands and electron-phonon matrix elements) for an efficient sampling of the Brillouin zone, and the solution of the Boltzmann equation is achieved via a fast and stable conjugate gradient scheme. We discuss the application of this approach to n -doped silicon. In particular, we discuss a number of thermoelectric properties such as the thermal and electrical conductivities of electrons, the Lorenz number and the Seebeck coefficient, including the phonon drag effect, in a range of temperatures and carrier concentrations. This approach gives results in good agreement with experimental data and provides a detailed characterization of the nature and the relative importance of the individual scattering mechanisms. Moreover, the access to the exact solution of the Boltzmann equation for a realistic system provides a direct way to assess the accuracy of different flavors of relaxation time approximation, as well as of models that are popular in the thermoelectric community to estimate transport coefficients.

  4. Computational uncertainty principle in nonlinear ordinary differential equations (I)——Numerical results

    Institute of Scientific and Technical Information of China (English)

    李建平[1; 曾庆存[2; 丑纪范[3

    2000-01-01

    In a majority of cases of long-time numerical integration for initial-value problems, roundoff error has received little attention. Using twenty-nine numerical methods, the influence of round-off error on numerical solutions is generally studied through a large number of numerical experiments. Here we find that there exists a strong dependence on machine precision (which is a new kind of dependence different from the sensitive dependence on initial conditions), maximally effective computation time (MECT) and optimal stepsize (OS) in solving nonlinear ordinary differential equations (ODEs) in finite machine precision. And an optimal searching method for evaluating MECT and OS under finite machine precision is presented. The relationships between MECT, OS, the order of numerical method and machine precision are found. Numerical results show that round-off error plays a significant role in the above phenomena. Moreover, we find two universal relations which are independent of the types of ODEs, initial val

  5. Comparative Study on the Kinetic Equations of Potassium Release from Soils

    Institute of Scientific and Technical Information of China (English)

    LUXIAO-NAN; LUYUN-FU

    1993-01-01

    Elovich,two-constant,parabolic diffusion,exponential,second-order,first-order and zero-order equations were used to describe the kinetic characteristics of potassium desorption from six paddy soils of Zhejiang Province in a constant electric field (44.4V/cm) of EUF.Results showed that the second-order and Elovich equations could describe the potassium desorption kinetics best,as evidenced by the highest correlation coefficients (r) and the lowest standard errors (SE).The first-order,two-constant and parabolic diffusion equations also described the K desorption kinetics well,as showed by the relatively high correlation coefficients and relatively low standard errors.The zero-order equation did not describe the K desorption satisfactorily with a relatively low correlation coefficient and relatively high standard error.However,the exponential equation could not be used to describe the K desorption kinetics,due to the lowest correlation coefficient and the highest standarderror.

  6. Drug release profile in core-shell nanofibrous structures: a study on Peppas equation and artificial neural network modeling.

    Science.gov (United States)

    Maleki, Mahboubeh; Amani-Tehran, Mohammad; Latifi, Masoud; Mathur, Sanjay

    2014-01-01

    Release profile of drug constituent encapsulated in electrospun core-shell nanofibrous mats was modeled by Peppas equation and artificial neural network. Core-shell fibers were fabricated by co-axial electrospinning process using tetracycline hydrochloride (TCH) as the core and poly(l-lactide-co-glycolide) (PLGA) or polycaprolactone (PCL) as the shell materials. The density and hydrophilicity of the shell polymers, feed rates and concentrations of core and shell phases, the contribution of TCH in core material and electrical field were the parameters fed to the perceptron network to predict Peppas constants in order to derive release pattern. This study demonstrated the viability of the prediction tool in determining drug release profile of electrospun core-shell nanofibrous scaffolds.

  7. First-Principles Calculation of Static Equation of State and Elastic Constants for GaSe

    Institute of Scientific and Technical Information of China (English)

    ZHANG Dong-Wen; JIN Feng-Tao; YUAN Jian-Min

    2006-01-01

    @@ The all-electron full potential augmented plane-wave plus local orbital (APW+1o) method with the local-density approximation (LDA) is used to calculate the static equation of state (EOS) and elastic constants of crystalline GaSe. After the full relaxation of atomic positions, the calculated band structure at ambient pressure is consistent with the experimental data to the extent expected to give the known limits of LDA one-electron energies. The equilibrium lattice parameters found here exhibit the usual LDA-induced contraction. However, constrained with the experimental cell volume, the interlayer separation exhibits an expansion due to the LDA underestimate of the weak interlayer bonding. The calculated values of elastic constants are in good agreement with acoustic measurements. The pressure derivatives of the lattice constants derived from the theoretical elastic constants are in very good agreement with x-ray spectra measurements. Two analytical EOSs have been determined at pressures up to 4.5 GPa. The pressure evolution of the structure indicates that the layer thickness decreasesslightly under pressure.

  8. The canonical equation of adaptive dynamics for life histories: from fitness-returns to selection gradients and Pontryagin's maximum principle.

    Science.gov (United States)

    Metz, Johan A Jacob; Staňková, Kateřina; Johansson, Jacob

    2016-03-01

    This paper should be read as addendum to Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013). Our goal is, using little more than high-school calculus, to (1) exhibit the form of the canonical equation of adaptive dynamics for classical life history problems, where the examples in Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013) are chosen such that they avoid a number of the problems that one gets in this most relevant of applications, (2) derive the fitness gradient occurring in the CE from simple fitness return arguments, (3) show explicitly that setting said fitness gradient equal to zero results in the classical marginal value principle from evolutionary ecology, (4) show that the latter in turn is equivalent to Pontryagin's maximum principle, a well known equivalence that however in the literature is given either ex cathedra or is proven with more advanced tools, (5) connect the classical optimisation arguments of life history theory a little better to real biology (Mendelian populations with separate sexes subject to an environmental feedback loop), (6) make a minor improvement to the form of the CE for the examples in Dieckmann et al. and Parvinen et al.

  9. Seismic tomography analysis using finite differential calculation of the eikonal equation and reciplocal principle; Eikonal equation no sabunkaiho to sohan genri wo riyoshita danseiha tomography kaiseki

    Energy Technology Data Exchange (ETDEWEB)

    Fujimoto, M.; Ashida, Y.; Watanabe, T.; Sassa, K. [Kyoto University, Kyoto (Japan)

    1996-10-01

    This paper describes the seismic tomography analysis of underground structures using finite differential calculation (FDC) and a reciprocal principle which points out that a propagation path is constant even if a source and receiver are exchanged with each other. Tomography analysis generally determines a ray length across each underground cell structure by ray tracing method to modify each cell slowness (inverse of velocity). Travel time field was determined by FDC of eikonal equation among ray tracing methods, and a wave propagation path was determined by reciprocity of elastic wave to carry out inversion. In conventional methods, since a wave length is assumed to be infinitesimal by ray theory, false modified slowness structures frequently appears depending on the density of a ray. Wave propagates in a certain width, and is affected by environment. The slowness was thus modified on the basis of the wave propagation path with a certain width by using not ray-tracing but reciprocity. By this modification, false structures were hardly found under a fine grid, and several propagation paths could be considered. 6 refs., 9 figs.

  10. First-principles equation-of-state table of beryllium based on density-functional theory calculations

    Science.gov (United States)

    Ding, Y. H.; Hu, S. X.

    2017-06-01

    Beryllium has been considered a superior ablator material for inertial confinement fusion (ICF) target designs. An accurate equation-of-state (EOS) of beryllium under extreme conditions is essential for reliable ICF designs. Based on density-functional theory (DFT) calculations, we have established a wide-range beryllium EOS table of density ρ = 0.001 to 500 g/cm3 and temperature T = 2000 to 108 K. Our first-principle equation-of-state (FPEOS) table is in better agreement with the widely used SESAME EOS table (SESAME 2023) than the average-atom INFERNO and Purgatorio models. For the principal Hugoniot, our FPEOS prediction shows ˜10% stiffer than the last two models in the maximum compression. Although the existing experimental data (only up to 17 Mbar) cannot distinguish these EOS models, we anticipate that high-pressure experiments at the maximum compression region should differentiate our FPEOS from INFERNO and Purgatorio models. Comparisons between FPEOS and SESAME EOS for off-Hugoniot conditions show that the differences in the pressure and internal energy are within ˜20%. By implementing the FPEOS table into the 1-D radiation-hydrodynamic code LILAC, we studied the EOS effects on beryllium-shell-target implosions. The FPEOS simulation predicts higher neutron yield (˜15%) compared to the simulation using the SESAME 2023 EOS table.

  11. A Maximum Principle for Controlled Time-Symmetric Forward-Backward Doubly Stochastic Differential Equation with Initial-Terminal Sate Constraints

    Directory of Open Access Journals (Sweden)

    Shaolin Ji

    2012-01-01

    Full Text Available We study the optimal control problem of a controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal state constraints. Applying the terminal perturbation method and Ekeland’s variation principle, a necessary condition of the stochastic optimal control, that is, stochastic maximum principle, is derived. Applications to backward doubly stochastic linear-quadratic control models are investigated.

  12. P-V-T equation of state of cubic CaSiO3 perovskite from first-principles computation

    Science.gov (United States)

    Kawai, Kenji; Tsuchiya, Taku

    2014-04-01

    Ca-perovskite (Pv) is considered to be one of the most abundant minerals in the Earth's lower mantle (LM) with an ideal cubic structure at LM pressures and temperatures. In this study, a pressure-volume-temperature (P-V-T) equation of state model for Ca-Pv is constructed using density functional first-principles molecular dynamics simulations. The calculated P-V-T data yield KT0 1000 K = 203.95 GPa, V0 1000 K = 46.17 Å3/formula unit, γ0 = 1.576, and q = 0.96 within the framework of the Mie-Grüneisen-Debye formulation. We compare the density and bulk sound velocity of Ca-Pv with those of iron-bearing Mg-Pv and seismological values. Along an adiabatic temperature gradient, Ca-Pv has ~2.5% higher density and ~0.7% faster bulk sound velocity than the preliminary reference Earth model, while it has ~3.8% higher density and ~2.7% slower bulk sound velocity than iron-bearing Mg-Pv. Our results indicate that a possible lateral variation in the Ca-Pv fraction in the LM could produce an anticorrelation between VΦ and ρ.

  13. Chemical release experiments to induce F region ionospheric plasma irregularities at the magnetic equator

    Science.gov (United States)

    Sultan, Peter Jared

    1994-01-01

    The largest-scale plasma instability that occurs naturally in the Earth's ionosphere is a turbulent upwelling of the equatorial F region known as equatorial spread-F (ESF). During an ESF event, high plasma density magnetic fluxtubes at the bottomside of the F region are thought to change places with lower plasma density flux-tubes from below in a Rayleigh-Taylor type (heavy fluid over light fluid) instability. This interchange creates a large-scale (10's of km) density perturbation locally, which rapidly penetrates through to the topside of the F region, creating a plume of cascading smaller-scale (meter to centimeter scale) irregularities from the sharp density gradients at the edges of the rising plasma 'bubble'. In a theoretical test of this overall scenario for ESF, a linear instability growth rate is derived following the magnetic fluxtube formalism of Haerendel. Using realistic atmospheric and ionospheric density model inputs, growth rates are calculated for a range of geophysical conditions. Time/altitude domains having positive growth rates are found to coincide with observed time/altitude patterns of ESF occurrence, thus supporting the fluxtube model. The physics also are tested experimentally by the deliberate creation of plasma bubbles in ambient ionospheres that the fluxtube model predicts are susceptible to the Rayleigh-Taylor instability. Two such artificial seed perturbations were generated during the 1990 NASA/Boston University CRRES-at-Kwajalein campaign, when clouds of sulfur hexafluoride (SF6) were released by sounding rockets to initiate plasma recombinations near the bottomside of the equatorial ionosphere. Multiple diagnostics (incoherent scatter radar, high frequency radar, optics, and satellite polarimeters at several sites) were used to monitor the prelaunch status of the ionosphere and the electron depleted regions that resulted from the chemical releases. Small ESF plumes were observed to form in the region of the artificial perturbation

  14. A Signal-On Fluorosensor Based on Quench-Release Principle for Sensitive Detection of Antibiotic Rapamycin

    Directory of Open Access Journals (Sweden)

    Hee-Jin Jeong

    2015-03-01

    Full Text Available An antibiotic rapamycin is one of the most commonly used immunosuppressive drugs, and also implicated for its anti-cancer activity. Hence, the determination of its blood level after organ transplantation or tumor treatment is of great concern in medicine. Although there are several rapamycin detection methods, many of them have limited sensitivity, and/or need complicated procedures and long assay time. As a novel fluorescent biosensor for rapamycin, here we propose “Q’-body”, which works on the fluorescence quench-release principle inspired by the antibody-based quenchbody (Q-body technology. We constructed rapamycin Q’-bodies by linking the two interacting domains FKBP12 and FRB, whose association is triggered by rapamycin. The fusion proteins were each incorporated position-specifically with one of fluorescence dyes ATTO520, tetramethylrhodamine, or ATTO590 using a cell-free translation system. As a result, rapid rapamycin dose-dependent fluorescence increase derived of Q’-bodies was observed, especially for those with ATTO520 with a lowest detection limit of 0.65 nM, which indicates its utility as a novel fluorescent biosensor for rapamycin.

  15. Advancements in Micrometeorological Technique for Monitoring CH4 Release from Remote Permafrost Regions: Principles, Emerging Research, and Latest Updates

    Science.gov (United States)

    Burba, George; Budishchev, Artem; Gioli, Beniamino; Haapanala, Sami; Helbig, Manuel; Losacco, Salvatore; Mammarella, Ivan; Moreaux, Virginie; Murphy, Patrick; Oechel, Walter; Peltola, Olli; Rinne, Janne; Sonnentag, Oliver; Sturtevant, Cove; Vesala, Timo; Zona, Donatella; Zulueta, Rommel

    2014-05-01

    in permafrost regions have mostly been made with static chamber techniques, and few were done with the eddy covariance approach using closed-path analyzers. Although chambers and closed-path analyzers have advantages, both techniques have significant limitations, especially for remote or portable research in cold regions. Static chamber measurements are discrete in time and space, and particularly difficult to use over polygonal tundra with highly non-uniform micro-topography and active soil layer. Closed-path gas analyzers for measuring CH4 eddy fluxes require climate control, employ high-power pumps, and generally require grid power and infrastructure. As a result, spatial coverage of eddy covariance CH4 flux measurements in cold regions remains limited. Existing stations are often located near grid power sources and roads rather than in the middle of the methane-producing ecosystem, while those that are placed appropriately may require extraordinary efforts to build and maintain them, with large investments into manpower and infrastructure. In this presentation, basic principles of eddy covariance flux measurements are explained, along with details on the CH4, CO2 and H2O exchange measurements using low-power flux stations. Also included are latest updates on the emerging research utilizing such stations in remote permafrost regions, and on the 2013-2014 development of fully automated remote unattended flux station capable of processing data on-the-go to continuously output final CH4 release rates.

  16. Discontinuous local semiflows for Kurzweil equations leading to LaSalle's invariance principle for differential systems with impulses at variable times

    Science.gov (United States)

    Afonso, S. M.; Bonotto, E. M.; Federson, M.; Schwabik, Š.

    2011-04-01

    In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle's invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle's invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times.

  17. Vanishing viscosity as a selection principle for the Euler equations: The case of 3D shear flow

    CERN Document Server

    Bardos, Claude; Wiedemann, Emil

    2012-01-01

    We show that for a certain family of initial data, there exist non-unique weak solutions to the 3D incompressible Euler equations satisfying the weak energy inequality, whereas the weak limit of every sequence of Leray-Hopf weak solutions for the Navier-Stokes equations, with the same initial data, and as the viscosity tends to zero, is uniquely determined and equals the shear flow solution of the Euler equations. This simple example suggests that, also in more general situations, the vanishing viscosity limit of the Navier-Stokes equations could serve as a uniqueness criterion for weak solutions of the Euler equations.

  18. The principle of minimum of partial local variations for determining convective flows in the numerical solution of one-dimensional nonlinear scalar hyperbolic equations

    Science.gov (United States)

    Goloviznin, V. M.; Kanaev, A. A.

    2011-05-01

    For the CABARET finite difference scheme, a new approach to the construction of convective flows for the one-dimensional nonlinear transport equation is proposed based on the minimum principle of partial local variations. The new approach ensures the monotonicity of solutions for a wide class of problems of a fairly general form including those involving discontinuous and nonconvex functions. Numerical results illustrating the properties of the proposed method are discussed.

  19. Influence of Hydrophilic Polymers on the β Factor in Weibull Equation Applied to the Release Kinetics of a Biologically Active Complex of Aesculus hippocastanum

    Directory of Open Access Journals (Sweden)

    Justyna Kobryń

    2017-01-01

    Full Text Available Triterpenoid saponins complex of biological origin, escin, exhibits significant clinical activity in chronic venous insufficiency, skin inflammation, epidermal abrasions, allergic dermatitis, and acute impact injuries, especially in topical application. The aim of the study is the comparison of various hydrogel formulations, as carriers for a horse chestnut seed extract (EH. Methylcellulose (MC, two polyacrylic acid derivatives (PA1 and PA2, and polyacrylate crosspolymer 11 (PC-11 were employed. The release rates of EH were examined and a comparison with the Weibull model equation was performed. Application of MC as the carrier in the hydrogel preparation resulted in fast release rate of EH, whereas in the case of the hydrogel composed with PC-11 the release was rather prolonged. Applied Weibull function adhered best to the experimental data. Due to the evaluated shape parameter β, in the Weibull equation, the systems under study released the active compound according to the Fickian diffusion.

  20. Variational Principles, Lie Point Symmetries, and Similarity Solutions of the Vector Maxwell Equations in Non-linear Optics

    DEFF Research Database (Denmark)

    Webb, Garry; Sørensen, Mads Peter; Brio, Moysey

    2004-01-01

    The vector Maxwell equations of nonlinear optics coupled to a single Lorentz oscillator and with instantaneous Kerr nonlinearity are investigated by using Lie symmetry group methods. Lagrangian and Hamiltonian formulations of the equations are obtained. The aim of the analysis is to explore......-second pulse propagation in which the NLS approximation is expected to break down. The canonical Hamiltonian description of the equations involves the solution of a polynomial equation for the electric field $E$, in terms of the the canonical variables, with possible multiple real roots for $E$. In order...... to circumvent this problem, non-canonical Poisson bracket formulations of the equations are obtained in which the electric field is one of the non-canonical variables. Noether's theorem, and the Lie point symmetries admitted by the equations are used to obtain four conservation laws, including...

  1. Lie-algebraic structure of Lax-Sato integrable heavenly equations and the Lagrange-d'Alembert principle

    Science.gov (United States)

    Hentosh, Oksana E.; Prykarpatsky, Yarema A.; Blackmore, Denis; Prykarpatski, Anatolij K.

    2017-10-01

    The work is devoted to recent investigations of the Lax-Sato compatible linear vector field equations, especially to the related Lie-algebraic structures and integrability properties of a very interesting class of nonlinear dynamical systems called the dispersionless heavenly type equations, which were initiated by Plebański and later analyzed in a series of articles. The AKS-algebraic and related R-structure schemes are used to study the orbits of the corresponding co-adjoint actions, which are intimately related to the classical Lie-Poisson structures on them. It is demonstrated that their compatibility condition coincides with the corresponding heavenly equation being considered. It is shown that all these equations originate in this way and can be represented as a Lax compatibility condition for specially constructed loop vector fields on the torus. The infinite hierarchy of conservations laws related to the heavenly equations is described, and its analytical structure connected with the Casimir invariants is mentioned. In addition, typical examples of such equations, demonstrating in detail their integrability via the scheme devised herein, are presented. The relationship of the very interesting Lagrange-d'Alembert type mechanical interpretation of the devised integrability scheme with the Lax-Sato equations is also discussed.

  2. Calculation of the release of total organic matter and total mineral using the hydrodynamic equations applied to palm oil mill effluent treatment by cascaded anaerobic ponds.

    Science.gov (United States)

    Fulazzaky, Mohamad Ali

    2013-01-01

    Anaerobic treatment processes to remove organic matter from palm oil mill effluent (POME) have been used widely in Malaysia. Still the amounts of total organic and total mineral released from POME that may cause degradation of the receiving environment need to be verified. This paper proposes the use of the hydrodynamic equations to estimate performance of the cascaded anaerobic ponds (CAP) and to calculate amounts of total organic matter and total mineral released from POME. The CAP efficiencies to remove biochemical oxygen demands, chemical oxygen demands, total solids and volatile solids (VS) as high as 94.5, 93.6, 96.3 and 98.2 %, respectively, are estimated. The amounts of total organic matter and total mineral as high as 538 kg VS/day and 895 kg FS/day, respectively, released from POME to the receiving water are calculated. The implication of the proposed hydrodynamic equations contributes to more versatile environmental assessment techniques, sometimes replacing laboratory analysis.

  3. First-principles studies on the equation of state, thermal conductivity, and opacity of deuterium-tritium (DT) and polystyrene (CH) for inertial confinement fusion applications

    Science.gov (United States)

    Hu, S. X.; Collins, L. A.; Goncharov, V. N.; Kress, J. D.; Boehly, T. R.; Epstein, R.; McCrory, R. L.; Skupsky, S.

    2016-05-01

    Using first-principles (FP) methods, we have performed ab initio compute for the equation of state (EOS), thermal conductivity, and opacity of deuterium-tritium (DT) in a wide range of densities and temperatures for inertial confinement fusion (ICF) applications. These systematic investigations have recently been expanded to accurately compute the plasma properties of CH ablators under extreme conditions. In particular, the first-principles EOS and thermal-conductivity tables of CH are self-consistently built from such FP calculations, which are benchmarked by experimental measurements. When compared with the traditional models used for these plasma properties in hydrocodes, significant differences have been identified in the warm dense plasma regime. When these FP-calculated properties of DT and CH were used in our hydrodynamic simulations of ICF implosions, we found that the target performance in terms of neutron yield and energy gain can vary by a factor of 2 to 3, relative to traditional model simulations.

  4. Inverse final observation problems for Maxwell's equations in the quasi-stationary magnetic approximation and stable sequential Lagrange principles for their solving

    Science.gov (United States)

    Kalinin, A. V.; Sumin, M. I.; Tyukhtina, A. A.

    2017-02-01

    An initial-boundary value problem for Maxwell's equations in the quasi-stationary magnetic approximation is investigated. Special gauge conditions are presented that make it possible to state the problem of independently determining the vector magnetic potential. The well-posedness of the problem is proved under general conditions on the coefficients. For quasi-stationary Maxwell equations, final observation problems formulated in terms of the vector magnetic potential are considered. They are treated as convex programming problems in a Hilbert space with an operator equality constraint. Stable sequential Lagrange principles are stated in the form of theorems on the existence of a minimizing approximate solution of the optimization problems under consideration. The possibility of applying algorithms of dual regularization and iterative dual regularization with a stopping rule is justified in the case of a finite observation error.

  5. Propensity scores as a basis for equating groups: basic principles and application in clinical treatment outcome research.

    Science.gov (United States)

    West, Stephen G; Cham, Heining; Thoemmes, Felix; Renneberg, Babette; Schulze, Julian; Weiler, Matthias

    2014-10-01

    A propensity score is the probability that a participant is assigned to the treatment group based on a set of baseline covariates. Propensity scores provide an excellent basis for equating treatment groups on a large set of covariates when randomization is not possible. This article provides a nontechnical introduction to propensity scores for clinical researchers. If all important covariates are measured, then methods that equate on propensity scores can achieve balance on a large set of covariates that mimics that achieved by a randomized experiment. We present an illustration of the steps in the construction and checking of propensity scores in a study of the effectiveness of a health coach versus treatment as usual on the well-being of seriously ill individuals. We then consider alternative methods of equating groups on propensity scores and estimating treatment effects including matching, stratification, weighting, and analysis of covariance. We illustrate a sensitivity analysis that can probe for the potential effects of omitted covariates on the estimate of the causal effect. Finally, we briefly consider several practical and theoretical issues in the use of propensity scores in applied settings. Propensity score methods have advantages over alternative approaches to equating groups particularly when the treatment and control groups do not fully overlap, and there are nonlinear relationships between covariates and the outcome.

  6. Hydrogen release at metal-oxide interfaces: A first principle study of hydrogenated Al/SiO2 interfaces

    Science.gov (United States)

    Huang, Jianqiu; Tea, Eric; Li, Guanchen; Hin, Celine

    2017-06-01

    The Anode Hydrogen Release (AHR) mechanism at interfaces is responsible for the generation of defects, that traps charge carriers and can induce dielectric breakdown in Metal-Oxide-Semiconductor Field Effect Transistors. The AHR has been extensively studied at Si/SiO2 interfaces but its characteristics at metal-silica interfaces remain unclear. In this study, we performed Density Functional Theory (DFT) calculations to study the hydrogen release mechanism at the typical Al/SiO2 metal-oxide interface. We found that interstitial hydrogen atoms can break interfacial Alsbnd Si bonds, passivating a Si sp3 orbital. Interstitial hydrogen atoms can also break interfacial Alsbnd O bonds, or be adsorbed at the interface on aluminum, forming stable Alsbnd Hsbnd Al bridges. We showed that hydrogenated Osbnd H, Sisbnd H and Alsbnd H bonds at the Al/SiO2 interfaces are polarized. The resulting bond dipole weakens the Osbnd H and Sisbnd H bonds, but strengthens the Alsbnd H bond under the application of a positive bias at the metal gate. Our calculations indicate that Alsbnd H bonds and Osbnd H bonds are more important than Sisbnd H bonds for the hydrogen release process.

  7. Applicability of three-parameter equation of state of solids: compatibility with first principles approaches and application to solids

    CERN Document Server

    Roy, P B

    2003-01-01

    In a recent paper we have proposed a three-parameter equation of state (EOS) of solids, and applied it to a few isotherms and shown that the fits are uniformly excellent. In this paper a comprehensive comparison of the applicability of our model is made with seven existing three-parameter EOSs. We have applied our model along with seven existing three-parameter EOSs, with no constraint on the parameters, to accurate and model-independent isotherms of nine solids and studied the fitting accuracy and agreement of the fit parameters with experiment. Further, each of these nine isotherms is divided into three subsets, and the resulting subsets fitted with all the eight EOSs. The stability of the fitted stress-free bulk modulus B sub 0 and its pressure derivatives B' sub 0 and B'' sub 0 with variation in the compression range is compared. Furthermore, our EOS is applied to a large number of inorganic as well as organic solids, including alloy, glasses, rubbers and plastics; of widely divergent bonding and structur...

  8. Technical principles underlying limit values for release of substances for the percolation test TS3: comparison DE and NL

    Energy Technology Data Exchange (ETDEWEB)

    Van Zomeren, A.; Dijkstra, J.J. [ECN Environment and Energy Engineering, Petten (Netherlands); Susset, B. [Consulting Office SiWaP (Germany)

    2013-10-15

    Within CEN TC 351 WG 1, standardized, horizontal test methods are developed to assess the release (leaching) of dangerous substances from construction as defined in ER3 of the CPD. For granular materials TS 3, a horizontal up-flow percolation test, was further developed by CEN TC 351 WG1 and will enter the validation phase in 2013. In CEN TC 351 WG1, there are still discussions regarding the sample preparation and some test conditions. Currently, two options for sample preparation and test conditions are specified. Controversy between DE and NL regarding sample preparation and test conditions and the need for two separate options in the TS 3 percolation test are possibly for a part caused by different approaches for risk assessment in the Netherlands and in Germany and the resulting regulatory concepts. One important reason for this is, that in soil and groundwater regulations the test method and the impact assessment method are systematically linked together but the impact assessment methods and lab methods in both countries are different. The discussions in CEN TC 351 WG 1 show that there is a need to have a better mutual understanding of the relation between test method and impact assessment on the one hand and a clear overview of differences in impact assessment approaches of each country on the other hand. The aim of this project is to explain and compare the assumptions, boundary conditions and conventions of the impact assessment approach that are implemented in the upcoming German Recycling Degree and in the Soil Quality Degree of the Netherlands. Ultimately, a better understanding of the impact assessment approaches provides a basis for further discussion in WG1 to agree on only one option for the percolation test conditions. The following report is prepared by the contractors of Germany and Netherlands together to compare the two country-specific concepts. This report summarizes and explains the presentation given on the 25th of April at TC 351 WG1 in

  9. Thermal equation of state of solid naphthalene to 13 GPa and 773 K: in situ X-ray diffraction study and first principles calculations.

    Science.gov (United States)

    Likhacheva, Anna Y; Rashchenko, Sergey V; Chanyshev, Artem D; Inerbaev, Talgat M; Litasov, Konstantin D; Kilin, Dmitry S

    2014-04-28

    In a wide range of P-T conditions, such fundamental characteristics as compressibility and thermoelastic properties remain unknown for most classes of organic compounds. Here we attempt to clarify this issue by the example of naphthalene as a model representative of polycyclic aromatic hydrocarbons (PAHs). The elastic behavior of solid naphthalene was studied by in situ synchrotron powder X-ray diffraction up to 13 GPa and 773 K and first principles computations to 20 GPa and 773 K. Fitting of the P-V experimental data to Vinet equation of state yielded T 0 = 8.4(3) GPa and T' = 7.2 (3) at V0 = 361 Å(3), whereas the thermal expansion coefficient was found to be extremely low at P > 3 GPa (about 10(-5) K(-1)), in agreement with theoretical estimation. Such a diminishing of thermal effects with the pressure increase clearly demonstrates a specific feature of the high-pressure behavior of molecular crystals like PAHs, associated with a low energy of intermolecular interactions.

  10. Variational principles

    CERN Document Server

    Moiseiwitsch, B L

    2004-01-01

    This graduate-level text's primary objective is to demonstrate the expression of the equations of the various branches of mathematical physics in the succinct and elegant form of variational principles (and thereby illuminate their interrelationship). Its related intentions are to show how variational principles may be employed to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities (such as the phase shifts) that arise in the theory of scattering. Chapter-by-chapter treatment consists of analytical dynamics; optics, wave mecha

  11. Scaling Equation for Invariant Measure

    Institute of Scientific and Technical Information of China (English)

    LIU Shi-Kuo; FU Zun-Tao; LIU Shi-Da; REN Kui

    2003-01-01

    An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.

  12. Dynamic sealing principles

    Science.gov (United States)

    Zuk, J.

    1976-01-01

    The fundamental principles governing dynamic sealing operation are discussed. Different seals are described in terms of these principles. Despite the large variety of detailed construction, there appear to be some basic principles, or combinations of basic principles, by which all seals function, these are presented and discussed. Theoretical and practical considerations in the application of these principles are discussed. Advantages, disadvantages, limitations, and application examples of various conventional and special seals are presented. Fundamental equations governing liquid and gas flows in thin film seals, which enable leakage calculations to be made, are also presented. Concept of flow functions, application of Reynolds lubrication equation, and nonlubrication equation flow, friction and wear; and seal lubrication regimes are explained.

  13. Microwave system engineering principles

    CERN Document Server

    Raff, Samuel J

    1977-01-01

    Microwave System Engineering Principles focuses on the calculus, differential equations, and transforms of microwave systems. This book discusses the basic nature and principles that can be derived from thermal noise; statistical concepts and binomial distribution; incoherent signal processing; basic properties of antennas; and beam widths and useful approximations. The fundamentals of propagation; LaPlace's Equation and Transmission Line (TEM) waves; interfaces between homogeneous media; modulation, bandwidth, and noise; and communications satellites are also deliberated in this text. This bo

  14. Optimal Release Control of Companion Satellite System Using Electromagnetic Forces

    Institute of Scientific and Technical Information of China (English)

    Zengwen Xu,Peng Shi; Yushan Zhao∗

    2015-01-01

    Electromagnetic forces generated by the inter⁃action of component satellites can be used to release companion satellites. Optimal release trajectories for companion satellite system using inter⁃electromagnetic forces were investigated. Firstly, nonlinear relative motion dynamic equations of a two⁃craft electromagnetic companion satellite system were derived in spatial polar coordinates. Then principles of electromagnetic satellite formation flying were introduced. Secondly, the characteristics of the electromagnetic companion satellites release were analyzed and optimal release trajectories of companion satellites using electromagnetic forces were obtained using Gauss pseudospectral method. Three performance criteria were chosen as minimum time, minimum acceleration of the separation distance and minimum control acceleration. Finally, three release examples including expansion along separation distance, rotation in orbital plane and stable formation reconfiguration were given to demonstrate the feasibility of this method. Results indicated that the release trajectories can converge to optimal solutions effectively and the concept of release companion satellites using electromagnetic forces is practicable.

  15. Correction to Euler's equations and elimination of the closure problem in turbulence

    CERN Document Server

    Zak, Michail

    2012-01-01

    It has been demonstrated that the Euler equations of inviscid fluid are incomplete: according to the principle of release of constraints, absence of shear stresses must be compensated by additional degrees of freedom, and leads to Reynolds-type multivalued velocity field. however unlike the Reynolds equations, the enlarged Euler's (EE) model provides additional equations for fluctuations, and that eliminates the closure problem. Therefore the (EE) equations are applicable to fully developed turbulent motions where the physical viscosity is vanishingly small compare to the turbulent viscosity, as well as to superfluids and atomized fluids.Analysis of coupled mean/fluctuation EE equations shows that fluctuations stabilize the whole system generating elastic shear waves and increasing speed of sound. Those turbulent motions that originated from instability of underlying laminar motions can be described by the modified Euler's equation with the closure provided by the stabilization principle: driven by instabilit...

  16. On enforcing maximum principles and achieving element-wise species balance for advection-diffusion-reaction equations under the finite element method

    Science.gov (United States)

    Mudunuru, M. K.; Nakshatrala, K. B.

    2016-01-01

    We present a robust computational framework for advective-diffusive-reactive systems that satisfies maximum principles, the non-negative constraint, and element-wise species balance property. The proposed methodology is valid on general computational grids, can handle heterogeneous anisotropic media, and provides accurate numerical solutions even for very high Péclet numbers. The significant contribution of this paper is to incorporate advection (which makes the spatial part of the differential operator non-self-adjoint) into the non-negative computational framework, and overcome numerical challenges associated with advection. We employ low-order mixed finite element formulations based on least-squares formalism, and enforce explicit constraints on the discrete problem to meet the desired properties. The resulting constrained discrete problem belongs to convex quadratic programming for which a unique solution exists. Maximum principles and the non-negative constraint give rise to bound constraints while element-wise species balance gives rise to equality constraints. The resulting convex quadratic programming problems are solved using an interior-point algorithm. Several numerical results pertaining to advection-dominated problems are presented to illustrate the robustness, convergence, and the overall performance of the proposed computational framework.

  17. Principle extremum of full action

    Directory of Open Access Journals (Sweden)

    Solomon I. Khmelnik

    2011-10-01

    Full Text Available A new variational principle extremum of full action is proposed, which extends the Lagrange formalism on dissipative systems. It is shown that this principle is applicable in electrical engineering, electrodynamics, mechanics and hydrodynamics, taking into account the friction forces. The proposed variational principle may be considered as a new formalism used as an universal method of physical equations derivation, and also as a method for solving these equations.

  18. First-principles calculations for $c$-coefficients of the isobaric mass multiplet equation in the $1p0f$ shell

    CERN Document Server

    Ormand, W E; Jensen, M Hjorth

    2016-01-01

    We present the first calculations for the $c$-coefficients of the isobaric mass multiplet equation (IMME) for nuclei from $A=42$ to $A=54$ based on input from several realistic nucleon-nucleon interactions. We show that there is clear dependence on the short-ranged charge-symmetry breaking (CSB) part of the strong interaction. There is a significant variation in the CSB part between the commonly used CD-Bonn, N$^3$LO and Argonne V18 nucleon-nucleon interactions. All of them give a CSB contribution that is too large when compared to experiment.

  19. High-Order Hamilton's Principle and the Hamilton's Principle of High-Order Lagrangian Function

    Institute of Scientific and Technical Information of China (English)

    ZHANG Ming-Jiang; ZHAO Hong-Xia; FANG Jian-Hui; MA Shan-Jun; LU Kai

    2008-01-01

    In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton's principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton's principle. Finally, the Hamilton's principle of high-order Lagrangian function is given.

  20. Modeling the material strength and equations of state of beta-HMX from both first-principles calculations and molecular dynamics simulations

    Science.gov (United States)

    Peng, Qing; Wang, Guangyu; Liu, G. R.; de, Suvranu

    2015-06-01

    We investigate the elastic constants and equations of state (EOS) of the β-polymorph of cyclotetramethylene tetranitramine (HMX) energetic molecular crystal using density functional theory (DFT) calculations. The combination of vdW-DF2 van der Waals functionals and PBE exchange-correlation functionals gives optimized results. The DFT results are used to optimize the Reactive Force Field (ReaxFF). The material strength and EOS of beta-HMX at finite temperatures are then predicted from ReaxFF molecular dynamics simulations. Our results suggest that the optimized ReaxFF predicts the mechanics and EOS of beta-HMX well. The authors would like to acknowledge the generous financial support from the Defense Threat Reduction Agency (DTRA) Grant # HDTRA1-13-1-0025.

  1. Conservation Laws of Differential Equations in Finance

    Institute of Scientific and Technical Information of China (English)

    QIN Mao-Chang; MEI Feng-Xiang; SHANG Mei

    2005-01-01

    Conservation laws of some differential equations in fiance are studied in this paper. This method does not involve the use or existence of a variational principle. As an alternative, linearize the given equation and find adjoint equation of the linearized equation, the conservation laws can be constructed directly from the symmetries and adjoint symmetries of the associated linearized equation and its adjoint equation.

  2. Electrical and electronic principles

    CERN Document Server

    Knight, SA

    1988-01-01

    Electrical and Electronic Principles, 3 focuses on the principles involved in electrical and electronic circuits, including impedance, inductance, capacitance, and resistance.The book first deals with circuit elements and theorems, D.C. transients, and the series circuits of alternating current. Discussions focus on inductance and resistance in series, resistance and capacitance in series, power factor, impedance, circuit magnification, equation of charge, discharge of a capacitor, transfer of power, and decibels and attenuation. The manuscript then examines the parallel circuits of alternatin

  3. Derivation of equations to define inflection point and its analysis in flattening filter free photon beams based on the principle of polynomial function

    Directory of Open Access Journals (Sweden)

    KR Muralidhar

    2015-03-01

    Full Text Available Purpose: The objective of this work is to (1 present a mechanism for calculating inflection points on profiles at various depths and field sizes, and (2 study the doses at the inflection points for various field sizes at depth of maximum dose (Dmax for flattening filter free (FFF photon beam profiles. Methods: Graphical representation was done on percentage of dose versus inflection points. Also, using the polynomial function, the author formulated equations for calculating spot-on inflection point on the profiles for both the 6MV and 10 MV energies for different field sizes at various depths. Results: In a 10 MV FFF radiation beam, the dose at inflection point of the profile decreases as the field size increases. However, in 6MV FFF radiation beam, the dose at the inflection point initially increases with an increase in the field size up to 10 ×10 cm2 and decreases after 10 ×10 cm2. The polynomial function was fitted for both the 6 MV and 10 MV FFF beams for all field sizes and depths. Conclusion: Polynomial function is one of the easiest ways of identifying the inflection point in FFF beam for various field sizes and depths. Graphical representation of dose versus inflection point for both FFF energies was derived.

  4. Basic principles for the development of a concept for environmental exposure assessments of single substances released from multiple uses under REACH

    Energy Technology Data Exchange (ETDEWEB)

    Gross, Rita; Bunke, Dirk [Oeko-Institut e.V. - Institut fuer Angewandte Oekologie e.V., Freiburg im Breisgau (Germany); Gartiser, Stefan [Hydrotox GmbH, Freiburg im Breisgau (Germany)

    2011-10-15

    The ECHA Guidance Documents R.12 to R.18 include detailed provisions on how to conduct an exposure assessment as part of the Chemical Safety Report. The guidance documents, however, only restrictedly address the consideration of a substance's emissions into the environment, if the local releases from various uses of the same substance result in a cumulative exposure. In a situation where a chemical has a number of applications in one site, it may however occur that the emissions of several uses which only have a low risk if considered separately will sum up and cause an unacceptable risk to the environment. Against this background, the objective of the present study is a further specification of the guidelines on cumulative risk assessment according to the REACH Regulation. Besides the definition of the key terminology, guidelines on cumulative exposure assessment already laid down in other legal regulations have been evaluated and their transferability to the environmental exposure assessment according to REACH has been investigated. Moreover, the fields of application for which a cumulative exposure assessment might be relevant have been worked out. A distinction was made between cases where the responsibility for cumulative exposure assessment falls into the hands of the registrant as part of the Chemical Safety Report and other cases, where the responsibility lies with the downstream users (DU) or the Member State Competent Authorities (MS-CA). Initial proposals have been elaborated for a technical implementation of the cumulative exposure assessment of chemicals as part of the preparation and evaluation of chemical dossiers by the registrant and the MS-CA, respectively, and as part of the responsibility of the DU. (orig.)

  5. Quantum mechanics principles and formalism

    CERN Document Server

    McWeeny, Roy

    2012-01-01

    Focusing on main principles of quantum mechanics and their immediate consequences, this graduate student-oriented volume develops the subject as a fundamental discipline, opening with review of origins of Schrödinger's equations and vector spaces.

  6. Onsager principle as a tool for approximation

    Institute of Scientific and Technical Information of China (English)

    Masao Doi

    2015-01-01

    Onsager principle is the variational principle proposed by Onsager in his celebrated paper on the reciprocal relation. The principle has been shown to be useful in deriving many evolution equations in soft matter physics. Here the principle is shown to be useful in solving such equations approximately. Two examples are discussed: the diffusion dynamics and gel dynamics. Both examples show that the present method is novel and gives new results which capture the essential dynamics in the system.

  7. Causality Principle

    OpenAIRE

    Chi, Do Minh

    2001-01-01

    We advance a famous principle - causality principle - but under a new view. This principle is a principium automatically leading to most fundamental laws of the nature. It is the inner origin of variation, rules evolutionary processes of things, and the answer of the quest for ultimate theories of the Universe.

  8. Partial differential equations

    CERN Document Server

    Evans, Lawrence C

    2010-01-01

    This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

  9. On basic equation of statistical physics

    Institute of Scientific and Technical Information of China (English)

    邢修三

    1996-01-01

    Considering that thermodynamic irreversibility, the principle of entropy increase and hydrodynamic equations cannot be derived rigorously and in a unified way from the Liouville equations, the anomalous Langevin equation in Liouville space or its equivalent generalized Liouville equation is proposed as a basic equation of statistical physics. This equation reflects the fact that the law of motion of statistical thermodynamics is stochastic, but not deterministic. From that the nonequilibrium entropy, the principle of entropy increase, the theorem of minimum entropy production and the BBGKY diffusion equation hierarchy have been derived. The hydrodynamic equations, such as the generalized Navier-Stokes equation and the mass drift-diffusion equation, etc. have been derived from the BBGKY diffusion equation hierarchy. This equation has the same equilibrium solution as that of the Liouville equation. All these are unified and rigorous without adding any extra assumption. But it is difficult to prove that th

  10. Studies on the equation of state of mixed carbide fuel

    Science.gov (United States)

    Joseph, M.; Mathews, C. K.; Rao, P. Bhaskar

    1989-12-01

    The equation of state of reactor fuels is required up to very high temperatures in order to assess the energy release in hypothetical core disruptive accidents (HCM). Though the mixed carbide of uranium and plutonium is a candidate fuel material for fast breeder reactors, much information is not available on its equation of state. This paper reports the results of our studies to obtain the equilibrium vapour pressures of uranium carbide and uranium-plutonium mixed carbide of varying compositions in the temperature range of 1300-9000 K. An extrapolation method based on the principles of equilibrium thermodynamics has been used as also the principle of corresponding states. The agreement between the different results are discussed and their implications in HCDA calculations brought out.

  11. Variational Principle for Planetary Interiors

    Science.gov (United States)

    Zeng, Li; Jacobsen, Stein B.

    2016-09-01

    In the past few years, the number of confirmed planets has grown above 2000. It is clear that they represent a diversity of structures not seen in our own solar system. In addition to very detailed interior modeling, it is valuable to have a simple analytical framework for describing planetary structures. The variational principle is a fundamental principle in physics, entailing that a physical system follows the trajectory, which minimizes its action. It is alternative to the differential equation formulation of a physical system. Applying the variational principle to the planetary interior can beautifully summarize the set of differential equations into one, which provides us some insight into the problem. From this principle, a universal mass-radius relation, an estimate of the error propagation from the equation of state to the mass-radius relation, and a form of the virial theorem applicable to planetary interiors are derived.

  12. Field equations or conservation laws?

    CERN Document Server

    Francaviglia, Mauro; Winterroth, Ekkehart

    2013-01-01

    We explicate some epistemological implications of stationary principles and in particular of Noether Theorems. Noether's contribution to the problem of covariance, in fact, is epistemologically relevant, since it moves the attention from equations to conservation laws.

  13. The quasilinear parabolic kirchhoff equation

    Directory of Open Access Journals (Sweden)

    Dawidowski Łukasz

    2017-04-01

    Full Text Available In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.

  14. New applications of the homogeneous balance principle

    Institute of Scientific and Technical Information of China (English)

    张金良; 王跃明; 王明亮; 方宗德

    2003-01-01

    The homogeneous balance principle has been widely applied to the exploration of nonlinear transformation, exact solutions (especially solitary wave solution), dromion and similarity reduction to the nonlinear partial differential equations in mathematical physics. In this paper, we use the homogeneous balance principle to derive Backlund transformations for nonlinear partial differential equations that have more nonlinear terms and more highest-order partial derivative terms. With the aid of the Backlund transformations derived here, we could obtain exact solutions to the nonlinear partial differential equations. The Davey-Stewartson equation and the Nizhnik-Novikov-Veselov equation are considered as the examples.

  15. Energy Conservation Equations of Motion

    CERN Document Server

    Vinokurov, Nikolay A

    2015-01-01

    A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities that is called energy is constant. This paper presents an alternative approach, namely derivation of a general form of equations of motion that keep the system energy, expressed as a function of generalized coordinates and corresponding velocities, constant. These are Lagrange equations with addition of gyroscopic forces. The important fact, that the energy is defined as the function on the tangent bundle of configuration manifold, is used explicitly for the derivation. The Lagrangian is derived from a known energy function. A development of generalized Hamilton and Lagrange equations without the use of variational principles is proposed. The use of new technique is applied to derivation of some equations.

  16. Variational Principle for Planetary Interiors

    CERN Document Server

    Zeng, Li

    2016-01-01

    In the past few years, the number of confirmed planets has grown above 2000. It is clear that they represent a diversity of structures not seen in our own solar system. In addition to very detailed interior modeling, it is valuable to have a simple analytical framework for describing planetary structures. Variational principle is a fundamental principle in physics, entailing that a physical system follows the trajectory which minimizes its action. It is alternative to the differential equation formulation of a physical system. Applying this principle to planetary interior can beautifully summarize the set of differential equations into one, which provides us some insight into the problem. From it, a universal mass-radius relation, an estimate of error propagation from equation of state to mass-radius relation, and a form of virial theorem applicable to planetary interiors are derived.

  17. Optic eikonal,Fermat's principle and the least action principle

    Institute of Scientific and Technical Information of China (English)

    TAN KangBo; LIANG ChangHong; SHI XiaoWei

    2008-01-01

    A generalized refractive index in the form of optic eikonal is defined through com-paring frame definitions of left-handed and right-handed sets and indicates the sign of the refractive index covered by the quadratic form of the eikonal equation.Fer-mat's principle is generalized,and the general refractive law is derived directly.Under this definition,the comparison between Fermat's principle and the least ac-tion principle is made through employing path integral and analogizing L.de Broglie's theory.

  18. Hill's equation

    CERN Document Server

    Magnus, Wilhelm

    2004-01-01

    The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period

  19. Genetic principles.

    Science.gov (United States)

    Abuelo, D

    1987-01-01

    The author discusses the basic principles of genetics, including the classification of genetic disorders and a consideration of the rules and mechanisms of inheritance. The most common pitfalls in clinical genetic diagnosis are described, with emphasis on the problem of the negative or misleading family history.

  20. Cosmological principle

    Energy Technology Data Exchange (ETDEWEB)

    Wesson, P.S.

    1979-10-01

    The Cosmological Principle states: the universe looks the same to all observers regardless of where they are located. To most astronomers today the Cosmological Principle means the universe looks the same to all observers because density of the galaxies is the same in all places. A new Cosmological Principle is proposed. It is called the Dimensional Cosmological Principle. It uses the properties of matter in the universe: density (rho), pressure (p), and mass (m) within some region of space of length (l). The laws of physics require incorporation of constants for gravity (G) and the speed of light (C). After combining the six parameters into dimensionless numbers, the best choices are: 8..pi..Gl/sup 2/ rho/c/sup 2/, 8..pi..Gl/sup 2/ rho/c/sup 4/, and 2 Gm/c/sup 2/l (the Schwarzchild factor). The Dimensional Cosmological Principal came about because old ideas conflicted with the rapidly-growing body of observational evidence indicating that galaxies in the universe have a clumpy rather than uniform distribution. (SC)

  1. Least Action Principle in Gait

    CERN Document Server

    Fan, Yifang; Fan, Yubo; Xu, Zongxiang; Li, Zhiyu; Luo, Donglin

    2009-01-01

    We apply the laws of human gait vertical ground reaction force and discover the existence of the phenomenon of least action principle in gait. Using a capacitive mat transducer system, we obtain the variations of human gait vertical ground reaction force and establish a structure equation for the resultant of such a force. Defining the deviation of vertical force as an action function, we observe from our gait optimization analysis the least action principle at half of the stride time. We develop an evaluation index of mechanical energy consumption based upon the least action principle in gait. We conclude that these observations can be employed to enhance the accountability of gait evaluation.

  2. Press Oil Final Release Survey

    Energy Technology Data Exchange (ETDEWEB)

    Whicker, Jeffrey Jay [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ruedig, Elizabeth [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2017-05-11

    There are forty-eight 55 gallon barrels filled with hydraulic oil that are candidates for release and recycle. This oil needs to be characterized prior to release. Principles of sampling as provided in MARSAME/MARSSIM approaches were used as guidance for sampling.

  3. Principles of thermodynamics

    CERN Document Server

    Kaufman, Myron

    2002-01-01

    Ideal for one- or two-semester courses that assume elementary knowledge of calculus, This text presents the fundamental concepts of thermodynamics and applies these to problems dealing with properties of materials, phase transformations, chemical reactions, solutions and surfaces. The author utilizes principles of statistical mechanics to illustrate key concepts from a microscopic perspective, as well as develop equations of kinetic theory. The book provides end-of-chapter question and problem sets, some using Mathcad™ and Mathematica™; a useful glossary containing important symbols, definitions, and units; and appendices covering multivariable calculus and valuable numerical methods.

  4. Principles of quantum chemistry

    CERN Document Server

    George, David V

    2013-01-01

    Principles of Quantum Chemistry focuses on the application of quantum mechanics in physical models and experiments of chemical systems.This book describes chemical bonding and its two specific problems - bonding in complexes and in conjugated organic molecules. The very basic theory of spectroscopy is also considered. Other topics include the early development of quantum theory; particle-in-a-box; general formulation of the theory of quantum mechanics; and treatment of angular momentum in quantum mechanics. The examples of solutions of Schroedinger equations; approximation methods in quantum c

  5. Polydimensional Supersymmetric Principles

    CERN Document Server

    Pezzaglia, W M

    1999-01-01

    Systems of equations are invariant under "polydimensional transformations" which reshuffle the geometry such that what is a line or a plane is dependent upon the frame of reference. This leads us to propose an extension of Clifford calculus in which each geometric element (vector, bivector) has its own coordinate. A new classical action principle is proposed in which particles take paths which minimize the distance traveled plus area swept out by the spin. This leads to a solution of the 50 year old conundrum of `what is the correct Lagrangian' in which to derive the Papapetrou equations of motion for spinning particles in curved space (including torsion). Based on talk given at: 5th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Ixtapa-Zihuatanejo, Mexico, June 27-July 4, 1999.

  6. Variational principles for multisymplectic second-order classical field theories

    Science.gov (United States)

    Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

    2015-06-01

    We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.

  7. Variational principles for multisymplectic second-order classical field theories

    OpenAIRE

    Román Roy, Narciso; Prieto Martínez, Pedro Daniel

    2015-01-01

    We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework. Peer Reviewed

  8. Gas Dynamics Equations: Computation

    CERN Document Server

    Chen, Gui-Qiang G

    2012-01-01

    Shock waves, vorticity waves, and entropy waves are fundamental discontinuity waves in nature and arise in supersonic or transonic gas flow, or from a very sudden release (explosion) of chemical, nuclear, electrical, radiation, or mechanical energy in a limited space. Tracking these discontinuities and their interactions, especially when and where new waves arise and interact in the motion of gases, is one of the main motivations for numerical computation for the gas dynamics equations. In this paper, we discuss some historic and recent developments, as well as mathematical challenges, in designing and formulating efficient numerical methods and algorithms to compute weak entropy solutions for the Euler equations for gas dynamics.

  9. On Discreteness of the Hopf Equation

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    The principle aim of this essay is to illustrate how different phenomena is captured by different discretizations of the Hopf equation and general hyperbolic conservation laws. This includes dispersive schemes, shock capturing schemes as well as schemes for computing multi-valued solutions of the underlying equation. We introduce some model equations which describe the behavior of the discrete equation more accurate than the original equation. These model equations can either be conveniently discretized for producing novel numerical schemes or further analyzed to enrich the theory of nonlinear partial differential equations.

  10. Integral equations

    CERN Document Server

    Moiseiwitsch, B L

    2005-01-01

    Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco

  11. Riccati equations

    Directory of Open Access Journals (Sweden)

    Lloyd K. Williams

    1987-01-01

    Full Text Available In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.

  12. Equation poems

    Science.gov (United States)

    Prentis, Jeffrey J.

    1996-05-01

    One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.

  13. Penetration equations

    Energy Technology Data Exchange (ETDEWEB)

    Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)

    1997-10-01

    In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.

  14. Principles of Quantum Mechanics

    Science.gov (United States)

    Landé, Alfred

    2013-10-01

    Preface; Introduction: 1. Observation and interpretation; 2. Difficulties of the classical theories; 3. The purpose of quantum theory; Part I. Elementary Theory of Observation (Principle of Complementarity): 4. Refraction in inhomogeneous media (force fields); 5. Scattering of charged rays; 6. Refraction and reflection at a plane; 7. Absolute values of momentum and wave length; 8. Double ray of matter diffracting light waves; 9. Double ray of matter diffracting photons; 10. Microscopic observation of ρ (x) and σ (p); 11. Complementarity; 12. Mathematical relation between ρ (x) and σ (p) for free particles; 13. General relation between ρ (q) and σ (p); 14. Crystals; 15. Transition density and transition probability; 16. Resultant values of physical functions; matrix elements; 17. Pulsating density; 18. General relation between ρ (t) and σ (є); 19. Transition density; matrix elements; Part II. The Principle of Uncertainty: 20. Optical observation of density in matter packets; 21. Distribution of momenta in matter packets; 22. Mathematical relation between ρ and σ; 23. Causality; 24. Uncertainty; 25. Uncertainty due to optical observation; 26. Dissipation of matter packets; rays in Wilson Chamber; 27. Density maximum in time; 28. Uncertainty of energy and time; 29. Compton effect; 30. Bothe-Geiger and Compton-Simon experiments; 31. Doppler effect; Raman effect; 32. Elementary bundles of rays; 33. Jeans' number of degrees of freedom; 34. Uncertainty of electromagnetic field components; Part III. The Principle of Interference and Schrödinger's equation: 35. Physical functions; 36. Interference of probabilities for p and q; 37. General interference of probabilities; 38. Differential equations for Ψp (q) and Xq (p); 39. Differential equation for фβ (q); 40. The general probability amplitude Φβ' (Q); 41. Point transformations; 42. General theorem of interference; 43. Conjugate variables; 44. Schrödinger's equation for conservative systems; 45. Schr

  15. Correction to Euler's equations and elimination of the closure problem in turbulence

    Directory of Open Access Journals (Sweden)

    Michail Zak

    2012-12-01

    Full Text Available It has been demonstrated that the Euler equations of inviscid fluid are incomplete: according to the principle of release of constraints, absence of shear stresses must be compensated by additional degrees of freedom, and that leads to a Reynolds-type multivalued velocity field. However, unlike the Reynolds equations, the enlarged Euler's (EE model provides additional equations for fluctuations, and that eliminates the closure problem. Therefore the EE equations are applicable to fully developed turbulent motions where the physical viscosity is vanishingly small compare to the turbulent viscosity, as well as to superfluids and atomized fluids. Analysis of coupled mean/fluctuation EE equations shows that fluctuations stabilize the whole system generating elastic shear waves and increasing speed of sound. Those turbulent motions that originated from instability of underlying laminar motions can be described by the modified Euler's equation with the closure provided by the stabilization principle: driven by instability of laminar motion, fluctuations grow until the new state attains a neutral stability in the enlarged (multivalued class of functions, and these fluctuations can be taken as boundary conditions for the EE model. The approach is illustrated by an example.

  16. Gamescape Principles

    DEFF Research Database (Denmark)

    Nobaew, Banphot; Ryberg, Thomas

    2011-01-01

    This paper proposes a new theoretical framework or visual grammar for analysing visual aspects of digital 3D games, and for understanding more deeply the notion of Visual Digital Game Literacy. The framework focuses on the development of a visual grammar by drawing on the digital literacy framewo...... as to understand how learners posses or can develop broader critical media literacies and visual digital literacies in education.......This paper proposes a new theoretical framework or visual grammar for analysing visual aspects of digital 3D games, and for understanding more deeply the notion of Visual Digital Game Literacy. The framework focuses on the development of a visual grammar by drawing on the digital literacy framework...... and interviews) collected during a game workshop where students, studying to become game designers, developed a number of games. The visual digital literacy framework we propose consists of five main major components: Gamescape Principles, Interpretation, Style, Experiences and Practices. For the purpose...

  17. Multipartition generalizations of the Schwinger variational principle

    Science.gov (United States)

    Goldflam, R.; Thaler, R. M.; Tobocman, W.

    1981-04-01

    Generalizations of the Schwinger variational principle are proposed which include rearrangement scattering. Functionals are given for the transition amplitude. The requirement that a functional be stationary with respect to variation of the scattering wave function leads to a set of simultaneous equations for the scattering wave function rather than a single equation. This is consistent with recent formalisms for many-body scattering.

  18. Differential equations

    CERN Document Server

    Tricomi, FG

    2013-01-01

    Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff

  19. Differential equations

    CERN Document Server

    Barbu, Viorel

    2016-01-01

    This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.

  20. Energy equation, the dissipation function and the Euler turbine equation

    Energy Technology Data Exchange (ETDEWEB)

    Mobarak, A. (Cairo Univ. (Egypt). Faculty of Engineering)

    1978-01-01

    The derivation of the energy equation for a rotating frame of coordinates is presented. The link between the thermodynamics and the fluid dynamics of viscous flow and which is generally given by the dissipation function is discussed in more detail. This work shows, that the published definition of the dissipation function is an improper one, and leads in connection with the energy equation to contradictory results when considering the principle of energy conservation. Further, the Euler turbine equation is discussed, and it is shown that the present form is only valid, if the flow condition in the rotor (the relative system) is steady.

  1. The strong maximum principle revisited

    Science.gov (United States)

    Pucci, Patrizia; Serrin, James

    In this paper we first present the classical maximum principle due to E. Hopf, together with an extended commentary and discussion of Hopf's paper. We emphasize the comparison technique invented by Hopf to prove this principle, which has since become a main mathematical tool for the study of second order elliptic partial differential equations and has generated an enormous number of important applications. While Hopf's principle is generally understood to apply to linear equations, it is in fact also crucial in nonlinear theories, such as those under consideration here. In particular, we shall treat and discuss recent generalizations of the strong maximum principle, and also the compact support principle, for the case of singular quasilinear elliptic differential inequalities, under generally weak assumptions on the quasilinear operators and the nonlinearities involved. Our principal interest is in necessary and sufficient conditions for the validity of both principles; in exposing and simplifying earlier proofs of corresponding results; and in extending the conclusions to wider classes of singular operators than previously considered. The results have unexpected ramifications for other problems, as will develop from the exposition, e.g. two point boundary value problems for singular quasilinear ordinary differential equations (Sections 3 and 4); the exterior Dirichlet boundary value problem (Section 5); the existence of dead cores and compact support solutions, i.e. dead cores at infinity (Section 7); Euler-Lagrange inequalities on a Riemannian manifold (Section 9); comparison and uniqueness theorems for solutions of singular quasilinear differential inequalities (Section 10). The case of p-regular elliptic inequalities is briefly considered in Section 11.

  2. Action principle for Coulomb collisions in plasmas

    Science.gov (United States)

    Hirvijoki, Eero

    2016-09-01

    An action principle for Coulomb collisions in plasmas is proposed. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.

  3. Action principle for Coulomb collisions in plasmas

    CERN Document Server

    Hirvijoki, Eero

    2015-01-01

    In this letter we derive an action principle for Coulomb collisions in plasmas. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth potentials. Exact conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles. Being suitable for discretization, the presented action allows construction of variational integrators. Numerical implementation is left for a future study.

  4. Microhydrodynamics principles and selected applications

    CERN Document Server

    Kim, Sangtae; Brenner, Howard

    1991-01-01

    Microhydrodynamics: Principles and Selected Applications presents analytical and numerical methods for describing motion of small particles suspended in viscous fluids. The text first covers the fundamental principles of low-Reynolds-number flow, including the governing equations and fundamental theorems; the dynamics of a single particle in a flow field; and hydrodynamic interactions between suspended particles. Next, the book deals with the advances in the mathematical and computational aspects of viscous particulate flows that point to innovations for large-scale simulations on parallel co

  5. The high pressure structure and equation of state of 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) up to 20 GPa: X-ray diffraction measurements and first principles molecular dynamics simulations

    Energy Technology Data Exchange (ETDEWEB)

    Stavrou, Elissaios, E-mail: stavrou1@llnl.gov; Riad Manaa, M., E-mail: manaa1@llnl.gov; Zaug, Joseph M.; Kuo, I-Feng W.; Pagoria, Philip F.; Crowhurst, Jonathan C.; Armstrong, Michael R. [Lawrence Livermore National Laboratory, Physical and Life Sciences Directorate, P.O. Box 808 L-350, Livermore, California 94550 (United States); Kalkan, Bora [Advanced Light Source, Lawrence Berkeley Laboratory, Berkeley, California 94720 (United States); Advanced Materials Research Laboratory, Department of Physics Engineering, Hacettepe University 06800, Beytepe, Ankara (Turkey)

    2015-10-14

    Recent theoretical studies of 2,6-diamino-3,5-dinitropyrazine-1-oxide (C{sub 4}H{sub 4}N{sub 6}O{sub 5} Lawrence Livermore Molecule No. 105, LLM-105) report unreacted high pressure equations of state that include several structural phase transitions, between 8 and 50 GPa, while one published experimental study reports equation of state (EOS) data up to a pressure of 6 GPa with no observed transition. Here we report the results of a synchrotron-based X-ray diffraction study and also ambient temperature isobaric-isothermal atomistic molecular dynamics simulations of LLM-105 up to 20 GPa. We find that the ambient pressure phase remains stable up to 20 GPa; there is no indication of a pressure induced phase transition. We do find a prominent decrease in b-axis compressibility starting at approximately 13 GPa and attribute the stiffening to a critical length where inter-sheet distance becomes similar to the intermolecular distance within individual sheets. The ambient temperature isothermal equation of state was determined through refinements of measured X-ray diffraction patterns. The pressure-volume data were fit using various EOS models to yield bulk moduli with corresponding pressure derivatives. We find very good agreement between the experimental and theoretically derived EOS.

  6. The high pressure structure and equation of state of 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) up to 20 GPa: X-ray diffraction measurements and first principles molecular dynamics simulations.

    Science.gov (United States)

    Stavrou, Elissaios; Riad Manaa, M; Zaug, Joseph M; Kuo, I-Feng W; Pagoria, Philip F; Kalkan, Bora; Crowhurst, Jonathan C; Armstrong, Michael R

    2015-10-14

    Recent theoretical studies of 2,6-diamino-3,5-dinitropyrazine-1-oxide (C4H4N6O5 Lawrence Livermore Molecule No. 105, LLM-105) report unreacted high pressure equations of state that include several structural phase transitions, between 8 and 50 GPa, while one published experimental study reports equation of state (EOS) data up to a pressure of 6 GPa with no observed transition. Here we report the results of a synchrotron-based X-ray diffraction study and also ambient temperature isobaric-isothermal atomistic molecular dynamics simulations of LLM-105 up to 20 GPa. We find that the ambient pressure phase remains stable up to 20 GPa; there is no indication of a pressure induced phase transition. We do find a prominent decrease in b-axis compressibility starting at approximately 13 GPa and attribute the stiffening to a critical length where inter-sheet distance becomes similar to the intermolecular distance within individual sheets. The ambient temperature isothermal equation of state was determined through refinements of measured X-ray diffraction patterns. The pressure-volume data were fit using various EOS models to yield bulk moduli with corresponding pressure derivatives. We find very good agreement between the experimental and theoretically derived EOS.

  7. Thermodynamic restrictions on the constitutive equations of electromagnetic theory

    Science.gov (United States)

    Coleman, B. D.; Dill, E. H.

    1971-01-01

    Thermodynamics second law restrictions on constitutive equations of electromagnetic theory for nonlinear materials with long-range gradually fading memory, considering dissipation principle consequences

  8. On the principles of quantum mechanics

    CERN Document Server

    Sakai, E

    2004-01-01

    We propose five principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, and probability principle. We deductively establish quantum mechanics on the basis of them. Then we adopt the following four guide lines. First, we do not premise the relations between dynamical variables in classical mechanics. Second, since energy and momentum are quantitatively defined in classical mechanics, we define them in quantum mechanics so that the corresponding conservation laws are satisfied in a coupling system of a quantum particle and a classical particle. Third, we define Planck's constant as a proportionality constant between energy and frequency due to one of Einstein-de Broglie formulas. Fourth, we define mass as a proportionality constant between momentum and velocity. We have succeeded to obtain the canonical commutation relations and the Schroedinger equation for a particle in an external field in the definiti...

  9. Impact of singularity of Navier-Stokes equation upon atmospheric motion equations

    Institute of Scientific and Technical Information of China (English)

    SHI Wei-hui; WANG Yue-peng

    2007-01-01

    Some conelusiolib about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for Navkr-Stokes equation are summarized.On the basis of this,by taking the basic system of equations of atmospheric motion via Bonssinesq approximation as example to explain in detail that the instability about some simplified models of the basic system of equations for atmospheric motion iscaused by the instability of Navier-Stokes equation,thereby,a principle to guarantee the stability of simplified equation is drawn in simplifying the basic system of equations.

  10. GLOBAL SOLUTIONS OF NONLINEAR SCHRODINGER EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Ye Yaojun

    2005-01-01

    In this paper we study the existence of global solutions to the Cauchy problem of nonlinear Schrodinger equation by establishing time weight function spaces and using the contraction mapping principle.

  11. Extension of the Schrodinger equation

    Science.gov (United States)

    Somsikov, Vyacheslav

    2017-03-01

    Extension of the Schrodinger equation is submitted by removing its limitations appearing due to the limitations of the formalism of Hamilton, based on which this equation was obtained. For this purpose the problems of quantum mechanics arising from the limitations of classical mechanics are discussed. These limitations, in particular, preclude the use of the Schrodinger equation to describe the time symmetry violation. The extension of the Schrodinger equation is realized based on the principle of duality symmetry. According to this principle the dynamics of the systems is determined by the symmetry of the system and by the symmetry of the space. The extension of the Schrodinger equation was obtained from the dual expression of energy, represented in operator form. For this purpose the independent micro - and macro-variables that determine respectively the dynamics of quantum particle system relative to its center of mass and the movement of the center of mass in space are used. The solution of the extended Schrodinger equation for the system near equilibrium is submitted. The main advantage of the extended Schrodinger equation is that it is applicable to describe the interaction and evolution of quantum systems in inhomogeneous field of external forces.

  12. Ordinary differential equations

    CERN Document Server

    Cox, William

    1995-01-01

    Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further

  13. Principles of modern physics

    CERN Document Server

    Saxena, A K

    2014-01-01

    Principles of Modern Physics, divided into twenty one chapters, begins with quantum ideas followed by discussions on special relativity, atomic structure, basic quantum mechanics, hydrogen atom (and Schrodinger equation) and periodic table, the three statistical distributions, X-rays, physics of solids, imperfections in crystals, magnetic properties of materials, superconductivity, Zeeman-, Stark- and Paschen Back- effects, Lasers, Nuclear physics (Yukawa's meson theory and various nuclear models), radioactivity and nuclear reactions, nuclear fission, fusion and plasma, particle accelerators and detectors, the universe, Elementary particles (classification, eight fold way and quark model, standard model and fundamental interactions), cosmic rays, deuteron problem in nuclear physics, and cathode ray oscilloscope. NEW TO THE FOURTH EDITION: The CO2 Laser Theory of magnetic moments on the basis of shell model Geological dating Laser Induced fusion and laser fusion reactor. Hawking radiation The cosmological red ...

  14. Nonlinear optics principles and applications

    CERN Document Server

    Li, Chunfei

    2017-01-01

    This book reflects the latest advances in nonlinear optics. Besides the simple, strict mathematical deduction, it also discusses the experimental verification and possible future applications, such as the all-optical switches. It consistently uses the practical unit system throughout. It employs simple physical images, such as "light waves" and "photons" to systematically explain the main principles of nonlinear optical effects. It uses the first-order nonlinear wave equation in frequency domain under the condition of “slowly varying amplitude approximation" and the classical model of the interaction between the light and electric dipole. At the same time, it also uses the rate equations based on the energy-level transition of particle systems excited by photons and the energy and momentum conservation principles to explain the nonlinear optical phenomenon. The book is intended for researchers, engineers and graduate students in the field of the optics, optoelectronics, fiber communication, information tech...

  15. Freidlin-Wentzell's Large Deviations for Stochastic Evolution Equations

    OpenAIRE

    Ren, Jiagang; Zhang, Xicheng

    2008-01-01

    We prove a Freidlin-Wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises. In particular, our general result can be used to deal with a large class of quasi linear stochastic partial differential equations, such as stochastic porous medium equations and stochastic reaction diffusion equations with polynomial growth zero order term and $p$-Laplacian second order term.

  16. A Large Deviation Principle of Capacity for the Markov Process Modulated by the Stochastic Evolution Equation%由随机发展方程调制的马氏过程的容度大偏差原理

    Institute of Scientific and Technical Information of China (English)

    马小翠

    2011-01-01

    给出了{(X^s(t),Z^ε(t));ε〉0,t∈[0,T]}的容度大偏差定理.其中X^ε(t)满足下面的随机微分方程:dX^ε(t)=(√εσ(t))dw(t)+b(X^ε(t),Z^ε(t))dt,Z^ε(t)为有限个状态的随机过程.%In this paper, We discuss a large deviation principle of capacity for {(X^s(t),Z^ε(t));ε〉0,t∈[0,T]}determined by dX^ε(t)=(√εσ(t))dw(t)+b(X^ε(t),Z^ε(t))dt,Z^ε(t)is an n- state process.

  17. Cosmological implications of Heisenberg's principle

    CERN Document Server

    Gonzalo, Julio A

    2015-01-01

    The aim of this book is to analyze the all important implications of Heisenberg's Uncertainty Principle for a finite universe with very large mass-energy content such as ours. The earlier and main contributors to the formulation of Quantum Mechanics are briefly reviewed regarding the formulation of Heisenberg's Principle. After discussing “indeterminacy” versus ”uncertainty”, the universal constants of physics are reviewed and Planck's units are given. Next, a novel set of units, Heisenberg–Lemaitre units, are defined in terms of the large finite mass of the universe. With the help of Heisenberg's principle, the time evolution of the finite zero-point energy for the universe is investigated quantitatively. Next, taking advantage of the rigorous solutions of Einstein's cosmological equation for a flat, open and mixed universe of finite mass, the most recent and accurate data on the “age” (to) and the expansion rate (Ho) of the universe and their implications are reconsidered.

  18. Principles of tendon transfers.

    Science.gov (United States)

    Coulet, B

    2016-04-01

    Tendon transfers are carried out to restore functional deficits by rerouting the remaining intact muscles. Transfers are highly attractive in the context of hand surgery because of the possibility of restoring the patient's ability to grip. In palsy cases, tendon transfers are only used when a neurological procedure is contraindicated or has failed. The strategy used to restore function follows a common set of principles, no matter the nature of the deficit. The first step is to clearly distinguish between deficient muscles and muscles that could be transferred. Next, the type of palsy will dictate the scope of the program and the complexity of the gripping movements that can be restored. Based on this reasoning, a surgical strategy that matches the means (transferable muscles) with the objectives (functions to restore) will be established and clearly explained to the patient. Every paralyzed hand can be described using three parameters. 1) Deficient segments: wrist, thumb and long fingers; 2) mechanical performance of muscles groups being revived: high energy-wrist extension and finger flexion that require strong transfers with long excursion; low energy-wrist flexion and finger extension movements that are less demanding mechanically, because they can be accomplished through gravity alone in some cases; 3) condition of the two primary motors in the hand: extrinsics (flexors and extensors) and intrinsics (facilitator). No matter the type of palsy, the transfer surgery follows the same technical principles: exposure, release, fixation, tensioning and rehabilitation. By performing an in-depth analysis of each case and by following strict technical principles, tendon transfer surgery leads to reproducible results; this allows the surgeon to establish clear objectives for the patient preoperatively.

  19. The Statistical Drake Equation

    Science.gov (United States)

    Maccone, Claudio

    2010-12-01

    function, apparently previously unknown and dubbed "Maccone distribution" by Paul Davies. DATA ENRICHMENT PRINCIPLE. It should be noticed that ANY positive number of random variables in the Statistical Drake Equation is compatible with the CLT. So, our generalization allows for many more factors to be added in the future as long as more refined scientific knowledge about each factor will be known to the scientists. This capability to make room for more future factors in the statistical Drake equation, we call the "Data Enrichment Principle," and we regard it as the key to more profound future results in the fields of Astrobiology and SETI. Finally, a practical example is given of how our statistical Drake equation works numerically. We work out in detail the case, where each of the seven random variables is uniformly distributed around its own mean value and has a given standard deviation. For instance, the number of stars in the Galaxy is assumed to be uniformly distributed around (say) 350 billions with a standard deviation of (say) 1 billion. Then, the resulting lognormal distribution of N is computed numerically by virtue of a MathCad file that the author has written. This shows that the mean value of the lognormal random variable N is actually of the same order as the classical N given by the ordinary Drake equation, as one might expect from a good statistical generalization.

  20. Some remarks on singular solutions of nonlinear elliptic equations. III: viscosity solutions, including parabolic operators

    CERN Document Server

    Caffarelli, Luis; Nirenberg, Louis

    2011-01-01

    The paper concerns singular solutions of nonlinear elliptic equations, which include removable singularities for viscosity solutions, a strengthening of the Hopf Lemma including parabolic equations, Strong maximum principle and Hopf Lemma for viscosity solutions including also parabolic equations.

  1. Multisymplectic Geometry for the Seismic Wave Equation

    Institute of Scientific and Technical Information of China (English)

    CHEN Jing-Bo

    2004-01-01

    The multisymplectic geometry for the seismic wave equation is presented in this paper.The local energy conservation law,the local momentum evolution equations,and the multisymplectic form are derived directly from the variational principle.Based on the covariant Legendre transform,the multisymplectic Hamiltonian formulation is developed.Multisymplectic discretization and numerical experiments are also explored.

  2. Equivalence principles and electromagnetism

    Science.gov (United States)

    Ni, W.-T.

    1977-01-01

    The implications of the weak equivalence principles are investigated in detail for electromagnetic systems in a general framework. In particular, it is shown that the universality of free-fall trajectories (Galileo weak equivalence principle) does not imply the validity of the Einstein equivalence principle. However, the Galileo principle plus the universality of free-fall rotation states does imply the Einstein principle.

  3. Dynamic equations for curved submerged floating tunnel

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    In virtue of reference Cartesian coordinates, geometrical relations of spatial curved structure are presented in orthogonal curvilinear coordinates. Dynamic equations for helical girder are derived by Hamilton principle. These equations indicate that four generalized displacements are coupled with each other. When spatial structure degenerates into planar curvilinear structure, two generalized displacements in two perpendicular planes are coupled with each other. Dynamic equations for arbitrary curvilinear structure may be obtained by the method used in this paper.

  4. First-principles investigation of the equation of state and elastic properties of perovskite-type SrW(O,N)3 under hydrostatic pressures up to 139 GPa

    Science.gov (United States)

    Zahedi, Ehsan; Hojamberdiev, Mirabbos

    2017-03-01

    Pressure dependence of the structural and elastic properties of perovskite-type cubic SrWO2.05N0.95 was studied using firstprinciples density functional theory (DFT) utilizing the plane wave pseudopotential and the exchange-correlation functionals within the generalized gradient approximation. The estimated bulk modulus and its pressure derivative values from the P - V data fitted to the third-order Birch-Murnaghan equation of state were close to the data obtained from the independent elastic constants. Based on the generalized Born stability criteria, SrWO2.05N0.95 is mechanically stable up to 139 GPa. The influence of hydrostatic pressure (0 to 139 GPa) on the bulk modulus, shear modulus, Young's modulus, Pugh's modulus ratio, Poisson's ratio, Vickers hardness, sound velocities, Debye temperature, Debye-Grüneisen parameter, minimum thermal conductivity and elastic anisotropy of SrWO2.05N0.95 was particularly studied in detail. It was found that SrWO2.05N0.95 is a ductile and hard solid with large bulk, shear and Young's modulus and displays an extraordinary low thermal conductivity. Since there are not any experimental or theoretical data available for comparison the results of the present study have revealed an important fundamental information about the elastic properties of perovskite-type cubic SrWO2.05N0.95 for future experimental studies.

  5. A hybrid framework of first principles molecular orbital calculations and a three-dimensional integral equation theory for molecular liquids: Multi-center molecular Ornstein–Zernike self-consistent field approach

    Energy Technology Data Exchange (ETDEWEB)

    Kido, Kentaro, E-mail: kido.kentaro@jaea.go.jp [Nuclear Safety Research Center, Japan Atomic Energy Agency, 2-4 Shirane, Shirakata, Tokai-mura, Naka-gun, Ibaraki 319-1195 (Japan); Kasahara, Kento [Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510 (Japan); Yokogawa, Daisuke [Department of Chemistry, Graduate School of Science, Nagoya University, Chikusa, Nagoya 464-8602 (Japan); Institute of Transformative Bio-Molecules (WPI-ITbM), Nagoya University, Chikusa, Nagoya 464-8062 (Japan); Sato, Hirofumi [Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510 (Japan); Elements Strategy Institute for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520 (Japan)

    2015-07-07

    In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein–Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple S{sub N}2 reaction (Cl{sup −} + CH{sub 3}Cl → ClCH{sub 3} + Cl{sup −}) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.

  6. Novel Principles and the Charge-Symmetric Design of Dirac's Quantum Mechanics: I. Enhanced Eriksen's Theorem and the Universal Charge-Index Formalism for Dirac's Equation in (Strong) External Static Fields

    Science.gov (United States)

    Kononets, Yu. V.

    2016-12-01

    The presented enhanced version of Eriksen's theorem defines an universal transform of the Foldy-Wouthuysen type and in any external static electromagnetic field (ESEMF) reveals a discrete symmetry of Dirac's equation (DE), responsible for existence of a highly influential conserved quantum number—the charge index distinguishing two branches of DE spectrum. It launches the charge-index formalism (CIF) obeying the charge-index conservation law (CICL). Via its unique ability to manipulate each spectrum branch independently, the CIF creates a perfect charge-symmetric architecture of Dirac's quantum mechanics (DQM), which resolves all the riddles of the standard DE theory (SDET). Besides the abstract CIF algebra, the paper discusses: (1) the novel accurate charge-symmetric definition of the electric-current density; (2) DE in the true-particle representation, where electrons and positrons coexist on equal footing; (3) flawless "natural" scheme of second quantization; and (4) new physical grounds for the Fermi-Dirac statistics. As a fundamental quantum law, the CICL originates from the kinetic-energy sign conservation and leads to a novel single-particle physics in strong-field situations. Prohibiting Klein's tunneling (KT) in Klein's zone via the CICL, the precise CIF algebra defines a new class of weakly singular DE solutions, strictly confined in the coordinate space and experiencing the total reflection from the potential barrier.

  7. An axiomatic approach to Maxwell's equations

    CERN Document Server

    Heras, José A

    2016-01-01

    This paper suggests an axiomatic approach to Maxwell's equations. The basis of this approach is a theorem formulated for two sets of functions localized in space and time. If each set satisfies a continuity equation then the theorem provides an integral representation for each function. A corollary of this theorem yields Maxwell's equations with magnetic monopoles. It is pointed out that the causality principle and the conservation of electric and magnetic charges are the most fundamental physical axioms underlying these equations. Another application of the corollary yields Maxwell's equations in material media. The theorem is also formulated in the Minkowski space-time and applied to obtain the covariant form of Maxwell's equations with magnetic monopoles and the covariant form of Maxwell's equations in material media. The approach makes use of the infinite-space Green function of the wave equation and is therefore suitable for an advanced course in electrodynamics.

  8. Stochastic optimal control, forward-backward stochastic differential equations and the Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)

    2016-07-01

    The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.

  9. Geophysical interpretation using integral equations

    CERN Document Server

    Eskola, L

    1992-01-01

    Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu­ med to have a back...

  10. Information Equation of State

    Directory of Open Access Journals (Sweden)

    M. Paul Gough

    2008-07-01

    Full Text Available Landauer’s principle is applied to information in the universe. Once stars began forming there was a constant information energy density as the increasing proportion of matter at high stellar temperatures exactly compensated for the expanding universe. The information equation of state was close to the dark energy value, w = -1, for a wide range of redshifts, 10 > z > 0.8, over one half of cosmic time. A reasonable universe information bit content of only 1087 bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem. In answering the ‘Why now?’ question we wonder ‘What next?’ as we expect the information equation of state to tend towards w = 0 in the future.c

  11. Chemical thermodynamics: principles and applications

    Energy Technology Data Exchange (ETDEWEB)

    Ott, J. Bevan; Boerio-Goates, Juliana [Brigham Young Univ., Provo, UT (United States)

    2000-06-01

    Chemical Thermodynamics: Principles and Applications presents a thorough development of the principles of thermodynamics--an old science to which the authors include the most modem applications, along with those of importance in developing the science and those of historical interest. The text is written in an informal but rigorous style, including anecdotes about some of the great thermodynamicists (with some of whom the authors have had a personal relationship), and focuses on 'real' systems in the discussion and figures, in contrast to the generic examples that are often used in other textbooks. The book provides a basic review of thermodynamic principles, equations, and applications of broad interest. It covers the development of thermodynamics as one of the pre-eminent examples of an exact science. A discussion of the standard state that emphasizes its significance and usefulness is also included, as well as a more rigorous and indepth treatment of thermodynamics. Outlines the development of the principles of thermodynamics, including the most modem applications along with those of importance in developing the science and those of historical interest . Provides a basic review of thermodynamic principles, equations, and applications of broad interest. Treats thermodynamics as one of the preeminent examples of an exact science. Provides a more rigorous and indepth treatment of thermodynamics and discussion of a wider variety of applications than are found in more broadly based physical chemistry undergraduate textbooks. Includes examples in the text and exercises and problems at the end of each chapter to assist the student in learning the subject. (Author)

  12. Integral equations

    CERN Document Server

    Tricomi, Francesco Giacomo

    1957-01-01

    This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful

  13. A minimum principle for chaotic dynamical systems

    Science.gov (United States)

    Bracken, Paul; Góra, Paweł; Boyarsky, Abraham

    2002-06-01

    Discrete time dynamical systems generated by the iteration of nonlinear maps, such as the logistic map or the tent map, provide interesting examples of chaotic systems. But what is the physical principle behind the emergence of these maps? In the continuous time settings, differential equations of mechanics arise from the minimization of the energy function (Hamiltonian). However, there is no general physical principle for the discrete time analogue of differential equations, namely, maps. In this note, we present an approach to this problem. Using a natural definition of energy for chaotic systems, we minimize energy subject to the constraint that the observed dynamical system has a known entropy. We consider the case where the natural invariant measure is Lebesgue. Invoking the Euler-Lagrange equation, we derive a nonlinear second order differential equation whose solution is the chaotic map that minimizes energy.

  14. Stochastic partial differential equations

    CERN Document Server

    Chow, Pao-Liu

    2014-01-01

    Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad

  15. A new principle of synthetic cascade utilization of chemical energy and physical energy

    Institute of Scientific and Technical Information of China (English)

    JIN; Hongguang; HONG; Hui; WANG; Baoqun; HAN; Wei; LIN; Rum

    2005-01-01

    We propose a new principle of the cascade utilization of both chemical energy and physical energy in energy systems with the integration of chemical processes and thermal cycles. Particularly, a general equation of energy levels of substance, Gibbs free energy of chemical reaction and physical energy is explicitly founded. On the basis of this equation, a chemical-looping combustion and an indirect combustion are investigated. Furthermore, a mechanism of energy release, with the combination of decreasing the energy level of Gibbs free energy and upgrading the energy level of low or middle- temperature thermal energy, is clarified. The promising results obtained here establish a theoretical basis for the further investigation of multi-function systems in which energy and the environment are compatible, and create a new approach to improve the performance of traditional thermal cycles.

  16. Asymptotic integration of differential and difference equations

    CERN Document Server

    Bodine, Sigrun

    2015-01-01

    This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers i...

  17. Synchronous Lagrangian variational principles in General Relativity

    CERN Document Server

    Cremaschini, Claudio

    2016-01-01

    The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in relativistic classical field theory which are either asynchronous or synchronous. The historical Einstein-Hilbert and Palatini variational formulations are found to belong to the first category. Nevertheless, it is shown that an alternative route exists which permits one to cast these principles in terms of equivalent synchronous Lagrangian variational formulations. The advantage is twofold. First, synchronous approaches allow one to overcome the lack of gauge symmetry of the asynchronous principles. Second, the property of manifest covariance of the theory is also restored at all levels, including the symbolic Euler-Lagrange equations, with the variational Lagrangian density being now identified with a $4-$scalar. As an application, a joint synchronous variational principle...

  18. Basic principles of stability.

    Science.gov (United States)

    Egan, William; Schofield, Timothy

    2009-11-01

    An understanding of the principles of degradation, as well as the statistical tools for measuring product stability, is essential to management of product quality. Key to this is management of vaccine potency. Vaccine shelf life is best managed through determination of a minimum potency release requirement, which helps assure adequate potency throughout expiry. Use of statistical tools such a least squares regression analysis should be employed to model potency decay. The use of such tools provides incentive to properly design vaccine stability studies, while holding stability measurements to specification presents a disincentive for collecting valuable data. The laws of kinetics such as Arrhenius behavior help practitioners design effective accelerated stability programs, which can be utilized to manage stability after a process change. Design of stability studies should be carefully considered, with an eye to minimizing the variability of the stability parameter. In the case of measuring the degradation rate, testing at the beginning and the end of the study improves the precision of this estimate. Additional design considerations such as bracketing and matrixing improve the efficiency of stability evaluation of vaccines.

  19. Principles of rock mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Turchaninov, I.A.; Iofis, M.A.; Kasparyan, E.V.

    1979-01-01

    This book presents the principles of rock mechanics in a systematic way, reflecting both the historic development and the contemporary status of theoretical and experimental techniques used for the determination of the properties and stress state of rock masses, calculation of elements of systems for exploitation of useful mineral deposits and the design of mine openings. The subject of rock mechanics is discussed and methods and basic approaches are analyzed. The most widely used methods for determining the properties of rock in specimens and in situ are described. Problems of determining the stress strain state of the rock around mine openings by both experimental and analytic methods are discussed. The primary results of the study of the stress state of rock around main, development and production openings are presented. Problems of the movement of rock due to extraction of minerals are analyzed in detail, as are the conditions and causes of the development of rock bursts and sudden release of rock and gas in both surface and underground mines. Procedures for preventing or localizing rock bursts or sudden outbursts are described. (313 refs.)

  20. Abstract Operators and Higher-order Linear Partial Differential Equation

    Institute of Scientific and Technical Information of China (English)

    BI Guang-qing; BI Yue-kai

    2011-01-01

    We summarize several relevant principles for the application of abstract operators in partial differential equations,and combine abstract operators with the Laplace transform.Thus we have developed the theory of partial differential equations of abstract operators and obtained the explicit solutions of initial value problems for a class of higher-order linear partial differential equations.

  1. Physical Consequences of Mathematical Principles

    Directory of Open Access Journals (Sweden)

    Comay E.

    2009-10-01

    Full Text Available Physical consequences are derived from the following mathematical structures: the variational principle, Wigner’s classifications of the irreducible representations of the Poincar ́ e group and the duality invariance of the homogeneous Maxwell equations. The analysis is carried out within the validity domain of special relativity. Hierarchical re- lations between physical theories are used. Some new results are pointed out together with their comparison with experimental data. It is also predicted that a genuine Higgs particle will not be detected.

  2. General proof of entropy principle in Einstein-Maxwell theory

    CERN Document Server

    Fang, Xiongjun

    2015-01-01

    We consider a static self-gravitating charged perfect fluid system in the Einstein-Maxwell theory. Assume Maxwell's equation and the Einstein constraint equation are satisfied, and the temperature of the fluid obeys Tolman's law. Then we prove that the total entropy of the fluid achieves an extremum implies other components of Einstein's equation for any variations of metric and electrical potential with fixed boundary values. Conversely, if Einstein's equation and Maxwell's equations hold, the total entropy achieves an extremum. Our work suggests that the maximum entropy principle is consistent with Einstein's equation when electric field is taken into account.

  3. Reader-Response and the Pathos Principle.

    Science.gov (United States)

    Johnson, Nan

    1988-01-01

    Reviews and equates theories of reader-response and rhetorical theories on audience response (the pathos principle). Concludes that the fundamental synonymity between them represents a significant bridge between analysis of literary texts and the dynamics of formal and social discourse and provides a theoretical foundation for teaching reading and…

  4. Prediction of drug release from HPMC matrices: effect of physicochemical properties of drug and polymer concentration.

    Science.gov (United States)

    Fu, X C; Wang, G P; Liang, W Q; Chow, M S S

    2004-03-05

    A working equation to predict drug release from hydroxypropyl methylcellulose (HPMC) matrices was derived using a training set of HPMC matrices having different HPMC concentration (w/w, 16.5-55%) and different drugs (solubilities of 1.126-125.5 g/100 ml in water and molecular volumes of 0.1569-0.4996 nm(3)). The equation was log(M(t)/M( infinity ))=-0.6747+1.027 log t -0.1759 (log C(s)) log t +0.4027 (log V) log t -1.041C(H) +0.3213 (log C(s)) C(H) -0.4101 (log V) C(H) -0.3521 (log V) log C(s) (n=263, r=0.9831), where M(t) is the amount of drug released at time t, M( infinity ) the amount of drug released over a very long time, which corresponds in principle to the initial loading, t the release time (h), C(s) the drug solubility in water (g/100 ml), V the volume of drug molecule (nm(3)), and C(H) is HPMC concentration (w/w). The benefit of the novel model is to predict M(t)/M( infinity ) values of a drug from formulation and its physicochemical properties, so applicable to the HPMC matrices of different polymer levels and different drugs including soluble drugs and slightly soluble drugs.

  5. State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities.

    Science.gov (United States)

    Korayem, M H; Nekoo, S R

    2015-07-01

    This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data.

  6. Treatment of coupled fluid-structure interaction problems by a mixed variational principle

    Science.gov (United States)

    Felippa, Carlos A.; Ohayon, Roger

    1989-01-01

    A general three-field variational principle is obtained for the motion of an acoustic fluid enclosed in a rigid or flexible container by the method of canonical decomposition applied to a modified form of the wave equation in the displacement potential. The general principle is specialized to a mixed two-field principle that contains the fluid displacement potential and pressure as independent fields. Semidiscrete finite-element equations of motion based on this principle are displayed.

  7. The principle of the Fermionic projector

    CERN Document Server

    Finster, Felix

    2006-01-01

    The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. This book begins with a brief review of relativity, relativistic quantum mechanics, and classical gauge theories, emphasizing the basic physical concepts and mathematical foundations. The external field problem and Klein's paradox are discussed and then resolved by introducing the fermionic projector, a global object in space-time that generalizes the notion of the Dirac sea. At the mathematical core of the book is a precise definition of the fermionic projector and the use of methods of hyperbolic differential equations for detailed analysis. The fermionic projector makes it possible to formulate a new type of variational principle in space-time. The mathematical tools are developed for the analysis of the corresponding Euler-Lagrange equations. A particular variational principle is proposed that gives rise to an effective...

  8. Turbulent lock release gravity current

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    The time evolution of a turbulent lock release gravity current, formed by a finite volume ofhomogeneous fluid released instantaneously into another fluid of slightly lower density, was studied byexperimental measurements of the density structure via elaborate digital image processing and by a nu-merical simulation of the flow and mixing using a two-equation turbulence model. The essential fact thatthe gravity current passes through an initial slumping phase in which the current head advances steadilyand a second self-similar phase in which the front velocity decreases like the negative third power of thetime after release is satisfactorily presented by the laboratory observation. An overall entrainment ratioproportional to the distance from the release point is found by the numerical simulation. The renormal-ization group (RNG) k- ε model for Reynolds-stress closure is validated to characterize the gravitycurrent with transitional and localized turbulence.

  9. Principles of project management

    Science.gov (United States)

    1982-01-01

    The basic principles of project management as practiced by NASA management personnel are presented. These principles are given as ground rules and guidelines to be used in the performance of research, development, construction or operational assignments.

  10. Renin release

    DEFF Research Database (Denmark)

    Schweda, Frank; Friis, Ulla; Wagner, Charlotte;

    2007-01-01

    The aspartyl-protease renin is the key regulator of the renin-angiotensin-aldosterone system, which is critically involved in salt, volume, and blood pressure homeostasis of the body. Renin is mainly produced and released into circulation by the so-called juxtaglomerular epithelioid cells, located......, salt, and volume overload. In contrast, the events controlling the function of renin-secreting cells at the organ and cellular level are markedly less clear and remain mysterious in certain aspects. The unravelling of these mysteries has led to new and interesting insights into the process of renin...

  11. Application of the principle of similarity fluid mechanics

    Science.gov (United States)

    Hendricks, R. C.; Sengers, J. V.

    1979-01-01

    Possible applications of the principle of similarity to fluid mechanics is described and illustrated. In correlating thermophysical properties of fluids, the similarity principle transcends the traditional corresponding states principle. In fluid mechanics the similarity principle is useful in correlating flow processes that can be modeled adequately with one independent variable (i.e., one-dimensional flows). In this paper we explore the concept of transforming the conservation equations by combining similarity principles for thermophysical properties with those for fluid flow. We illustrate the usefulness of the procedure by applying such a transformation to calculate two phase critical mass flow through a nozzle.

  12. Chemical Principles Exemplified

    Science.gov (United States)

    Plumb, Robert C.

    1970-01-01

    This is the first of a new series of brief ancedotes about materials and phenomena which exemplify chemical principles. Examples include (1) the sea-lab experiment illustrating principles of the kinetic theory of gases, (2) snow-making machines illustrating principles of thermodynamics in gas expansions and phase changes, and (3) sunglasses that…

  13. How Einstein Got His Field Equations

    CERN Document Server

    Walters, Sam

    2016-01-01

    We study the pages in Albert Einstein's 1916 landmark paper in the Annalen der Physik where he derived his field equations for gravity. Einstein made two heuristic and physically insightful steps. The first was to obtain the field equations in vacuum in a rather geometric fashion. The second step was obtaining the field equations in the presence of matter from the field equations in vacuum. (This transition is an essential principle in physics, much as the principle of local gauge invariance in quantum field theory.) To this end, we go over some quick differential geometric background related to curvilinear coordinates, vectors, tensors, metric tensor, Christoffel symbols, Riemann curvature tensor, Ricci tensor, and see how Einstein used geometry to model gravity.

  14. Moderate Deviation Principles for Stochastic Differential Equations with Jumps

    Science.gov (United States)

    2014-01-15

    random measure and an in�nite dimensional Brownian motion) was derived. As in the Brownian motion case, the representation is motivated in part by...deviations of a smaller order than in large deviation theory . Consider for example an independent and identically distributed (iid) sequence fYigi1 of...8217") " E " 1 2 Z X[0;T ] ( ")21fj "jB"gdT + F G "("N " 1’") # " 1 2 3M 2(1); (3.6) where the last inequality follows from (3.5) on

  15. SCIENTIFIC PRINCIPLES AND MATHEMATICAL MODELS OF PROCESSES OF MINING

    OpenAIRE

    Kriuchkov, Anatolii Ivanovych

    2016-01-01

    The connection between mathematical models of the mining industry with the basic scientific principles. The method of simulation of random non-stationary processes in the form of a set of Hamilton-Jacobi equations and Fokker-Planck-Kolmogorov using the principle of duality movement of mass in space

  16. Comparison Principles in Nonlinear Mechanics and Their Application

    Institute of Scientific and Technical Information of China (English)

    王照林; 楚天广

    1994-01-01

    A kind of infinite demensional nonlinear dynamical system described by functional differential equations with finite time delay is investigated in this paper The comparison principles of LRC type are established and applied to the problems of averaging principle and practical stability in terms of two measures for the system with time delay

  17. Emmy Noether and Linear Evolution Equations

    Directory of Open Access Journals (Sweden)

    P. G. L. Leach

    2013-01-01

    Full Text Available Noether’s Theorem relates the Action Integral of a Lagrangian with symmetries which leave it invariant and the first integrals consequent upon the variational principle and the existence of the symmetries. These each have an equivalent in the Schrödinger Equation corresponding to the Lagrangian and by extension to linear evolution equations in general. The implications of these connections are investigated.

  18. On the Dirac equation for a quark

    CERN Document Server

    Pestov, I B

    2003-01-01

    It is argued from geometrical, group-theoretical and physical points of view that in the framework of QCD it is not only necessary but also possible to modify the Dirac equation so that correspondence principle holds valid. The Dirac wave equation for a quark is proposed and some consequences are considered. In particular, it is shown that interquark potential expresses the Coulomb law for the quarks and, in fact, coincides with the known Cornell potential.

  19. Optic eikonal, Fermat’s principle and the least action principle

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    A generalized refractive index in the form of optic eikonal is defined through com- paring frame definitions of left-handed and right-handed sets and indicates the sign of the refractive index covered by the quadratic form of the eikonal equation. Fer- mat’s principle is generalized, and the general refractive law is derived directly. Under this definition, the comparison between Fermat’s principle and the least ac- tion principle is made through employing path integral and analogizing L. de Broglie’s theory.

  20. REGION-WISE VARIATIONAL PRINCIPLES AND GENERALIZED VARIATIONAL PRINCIPLES ON LARGE STRAIN FOR CONSOLIDATION THEORY

    Institute of Scientific and Technical Information of China (English)

    LUO Xiao-hui; LI Yong-le; LUO Xin

    2005-01-01

    The difference of constitutive character and large deformation as to soil mass are basic questions to analyze deformational feature. According to the description method of limited deformation, the large deformation consolidation equations of soil mass were created and its variational principles were rigorously testified. The regionwise variational principles of consolidation theory were deduced using sub-structure continuous condition of region-wise. Quoting the method of Lagrangian multiplier operator, generalized variational principles of region-wise of large deformation consolidation in the nonconstrained condition were created and approved.

  1. POSITIVE SOLUTIONS OF FULLY NONLINEAR ELLIPTIC EQUATIONS ON GENERAL BOUNDED DOMAINS

    Institute of Scientific and Technical Information of China (English)

    Li Meisheng; Bao Jiguang

    2001-01-01

    We prove the refined ABP maximum principle, comparison principle, and related existence and uniqueness theorem for the positive solutions of the Dirich let problems of second order fully nonlinear elliptic equations on arbitrary bounded domains.

  2. An introduction to partial differential equations with Matlab

    CERN Document Server

    Coleman, Matthew P

    2013-01-01

    Introduction What are Partial Differential Equations? PDEs We Can Already Solve Initial and Boundary Conditions Linear PDEs-Definitions Linear PDEs-The Principle of Superposition Separation of Variables for Linear, Homogeneous PDEs Eigenvalue Problems The Big Three PDEsSecond-Order, Linear, Homogeneous PDEs with Constant CoefficientsThe Heat Equation and Diffusion The Wave Equation and the Vibrating String Initial and Boundary Conditions for the Heat and Wave EquationsLaplace's Equation-The Potential Equation Using Separation of Variables to Solve the Big Three PDEs Fourier Series Introduction

  3. Partial Differential Equations

    CERN Document Server

    1988-01-01

    The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.

  4. Ground state solutions for asymptotically periodic Schrodinger equations with critical growth

    Directory of Open Access Journals (Sweden)

    Hui Zhang

    2013-10-01

    Full Text Available Using the Nehari manifold and the concentration compactness principle, we study the existence of ground state solutions for asymptotically periodic Schrodinger equations with critical growth.

  5. General Large Deviations and Functional Iterated Logarithm Law for Multivalued Stochastic Differential Equations

    OpenAIRE

    Ren, Jiagang; Wu, Jing; Zhang, Hua

    2015-01-01

    In this paper, we prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations. As an application, we derive a functional iterated logarithm law for the solutions of multivalued stochastic differential equations.

  6. Algebroid Solutions of Second Order Complex Differential Equations

    Directory of Open Access Journals (Sweden)

    Lingyun Gao

    2014-01-01

    Full Text Available Using value distribution theory and maximum modulus principle, the problem of the algebroid solutions of second order algebraic differential equation is investigated. Examples show that our results are sharp.

  7. Optimal Control of Non-well-posed Heat Equations

    Institute of Scientific and Technical Information of China (English)

    Geng Sheng WANG

    2005-01-01

    This work is concerned with Pontryagin's maximum principle of optimal control problems governed by some non-well-posed semilinear heat equations. A type of approach to the non-well-posed optimal control problem is given.

  8. Large Deviations for Multi-valued Stochastic Differential Equations

    CERN Document Server

    Ren, Jiagang; Zhang, Xicheng

    2009-01-01

    We prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations with monotone drifts, which in particular contains a class of SDEs with reflection in a convex domain.

  9. Some remarks on a second order evolution equation

    Directory of Open Access Journals (Sweden)

    Mohammed Aassila

    1998-07-01

    Full Text Available We prove the strong asymptotic stability of solutions to a second order evolution equation when the LaSalle's invariance principle cannot be applied due to the lack of monotonicity and compactness.

  10. Individualized optimal release angles in discus throwing.

    Science.gov (United States)

    Leigh, Steve; Liu, Hui; Hubbard, Mont; Yu, Bing

    2010-02-10

    The purpose of this study was to determine individualized optimal release angles for elite discus throwers. Three-dimensional coordinate data were obtained for at least 10 competitive trials for each subject. Regression relationships between release speed and release angle, and between aerodynamic distance and release angle were determined for each subject. These relationships were linear with subject-specific characteristics. The subject-specific relationships between release speed and release angle may be due to subjects' technical and physical characteristics. The subject-specific relationships between aerodynamic distance and release angle may be due to interactions between the release angle, the angle of attack, and the aerodynamic distance. Optimal release angles were estimated for each subject using the regression relationships and equations of projectile motion. The estimated optimal release angle was different for different subjects, and ranged from 35 degrees to 44 degrees . The results of this study demonstrate that the optimal release angle for discus throwing is thrower-specific. The release angles used by elite discus throwers in competition are not necessarily optimal for all discus throwers, or even themselves. The results of this study provide significant information for understanding the biomechanics of discus throwing techniques.

  11. Biomechanics principles and practices

    CERN Document Server

    Peterson, Donald R

    2014-01-01

    Presents Current Principles and ApplicationsBiomedical engineering is considered to be the most expansive of all the engineering sciences. Its function involves the direct combination of core engineering sciences as well as knowledge of nonengineering disciplines such as biology and medicine. Drawing on material from the biomechanics section of The Biomedical Engineering Handbook, Fourth Edition and utilizing the expert knowledge of respected published scientists in the application and research of biomechanics, Biomechanics: Principles and Practices discusses the latest principles and applicat

  12. Heisenberg's uncertainty principle

    OpenAIRE

    Busch, Paul; Heinonen, Teiko; Lahti, Pekka

    2007-01-01

    Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and...

  13. Fusion research principles

    CERN Document Server

    Dolan, Thomas James

    2013-01-01

    Fusion Research, Volume I: Principles provides a general description of the methods and problems of fusion research. The book contains three main parts: Principles, Experiments, and Technology. The Principles part describes the conditions necessary for a fusion reaction, as well as the fundamentals of plasma confinement, heating, and diagnostics. The Experiments part details about forty plasma confinement schemes and experiments. The last part explores various engineering problems associated with reactor design, vacuum and magnet systems, materials, plasma purity, fueling, blankets, neutronics

  14. Chemical Principle and PDE of Variational Electrodynamics

    CERN Document Server

    De Luca, Jayme

    2016-01-01

    We study the problem of selecting a bounded two-body orbit exerting a vanishing electrical force on a third charge located outside a core region. The former infinite-dimensional PDE problem is called here the Chemical principle for the hydrogenoid atom of variational electrodynamics. For orbits with velocity discontinuities satisfying mild conditions at breaking points we introduce the delay and synchronization functions and prove a musical Lemma of synchronization-at-a-distance. We derive the leading PDE of the Chemical principle by removing the accelerations using the equations of motion approximated by keeping only the terms with the most singular denominators.

  15. Database principles programming performance

    CERN Document Server

    O'Neil, Patrick

    2014-01-01

    Database: Principles Programming Performance provides an introduction to the fundamental principles of database systems. This book focuses on database programming and the relationships between principles, programming, and performance.Organized into 10 chapters, this book begins with an overview of database design principles and presents a comprehensive introduction to the concepts used by a DBA. This text then provides grounding in many abstract concepts of the relational model. Other chapters introduce SQL, describing its capabilities and covering the statements and functions of the programmi

  16. Principles of private law

    OpenAIRE

    Andraško, Richard

    2011-01-01

    Principles of private law The reason of choosing "Principles of private law" for my thesis is that private law is built on untouchable values. For example, basic values like freedom and equality, which are represented by these principles. Many of them are indispensable in the relation of functionality of the whole system of law. Most of them have Roman law origin. The purpose of my thesis is to describe and summarize the main principles of private law that mostly appear in Czech law, especial...

  17. Fractional Order Differential Equations Involving Caputo Derivative

    Directory of Open Access Journals (Sweden)

    Zoubir Dahmani

    2014-04-01

    Full Text Available In this paper, the Banach contraction principle and Schaefer theorem are applied to establish new results for the existence and uniqueness of solutions for some Caputo fractional differential equations. Some examples are also discussed to illustrate the main results.

  18. On a Volterra Stieltjes integral equation

    Directory of Open Access Journals (Sweden)

    P. T. Vaz

    1990-01-01

    Full Text Available The paper deals with a study of linear Volterra integral equations involving Lebesgue-Stieltjes integrals in two independent variables. The authors prove an existence theorem using the Banach fixed-point principle. An explicit example is also considered.

  19. Food Web Assembly Rules for Generalized Lotka-Volterra Equations

    DEFF Research Database (Denmark)

    Härter, Jan Olaf Mirko; Mitarai, Namiko; Sneppen, Kim

    2016-01-01

    In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this......In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show...

  20. Jourdain Principle of a Super-Thin Elastic Rod Dynamics

    Institute of Scientific and Technical Information of China (English)

    XUE Yun; SHANG Hui-Lin

    2009-01-01

    A super thin elastic rod is modeled with a background of DNA super coiling structure, and its dynamics is discussed based on the Jourdain variation. The cross section of the rod is taken as the object of this study and two velocity spaces about arc coordinate and the time are obtained respectively. Virtual displacements of the section on the two velocity spaces are defined and can be expressed in terms of Jourdaln variation. Jourdain principles of a super thin elastic rod dynamics on arc coordinate and the time velocity space are established,respectively, which show that there are two ways to realize the constraint conditions. If the constitutive relation of the rod is linear, the Jourdaln principle takes the Euler-Lagrange form with generalized coordinates. The Kirchhoff equation, Lagrange equation and Appell equation can be derived from the present Jourdaln principle.While the rod subjected to a surface constraint, Lagrange equation with undetermined multipliers may be derived.

  1. Exact solutions to a class of nonlinear Schrödinger-type equations

    Indian Academy of Sciences (India)

    Jin-Liang Zhang; Ming-Liang Wing

    2006-12-01

    A class of nonlinear Schrödinger-type equations, including the Rangwala–Rao equation, the Gerdjikov–Ivanov equation, the Chen–Lee–Lin equation and the Ablowitz–Ramani–Segur equation are investigated, and the exact solutions are derived with the aid of the homogeneous balance principle, and a set of subsidiary higher order ordinary differential equations (sub-ODEs for short).

  2. Multisymplectic Geometry and Its Appiications for the Schr(o)dinger Equation in Quantum Mechanics

    Institute of Scientific and Technical Information of China (English)

    CHEN Jing-Bo

    2007-01-01

    Multisymplectic geometry for the Schr(o)dinger equation in quantum mechanics is presented. This formalism of multisymplectic geometry provides a concise and complete introduction to the Schr(o)dinger equation. The Schr(o)dinger equation, its associated energy and momentum evolution equations, and the multisymplectic form are derived directly from the variational principle. Some applications are also explored.

  3. The third-order Lagrange equation for mechanical systems of variable mass

    Institute of Scientific and Technical Information of China (English)

    Ma Shan-Jun; Ge Wei-Guo; Huang Pei-Tian

    2005-01-01

    In this paper, based on the third-order D'Alembert-Lagrange principle for mechanical systems of variable mass,the third-order Lagrange equations of mechanical systems of variable mass are obtained From the equations the motion of mechanical systems of variable mass can be studied. In addition, the equations may enrich the theory of third-order differential equation.

  4. 78 FR 32988 - Core Principles and Other Requirements for Designated Contract Markets; Correction

    Science.gov (United States)

    2013-06-03

    ... COMMISSION 17 CFR Part 38 RIN 3038-AD09 Core Principles and Other Requirements for Designated Contract...: This document corrects the Federal Register release of the final rule regarding Core Principles and... language for the previously published Federal Register release of the final rule regarding Core...

  5. Principles of snow hydrology

    National Research Council Canada - National Science Library

    DeWalle, David R; Rango, Albert

    2008-01-01

    ... Hydrology describes the factors that control the accumulation, melting, and runoff of water from seasonal snowpacks over the surface of the earth. The book addresses not only the basic principles governing snow in the hydrologic cycle, but also the latest applications of remote sensing, and principles applicable to modelling streamflow from snowmelt across lar...

  6. Great Principles of Computing

    OpenAIRE

    Denning, Peter J.

    2008-01-01

    The Great Principles of Computing is a framework for understanding computing as a field of science. The website ...April 2008 (Rev. 8/31/08) The Great Principles of Computing is a framework for understanding computing as a field of science.

  7. Basic principle of superconductivity

    OpenAIRE

    De Cao, Tian

    2007-01-01

    The basic principle of superconductivity is suggested in this paper. There have been two vital wrong suggestions on the basic principle, one is the relation between superconductivity and the Bose-Einstein condensation (BEC), and another is the relation between superconductivity and pseudogap.

  8. Cosmography: Cosmology without the Einstein equations

    CERN Document Server

    Visser, M

    2004-01-01

    How much of modern cosmology is really cosmography? How much of modern cosmology is independent of the Einstein equations? (Independent of the Friedmann equations?) These questions are becoming increasingly germane -- as the models cosmologists use for the stress-energy content of the universe become increasingly baroque, it behoves us to step back a little and carefully disentangle cosmological kinematics from cosmological dynamics. The use of basic symmetry principles (such as the cosmological principle) permits us to do a considerable amount, without ever having to address the vexatious issues of just how much "dark energy", "dark matter", "quintessence", and/or "phantom matter" is needed in order to satisfy the Einstein equations. This is the sub-sector of cosmology that Weinberg refers to as "cosmography", and in this article I will explore the extent to which cosmography is sufficient for analyzing the Hubble law and so describing many of the features of the universe around us.

  9. Effect of the principle for soothing the liver and strengthening the spleen, regulating stomach and refresh spirit on corticotropin releasing hormone content of functional diarrhoea rats%疏肝健脾、安神和胃法治疗功能性腹泻模型大鼠的作用机制

    Institute of Scientific and Technical Information of China (English)

    吴文江; 陶双友; 韩棉梅; 梁嘉恺; 罗琦; 何丽英; 周福生

    2013-01-01

    corticotropin releasing hormone level expression was tested. Results After 2 weeks of the treatment, intestinal propulsion rate of functional diarrhoea rats was significantly reduced (P < 0. 05 ). Compared with the normal group, the corticotropin releasing hormone level of model group was significantly increased (P <0. 05). Conclusions The corticotropin releasing hormone expression levels in brain stem, hypothalamus, intestinal mucosa of functional diarrhoea rat are often associated with the pathogenesis of functional diarrhoea. The principle for soothing the liver and strengthening the spleen, regulating stomach and refresh spirit lower the expression of corticotropin releasing hormone explains the pathogenesis of functional diarrhoea.

  10. Variational principles in physics

    CERN Document Server

    Basdevant, Jean-Louis

    2007-01-01

    Optimization under constraints is an essential part of everyday life. Indeed, we routinely solve problems by striking a balance between contradictory interests, individual desires and material contingencies. This notion of equilibrium was dear to thinkers of the enlightenment, as illustrated by Montesquieu’s famous formulation: "In all magistracies, the greatness of the power must be compensated by the brevity of the duration." Astonishingly, natural laws are guided by a similar principle. Variational principles have proven to be surprisingly fertile. For example, Fermat used variational methods to demonstrate that light follows the fastest route from one point to another, an idea which came to be known as Fermat’s principle, a cornerstone of geometrical optics. Variational Principles in Physics explains variational principles and charts their use throughout modern physics. The heart of the book is devoted to the analytical mechanics of Lagrange and Hamilton, the basic tools of any physicist. Prof. Basdev...

  11. Equivalence principles exotica

    Institute of Scientific and Technical Information of China (English)

    C.S. UNNIKRISHNAN; George T. GILLIES

    2008-01-01

    This is a short review of the different prin-ciples of equivalence stated and used in the context of the gravitational interaction. We emphasize the need for precision in stating and differentiating these different equivalence principles, especially in the context of preva-lent confusion regarding the applicability of the weak equivalence principle in quantum mechanics. We discuss several empirical results pertaining to the validity of the equivalence principle in exotic physical sitautions not di-rectly amenable to experimental tests. We conclude with a section on the physical basis of the universal validity of the equivalence principle, as manifest in the universality of free fall, and discuss its link to cosmic gravity.

  12. Software citation principles

    Directory of Open Access Journals (Sweden)

    Arfon M. Smith

    2016-09-01

    Full Text Available Software is a critical part of modern research and yet there is little support across the scholarly ecosystem for its acknowledgement and citation. Inspired by the activities of the FORCE11 working group focused on data citation, this document summarizes the recommendations of the FORCE11 Software Citation Working Group and its activities between June 2015 and April 2016. Based on a review of existing community practices, the goal of the working group was to produce a consolidated set of citation principles that may encourage broad adoption of a consistent policy for software citation across disciplines and venues. Our work is presented here as a set of software citation principles, a discussion of the motivations for developing the principles, reviews of existing community practice, and a discussion of the requirements these principles would place upon different stakeholders. Working examples and possible technical solutions for how these principles can be implemented will be discussed in a separate paper.

  13. Principles of computational fluid dynamics

    CERN Document Server

    Wesseling, Pieter

    2001-01-01

    The book is aimed at graduate students, researchers, engineers and physicists involved in flow computations. An up-to-date account is given of the present state-of-the-art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary mathematical analysis. Attention is given to difficulties arising from geometric complexity of the flow domain and of nonuniform structured boundary-fitted grids. Uniform accuracy and efficiency for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Much attention is given to stability analysis, and useful stability conditions are provided, some of them new, for many numerical schemes used in practice. Unified methods for compressible and incompressible flows are discussed. Numerical analysis of the shallow-water equations is included. The theory of hyperbolic conservation laws is treated. Godunov's order barrier and ho...

  14. Action principle for Numerical Relativity evolution systems

    CERN Document Server

    Bona, C; Palenzuela, C

    2010-01-01

    A Lagrangian density is provided, that allows to recover the Z4 evolution system from an action principle. The resulting system is then strongly hyperbolic when supplemented by gauge conditions like '1+log' or 'freezing shift', suitable for numerical evolution. The physical constraint $Z_\\mu = 0$ can be imposed just on the initial data. The corresponding Hamiltonian and canonical equations are also provided. This opens the door to analogous results for other numerical-relativity formalisms, like BSSN, that can be derived from Z4 by a symmetry-breaking procedure. The harmonic formulation can be easily recovered by a slight modification of the procedure. This provides a mechanism for deriving both the field evolution equations and the gauge conditions from the action principle, with a view on using simplectic integrators for a constraint-preserving numerical evolution.

  15. Proton-pumping mechanism of cytochrome c oxidase: A kinetic master-equation approach

    Science.gov (United States)

    Kim, Young C.; Hummer, Gerhard

    2011-01-01

    Cytochrome c oxidase (CcO) is an efficient energy transducer that reduces oxygen to water and converts the released chemical energy into an electrochemical membrane potential. As a true proton pump, CcO translocates protons across the membrane against this potential. Based on a wealth of experiments and calculations, an increasingly detailed picture of the reaction intermediates in the redox cycle has emerged. However, the fundamental mechanism of proton pumping coupled to redox chemistry remains largely unresolved. Here we examine and extend a kinetic master-equation approach to gain insight into redox-coupled proton pumping in CcO. Basic principles of the CcO proton pump emerge from an analysis of the simplest kinetic models that retain essential elements of the experimentally determined structure, energetics, and kinetics, and that satisfy fundamental physical principles. The master-equation models allow us to address the question of how pumping can be achieved in a system in which all reaction steps are reversible. Whereas proton pumping does not require the direct modulation of microscopic reaction barriers, such kinetic gating greatly increases the pumping efficiency. Further efficiency gains can be achieved by partially decoupling the proton uptake pathway from the ative-site region. Such a mechanism is consistent with the proposed Glu valve, in which the side chain of a key glutamic acid shuttles between the D channel and the active-site region. We also show that the models predict only small proton leaks even in the absence of turnover. The design principles identified here for CcO provide a blueprint for novel biology-inspired fuel cells, and the master-equation formulation should prove useful also for other molecular machines. PMID:21946020

  16. Proton-pumping mechanism of cytochrome c oxidase: a kinetic master-equation approach.

    Science.gov (United States)

    Kim, Young C; Hummer, Gerhard

    2012-04-01

    Cytochrome c oxidase is an efficient energy transducer that reduces oxygen to water and converts the released chemical energy into an electrochemical membrane potential. As a true proton pump, cytochrome c oxidase translocates protons across the membrane against this potential. Based on a wealth of experiments and calculations, an increasingly detailed picture of the reaction intermediates in the redox cycle has emerged. However, the fundamental mechanism of proton pumping coupled to redox chemistry remains largely unresolved. Here we examine and extend a kinetic master-equation approach to gain insight into redox-coupled proton pumping in cytochrome c oxidase. Basic principles of the cytochrome c oxidase proton pump emerge from an analysis of the simplest kinetic models that retain essential elements of the experimentally determined structure, energetics, and kinetics, and that satisfy fundamental physical principles. The master-equation models allow us to address the question of how pumping can be achieved in a system in which all reaction steps are reversible. Whereas proton pumping does not require the direct modulation of microscopic reaction barriers, such kinetic gating greatly increases the pumping efficiency. Further efficiency gains can be achieved by partially decoupling the proton uptake pathway from the active-site region. Such a mechanism is consistent with the proposed Glu valve, in which the side chain of a key glutamic acid shuttles between the D channel and the active-site region. We also show that the models predict only small proton leaks even in the absence of turnover. The design principles identified here for cytochrome c oxidase provide a blueprint for novel biology-inspired fuel cells, and the master-equation formulation should prove useful also for other molecular machines. .

  17. 76 FR 14825 - Core Principles and Other Requirements for Designated Contact Markets

    Science.gov (United States)

    2011-03-18

    ... COMMISSION 17 CFR Parts 1, 16, and 38 RIN 3038-AD09 Core Principles and Other Requirements for Designated... Commission in the Federal Register release for the notice of proposed rulemaking for ``Core Principles and... comment period for the proposed rulemaking closed on February 22, 2011. \\2\\ See Core Principles and...

  18. Introducing the Accounting Equation with M&M's®

    Science.gov (United States)

    Scofield, Barbara W.; Dye, Wilma

    2009-01-01

    On the first day of Principles of Accounting classes, students learn the fundamental accounting equation from which all financial accounting practice emerge. The accounting equation is the criterion by which companies are valued and by which company performance is measured. This activity simplifies assets, liabilities, and owners' equity to the…

  19. Invariant Measures for a Random Evolution Equation with Small Perturbations

    Institute of Scientific and Technical Information of China (English)

    Fu Bao XI

    2001-01-01

    In this paper we consider a random evolution equation with small perturbations, and show how to construct coupled solutions to the equation. As applications, we prove the Feller continuity of the solutions and the existence and uniqueness of invariant measures. Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations tend to zero.

  20. Quantization of Equations of Motion

    Directory of Open Access Journals (Sweden)

    D. Kochan

    2007-01-01

    Full Text Available The Classical Newton-Lagrange equations of motion represent the fundamental physical law of mechanics. Their traditional Lagrangian and/or Hamiltonian precursors when available are essential in the context of quantization. However, there are situations that lack Lagrangian and/or Hamiltonian settings. This paper discusses a description of classical dynamics and presents some irresponsible speculations about its quantization by introducing a certain canonical two-form ?. By its construction ? embodies kinetic energy and forces acting within the system (not their potential. A new type of variational principle employing differential two-form ? is introduced. Variation is performed over “umbilical surfaces“ instead of system histories. It provides correct Newton-Lagrange equations of motion. The quantization is inspired by the Feynman path integral approach. The quintessence is to rearrange it into an “umbilical world-sheet“ functional integral in accordance with the proposed variational principle. In the case of potential-generated forces, the new approach reduces to the standard quantum mechanics. As an example, Quantum Mechanics with friction is analyzed in detail. 

  1. Kinetic energy equations for the average-passage equation system

    Science.gov (United States)

    Johnson, Richard W.; Adamczyk, John J.

    1989-01-01

    Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.

  2. Kinetic energy equations for the average-passage equation system

    Science.gov (United States)

    Johnson, Richard W.; Adamczyk, John J.

    1989-01-01

    Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.

  3. Principles of dynamics

    CERN Document Server

    Hill, Rodney

    2013-01-01

    Principles of Dynamics presents classical dynamics primarily as an exemplar of scientific theory and method. This book is divided into three major parts concerned with gravitational theory of planetary systems; general principles of the foundations of mechanics; and general motion of a rigid body. Some of the specific topics covered are Keplerian Laws of Planetary Motion; gravitational potential and potential energy; and fields of axisymmetric bodies. The principles of work and energy, fictitious body-forces, and inertial mass are also looked into. Other specific topics examined are kinematics

  4. Biomedical engineering principles

    CERN Document Server

    Ritter, Arthur B; Valdevit, Antonio; Ascione, Alfred N

    2011-01-01

    Introduction: Modeling of Physiological ProcessesCell Physiology and TransportPrinciples and Biomedical Applications of HemodynamicsA Systems Approach to PhysiologyThe Cardiovascular SystemBiomedical Signal ProcessingSignal Acquisition and ProcessingTechniques for Physiological Signal ProcessingExamples of Physiological Signal ProcessingPrinciples of BiomechanicsPractical Applications of BiomechanicsBiomaterialsPrinciples of Biomedical Capstone DesignUnmet Clinical NeedsEntrepreneurship: Reasons why Most Good Designs Never Get to MarketAn Engineering Solution in Search of a Biomedical Problem

  5. Modern electronic maintenance principles

    CERN Document Server

    Garland, DJ

    2013-01-01

    Modern Electronic Maintenance Principles reviews the principles of maintaining modern, complex electronic equipment, with emphasis on preventive and corrective maintenance. Unfamiliar subjects such as the half-split method of fault location, functional diagrams, and fault finding guides are explained. This book consists of 12 chapters and begins by stressing the need for maintenance principles and discussing the problem of complexity as well as the requirements for a maintenance technician. The next chapter deals with the connection between reliability and maintenance and defines the terms fai

  6. Developing principles of growth

    DEFF Research Database (Denmark)

    Neergaard, Helle; Fleck, Emma

    of the principles of growth among women-owned firms. Using an in-depth case study methodology, data was collected from women-owned firms in Denmark and Ireland, as these countries are similar in contextual terms, e.g. population and business composition, dominated by micro, small and medium-sized enterprises....... Extending on principles put forward in effectuation theory, we propose that women grow their firms according to five principles which enable women’s enterprises to survive in the face of crises such as the current financial world crisis....

  7. [Nutrient release characteristics and use efficiency of slow- and controlled release fertilizers].

    Science.gov (United States)

    Duan, Lu-Lu; Zhang, Min; Liu, Gang; Shang, Zhao-Cong; Yang, Yi

    2009-05-01

    Water extraction method and soil incubation method were used to study the nutrient release characteristics of four slow- and controlled release fertilizers (CRF1, CRF2, SCU, and IBDU), and pot experiment was conducted to assess the effects of the release characteristics on the nutrient requirements of canola (Brassica napus L.). The nutrient release curves of test fertilizers in water were S pattern for CRF1 and CRF2, burst pattern for SCU, and reverse L pattern for IBDU. The nutrient release characteristics of the four fertilizers in water and in soil all fitted binomial equations, suggesting that there existed some similarities in the nutrient release in the two media. The nutrient uptake and biomass of canola plants treated with CRF1 and CRF2 were significantly higher than those treated with SCU and IBDU, and CRF2 had the greatest effect. The nutrient release curves of CRF1 and CRF2 accorded more closely with the nutrient requirements of canola.

  8. The Hamilton principle for fluid binary mixtures with two temperatures

    CERN Document Server

    Gouin, Henri

    2009-01-01

    For binary mixtures of fluids without chemical reactions, but with components having different temperatures, the Hamilton principle of least action is able to produce the equation of motion for each component and a balance equation of the total heat exchange between components. In this nonconservative case, a Gibbs dynamical identity connecting the equations of momenta, masses, energy and heat exchange allows to deduce the balance equation of energy of the mixture. Due to the unknown exchange of heat between components, the number of obtained equations is less than the number of field variables. The second law of thermodynamics constrains the possible expression of a supplementary constitutive equation closing the system of equations. The exchange of energy between components produces an increasing rate of entropy and creates a dynamical pressure term associated with the difference of temperature between components. This new dynamical pressure term fits with the results obtained by classical thermodynamical a...

  9. Generalized Dromion Structures of New (2 + 1)-Dimensional Nonlinear EvolutionEquation

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jie-Fang

    2001-01-01

    We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this system are released.

  10. Solving Nonlinear Wave Equations by Elliptic Equation

    Institute of Scientific and Technical Information of China (English)

    FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo

    2003-01-01

    The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.

  11. Bateman's principle and immunity

    National Research Council Canada - National Science Library

    Jens Rolff

    2002-01-01

    .... This alternative is based on Bateman's principle, that males gain fitness by increasing their mating success whilst females increase fitness through longevity because their reproductive effort is much higher...

  12. The Symmetry Principle

    Directory of Open Access Journals (Sweden)

    Joe Rosen

    2005-12-01

    Full Text Available Abstract: The symmetry principle is described in this paper. The full details are given in the book: J. Rosen, Symmetry in Science: An Introduction to the General Theory (Springer-Verlag, New York, 1995.

  13. Archimedes' Principle in Action

    Science.gov (United States)

    Kires, Marian

    2007-01-01

    The conceptual understanding of Archimedes' principle can be verified in experimental procedures which determine mass and density using a floating object. This is demonstrated by simple experiments using graduated beakers. (Contains 5 figures.)

  14. Principles of nanomagnetism

    CERN Document Server

    Guimarães, Alberto P

    2017-01-01

    This is the first monograph on nanomagnetism. It emphasizes general principles and mechanisms relevant to the understanding of the intriguing properties of nanomagnetic objects including thin films, nanoparticles, nanowires, nanodisks and nanorings.

  15. Archimedes' Principle in Action

    Science.gov (United States)

    Kires, Marian

    2007-01-01

    The conceptual understanding of Archimedes' principle can be verified in experimental procedures which determine mass and density using a floating object. This is demonstrated by simple experiments using graduated beakers. (Contains 5 figures.)

  16. Principles Scientifiques, Principes Philosophiques

    Directory of Open Access Journals (Sweden)

    Gilles-Gaston Granger

    1999-06-01

    Full Text Available A principle is a starting point of departure as well as a rule. In science principles are either alleged evident rules or generalizations of already accepted laws, or formal determinations for objects in a given domain. Thus two problems arise: first, does their nature have a conventional character? and sencond, what kind of truth is to be assigned to them. In philosophy principles are taken as a method of thinking as well as fundamental experiences. Even though they are points of departure, their true meaning is known only after a philosophical job is done. Thus, paradoxically enough, we can say that in both science and philosophy a principle is at the same time in the begining and in the end.

  17. Stability of the second order partial differential equations

    OpenAIRE

    Ghaemi MB; Cho YJ; Alizadeh B; Gordji M Eshaghi

    2011-01-01

    Abstract We say that a functional equation (ξ) is stable if any function g satisfying the functional equation (ξ) approximately is near to a true solution of (ξ). In this paper, by using Banach's contraction principle, we prove the stability of nonlinear partial differential equations of the following forms: y x ( x , t ) = f ( x , t , y ( x , t ) ) , a y x ( x , t ) + b y t ( x , t ) = f ( x , t , y ( x , t ) ) , p (...

  18. A Generalized Equation of State for High-Pressure Liquids

    Institute of Scientific and Technical Information of China (English)

    LIANG Yan-bo; TONG Jing-shan

    2005-01-01

    An equation of state (EOS) for high-pressure liquids, I.e., Tait EOS, is deduced according to isothermal compressibility KT=-1/V·((а)V/(а)p)T·.Based on the equation, a generalized EOS for high pressure-liquids is established by using the reduced state principle and introducing a characteristic parameter-configuration factorξ.Reasonably satisfactory P-V-T data for many organic compounds, including some polar components, were calculated by using the equation.

  19. The Hamiltonian Structure of the Maxwell-Vlasov Equations.

    Science.gov (United States)

    1981-02-01

    principle of Percival [1979). 4. By using an appropriate Darboux theorem, (see Marsden [1981], lecture 1), one can show that Of admits canonically...get the Vlasov-Poisson equation. It would also be of interest to realize both the Vlasov-Maxwell and MHD equations as limiting cases of a grand...de Vries equation, Springer Lecture Notes, #755, 1-15 and Inv. Math. 50, 219-248. J. Arms (1979]. Linearization stability of gravitational and gauge

  20. News/Press Releases

    Data.gov (United States)

    Office of Personnel Management — A press release, news release, media release, press statement is written communication directed at members of the news media for the purpose of announcing programs...

  1. Heisenberg's observability principle

    OpenAIRE

    Wolff, JE

    2014-01-01

    Werner Heisenberg's 1925 paper ‘Quantum-theoretical re-interpretation of kinematic and mechanical relations’ marks the beginning of quantum mechanics. Heisenberg famously claims that the paper is based on the idea that the new quantum mechanics should be ‘founded exclusively upon relationships between quantities which in principle are observable’. My paper is an attempt to understand this observability principle, and to see whether its employment is philosophically defensible. Against interpr...

  2. Electrical and electronic principles

    CERN Document Server

    Knight, S A

    1991-01-01

    Electrical and Electronic Principles, 2, Second Edition covers the syllabus requirements of BTEC Unit U86/329, including the principles of control systems and elements of data transmission. The book first tackles series and parallel circuits, electrical networks, and capacitors and capacitance. Discussions focus on flux density, electric force, permittivity, Kirchhoff's laws, superposition theorem, arrangement of resistors, internal resistance, and powers in a circuit. The text then takes a look at capacitors in circuit, magnetism and magnetization, electromagnetic induction, and alternating v

  3. Ternary optical computer principle

    Institute of Scientific and Technical Information of China (English)

    金翊; 何华灿; 吕养天

    2003-01-01

    The fundamental principle and the characteristics of ternary optical computer, using horizontal polarized light, vertical polarized light and no-intensity to express information, are propounded in thispaper. The practicability to make key parts of the ternary optical computer from modern micro or integrated optical devices, opto-electronic and electro-photonic elements is discussed. The principle can be applied in three-state optical fiber communication via horizontal and vertical polarized light.

  4. PRINCIPLES OF ANIMAL BREEDING

    OpenAIRE

    2014-01-01

    University textbook Principles of Animal Breeding is intended for students of agriculture and veterinary medicine. The material is the adapted curricula of undergraduate and graduate level studies in the framework of which the modules Principles of animal breeding as well as Basics of genetics and selection of animals attended are listened. The textbook contains 14 chapters and a glossary of terms. Its concept enables combining fundamental and modern knowledge in the ...

  5. Microprocessors principles and applications

    CERN Document Server

    Debenham, Michael J

    1979-01-01

    Microprocessors: Principles and Applications deals with the principles and applications of microprocessors and covers topics ranging from computer architecture and programmed machines to microprocessor programming, support systems and software, and system design. A number of microprocessor applications are considered, including data processing, process control, and telephone switching. This book is comprised of 10 chapters and begins with a historical overview of computers and computing, followed by a discussion on computer architecture and programmed machines, paying particular attention to t

  6. Electrophysiology of living organs from first principles

    CERN Document Server

    Scharf, Günter

    2010-01-01

    Based on the derivation of the macroscopic Maxwell's equations by spatial averaging of the microscopic equations, we discuss the electrophysiology of living organs. Other methods of averaging (or homogenization) like the bidomain model are not compatible with Maxwell's theory. We also point out that modeling the active cells by source currents is not a suitable description of the situation from first principles. Instead, it turns out that the main source of the measured electrical potentials is the polarization charge density which exists at the membranes of the active cells and adds up to a macroscopic polarization. The latter is the source term in the Laplace equation, the solution of which gives the measured far-field potential. As a consequence it is the polarization or dipole density which is best suited for localization of cardiac arrhythmia.

  7. Unconventional Hamilton-type variational principles for electromagnetic elastodynamics

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electromagnetic elastodynamics can be established systematically. This new variational principles can fully characterize the initial-boundary-value problem of this dynamics. In this paper, the expression of the generalized principle of virtual work for electromagnetic dynamics is given. Based on this equation, it is possible not only to obtain the principle of virtual work in electromagnetic dynamics, but also to derive systematically the complementary functionals for eleven-field, nine-field and six-field unconventional Hamilton-type variational principles for electromagnetic elastodynamics, and the potential energy functionals for four-field and three-field ones by the generalized Legendre transformation given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.

  8. Generalized uncertainty principles

    CERN Document Server

    Machluf, Ronny

    2008-01-01

    The phenomenon in the essence of classical uncertainty principles is well known since the thirties of the last century. We introduce a new phenomenon which is in the essence of a new notion that we introduce: "Generalized Uncertainty Principles". We show the relation between classical uncertainty principles and generalized uncertainty principles. We generalized "Landau-Pollak-Slepian" uncertainty principle. Our generalization relates the following two quantities and two scaling parameters: 1) The weighted time spreading $\\int_{-\\infty}^\\infty |f(x)|^2w_1(x)dx$, ($w_1(x)$ is a non-negative function). 2) The weighted frequency spreading $\\int_{-\\infty}^\\infty |\\hat{f}(\\omega)|^2w_2(\\omega)d\\omega$. 3) The time weight scale $a$, ${w_1}_a(x)=w_1(xa^{-1})$ and 4) The frequency weight scale $b$, ${w_2}_b(\\omega)=w_2(\\omega b^{-1})$. "Generalized Uncertainty Principle" is an inequality that summarizes the constraints on the relations between the two spreading quantities and two scaling parameters. For any two reason...

  9. Introduction to differential equations

    CERN Document Server

    Taylor, Michael E

    2011-01-01

    The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen

  10. The Modified Magnetohydrodynamical Equations

    Institute of Scientific and Technical Information of China (English)

    EvangelosChaliasos

    2003-01-01

    After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.

  11. Schrodinger Equation As a General Optimization Algorithm

    CERN Document Server

    Huang, Xiaofei

    2009-01-01

    One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrodinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the quantum state of a physical system. It has been found that the time-independent version of the equation can be derived from a general optimization algorithm. Instead of arguing for a new interpretation and possible deeper principle for quantum mechanics, this paper elaborates a few points of the equation as a general global optimization algorithm. Benchmarked against randomly generated hard optimization problems, this paper shows that the algorithm significantly outperformed a classic local optimization algorithm. The former found a solution in one second with a single trial better than the best one found by the latter around one hour after one hundred thousand trials.

  12. Partial differential equations mathematical techniques for engineers

    CERN Document Server

    Epstein, Marcelo

    2017-01-01

    This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate s...

  13. Moving interfaces and quasilinear parabolic evolution equations

    CERN Document Server

    Prüss, Jan

    2016-01-01

    In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions...

  14. One dimensional Newton's equation with variable mass

    CERN Document Server

    Mazharimousavi, S Habib

    2013-01-01

    We revisit Newton's equation of motion in one dimension when the moving particle has a variable mass m(x,t) depending both on position (x) and time (t). Geometrically the mass function is identified with one of the metric function in a 1+1-dimensional spacetime. As a reflection of the equivalence principle geodesics equation gives the Newton's law of motion leaving the right hand side to be supplemented by the external forces. The resulting equation involves the speed of light so that our equation of motion addresses a wider scope than the customary classical mechanics. In the limit of infinite light speed which amounts to instantaneous interaction we recover the classical results.

  15. Physical entropy, information entropy and their evolution equations

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Inspired by the evolution equation of nonequilibrium statistical physics entropy and the concise statistical formula of the entropy production rate, we develop a theory of the dynamic information entropy and build a nonlinear evolution equation of the information entropy density changing in time and state variable space. Its mathematical form and physical meaning are similar to the evolution equation of the physical entropy: The time rate of change of information entropy density originates together from drift, diffusion and production. The concise statistical formula of information entropy production rate is similar to that of physical entropy also. Furthermore, we study the similarity and difference between physical entropy and information entropy and the possible unification of the two statistical entropies, and discuss the relationship among the principle of entropy increase, the principle of equilibrium maximum entropy and the principle of maximum information entropy as well as the connection between them and the entropy evolution equation.

  16. On the Raychaudhuri equation

    Indian Academy of Sciences (India)

    George F R Ellis

    2007-07-01

    The Raychaudhuri equation is central to the understanding of gravitational attraction in astrophysics and cosmology, and in particular underlies the famous singularity theorems of general relativity theory. This paper reviews the derivation of the equation, and its significance in cosmology.

  17. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2014-01-01

    A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or

  18. Renormalizing Partial Differential Equations

    OpenAIRE

    Bricmont, J.; Kupiainen, A.

    1994-01-01

    In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.

  19. Ordinary differential equations

    CERN Document Server

    Greenberg, Michael D

    2014-01-01

    Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

  20. The Pseudo-Maxwell Equations Revisited

    Science.gov (United States)

    Stavroudis, Orestes N.

    1982-02-01

    The so-called pseudo-Maxwell are a set of partial differential eauations that strongly resemble the Maxwell equations, yet are based only on Fermat's principle, the idea of an orthotomic system of rays, and certain theorems from differential gecmetry. From Fermat's principle, applying the Euler equation from the variational calculus, one obtains the ray equation whose solutions describe ray paths in an inhomogeneous medium. We define an aggregate of such rays as an orthotomic system if it is possible to find a sur-face orthogonal to all rays in the aggregate. Making use of the Frenet equations from differential geometry, one may derive relationships between certain geometrical vectors and their derivatives. These are the pseudo-Maxwell equations. Their existence is' paradoxical. Are they merely a mathematical artifact, an accidental quirk of the notation we are accustomed to use? Or do they indicate that there is more geometry lurking in the physics of electricity and magnetism than we ever dreamed of in our philosophies?

  1. GENERAL PRINCIPLES OF LAW

    Directory of Open Access Journals (Sweden)

    Elena ANGHEL

    2016-05-01

    Full Text Available According to Professor Djuvara “law can be a science, and legal knowledge can also become science when, referring to a number as large as possible of acts of those covered by law, sorts and connects them by their essential characters upon legal concepts or principles which are universally valid, just like the laws of nature”. The general principles of law take a privileged place in the positive legal order and represent the foundation of any legal construction. The essence of the legal principles resides in their generality. In respect of the term “general”, Franck Moderne raised the question on the degree of generality used in order to define a principle as being general – at the level of an institution, of a branch of the law or at the level of the entire legal order. The purpose of this study is to find out the characteristics of law principles. In our opinion, four characteristics can be mentioned.

  2. A Principle of Intentionality

    Science.gov (United States)

    Turner, Charles K.

    2017-01-01

    The mainstream theories and models of the physical sciences, including neuroscience, are all consistent with the principle of causality. Wholly causal explanations make sense of how things go, but are inherently value-neutral, providing no objective basis for true beliefs being better than false beliefs, nor for it being better to intend wisely than foolishly. Dennett (1987) makes a related point in calling the brain a syntactic (procedure-based) engine. He says that you cannot get to a semantic (meaning-based) engine from there. He suggests that folk psychology revolves around an intentional stance that is independent of the causal theories of the brain, and accounts for constructs such as meanings, agency, true belief, and wise desire. Dennett proposes that the intentional stance is so powerful that it can be developed into a valid intentional theory. This article expands Dennett’s model into a principle of intentionality that revolves around the construct of objective wisdom. This principle provides a structure that can account for all mental processes, and for the scientific understanding of objective value. It is suggested that science can develop a far more complete worldview with a combination of the principles of causality and intentionality than would be possible with scientific theories that are consistent with the principle of causality alone. PMID:28223954

  3. Nonlinear unified equations for water waves propagating over uneven bottoms in the nearshore region

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Considering the continuous characteristics for water waves propagating over complex topography in the nearshore region, the unified nonlinear equations, based on the hypothesis for a typical uneven bottom, are presented by employing the Hamiltonian variational principle for water waves. It is verified that the equations include the following special cases: the extension of Airy's nonlinear shallow-water equations, the generalized mild-slope equation, the dispersion relation for the second-order Stokes waves and the higher order Boussinesq-type equations.

  4. Nonlinear Biharmonic Equations with Critical Potential

    Institute of Scientific and Technical Information of China (English)

    Hui XIONG; Yao Tian SHEN

    2005-01-01

    In this paper, we study two semilinear singular biharmonic equations: one with subcritical exponent and critical potential, another with sub-critical potential and critical exponent. By Pohozaev identity for singular solution, we prove there is no nontrivial solution for equations with critical exponent and critical potential. And by using the concentrate compactness principle and Mountain Pass theorem, respectively, we get two existence results for the two problems. Meanwhile,we have compared the changes of the critical dimensions in singular and non-singular cases, and we get an interesting result.

  5. Surveys in differential-algebraic equations III

    CERN Document Server

    Reis, Timo

    2015-01-01

    The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - Flexibility of DAE formulations - Reachability analysis and deterministic global optimization - Numerical linear algebra methods - Boundary value problems The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

  6. Surveys in differential-algebraic equations II

    CERN Document Server

    Reis, Timo

    2015-01-01

    The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - Observers for DAEs - DAEs in chemical processes - Optimal control of DAEs - DAEs from a functional-analytic viewpoint - Algebraic methods for DAEs The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

  7. Surveys in differential-algebraic equations IV

    CERN Document Server

    Reis, Timo

    2017-01-01

    The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs) which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - History of DAEs - DAE aspects of mechanical multibody systems - Model reduction of DAEs - Observability for DAEs - Numerical Analysis for DAEs The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

  8. Concentration phenomena in the semilinear parabolic equation

    Institute of Scientific and Technical Information of China (English)

    TAN; Zhong

    2001-01-01

    [1]Fujita, H., On the blowing up of solutions of the Chauch problem for u=Δu+u1+α, J. Fac. Sci. Univ. Tokyo Sect. I, 966, 3: 09.[2]Ni, W. -M., Sacks, P. E., Tavantzis, J., On the asymptotic behavior of solutions of certain quasilinear equations of parabolic type, J. Differential Equations, 984, 54: 97.[3]Cazenave, T., Lions, P. L., Solutions globales d'equations de la chaleur semilineaires, Comm. in Partial Differential Equations, 984, 9(0): 955.[4]Giga, Y., A bound for global solutions of semilinear heat equations, Commun. Math. Phys., 986, 03: 45.[5]Galaktionov, V., Vazquez, J. L., Continuation of blow-up solutions of nonlinear heat equations in several space dimensions, Comm. Pure Appl. Math., 997, 50: .[6]Rey, O., The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Func. Anal., 990, 89: .[7]Wei Juncheng, Asymptotic behavior of least energy solution to a semilinear Dirichlet problem near the critical exponent, J. Math. Soc. Japan, 998, 50(): 39.[8]Lions, P. L., The concentration-compactness principle in the calculus of variations, The limit case ,2, Rev. Mat. Iberoamerioana, 985, : 45, 45.[9]Brezis, H., Elliptic equations with limiting Sobolev exponents——the impact of topology, Commun. Pure and Appl. Math., 986, XXXXIX: S7.[10]Sacks, J., Uhlenbeck, K., The existence of minimal immersions of 2-spheres, Ann. Math., 98, 3: .[11]Zhu Xiping, Nontrivial solutions of quasilinear elliptic equation involving critical growth, Science in China (in Chinese), Ser. A, 988, (3): 225.[12]Pohozaev, S. I., Eigenfunctions of the equation -Δu+λf(u)=0, Soviet. Math. Dold., 965, 6: 408.[13]Gidas, B., Ni, W. -M., Nirenberg, L., Symmetry and related properties via the maximum principle, Comm. Math. Phys., 979, 68: 209.[14]Ni, W. -M., Sacks, P. E., Singular behaviour in nonlinear parabolic equations, Tran. of the AMS, 985, 287(2): 657.[15]Ni, W. -M., Sacks, P. E

  9. Novel natural convection heat sink design concepts from first principles

    OpenAIRE

    Fletcher, Derek E.

    2016-01-01

    Approved for public release; distribution is unlimited This was a two-part numerical study using ANSYS Fluent to develop novel heat sink concepts from first principles. The objective of this research was to highlight geometric structures that incorporate the principles of the stack effect to improve the heat transfer capability of a heat sink under natural convection. The first part investigated the heat transfer/fluid flow characteristics of vertically aligned tubes. The gaps between tube...

  10. Cultivating the Grapevine: An Analysis of Rumor Principles and Concepts

    Science.gov (United States)

    2015-12-01

    NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS Approved for public release; distribution is unlimited CULTIVATING THE...REPORT TYPE AND DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE CULTIVATING THE GRAPEVINE: AN ANALYSIS OF RUMOR PRINCIPLES AND CONCEPTS 5...Specifically, this study draws from a review of current and historical literature on rumor theory to distill a set of principles to guide the successful

  11. Basic Principles of Chromatography

    Science.gov (United States)

    Ismail, Baraem; Nielsen, S. Suzanne

    Chromatography has a great impact on all areas of analysis and, therefore, on the progress of science in general. Chromatography differs from other methods of separation in that a wide variety of materials, equipment, and techniques can be used. [Readers are referred to references (1-19) for general and specific information on chromatography.]. This chapter will focus on the principles of chromatography, mainly liquid chromatography (LC). Detailed principles and applications of gas chromatography (GC) will be discussed in Chap. 29. In view of its widespread use and applications, high-performance liquid chromatography (HPLC) will be discussed in a separate chapter (Chap. 28). The general principles of extraction are first described as a basis for understanding chromatography.

  12. Principles of musical acoustics

    CERN Document Server

    Hartmann, William M

    2013-01-01

    Principles of Musical Acoustics focuses on the basic principles in the science and technology of music. Musical examples and specific musical instruments demonstrate the principles. The book begins with a study of vibrations and waves, in that order. These topics constitute the basic physical properties of sound, one of two pillars supporting the science of musical acoustics. The second pillar is the human element, the physiological and psychological aspects of acoustical science. The perceptual topics include loudness, pitch, tone color, and localization of sound. With these two pillars in place, it is possible to go in a variety of directions. The book treats in turn, the topics of room acoustics, audio both analog and digital, broadcasting, and speech. It ends with chapters on the traditional musical instruments, organized by family. The mathematical level of this book assumes that the reader is familiar with elementary algebra. Trigonometric functions, logarithms and powers also appear in the book, but co...

  13. Generalized invariance principles and the theory of stability.

    Science.gov (United States)

    Lasalle, J. P.

    1971-01-01

    Description of some recent extensions of the invariance principle to more generalized dynamical systems where the state space is not locally compact and the flow is unique only in the forward direction of time. A sufficient condition for asymptotic stability of an invariant set is obtained which does not require that the Liapunov function be positive-definite. A recently developed generalized invariance principle is described which is applicable to functional differential equations, partial differential equations, and, in particular, to certain stability problems arising in thermoelasticity, viscoelasticity, and distributed nonlinear networks.

  14. The action principle for generalized fluid motion including gyroviscosity

    CERN Document Server

    Lingam, M

    2014-01-01

    A general set of fluid equations that allow for energy-conserving momentum transport by gyroscopic motion of fluid elements is obtained. The equations are produced by a class of action principles that yield a large subset of the known fluid and magnetofluid models, including gyroviscosity. Analysis of the action principle yields broad, model-independent results regarding the conservation laws of energy and linear and angular momenta. The formalism is illustrated by studying fluid models with intrinsic angular momentum that may appear in the contexts of condensed matter, biological, and other areas of physics.

  15. Three Principles of Water Flow in Soils

    Science.gov (United States)

    Guo, L.; Lin, H.

    2016-12-01

    Knowledge of water flow in soils is crucial to understanding terrestrial hydrological cycle, surface energy balance, biogeochemical dynamics, ecosystem services, contaminant transport, and many other Critical Zone processes. However, due to the complex and dynamic nature of non-uniform flow, reconstruction and prediction of water flow in natural soils remain challenging. This study synthesizes three principles of water flow in soils that can improve modeling water flow in soils of various complexity. The first principle, known as the Darcy's law, came to light in the 19th century and suggested a linear relationship between water flux density and hydraulic gradient, which was modified by Buckingham for unsaturated soils. Combining mass balance and the Buckingham-Darcy's law, L.A. Richards quantitatively described soil water change with space and time, i.e., Richards equation. The second principle was proposed by L.A. Richards in the 20th century, which described the minimum pressure potential needed to overcome surface tension of fluid and initiate water flow through soil-air interface. This study extends this principle to encompass soil hydrologic phenomena related to varied interfaces and microscopic features and provides a more cohesive explanation of hysteresis, hydrophobicity, and threshold behavior when water moves through layered soils. The third principle is emerging in the 21st century, which highlights the complex and evolving flow networks embedded in heterogeneous soils. This principle is summarized as: Water moves non-uniformly in natural soils with a dual-flow regime, i.e., it follows the least-resistant or preferred paths when "pushed" (e.g., by storms) or "attracted" (e.g., by plants) or "restricted" (e.g., by bedrock), but moves diffusively into the matrix when "relaxed" (e.g., at rest) or "touched" (e.g., adsorption). The first principle is a macroscopic view of steady-state water flow, the second principle is a microscopic view of interface

  16. Analytical solution of diffusion model for nutrient release from controlled release fertilizer

    Science.gov (United States)

    Ameenuddin Irfan, Sayed; Razali, Radzuan; KuShaari, KuZilati; Mansor, Nurlidia; Azeem, Babar

    2017-09-01

    An analytical method has been developed to solve the initial value problem which arises from Fick’s diffusion equation encountered in the modelling of the Controlled Release Fertilizers. The proposed analytical solution is developed using the modified Adomian decomposition method. This method does not require the discretization method, reliability and efficiency of this method is more and it also reduces the calculation time. The model has predicted the effect of granule radius and diffusion coefficient on the nutrient release and total release time of Controlled Release Fertilizer. Model has predicted that increase in the radius of granule reduces the release and vice versa in case of diffusion coefficient. Detailed understanding of these parameters helps in improved designing of Controlled Release Fertilizer.

  17. On Figures of speech, Cooperative Principle and Politeness Principle

    Institute of Scientific and Technical Information of China (English)

    于永丽; 朱丽萍

    2008-01-01

    To accomplish the communication efficiently and successfully, the people usually follow some certain principle in conversation. Grice named this principle as the cooperative principle. The politeness principle that Leech has developed can explain some phenomenon from a different perspective that the cooperative principle cannot. Nowadays, the use of the figures of speech is becoming more and more often. What we should pay attention to is the fact that the use of the figures of speech violates the cooperative principle, while following the politeness principle to a certain extent. And this paper aims to discuss the relationship among them, to provide some information for the readers.

  18. Mechanical engineering principles

    CERN Document Server

    Bird, John

    2014-01-01

    A student-friendly introduction to core engineering topicsThis book introduces mechanical principles and technology through examples and applications, enabling students to develop a sound understanding of both engineering principles and their use in practice. These theoretical concepts are supported by 400 fully worked problems, 700 further problems with answers, and 300 multiple-choice questions, all of which add up to give the reader a firm grounding on each topic.The new edition is up to date with the latest BTEC National specifications and can also be used on undergraduate courses in mecha

  19. Itch Management: General Principles.

    Science.gov (United States)

    Misery, Laurent

    2016-01-01

    Like pain, itch is a challenging condition that needs to be managed. Within this setting, the first principle of itch management is to get an appropriate diagnosis to perform an etiology-oriented therapy. In several cases it is not possible to treat the cause, the etiology is undetermined, there are several causes, or the etiological treatment is not effective enough to alleviate itch completely. This is also why there is need for symptomatic treatment. In all patients, psychological support and associated pragmatic measures might be helpful. General principles and guidelines are required, yet patient-centered individual care remains fundamental.

  20. Electrical principles 3 checkbook

    CERN Document Server

    Bird, J O

    2013-01-01

    Electrical Principles 3 Checkbook aims to introduce students to the basic electrical principles needed by technicians in electrical engineering, electronics, and telecommunications.The book first tackles circuit theorems, single-phase series A.C. circuits, and single-phase parallel A.C. circuits. Discussions focus on worked problems on parallel A.C. circuits, worked problems on series A.C. circuits, main points concerned with D.C. circuit analysis, worked problems on circuit theorems, and further problems on circuit theorems. The manuscript then examines three-phase systems and D.C. transients

  1. Principles of quantum electronics

    CERN Document Server

    Marcuse, Dietrich

    1980-01-01

    Principles of Quantum Electronics focuses on the concept of quantum electronics as the application of quantum theory to engineering problems. It examines the principles that govern specific quantum electronics devices and presents their theoretical applications to typical problems. Comprised of 10 chapters, this book starts with an overview of the Dirac formulation of quantum mechanics. This text then considers the derivation of the formalism of field quantization and discusses the properties of photons and phonons. Other chapters examine the interaction between the electromagnetic field and c

  2. Principles of engineering geology

    Energy Technology Data Exchange (ETDEWEB)

    Attewell, P.B.; Farmer, I.W.

    1976-01-01

    This book discusses basic principles as well as the practical applications of geological survey and analysis. Topics covered include the mechanical and physical response of rocks, rock masses and soils to changes in environmental conditions, and the principles of groundwater flow. The core of the book deals with the collection of geological and technical data, its subsequent analysis, and application to design. The combination of rigorous and detailed discussion of theory and well-illustrated examples made the book an indispensable reference source and ideal course book for both geologists and civil engineers.

  3. Principles of statistics

    CERN Document Server

    Bulmer, M G

    1979-01-01

    There are many textbooks which describe current methods of statistical analysis, while neglecting related theory. There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again fo

  4. The Modified Magnetohydrodynamical Equations

    Institute of Scientific and Technical Information of China (English)

    Evangelos Chaliasos

    2003-01-01

    After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similarfashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is doneby replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vectorpotential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vectoranalysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHDequations.

  5. Singular stochastic differential equations

    CERN Document Server

    Cherny, Alexander S

    2005-01-01

    The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

  6. Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Jianping Zhao

    2012-01-01

    Full Text Available An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving fractional differential equations.

  7. BIRKHOFF'S EQUATIONS AND GEOMETRICAL THEORY OF ROTATIONAL RELATIVISTIC SYSTEM

    Institute of Scientific and Technical Information of China (English)

    LUO SHAO-KAI; CHEN XIANG-WEI; FU JING-LI

    2001-01-01

    The Birkhoffian and Birkhoff's functions of a rotational relativistic system are constructed, the Pfaff action of rotational relativistic system is defined, the Pfaff-Birkhoff principle of a rotational relativistic system is given, and the Pfaff-Birkhoff-D'Alembert principles and Birkhoff's equations of rotational relativistic system are constructed. The geometrical description of a rotational relativistic system is studied, and the exact properties of Birkhoff's equations and their forms onR × T*M for a rotational relativistic system are obtained. The global analysis of Birkhoff's equations for a rotational relativistic system is studied, the global properties of autonomous, semi-autonomous and non-autonomous rotational relativistic Birkhoff's equations, and the geometrical properties of energy change for rotational relativistic Birkhoff's equations are given.

  8. Non-differentiable variational principles

    Science.gov (United States)

    Cresson, Jacky

    2005-07-01

    We develop a calculus of variations for functionals which are defined on a set of non-differentiable curves. We first extend the classical differential calculus in a quantum calculus, which allows us to define a complex operator, called the scale derivative, which is the non-differentiable analogue of the classical derivative. We then define the notion of extremals for our functionals and obtain a characterization in term of a generalized Euler-Lagrange equation. We finally prove that solutions of the Schrödinger equation can be obtained as extremals of a non-differentiable variational principle, leading to an extended Hamilton's principle of least action for quantum mechanics. We compare this approach with the scale relativity theory of Nottale, which assumes a fractal structure of space-time.Résumé (Principes variationnels non différentiable). Nous développons un calcul des variations pour des fonctionnelles définies sur un ensemble de courbes non différentiables. Pour cela, nous étendons le calcul différentiel classique, en calcul appelé calcul quantique, qui nous permet de définir un opérateur à valeur complexes, appelé dérivée d'échelle, qui est l'analogue non différentiable de la dérivée usuelle. On définit alors la notion d'extremale pour ces fonctionnelles pour lesquelles nous obtenons une caractérisation via une équation d'Euler-Lagrange généralisée. On prouve enfin que les solutions de l'équation de Schrödinger peuvent s'obtenir comme solution d'un problème variationnel non différentiable, étendant ainsi le principe de moindre action de Hamilton au cadre de la mécanique quantique. On discute enfin la connexion entre ce travail et la théorie de la relativité d'échelle développée par Nottale, et qui suppose une structure fractale de l'espace-temps.

  9. Interplay of Boltzmann equation and continuity equation for accelerated electrons in solar flares

    CERN Document Server

    Codispoti, Anna

    2015-01-01

    During solar flares a large amount of electrons are accelerated within the plasma present in the solar atmosphere. Accurate measurements of the motion of these electrons start becoming available from the analysis of hard X-ray imaging-spectroscopy observations. In this paper, we discuss the linearized perturbations of the Boltzmann kinetic equation describing an ensemble of electrons accelerated by the energy release occurring during solar flares. Either in the limit of high energy or at vanishing background temperature such an equation reduces to a continuity equation equipped with an extra force of stochastic nature. This stochastic force is actually described by the well known energy loss rate due to Coulomb collision with ambient particles, but, in order to match the collision kernel in the linearized Boltzmann equation it needs to be treated in a very specific manner. In the second part of the paper the derived continuity equation is solved with some hyperbolic techniques, and the obtained solution is wr...

  10. THE EIGENVALUE PROBLEM FOR THE LAPLACIAN EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    This article studies the Dirichlet eigenvalue problem for the Laplacian equations △u = -λu, x ∈Ω, u = 0, x ∈ (δ)Ω, where Ω (∩) Rn is a smooth bounded convex domain. By using the method of appropriate barrier function combined with the maximum principle, authors obtain a sharp lower bound of the difference of the first two eigenvalues for the Dirichlet eigenvalue problem. This study improves the result of S.T.Yau et al.

  11. Ground states for the fractional Schrodinger equation

    Directory of Open Access Journals (Sweden)

    Binhua Feng

    2013-05-01

    Full Text Available In this article, we show the existence of ground state solutions for the nonlinear Schrodinger equation with fractional Laplacian $$ (-Delta ^alpha u+ V(xu =lambda |u|^{p}uquadhbox{in $mathbb{R}^N$ for $alpha in (0,1$}. $$ We use the concentration compactness principle in fractional Sobolev spaces $H^alpha$ for $alpha in (0,1$. Our results generalize the corresponding results in the case $alpha =1$.

  12. Principles of Bridge Reliability

    DEFF Research Database (Denmark)

    Thoft-Christensen, Palle; Nowak, Andrzej S.

    The paper gives a brief introduction to the basic principles of structural reliability theory and its application to bridge engineering. Fundamental concepts like failure probability and reliability index are introduced. Ultimate as well as serviceability limit states for bridges are formulated...

  13. Principles of Proper Validation

    DEFF Research Database (Denmark)

    Esbensen, Kim; Geladi, Paul

    2010-01-01

    Validation in chemometrics is presented using the exemplar context of multivariate calibration/prediction. A phenomenological analysis of common validation practices in data analysis and chemometrics leads to formulation of a set of generic Principles of Proper Validation (PPV), which is based...

  14. On Weak Markov's Principle

    DEFF Research Database (Denmark)

    Kohlenbach, Ulrich Wilhelm

    2002-01-01

    We show that the so-called weak Markov's principle (WMP) which states that every pseudo-positive real number is positive is underivable in E-HA + AC. Since allows one to formalize (atl eastl arge parts of) Bishop's constructive mathematics, this makes it unlikely that WMP can be proved within the...

  15. The traveltime holographic principle

    KAUST Repository

    Huang, Y.

    2014-11-06

    Fermat\\'s interferometric principle is used to compute interior transmission traveltimes τpq from exterior transmission traveltimes τsp and τsq. Here, the exterior traveltimes are computed for sources s on a boundary B that encloses a volume V of interior points p and q. Once the exterior traveltimes are computed, no further ray tracing is needed to calculate the interior times τpq. Therefore this interferometric approach can be more efficient than explicitly computing interior traveltimes τpq by ray tracing. Moreover, the memory requirement of the traveltimes is reduced by one dimension, because the boundary B is of one fewer dimension than the volume V. An application of this approach is demonstrated with interbed multiple (IM) elimination. Here, the IMs in the observed data are predicted from the migration image and are subsequently removed by adaptive subtraction. This prediction is enabled by the knowledge of interior transmission traveltimes τpq computed according to Fermat\\'s interferometric principle. We denote this principle as the ‘traveltime holographic principle’, by analogy with the holographic principle in cosmology where information in a volume is encoded on the region\\'s boundary.

  16. Principles of Protocol Design

    DEFF Research Database (Denmark)

    Sharp, Robin

    This is a new and updated edition of a book first published in 1994. The book introduces the reader to the principles used in the construction of a large range of modern data communication protocols, as used in distributed computer systems of all kinds. The approach taken is rather a formal one...

  17. Principles of sound ecotoxicology.

    Science.gov (United States)

    Harris, Catherine A; Scott, Alexander P; Johnson, Andrew C; Panter, Grace H; Sheahan, Dave; Roberts, Mike; Sumpter, John P

    2014-03-18

    We have become progressively more concerned about the quality of some published ecotoxicology research. Others have also expressed concern. It is not uncommon for basic, but extremely important, factors to apparently be ignored. For example, exposure concentrations in laboratory experiments are sometimes not measured, and hence there is no evidence that the test organisms were actually exposed to the test substance, let alone at the stated concentrations. To try to improve the quality of ecotoxicology research, we suggest 12 basic principles that should be considered, not at the point of publication of the results, but during the experimental design. These principles range from carefully considering essential aspects of experimental design through to accurately defining the exposure, as well as unbiased analysis and reporting of the results. Although not all principles will apply to all studies, we offer these principles in the hope that they will improve the quality of the science that is available to regulators. Science is an evidence-based discipline and it is important that we and the regulators can trust the evidence presented to us. Significant resources often have to be devoted to refuting the results of poor research when those resources could be utilized more effectively.

  18. Principles of Cancer Screening.

    Science.gov (United States)

    Pinsky, Paul F

    2015-10-01

    Cancer screening has long been an important component of the struggle to reduce the burden of morbidity and mortality from cancer. Notwithstanding this history, many aspects of cancer screening remain poorly understood. This article presents a summary of basic principles of cancer screening that are relevant for researchers, clinicians, and public health officials alike. Published by Elsevier Inc.

  19. Geoethics and its principles

    Directory of Open Access Journals (Sweden)

    Szabó Štefan

    1997-12-01

    Full Text Available Mining and mineral processing belong to the activities with a mostly negative impact on the environment. GAIA hypothesis should help us to understand the basic mechanisms of planetary homeostasis, influenced by human activities. Principles of the geoethics should help to respect the limits of disturbances and loading capacity of ecosystems, which have the essential importance for our survival.

  20. Principles of economics textbooks

    DEFF Research Database (Denmark)

    Madsen, Poul Thøis

    2012-01-01

    Has the financial crisis already changed US principles of economics textbooks? Rather little has changed in individual textbooks, but taken as a whole ten of the best-selling textbooks suggest rather encompassing changes of core curriculum. A critical analysis of these changes shows how individual...

  1. Classical Equations for Quantum Systems

    CERN Document Server

    Gell-Mann, Murray; Gell-Mann, Murray; Hartle, James B.

    1993-01-01

    The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. We investigate the requirements for coarse grainings to yield decoherent sets of histories that are quasiclassical, i.e. such that the individual histories obey, with high probability, effective classical equations of motion interrupted continually by small fluctuations and occasionally by large ones. We discuss these requirements generally but study them specifically for coarse grainings of the type that follows a distinguished subset of a complete set of variables while ignoring the rest. More coarse graining is needed to achieve decoherence than would be suggested by naive arguments based on the uncertainty principle. Even coarser graining is required in the distinguished variables for them to have the necessary inertia to approach classical predictability in the presence of t...

  2. Principles of magnetostatics

    CERN Document Server

    Fernow, Richard C

    2016-01-01

    The subject of magnetostatics - the mathematical theory that describes the forces and fields resulting from the steady flow of electrical currents - has a long history. By capturing the basic concepts, and building towards the computation of magnetic fields, this book is a self-contained discussion of the major subjects in magnetostatics. Overviews of Maxwell's equations, the Poisson equation, and boundary value problems pave the way for dealing with fields from transverse, axial and periodic magnetic arrangements and assemblies of permanent magnets. Examples from accelerator and beam physics give up-to-date context to the theory. Furthermore, both complex contour integration and numerical techniques (including finite difference, finite element, and integral equation methods) for calculating magnetic fields are discussed in detail with plentiful examples. Both theoretical and practical information on carefully selected topics make this a one-stop reference for magnet designers, as well as for physics and elec...

  3. A practical course in differential equations and mathematical modeling

    CERN Document Server

    Ibragimov , Nail H

    2009-01-01

    A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame

  4. Positive solutions to logistic type equations with harvesting

    Science.gov (United States)

    Girão, Pedro; Tehrani, Hossein

    We use comparison principles, variational arguments and a truncation method to obtain positive solutions to logistic type equations with harvesting both in R and in a bounded domain Ω⊂R, with N⩾3, when the carrying capacity of the environment is not constant. By relaxing the growth assumption on the coefficients of the differential equation we derive a new equation which is easily solved. The solution of this new equation is then used to produce a positive solution of our original problem.

  5. Politeness Principle and Intercultural Communication

    Institute of Scientific and Technical Information of China (English)

    周宇岚

    2007-01-01

    There are many potential problems in intercultural communications. Politeness principle is very important in helping improving intercultural communications. But different cultures have various standard of politeness principle. This essay discusses the very different points of view on politeness principle between Chinese people and westerners, and studies how the context and settings affect the practice of politeness principle. At the ending of the essay, the guiding significance of politeness principle is p...

  6. The Pauli exclusion principle origin, verifications and applications

    CERN Document Server

    Kaplan, Ilya G

    2017-01-01

    This is the first scientific book devoted to the Pauli Exclusion Principle, which is a fundamental principle of quantum mechanics and is permanently applied in chemistry, physics, molecular biology and in physical astronomy. However, while the principle has been studied for more than 90 years, rigorous theoretical foundations still have not been established and many unsolved problems remain. Following an introduction and historical survey, this book discusses the still unresolved questions around this fundamental principle. For instance, why, according to the Pauli Exclusion Principle, are only symmetric and antisymmetric permutation symmetries for identical particles realized, while the Schrödinger equation is satisfied by functions with any permutation symmetry? Chapter 3 covers possible answers to this, while chapter 4 presents effective and elegant methods for finding the Pauli-allowed states in atomic, molecular and nuclear spectroscopy. Chapter 5 discusses parastatistics and fractional statistics, dem...

  7. Food Web Assembly Rules for Generalized Lotka-Volterra Equations.

    Directory of Open Access Journals (Sweden)

    Jan O Haerter

    2016-02-01

    Full Text Available In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help obtain coexistence in food webs. Hence, omnivory may be the glue that keeps communities intact even under extinction or ecological release of species.

  8. Food Web Assembly Rules for Generalized Lotka-Volterra Equations.

    Science.gov (United States)

    Haerter, Jan O; Mitarai, Namiko; Sneppen, Kim

    2016-02-01

    In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help obtain coexistence in food webs. Hence, omnivory may be the glue that keeps communities intact even under extinction or ecological release of species.

  9. An Effective Method for Seeking Conservation Laws of Partial Differential Equations

    Institute of Scientific and Technical Information of China (English)

    QIN Mao-Chang; MEI Feng-Xiang; FAN Gui-Hong

    2006-01-01

    This paper introduces an effective method for seeking localconservation laws of general partial differential equations (PDEs). The well-known variational principle does not involve in this method. Alternatively, the conservation laws can be derived from symmetries, which include the symmetries of the associated linearized equation of the PDEs,and the adjoint symmetries of the adjoint equation of the PDEs.

  10. APPLYING THE PRINCIPLES OF ACCOUNTING IN

    Directory of Open Access Journals (Sweden)

    NAGY CRISTINA MIHAELA

    2015-05-01

    Full Text Available The application of accounting principles (accounting principle on accrual basis; principle of business continuity; method consistency principle; prudence principle; independence principle; the principle of separate valuation of assets and liabilities; intangibility principle; non-compensation principle; the principle of substance over form; the principle of threshold significance to companies that are in bankruptcy procedure has a number of particularities. Thus, some principles cannot be applied to bankruptcy procedures (accounting principle on accrual basis, principle of business continuity, independence principle, intangibility principle and the principle of substance over form, some are available only in certain situations (method consistency principle and the prudence principle and others do not apply to bankruptcy (the principle of separate valuation of assets and liabilities; noncompensation principle and the principle of threshold significance.

  11. The new pooled cohort equations risk calculator

    DEFF Research Database (Denmark)

    Preiss, David; Kristensen, Søren L

    2015-01-01

    total cardiovascular risk score. During development of joint guidelines released in 2013 by the American College of Cardiology (ACC) and American Heart Association (AHA), the decision was taken to develop a new risk score. This resulted in the ACC/AHA Pooled Cohort Equations Risk Calculator. This risk...... disease and any measure of social deprivation. An early criticism of the Pooled Cohort Equations Risk Calculator has been its alleged overestimation of ASCVD risk which, if confirmed in the general population, is likely to result in statin therapy being prescribed to many individuals at lower risk than...

  12. Differential equations for dummies

    CERN Document Server

    Holzner, Steven

    2008-01-01

    The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.

  13. Nonlinear Dirac Equations

    Directory of Open Access Journals (Sweden)

    Wei Khim Ng

    2009-02-01

    Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

  14. Fractional Chemotaxis Diffusion Equations

    CERN Document Server

    Langlands, T A M

    2010-01-01

    We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.

  15. Huygens-Fresnel Principle in Superspace

    CERN Document Server

    de Gomes, H A

    2006-01-01

    We first roughly present a summary of the optico-mechanical analogy, which has always been so profitable in physics. Then we put forward a geometrodynamical formulation of gravity suitable to our intentions, both formally and conceptually. We present difficulties in some approaches to canonically quantize gravity which can be ammended by the idea put forward in this paper, which we introduce in the last section. It consists basically in trying to find an intermediary between the quantization step going from the classical superhamiltonian constraint to the Wheeler-DeWitt equation. This is accomplished by inputing interference beyond the WKB approximation, through a sort of Huygens-Fresnel Principle (HFP) in superspace. It turns out that we can derive wave-like character for both domains from this principle by allowing backward angles of diffraction, and what is more, approximate to a high degree of accuracy Feynman's path integral method in any domain.

  16. Multipartite cellular automata and the superposition principle

    Science.gov (United States)

    Elze, Hans-Thomas

    2016-05-01

    Cellular automata (CA) can show well known features of quantum mechanics (QM), such as a linear updating rule that resembles a discretized form of the Schrödinger equation together with its conservation laws. Surprisingly, a whole class of “natural” Hamiltonian CA, which are based entirely on integer-valued variables and couplings and derived from an action principle, can be mapped reversibly to continuum models with the help of sampling theory. This results in “deformed” quantum mechanical models with a finite discreteness scale l, which for l→0 reproduce the familiar continuum limit. Presently, we show, in particular, how such automata can form “multipartite” systems consistently with the tensor product structures of non-relativistic many-body QM, while maintaining the linearity of dynamics. Consequently, the superposition principle is fully operative already on the level of these primordial discrete deterministic automata, including the essential quantum effects of interference and entanglement.

  17. Optical potential from first principles

    CERN Document Server

    Rotureau, J; Hagen, G; Nunes, F; Papenbrock, T

    2016-01-01

    We develop a method to construct a microscopic optical potential from chiral interactions for nucleon-nucleus scattering at arbitrary energies. The optical potential is constructed by combining the Green's function approach with the coupled-cluster method. Using this approach, we perform a proof-of-principle calculation of the optical potential for the elastic neutron scattering on $^{16}{\\rm O}$. We verify the convergence of the optical potential and scattering phase shifts with respect to the model-space size and we also investigate the absorptive component of the optical potential. We find an almost negligible absorption at low-energies. To shed light on this result, we computed excited states of $^{16}{\\rm O}$ using equation-of-motion coupled-cluster with singles-and-doubles excitations and we found no low-lying excited states below 10~MeV. We conclude that the reduced absorption at low-energies can be attributed to a lack of correlations coming from the low-order cluster truncation in the employed couple...

  18. A two-zone method with an enhanced accuracy for a numerical solution of the diffusion equation

    Science.gov (United States)

    Cheon, Jin-Sik; Koo, Yang-Hyun; Lee, Byung-Ho; Oh, Je-Yong; Sohn, Dong-Seong

    2006-12-01

    A variational principle is applied to the diffusion equation to numerically obtain the fission gas release from a spherical grain. The two-zone method, originally proposed by Matthews and Wood, is modified to overcome its insufficient accuracy for a low release. The results of the variational approaches are examined by observing the gas concentration along the grain radius. At the early stage, the concentration near the grain boundary is higher than that at the inner points of the grain in the cases of the two-zone method as well as the finite element analysis with the number of the elements at as many as 10. The accuracy of the two-zone method is considerably enhanced by relocating the nodal points of the two zones. The trial functions are derived as a function of the released fraction. During the calculations, the number of degrees of freedom needs to be reduced to guarantee physically admissible concentration profiles. Numerical verifications are performed extensively. By taking a computational time comparable to the algorithm by Forsberg and Massih, the present method provides a solution with reasonable accuracy in the whole range of the released fraction.

  19. Drift-Diffusion Equation

    Directory of Open Access Journals (Sweden)

    K. Banoo

    1998-01-01

    equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.

  20. Developmental Partial Differential Equations

    OpenAIRE

    Duteil, Nastassia Pouradier; Rossi, Francesco; Boscain, Ugo; Piccoli, Benedetto

    2015-01-01

    In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's evolution. In other words, the manifold's evolution depends on the solution to the PDE, and vice versa the differential operator of the PDE depends on the manifold's geometry. DPDE is used to study a diffusion equation with source on a growing surface whose gro...

  1. Differential equations I essentials

    CERN Document Server

    REA, Editors of

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.

  2. Nonequilibrium thermodynamics of fuel cells: Heat release mechanisms and voltage

    Energy Technology Data Exchange (ETDEWEB)

    Wilemski, G.

    1980-01-01

    Nonequilibrium thermodynamics is used to analyze the spatial distribution of heat release mechanisms occurring in fuel cells operating under load in nonisothermal steady states. Novel contributions to heat release in the bulk electrolyte are found which are analogous to Peltier and Thomson effects in metallic conductors. Expresions for the heat release at individual electrodes are presented. An equation for the voltage of these cells is also derived.

  3. Ordinary differential equations

    CERN Document Server

    Pontryagin, Lev Semenovich

    1962-01-01

    Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.

  4. Quantum simulation of the Dirac equation

    Energy Technology Data Exchange (ETDEWEB)

    Gerritsma, Rene; Kirchmair, Gerhard; Zaehringer, Florian; Blatt, Rainer; Roos, Christian [Institut fuer Quantenoptik und Quanteninformation, 6020 Innsbruck (Austria); Solano, Enrique [Departamento de Quimica Fisica, Universidad del Pais Vasco - Euskal Herriko Unibertsitatea, Bilbao (Spain)

    2010-07-01

    The Dirac equation is a cornerstone in the history of physics, merging successfully quantum mechanics with special relativity, providing a natural description of the electron spin and predicting the existence of anti-matter. However, the Dirac equation also predicts some peculiar effects such as Klein's paradox and Zitterbewegung, an unexpected quivering motion of a free relativistic quantum particle first examined by Schroedinger. In this talk, we report on a proof-of-principle quantum simulation of the one-dimensional Dirac equation using a single trapped ion, which is set to behave as a free relativistic quantum particle. We measure as a function of time the particle position and study Zitterbewegung for different initial superpositions of positive and negative energy spinor states, as well as the cross-over from relativistic to nonrelativistic dynamics.

  5. Classical equations for quantum systems

    Energy Technology Data Exchange (ETDEWEB)

    Gell-Mann, M. (Theoretical Astrophysics Group (T-6), Los Alamos National Laboratory, Los Alamos, New Mexico 87545) (United States) (Santa Fe Institute, 1660 Old Pecos Trail, Santa Fe, New Mexico 87501); Hartle, J.B. (Department of Physics, University of California enSanta Barbara, Santa Barbara, (California) 93106)

    1993-04-15

    The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. A formulation of quantum mechanics is used that predicts probabilities for the individual members of a set of alternative coarse-grained histories that [ital decohere], which means that there is negligible quantum interference between the individual histories in the set. We investigate the requirements for coarse grainings to yield decoherent sets of histories that are quasiclassical, i.e., such that the individual histories obey, with high probability, effective classical equations of motion interrupted continually by small fluctuations and occasionally by large ones. We discuss these requirements generally but study them specifically for coarse grainings of the type that follows a distinguished subset of a complete set of variables while ignoring the rest. More coarse graining is needed to achieve decoherence than would be suggested by naive arguments based on the uncertainty principle. Even coarser graining is required in the distinguished variables for them to have the necessary inertia to approach classical predictability in the presence of the noise consisting of the fluctuations that typical mechanisms of decoherence produce. We describe the derivation of phenomenological equations of motion explicitly for a particular class of models.

  6. Principles of photonics

    CERN Document Server

    Liu, Jia-Ming

    2016-01-01

    With this self-contained and comprehensive text, students will gain a detailed understanding of the fundamental concepts and major principles of photonics. Assuming only a basic background in optics, readers are guided through key topics such as the nature of optical fields, the properties of optical materials, and the principles of major photonic functions regarding the generation, propagation, coupling, interference, amplification, modulation, and detection of optical waves or signals. Numerous examples and problems are provided throughout to enhance understanding, and a solutions manual containing detailed solutions and explanations is available online for instructors. This is the ideal resource for electrical engineering and physics undergraduates taking introductory, single-semester or single-quarter courses in photonics, providing them with the knowledge and skills needed to progress to more advanced courses on photonic devices, systems and applications.

  7. Principles of geodynamics

    CERN Document Server

    Scheidegger, Adrian E

    1982-01-01

    Geodynamics is commonly thought to be one of the subjects which provide the basis for understanding the origin of the visible surface features of the Earth: the latter are usually assumed as having been built up by geodynamic forces originating inside the Earth ("endogenetic" processes) and then as having been degrad­ ed by geomorphological agents originating in the atmosphere and ocean ("exogenetic" agents). The modem view holds that the sequence of events is not as neat as it was once thought to be, and that, in effect, both geodynamic and geomorphological processes act simultaneously ("Principle of Antagonism"); however, the division of theoretical geology into the principles of geodynamics and those of theoretical geomorphology seems to be useful for didactic purposes. It has therefore been maintained in the present writer's works. This present treatise on geodynamics is the first part of the author's treatment of theoretical geology, the treatise on Theoretical Geomorphology (also published by the Sprin...

  8. Principles of Fourier analysis

    CERN Document Server

    Howell, Kenneth B

    2001-01-01

    Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author''s development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based ...

  9. Principles of systems science

    CERN Document Server

    Mobus, George E

    2015-01-01

    This pioneering text provides a comprehensive introduction to systems structure, function, and modeling as applied in all fields of science and engineering. Systems understanding is increasingly recognized as a key to a more holistic education and greater problem solving skills, and is also reflected in the trend toward interdisciplinary approaches to research on complex phenomena. The subject of systems science, as a basis for understanding the components and drivers of phenomena at all scales, should be viewed with the same importance as a traditional liberal arts education. Principles of Systems Science contains many graphs, illustrations, side bars, examples, and problems to enhance understanding. From basic principles of organization, complexity, abstract representations, and behavior (dynamics) to deeper aspects such as the relations between information, knowledge, computation, and system control, to higher order aspects such as auto-organization, emergence and evolution, the book provides an integrated...

  10. Common Principles and Multiculturalism

    Science.gov (United States)

    Zahedi, Farzaneh; Larijani, Bagher

    2009-01-01

    Judgment on rightness and wrongness of beliefs and behaviors is a main issue in bioethics. Over centuries, big philosophers and ethicists have been discussing the suitable tools to determine which act is morally sound and which one is not. Emerging the contemporary bioethics in the West has resulted in a misconception that absolute westernized principles would be appropriate tools for ethical decision making in different cultures. We will discuss this issue by introducing a clinical case. Considering various cultural beliefs around the world, though it is not logical to consider all of them ethically acceptable, we can gather on some general fundamental principles instead of going to the extremes of relativism and absolutism. Islamic teachings, according to the presented evidence in this paper, fall in with this idea. PMID:23908720

  11. Principles of harmonic analysis

    CERN Document Server

    Deitmar, Anton

    2014-01-01

    This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.

  12. Principles of Mobile Communication

    CERN Document Server

    Stüber, Gordon L

    2012-01-01

    This mathematically rigorous overview of physical layer wireless communications is now in a third, fully revised and updated edition. Along with coverage of basic principles sufficient for novice students, the volume includes plenty of finer details that will satisfy the requirements of graduate students aiming to research the topic in depth. It also has a role as a handy reference for wireless engineers. The content stresses core principles that are applicable to a broad range of wireless standards. Beginning with a survey of the field that introduces an array of issues relevant to wireless communications and which traces the historical development of today’s accepted wireless standards, the book moves on to cover all the relevant discrete subjects, from radio propagation to error probability performance and cellular radio resource management. A valuable appendix provides a succinct and focused tutorial on probability and random processes, concepts widely used throughout the book. This new edition, revised...

  13. Principles of mobile communication

    CERN Document Server

    Stüber, Gordon L

    2017-01-01

    This mathematically rigorous overview of physical layer wireless communications is now in a 4th, fully revised and updated edition. The new edition features new content on 4G cellular systems, 5G cellular outlook, bandpass signals and systems, and polarization, among many other topics, in addition to a new chapters on channel assignment techniques. Along with coverage of fundamentals and basic principles sufficient for novice students, the volume includes finer details that satisfy the requirements of graduate students aiming to conduct in-depth research. The book begins with a survey of the field, introducing issues relevant to wireless communications. The book moves on to cover relevant discrete subjects, from radio propagation, to error probability performance, and cellular radio resource management. An appendix provides a tutorial on probability and random processes. The content stresses core principles that are applicable to a broad range of wireless standards. New examples are provided throughout the bo...

  14. Common principles and multiculturalism.

    Science.gov (United States)

    Zahedi, Farzaneh; Larijani, Bagher

    2009-01-01

    Judgment on rightness and wrongness of beliefs and behaviors is a main issue in bioethics. Over centuries, big philosophers and ethicists have been discussing the suitable tools to determine which act is morally sound and which one is not. Emerging the contemporary bioethics in the West has resulted in a misconception that absolute westernized principles would be appropriate tools for ethical decision making in different cultures. We will discuss this issue by introducing a clinical case. Considering various cultural beliefs around the world, though it is not logical to consider all of them ethically acceptable, we can gather on some general fundamental principles instead of going to the extremes of relativism and absolutism. Islamic teachings, according to the presented evidence in this paper, fall in with this idea.

  15. Principles of mathematical modeling

    CERN Document Server

    Dym, Clive

    2004-01-01

    Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...

  16. Toxics Release Inventory (TRI)

    Data.gov (United States)

    U.S. Environmental Protection Agency — The Toxics Release Inventory (TRI) is a dataset compiled by the U.S. Environmental Protection Agency (EPA). It contains information on the release and waste...

  17. Computational principles of memory.

    Science.gov (United States)

    Chaudhuri, Rishidev; Fiete, Ila

    2016-03-01

    The ability to store and later use information is essential for a variety of adaptive behaviors, including integration, learning, generalization, prediction and inference. In this Review, we survey theoretical principles that can allow the brain to construct persistent states for memory. We identify requirements that a memory system must satisfy and analyze existing models and hypothesized biological substrates in light of these requirements. We also highlight open questions, theoretical puzzles and problems shared with computer science and information theory.

  18. Principles of artificial intelligence

    CERN Document Server

    Nilsson, Nils J

    1980-01-01

    A classic introduction to artificial intelligence intended to bridge the gap between theory and practice, Principles of Artificial Intelligence describes fundamental AI ideas that underlie applications such as natural language processing, automatic programming, robotics, machine vision, automatic theorem proving, and intelligent data retrieval. Rather than focusing on the subject matter of the applications, the book is organized around general computational concepts involving the kinds of data structures used, the types of operations performed on the data structures, and the properties of th

  19. A correspondence principle

    Science.gov (United States)

    Hughes, Barry D.; Ninham, Barry W.

    2016-02-01

    A single mathematical theme underpins disparate physical phenomena in classical, quantum and statistical mechanical contexts. This mathematical "correspondence principle", a kind of wave-particle duality with glorious realizations in classical and modern mathematical analysis, embodies fundamental geometrical and physical order, and yet in some sense sits on the edge of chaos. Illustrative cases discussed are drawn from classical and anomalous diffusion, quantum mechanics of single particles and ideal gases, quasicrystals and Casimir forces.

  20. The Principle of Proportionality

    DEFF Research Database (Denmark)

    Bennedsen, Morten; Meisner Nielsen, Kasper

    2005-01-01

    Recent policy initiatives within the harmonization of European company laws have promoted a so-called "principle of proportionality" through proposals that regulate mechanisms opposing a proportional distribution of ownership and control. We scrutinize the foundation for these initiatives...... in relationship to the process of harmonization of the European capital markets.JEL classifications: G30, G32, G34 and G38Keywords: Ownership Structure, Dual Class Shares, Pyramids, EU companylaws....

  1. The Principle of Proportionality

    DEFF Research Database (Denmark)

    Bennedsen, Morten; Meisner Nielsen, Kasper

    2005-01-01

    Recent policy initiatives within the harmonization of European company laws have promoted a so-called "principle of proportionality" through proposals that regulate mechanisms opposing a proportional distribution of ownership and control. We scrutinize the foundation for these initiatives...... in relationship to the process of harmonization of the European capital markets.JEL classifications: G30, G32, G34 and G38Keywords: Ownership Structure, Dual Class Shares, Pyramids, EU companylaws....

  2. Principles of electrical safety

    CERN Document Server

    Sutherland, Peter E

    2015-01-01

    Principles of Electrical Safety discusses current issues in electrical safety, which are accompanied by series' of practical applications that can be used by practicing professionals, graduate students, and researchers. .  Provides extensive introductions to important topics in electrical safety Comprehensive overview of inductance, resistance, and capacitance as applied to the human body Serves as a preparatory guide for today's practicing engineers

  3. On Rayleigh's Principle

    DEFF Research Database (Denmark)

    Andersen, Kurt Munk

    1997-01-01

    Rayleigh's principle expresses that the smallest eigenvalue of a regular Sturm-Liouville problem with regular boundary conditions is the minimum value of a certain functional, the so called Rayleigh's quotient, and that this value is attained at the corresponding eigenfunctions only. This can...... be proved by means of more advanced methods. However, it turns out that there is an elementary proof, which is presented in the report....

  4. PREFERENCE, PRINCIPLE AND PRACTICE

    DEFF Research Database (Denmark)

    Skovsgaard, Morten; Bro, Peter

    2011-01-01

    journalists justify themselves and their work. This article introduces an analytical framework for understanding legitimacy in a journalistic context. A framework based on a review of material ranging from historical accounts to research articles, and book-length studies. The framework comprises three...... distinct, but interconnected categories*preference, principle, and practice. Through this framework, historical attempts to justify journalism and journalists are described and discussed in the light of the present challenges for the profession....

  5. PRINCIPLES OF CHANGE MANAGEMENT

    Directory of Open Access Journals (Sweden)

    Eduard IONESCU

    2014-03-01

    Full Text Available Change management process needs to define certain principles and apply them effectively in order to achieve the best possible results. Understanding how certain members of the organization react to change will greatly influence how they will cope with the implementation of change, how their work will be productive during and after the implementation of change and that will be the result the end of the process.

  6. PREFERENCE, PRINCIPLE AND PRACTICE

    DEFF Research Database (Denmark)

    Skovsgaard, Morten; Bro, Peter

    2011-01-01

    Legitimacy has become a central issue in journalism, since the understanding of what journalism is and who journalists are has been challenged by developments both within and outside the newsrooms. Nonetheless, little scholarly work has been conducted to aid conceptual clarification as to how jou...... distinct, but interconnected categories*preference, principle, and practice. Through this framework, historical attempts to justify journalism and journalists are described and discussed in the light of the present challenges for the profession....

  7. Excitability in a stochastic differential equation model for calcium puffs.

    Science.gov (United States)

    Rüdiger, S

    2014-06-01

    Calcium dynamics are essential to a multitude of cellular processes. For many cell types, localized discharges of calcium through small clusters of intracellular channels are building blocks for all spatially extended calcium signals. Because of the large noise amplitude, the validity of noise-approximating model equations for this system has been questioned. Here we revisit the master equations for local calcium release, examine the multiple scales of calcium concentrations in the cluster domain, and derive adapted stochastic differential equations. We show by comparison of discrete and continuous trajectories that the Langevin equations can be made consistent with the master equations even for very small channel numbers. In its deterministic limit, the model reveals that excitability, a dynamical phenomenon observed in many natural systems, is at the core of calcium puffs. The model also predicts a bifurcation from transient to sustained release which may link local and global calcium signals in cells.

  8. Bioavailability of sustained-release theophylline formulations.

    Science.gov (United States)

    Bonora Regazzi, M; Rondanelli, R; Vidale, E; Cristiani, D

    1983-05-01

    Sustained-release formulations of theophylline as well as of other drugs are designed to effect a delayed but constant release of the active principle in the gastrointestinal tract, thus ensuring more prolonged blood level curves. This study was made to assess the bioavailability of two sustained-release microencapsulated formulations and one sustained-release Diffucaps formulation, in comparison with an equivalent dose of theophylline solution. As regards bioavailability, none of the three formulations differed significantly from the reference formulation. The blood levels at steady state were estimated on the basis of data obtained after a single-dose study. All three sustained release formulations showed good results after prolonged administration in terms of peaks and troughs. The time duration at which the theophylline plasma levels remain higher than 75% of the maximum steady-state levels, following 12-h dosing interval, was evaluated: for the sustained-release microencapsulated formulations this time duration reaches 100% of the dosing interval. A multiple-dose administration of the sustained-release formulations used in this study should guarantee almost complete time coverage, with blood levels sharply exceeding the minimum threshold level of the theophylline therapeutic range.

  9. Principled Missing Data Treatments.

    Science.gov (United States)

    Lang, Kyle M; Little, Todd D

    2016-04-04

    We review a number of issues regarding missing data treatments for intervention and prevention researchers. Many of the common missing data practices in prevention research are still, unfortunately, ill-advised (e.g., use of listwise and pairwise deletion, insufficient use of auxiliary variables). Our goal is to promote better practice in the handling of missing data. We review the current state of missing data methodology and recent missing data reporting in prevention research. We describe antiquated, ad hoc missing data treatments and discuss their limitations. We discuss two modern, principled missing data treatments: multiple imputation and full information maximum likelihood, and we offer practical tips on how to best employ these methods in prevention research. The principled missing data treatments that we discuss are couched in terms of how they improve causal and statistical inference in the prevention sciences. Our recommendations are firmly grounded in missing data theory and well-validated statistical principles for handling the missing data issues that are ubiquitous in biosocial and prevention research. We augment our broad survey of missing data analysis with references to more exhaustive resources.

  10. PRINCIPLES OF ANIMAL BREEDING

    Directory of Open Access Journals (Sweden)

    Sonja Jovanovac

    2014-06-01

    Full Text Available University textbook Principles of Animal Breeding is intended for students of agriculture and veterinary medicine. The material is the adapted curricula of undergraduate and graduate level studies in the framework of which the modules Principles of animal breeding as well as Basics of genetics and selection of animals attended are listened. The textbook contains 14 chapters and a glossary of terms. Its concept enables combining fundamental and modern knowledge in the breeding and selection of animals based on balanced and quality manner. The textbook material can be divided into several thematic sections. The first one relates to the classical notions of domestic animals breeding such as the history of breeding, domestication, breed, hereditary and non-hereditary variability and description of general and production traits. The second section focuses on the basic concepts in population and quantitative genetics, as well as biometrics. The third unit is dedicated to the principles of selection and domestic animals improving. The fourth unit relates to the current concepts and objectives of the molecular markers use in domestic animals selection and breeding. The above material has been submitted to the Croatian universities, but so far it has not been published as a textbook. The Ministry of Science, Education and Sports of Republic of Croatia approved financial support for the textbook publication.

  11. Building an Efficient Model for Afterburn Energy Release

    Energy Technology Data Exchange (ETDEWEB)

    Alves, S; Kuhl, A; Najjar, F; Tringe, J; McMichael, L; Glascoe, L

    2012-02-03

    Many explosives will release additional energy after detonation as the detonation products mix with the ambient environment. This additional energy release, referred to as afterburn, is due to combustion of undetonated fuel with ambient oxygen. While the detonation energy release occurs on a time scale of microseconds, the afterburn energy release occurs on a time scale of milliseconds with a potentially varying energy release rate depending upon the local temperature and pressure. This afterburn energy release is not accounted for in typical equations of state, such as the Jones-Wilkins-Lee (JWL) model, used for modeling the detonation of explosives. Here we construct a straightforward and efficient approach, based on experiments and theory, to account for this additional energy release in a way that is tractable for large finite element fluid-structure problems. Barometric calorimeter experiments have been executed in both nitrogen and air environments to investigate the characteristics of afterburn for C-4 and other materials. These tests, which provide pressure time histories, along with theoretical and analytical solutions provide an engineering basis for modeling afterburn with numerical hydrocodes. It is toward this end that we have constructed a modified JWL equation of state to account for afterburn effects on the response of structures to blast. The modified equation of state includes a two phase afterburn energy release to represent variations in the energy release rate and an afterburn energy cutoff to account for partial reaction of the undetonated fuel.

  12. Basic economic principles of road pricing: From theory to applications

    NARCIS (Netherlands)

    Rouwendal, J.; Verhoef, E.T.

    2006-01-01

    This paper presents, a non-technical introduction to the economic principles relevant for transport pricing design and analysis. We provide the basic rationale behind pricing of externalities, discuss why simple Pigouvian tax rules that equate charges to marginal external costs are not optimal in 's

  13. Basic economic principles of road pricing: From theory to applications

    NARCIS (Netherlands)

    Rouwendal, J.; Verhoef, E.T.

    2006-01-01

    This paper presents, a non-technical introduction to the economic principles relevant for transport pricing design and analysis. We provide the basic rationale behind pricing of externalities, discuss why simple Pigouvian tax rules that equate charges to marginal external costs are not optimal in 's

  14. The Calculus of Variations and the Ideal MHD Energy Principle

    Science.gov (United States)

    Schnack, Dalton D.

    In Lecture 22, we showed that the ideal MHD force operator is self-adjoint and suggested that this allowed a formulation in which the stability of a system could be determined without solving a differential equation. Going further requires a little background in the calculus of variations. In the lecture we begin this discussion,1 and formulate the ideal MHD energy principle.

  15. Variational principles for stochastic fluid dynamics.

    Science.gov (United States)

    Holm, Darryl D

    2015-04-08

    This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler-Boussinesq and quasi-geostropic approximations.

  16. The Wouthuysen equation

    NARCIS (Netherlands)

    Hazewinkel, M.

    1995-01-01

    Dedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an original space-

  17. Functional Cantor equation

    Science.gov (United States)

    Shabat, A. B.

    2016-12-01

    We consider the class of entire functions of exponential type in relation to the scattering theory for the Schrödinger equation with a finite potential that is a finite Borel measure. These functions have a special self-similarity and satisfy q-difference functional equations. We study their asymptotic behavior and the distribution of zeros.

  18. Dissipative Boussinesq equations

    CERN Document Server

    Dutykh, D; Dias, Fr\\'{e}d\\'{e}ric; Dutykh, Denys

    2007-01-01

    The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated numerically.

  19. Navier-Stokes equation

    Directory of Open Access Journals (Sweden)

    Hannelore Breckner

    2000-01-01

    Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.

  20. Differential Equation of Equilibrium

    African Journals Online (AJOL)

    user

    than the classical method in the solution of the aforementioned differential equation. Keywords: ... present a successful approximation of shell ... displacement function. .... only applicable to cylindrical shell subject to ..... (cos. 4. 4. 4. 3 β. + β. + β. -. = β. - β x x e ex. AL. xA w. Substituting equations (29); (30) and (31) into.

  1. The Action Principle in Relativistic Cosmology and the Cosmological Constant Problem

    CERN Document Server

    Totani, Tomonori

    2015-01-01

    Deriving the Einstein field equations (EFE) with matter fluid from the action principle includes a rather strange step; the rest-frame mass density must also be varied at the same time with metric $g_{\\mu\

  2. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2004-01-01

    This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...

  3. The action principle for generalized fluid motion including gyroviscosity

    Energy Technology Data Exchange (ETDEWEB)

    Lingam, M., E-mail: manasvi@physics.utexas.edu; Morrison, P.J., E-mail: morrison@physics.utexas.edu

    2014-11-07

    Highlights: • Method for constructing action principles for a diverse class of fluids with gyroscopic momentum transport is described. • General criteria for the conservation of momentum and angular momentum via Noether's theorem are obtained. • Fluids with intrinsic angular momentum are built as an illustration of the method. - Abstract: A general set of fluid equations that allow for energy-conserving momentum transport by gyroscopic motion of fluid elements is obtained. The equations are produced by a class of action principles that yield a large subset of the known fluid and magnetofluid models, including gyroviscosity. Analysis of the action principle yields broad, model-independent results regarding the conservation laws of energy and linear and angular momenta. The formalism is illustrated by studying fluid models with intrinsic angular momentum that may appear in the contexts of condensed matter, biological, and other areas of physics.

  4. Principles of visual attention

    DEFF Research Database (Denmark)

    Bundesen, Claus; Habekost, Thomas

    The nature of attention is one of the oldest and most central problems in psychology. A huge amount of research has been produced on this subject in the last half century, especially on attention in the visual modality, but a general explanation has remained elusive. Many still view attention...... research as a field that is fundamentally fragmented. This book takes a different perspective and presents a unified theory of visual attention: the TVA model. The TVA model explains the many aspects of visual attention by just two mechanisms for selection of information: filtering and pigeonholing....... These mechanisms are described in a set of simple equations, which allow TVA to mathematically model a large number of classical results in the attention literature. The theory explains psychological and neuroscientific findings by the same equations; TVA is a complete theory of visual attention, linking mind...

  5. Variational formulation of ideal fluid flows according to gauge principle

    Energy Technology Data Exchange (ETDEWEB)

    Kambe, Tsutomu [IDS, Higashi-yama 2-11-3, Meguro-ku, Tokyo 153-0043 (Japan)], E-mail: kambe@ruby.dti.ne.jp

    2008-06-30

    On the basis of the gauge principle of field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized by symmetries of translation and rotation. The rotational transformations are regarded as gauge transformations as well as the translational ones. In addition to the Lagrangians representing the translation symmetry, a structure of rotation symmetry is equipped with a Lagrangian {lambda}{sub A} including the vorticity and a vector potential bilinearly. Euler's equation of motion is derived from variations according to the action principle. In addition, the equations of continuity and entropy are derived from the variations. Equations of conserved currents are deduced as the Noether theorem in the space of Lagrangian coordinate a. Without {lambda}{sub A}, the action principle results in the Clebsch solution with vanishing helicity. The Lagrangian {lambda}{sub A} yields non-vanishing vorticity and provides a source term of non-vanishing helicity. The vorticity equation is derived as an equation of the gauge field, and the {lambda}{sub A} characterizes topology of the field. The present formulation is comprehensive and provides a consistent basis for a unique transformation between the Lagrangian a space and the Eulerian x space. In contrast, with translation symmetry alone, there is an arbitrariness in the transformation between these spaces.

  6. Einstein's first gravitational field equation 101 years latter

    CERN Document Server

    Betancort-Rijo, Juan

    2014-01-01

    We review and strengthen the arguments given by Einstein to derive his first gravitational field equation for static fields and show that, although it was ultimately rejected, it follows from General Relativity (GR) for negligible pressure. Using this equation and considerations folowing directly from the equivalence principle (EP), we show how Schwarzschild metric and other vacum metrics can be obtained immediately. With this results and some basic principles, we obtain the metric in the general spherically symmetric case and the corresponding hydrostatic equilibrium equation. For this metrics we obtain the motion equations in a simple and exact manner that clearly shows the three sources of difference (implied by various aspects of the EP) with respect to the Newtonian case and use them to study the classical tests of GR. We comment on the origin of the problems of Einstein first theory of gravity and discuss how, by removing it the theory could be made consistent and extended to include rotations, we also ...

  7. Leech's Politeness Principle

    Institute of Scientific and Technical Information of China (English)

    李日

    2011-01-01

    Leech thinks that people sometimes disobey Grice's Cooperative Principle in order to express themselves politely in interaction.Therefore he postulates the Politeness Principle and believes that it should be obeyed in communication.This paper analyzes his

  8. ELECTROMAGNETIC RELEASE MECHANISM

    Science.gov (United States)

    Michelson, C.

    1960-09-13

    An electromagnetic release mechanism is offered that may be used, for example, for supporting a safety rod for a nuclear reactor. The release mechanism is designed to have a large excess holding force and a rapid, uniform, and dependable release. The fast release is accomplished by providing the electromagnet with slotttd polts separated by an insulating potting resin, and by constructing the poles with a ferro-nickel alloy. The combination of these two features materially reduces the eddy current power density whenever the magnetic field changes during a release operation. In addition to these features, the design of the armature is such as to provide ready entrance of fluid into any void that might tend to form during release of the armature. This also improves the release time for the mechanism. The large holding force for the mechanism is accomplished by providing a small, selected, uniform air gap between the inner pole piece and the armature.

  9. Speed Gradient and MaxEnt Principles for Shannon and Tsallis Entropies

    OpenAIRE

    Fradkov, Alexander L.; Shalymov, Dmitry S.

    2015-01-01

    In this paper we consider dynamics of non-stationary processes that follow the MaxEnt principle. We derive a set of equations describing dynamics of a system for Shannon and Tsallis entropies. Systems with discrete probability distribution are considered under mass conservation and energy conservation constraints. The existence and uniqueness of solution are established and asymptotic stability of the equilibrium is proved. Equations are derived based on the speed-gradient principle originate...

  10. Release Characteristics of Different N Forms in an Uncoated Slow/Controlled Release Compound Fertilizer

    Institute of Scientific and Technical Information of China (English)

    DONG Yan; WANG Zheng-yin

    2007-01-01

    This study examined the release characteristics of different N forms in an uncoated slow/controlled-release compound fertilizer (UCRF) and the N uptake and N-use efficiency by rice plants. Water dissolution, soil leaching, and pot experiments were employed. The dynamics of N release from the UCRF could be quantitatively described by three equations: the first-order kinetics equation [Nt = N0 (1-e-kt)], Elovich equation (Nt = a + blnt), and parabola equation (Nt = a + bt0.5), with the best fitting by the first-order kinetics equation for different N (r= 0.9569**-0.9999**). The release potentials (N0 values estimated by the first-order kinetics equation) of different N in the UCRF decreased in the order of total N > DON > urea-N > NH4+-N > NO3--N in water, and total N > NH4+-N > DON > urea-N > NO3--N in soil, respectively,being in accordance with cumulative amounts of N release. The constants of N release rate (k values and b values) for different N forms were in decreasing order of total N > DON > NH4+-N > NO3--N in water, whereas the k values were urea-N >DON > NH4+-N > total N > NO3--N, and the b values were total N > NH4+-N > DON > NO3--N > urea-N in soil. Compared with a common compound fertilizer, the N-use efficiency, N-agronomy efficiency, and N-physiological efficiency of the UCRF were increased by 11.4%, 8.32 kg kg-1, and 5.17 kg kg-1, respectively. The ratios of different N to total N in the UCRF showed significant correlation with N uptake by rice plants. The findings showed that the first-order kinetics equation [Nt=N0(1-e-kt)] could be used to describe the release characteristics of different N forms in the fertilizer. The UCRF containing different N forms was more effective in facilitating N uptake by rice compared with the common compound fertilizer containing single urea-N form.

  11. Efficient reconstruction of contaminant release history

    Energy Technology Data Exchange (ETDEWEB)

    Alezander, Francis [Los Alamos National Laboratory; Anghel, Marian [Los Alamos National Laboratory; Gulbahce, Natali [NON LANL; Tartakovsky, Daniel [NON LANL

    2009-01-01

    We present a generalized hybrid Monte Carlo (GHMC) method for fast, statistically optimal reconstruction of release histories of reactive contaminants. The approach is applicable to large-scale, strongly nonlinear systems with parametric uncertainties and data corrupted by measurement errors. The use of discrete adjoint equations facilitates numerical implementation of GHMC, without putting any restrictions on the degree of nonlinearity of advection-dispersion-reaction equations that are used to described contaminant transport in the subsurface. To demonstrate the salient features of the proposed algorithm, we identify the spatial extent of a distributed source of contamination from concentration measurements of a reactive solute.

  12. Reaction-Multi Diffusion Model for Nutrient Release and Autocatalytic Degradation of PLA-Coated Controlled-Release Fertilizer

    Directory of Open Access Journals (Sweden)

    Sayed Ameenuddin Irfan

    2017-03-01

    Full Text Available A mathematical model for the reaction-diffusion equation is developed to describe the nutrient release profiles and degradation of poly(lactic acid (PLA-coated controlled-release fertilizer. A multi-diffusion model that consists of coupled partial differential equations is used to study the diffusion and chemical reaction (autocatalytic degradation simultaneously. The model is solved using an analytical-numerical method. Firstly, the model equation is transformed using the Laplace transformation as the Laplace transform cannot be inverted analytically. Numerical inversion of the Laplace transform is used by employing the Zakian method. The solution is useful in predicting the nutrient release profiles at various diffusivity, concentration of extraction medium, and reaction rates. It also helps in explaining the transformation of autocatalytic concentration in the coating material for various reaction rates, times of reaction, and reaction-multi diffusion. The solution is also applicable to the other biodegradable polymer-coated controlled-release fertilizers.

  13. Derivation of stable Burnett equations for rarefied gas flows

    Science.gov (United States)

    Singh, Narendra; Jadhav, Ravi Sudam; Agrawal, Amit

    2017-07-01

    A set of constitutive relations for the stress tensor and heat flux vector for the hydrodynamic description of rarefied gas flows is derived in this work. A phase density function consistent with Onsager's reciprocity principle and H theorem is utilized to capture nonequilibrium thermodynamics effects. The phase density function satisfies the linearized Boltzmann equation and the collision invariance property. Our formulation provides the correct value of the Prandtl number as it involves two different relaxation times for momentum and energy transport by diffusion. Generalized three-dimensional constitutive equations for different kinds of molecules are derived using the phase density function. The derived constitutive equations involve cross single derivatives of field variables such as temperature and velocity, with no higher-order derivative in higher-order terms. This is remarkable feature of the equations as the number of boundary conditions required is the same as needed for conventional Navier-Stokes equations. Linear stability analysis of the equations is performed, which shows that the derived equations are unconditionally stable. A comparison of the derived equations with existing Burnett-type equations is presented and salient features of our equations are outlined. The classic internal flow problem, force-driven compressible plane Poiseuille flow, is chosen to verify the stable Burnett equations and the results for equilibrium variables are presented.

  14. RFID design principles

    CERN Document Server

    Lehpamer, Harvey

    2012-01-01

    This revised edition of the Artech House bestseller, RFID Design Principles, serves as an up-to-date and comprehensive introduction to the subject. The second edition features numerous updates and brand new and expanded material on emerging topics such as the medical applications of RFID and new ethical challenges in the field. This practical book offers you a detailed understanding of RFID design essentials, key applications, and important management issues. The book explores the role of RFID technology in supply chain management, intelligent building design, transportation systems, military

  15. Principles of speech coding

    CERN Document Server

    Ogunfunmi, Tokunbo

    2010-01-01

    It is becoming increasingly apparent that all forms of communication-including voice-will be transmitted through packet-switched networks based on the Internet Protocol (IP). Therefore, the design of modern devices that rely on speech interfaces, such as cell phones and PDAs, requires a complete and up-to-date understanding of the basics of speech coding. Outlines key signal processing algorithms used to mitigate impairments to speech quality in VoIP networksOffering a detailed yet easily accessible introduction to the field, Principles of Speech Coding provides an in-depth examination of the

  16. Process Principle of Information

    Institute of Scientific and Technical Information of China (English)

    张高锋; 任君

    2006-01-01

    Ⅰ.IntroductionInformation structure is the organization modelof given and New information in the course ofinformation transmission.A discourse contains avariety of information and not all the informationlisted in the discourse is necessary and useful to us.When we decode a discourse,usually,we do not needto read every word in the discourse or text but skimor scan the discourse or text to search what we thinkis important or useful to us in the discourse as quicklyas possible.Ⅱ.Process Principles of Informati...

  17. Principles of copula theory

    CERN Document Server

    Durante, Fabrizio

    2015-01-01

    Principles of Copula Theory explores the state of the art on copulas and provides you with the foundation to use copulas in a variety of applications. Throughout the book, historical remarks and further readings highlight active research in the field, including new results, streamlined presentations, and new proofs of old results.After covering the essentials of copula theory, the book addresses the issue of modeling dependence among components of a random vector using copulas. It then presents copulas from the point of view of measure theory, compares methods for the approximation of copulas,

  18. Principles of fluorescence techniques

    CERN Document Server

    2016-01-01

    Fluorescence techniques are being used and applied increasingly in academics and industry. The Principles of Fluorescence Techniques course will outline the basic concepts of fluorescence techniques and the successful utilization of the currently available commercial instrumentation. The course is designed for students who utilize fluorescence techniques and instrumentation and for researchers and industrial scientists who wish to deepen their knowledge of fluorescence applications. Key scientists in the field will deliver theoretical lectures. The lectures will be complemented by the direct utilization of steady-state and lifetime fluorescence instrumentation and confocal microscopy for FLIM and FRET applications provided by leading companies.

  19. Principles of lithography

    CERN Document Server

    Levinson, Harry J

    2011-01-01

    The publication of Principles of Lithography, Third Edition just five years after the previous edition is evidence of the quickly changing and exciting nature of lithography as applied to the production of integrated circuits and other micro- and nanoscale devices. This text is intended to serve as an introduction to the science of microlithography, but also covers several subjects in depth, making it useful to the experienced lithographer as well. Topics directly related to manufacturing tools are addressed, including overlay, the stages of exposure, tools, and light sources. This updated edi

  20. Principles of meteoritics

    CERN Document Server

    Krinov, E L

    1960-01-01

    Principles of Meteoritics examines the significance of meteorites in relation to cosmogony and to the origin of the planetary system. The book discusses the science of meteoritics and the sources of meteorites. Scientists study the morphology of meteorites to determine their motion in the atmosphere. The scope of such study includes all forms of meteorites, the circumstances of their fall to earth, their motion in the atmosphere, and their orbits in space. Meteoric bodies vary in sizes; in calculating their motion in interplanetary space, astronomers apply the laws of Kepler. In the region of

  1. Protective relay principles

    CERN Document Server

    Sleva, Anthony F

    2009-01-01

    This title lets you improve failure detection and optimize protection. In the ever-evolving field of protective relay technology, an engineer's personal preference and professional judgment are as important to power system protection as the physical relays used to detect and isolate abnormal conditions. With invaluable insights from an experienced expert, ""Protective Relay Principles"" focuses on probable power system failure modes and the important characteristics of the protective relays used to detect these postulated failures.This book presents useful new concepts in a way that is easier

  2. Principles of Liquid Chromatography

    Science.gov (United States)

    Bakalyar, Stephen R.

    This article reviews the basic principles of high performance liquid chromatography (HPLC). The introductory section provides an overview of the HPLC technique, placing it in historical context and discussing the elementary facts of the separation mechanism. The next section discusses the nature of resolution, describing the two principal aspects, zone center separation and zone spreading. The third section takes a detailed look at how HPLC is used in practice to achieve a separation. It discusses the three key variables that need to be adjusted: retention, efficiency, and selectivity. A fourth section is concerned with various relationships of practical importance: flow rate, temperature, and pressure. A final section discusses future trends in HPLC.

  3. Developing principles of growth

    DEFF Research Database (Denmark)

    Neergaard, Helle; Fleck, Emma

    Although it has been widely recognized that the growth of women-owned businesses is central to wealth creation, innovation and economic development; limited attention has been devoted to understanding small business growth from a female perspective.This research seeks to develop an understanding...... of the principles of growth among women-owned firms. Using an in-depth case study methodology, data was collected from women-owned firms in Denmark and Ireland, as these countries are similar in contextual terms, e.g. population and business composition, dominated by micro, small and medium-sized enterprises...

  4. Principles of smile design

    Directory of Open Access Journals (Sweden)

    Bhuvaneswaran Mohan

    2010-01-01

    Full Text Available An organized and systematic approach is required to evaluate, diagnose and resolve esthetic problems predictably. It is of prime importance that the final result is not dependent only on the looks alone. Our ultimate goal as clinicians is to achieve pleasing composition in the smile by creating an arrangement of various esthetic elements. This article reviews the various principles that govern the art of smile designing. The literature search was done using PubMed search and Medline. This article will provide a basic knowledge to the reader to bring out a functional stable smile.

  5. Principles of smile design.

    Science.gov (United States)

    Bhuvaneswaran, Mohan

    2010-10-01

    An organized and systematic approach is required to evaluate, diagnose and resolve esthetic problems predictably. It is of prime importance that the final result is not dependent only on the looks alone. Our ultimate goal as clinicians is to achieve pleasing composition in the smile by creating an arrangement of various esthetic elements. This article reviews the various principles that govern the art of smile designing. The literature search was done using PubMed search and Medline. This article will provide a basic knowledge to the reader to bring out a functional stable smile.

  6. Principles of chemical kinetics

    CERN Document Server

    House, James E

    2007-01-01

    James House's revised Principles of Chemical Kinetics provides a clear and logical description of chemical kinetics in a manner unlike any other book of its kind. Clearly written with detailed derivations, the text allows students to move rapidly from theoretical concepts of rates of reaction to concrete applications. Unlike other texts, House presents a balanced treatment of kinetic reactions in gas, solution, and solid states. The entire text has been revised and includes many new sections and an additional chapter on applications of kinetics. The topics covered include quantitative rela

  7. Principles of compilers

    CERN Document Server

    Su, Yunlin

    2011-01-01

    ""Principles of Compilers: A New Approach to Compilers Including the Algebraic Method"" introduces the ideas of the compilation from the natural intelligence of human beings by comparing similarities and differences between the compilations of natural languages and programming languages. The notation is created to list the source language, target languages, and compiler language, vividly illustrating the multilevel procedure of the compilation in the process. The book thoroughly explains the LL(1) and LR(1) parsing methods to help readers to understand the how and why. It not only covers estab

  8. Academic Principles: A Brief Introduction

    Science.gov (United States)

    Association of American Universities, 2013

    2013-01-01

    For many decades certain core principles have guided the conduct of teaching, research, and scholarship at American universities, as well as the ways in which these institutions are governed. There is ample evidence that these principles have strongly contributed to the quality of American universities. The principles have also made these…

  9. Archimedes' Principle in General Coordinates

    Science.gov (United States)

    Ridgely, Charles T.

    2010-01-01

    Archimedes' principle is well known to state that a body submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body. Herein, Archimedes' principle is derived from first principles by using conservation of the stress-energy-momentum tensor in general coordinates. The resulting expression for the force is…

  10. Euphemism and the Politeness Principle

    Institute of Scientific and Technical Information of China (English)

    杨馥榕

    2014-01-01

    In linguistic communication, euphemism is a lubricant, whereas the politeness principle is a norm of moderating lin⁃guistic behavior. This paper aims to analyze the euphemism and the politeness principle, showing the relationship between euphe⁃mism and the politeness principle. In order to help people know how to behave in the daily communication and make their talk more effective.

  11. Archimedes' Principle in General Coordinates

    Science.gov (United States)

    Ridgely, Charles T.

    2010-01-01

    Archimedes' principle is well known to state that a body submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body. Herein, Archimedes' principle is derived from first principles by using conservation of the stress-energy-momentum tensor in general coordinates. The resulting expression for the force is…

  12. Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation

    OpenAIRE

    Gamba, I. M.; Panferov, V.; Villani, C.

    2007-01-01

    For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The main technique is based on a comparison principle that uses a certain dissipative property of the linear Boltzmann equation. Implications of the technique to propagation of upper Maxwellian bounds in the spatially-inhomogeneous case are discussed.

  13. Asymptotic Behavior for a Strongly Damped Nonlinear Wave Equation.

    Science.gov (United States)

    1980-06-01

    principle to reaction- diffusion equations, J. Differential Equations 33(1979), 201-225. [2] Billotti, J.E. and J.P. LaSalle , Periodic dissipative...results of Alikakos. Invariant sets in one space are automatically invariant sets in many spaces (which implies smoothness properties of invariant sets...of a "very smooth" maximal compact invariant set under a very weak dissipative assumption, along with its strong stability and attractivity properties

  14. Stochastic Cahn-Hilliard equation with singular nonlinearity and reflection

    OpenAIRE

    Goudenège, Ludovic

    2008-01-01

    International audience; We consider a stochastic partial differential equation with logarithmic (or negative power) nonlinearity, with one reflection at 0 and with a constraint of conservation of the space average. The equation, driven by the derivative in space of a space-time white noise, contains a bi-Laplacian in the drift. The lack of the maximum principle for the bi-Laplacian generates difficulties for the classical penalization method, which uses a crucial monotonicity property. Being ...

  15. Basic equations of the quasiparticle-phonon nuclear model for odd spherical nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Vdovin, A.I.; Tien Khoa, D.; Voronov, V.V.

    1986-02-01

    This paper obtains, in general form, the system of basic equations of the quasiparticle-phonon nuclear model for odd spherical nuclei. The equations take into account the anharmonicity of the vibrations of the even-even core and the corrections made necessary by the Pauli principle. It is shown that the system of equations contains all the variants of approximate equations of the quasiparticle-phonon model that are widely used in calculations.

  16. Generalized Jacobi Elliptic Function Solution to a Class of Nonlinear Schrödinger-Type Equations

    Directory of Open Access Journals (Sweden)

    Zeid I. A. Al-Muhiameed

    2011-01-01

    Full Text Available With the help of the generalized Jacobi elliptic function, an improved Jacobi elliptic function method is used to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Lin equation are investigated, and the exact solutions are derived with the aid of the homogenous balance principle.

  17. The Effective Equation Method

    Science.gov (United States)

    Kuksin, Sergei; Maiocchi, Alberto

    In this chapter we present a general method of constructing the effective equation which describes the behavior of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behavior of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three- and four-wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanography.

  18. Plastic variational principle based on the least work consumption principle

    Institute of Scientific and Technical Information of China (English)

    唐松花; 罗迎社; 周筑宝; 王智超

    2008-01-01

    Plastic variational principles are foundation to solve the boundary-value problems of plastic mechanics with the variational method(or energy method) and finite element method.The most convenient way of establishing different kinds of variational principles is to set up the extreme principle related to the studied problem.Based on a general new extreme principle-the Least work consumption principle,the variational principles of the rigid-plastic and rigid-viscoplastic material were derived.In comparison with existing methods,the method in this paper is more clear and direct,and the physical meaning is clear-cut.This method can offer a new way for establishing other kinds of variational principles.

  19. Differential equations problem solver

    CERN Document Server

    Arterburn, David R

    2012-01-01

    REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and

  20. Ordinary differential equations

    CERN Document Server

    Miller, Richard K

    1982-01-01

    Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,

  1. Stochastic Gauss equations

    Science.gov (United States)

    Pierret, Frédéric

    2016-02-01

    We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.

  2. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2011-01-01

    A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres

  3. Hyperbolic partial differential equations

    CERN Document Server

    Witten, Matthew

    1986-01-01

    Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M

  4. Nonlinear diffusion equations

    CERN Document Server

    Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning

    2001-01-01

    Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which

  5. Partial differential equations

    CERN Document Server

    Friedman, Avner

    2008-01-01

    This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of we

  6. Introduction to functional equations

    CERN Document Server

    Sahoo, Prasanna K

    2011-01-01

    Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections hig

  7. Uncertain differential equations

    CERN Document Server

    Yao, Kai

    2016-01-01

    This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.

  8. THE RESPONSIBILITY PRINCIPLE

    Directory of Open Access Journals (Sweden)

    Elena ANGHEL

    2015-07-01

    Full Text Available "I'm wishing Law this: all legal obligations sholud be executed with the scrupulosity with which moral obligations are being performed by those people who feel bound by them ...", so beautifully portraited by Nicolae Titulescu`s words1. Life in the society means more than a simple coexistence of human beings, it actually means living together, collaborating and cooperating; that is why I always have to relate to other people and to be aware that only by limiting my freedom of action, the others freedom is feasible. Neminem laedere should be a principle of life for each of us. The individual is a responsible being. But responsibility exceeds legal prescriptions. Romanian Constitution underlines that I have to exercise my rights and freedoms in good faith, without infringing the rights and freedoms of others. The legal norm, developer of the constitutional principles, is endowed with sanction, which grants it exigibility. But I wonder: If I choose to obey the law, is my decision essentially determined only due of the fear of punishment? Is it not because I am a rational being, who developed during its life a conscience towards values, and thus I understand that I have to respect the law and I choose to comply with it?

  9. Principles of Mechanical Excavation

    Energy Technology Data Exchange (ETDEWEB)

    Lislerud, A. [Tamrock Corp., Tampere (Finland)

    1997-12-01

    Mechanical excavation of rock today includes several methods such as tunnel boring, raiseboring, roadheading and various continuous mining systems. Of these raiseboring is one potential technique for excavating shafts in the repository for spent nuclear fuel and dry blind boring is promising technique for excavation of deposition holes, as demonstrated in the Research Tunnel at Olkiluoto. In addition, there is potential for use of other mechanical excavation techniques in different parts of the repository. One of the main objectives of this study was to analyze the factors which affect the feasibility of mechanical rock excavation in hard rock conditions and to enhance the understanding of factors which affect rock cutting so as to provide an improved basis for excavator performance prediction modeling. The study included the following four main topics: (a) phenomenological model based on similarity analysis for roller disk cutting, (b) rock mass properties which affect rock cuttability and tool life, (c) principles for linear and field cutting tests and performance prediction modeling and (d) cutter head lacing design procedures and principles. As a conclusion of this study, a test rig was constructed, field tests were planned and started up. The results of the study can be used to improve the performance prediction models used to assess the feasibility of different mechanical excavation techniques at various repository investigation sites. (orig.). 21 refs.

  10. The Exhaustive Lexicalisation Principle

    Directory of Open Access Journals (Sweden)

    Antonio Fábregas

    2007-12-01

    Full Text Available In this article I revisit the well-known empirical problem of manner of motion verbs with directional complements in Spanish. I present some data that, to my mind, had not received due attention in previous studies and I show that some manner of motion verbs actually allow directionals with the preposition a, while all of them allow them with prepositions like hacia or hasta. I argue that this pattern is due to a principle that states that every syntactic feature must be identified by lexical insertion, the Exhaustive Lexicalisation Principle. The crucial problem with directional complements is that the Spanish preposition a is locative, in contrast with English to, and, therefore, unable to identify the Path feature. Some verbs license the directional with a because they can lexicalise Path altogether with the verb; all verbs can combine with hasta or hacia because these prepositions lexicalise Path. When neither the verb nor the preposition lexicalise the Path, the construction is ungrammatical.

  11. Principles of safety pharmacology.

    Science.gov (United States)

    Pugsley, M K; Authier, S; Curtis, M J

    2008-08-01

    Safety Pharmacology is a rapidly developing discipline that uses the basic principles of pharmacology in a regulatory-driven process to generate data to inform risk/benefit assessment. The aim of Safety Pharmacology is to characterize the pharmacodynamic/pharmacokinetic (PK/PD) relationship of a drug's adverse effects using continuously evolving methodology. Unlike toxicology, Safety Pharmacology includes within its remit a regulatory requirement to predict the risk of rare lethal events. This gives Safety Pharmacology its unique character. The key issues for Safety Pharmacology are detection of an adverse effect liability, projection of the data into safety margin calculation and finally clinical safety monitoring. This article sets out to explain the drivers for Safety Pharmacology so that the wider pharmacology community is better placed to understand the discipline. It concludes with a summary of principles that may help inform future resolution of unmet needs (especially establishing model validation for accurate risk assessment). Subsequent articles in this issue of the journal address specific aspects of Safety Pharmacology to explore the issues of model choice, the burden of proof and to highlight areas of intensive activity (such as testing for drug-induced rare event liability, and the challenge of testing the safety of so-called biologics (antibodies, gene therapy and so on.).

  12. [Principles of callus distraction].

    Science.gov (United States)

    Hankemeier, S; Bastian, L; Gosling, T; Krettek, C

    2004-10-01

    Callus distraction is based on the principle of regenerating bone by continuous distraction of proliferating callus tissue. It has become the standard treatment of significant leg shortening and large bone defects. Due to many problems and complications, exact preoperative planning, operative technique and careful postoperative follow-up are essential. External fixators can be used for all indications of callus distraction. However, due to pin tract infections, pain and loss of mobility caused by soft tissue transfixation, fixators are applied in patients with open growth plates, simultaneous lengthening with continuous deformity corrections, and increased risk of infection. Distraction over an intramedullary nail allows removal of the external fixator at the end of distraction before callus consolidation (monorail method). The intramedullary nail protects newly formed callus tissue and reduces the risk of axial deviation and refractures. Recently developed, fully intramedullary lengthening devices eliminate fixator-associated complications and accelerate return to normal daily activities. This review describes principles of callus distraction, potential complications and their management.

  13. A Comparison of IRT Equating and Beta 4 Equating.

    Science.gov (United States)

    Kim, Dong-In; Brennan, Robert; Kolen, Michael

    Four equating methods were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional mean squared error (CMSE) difference, and the equipercentile equating property. The four methods were: (1) three parameter logistic (3PL) model true score equating; (2) 3PL observed score equating; (3) beta 4 true…

  14. GURTIN-TYPE REGION-WISE VARIATIONAL PRINCIPLES FOR THERMOPIEZOELECTRIC ELASTODYNAMICS

    Institute of Scientific and Technical Information of China (English)

    黄泊

    2003-01-01

    The variation of new Gurtin-type region-wise variational principles results incontinuous conditions, boundary conditions, all equations and relations in linearthermopiezoelectric elastodynamics. Gurtin-type region-wise variational principles comprisevery important parts of linear thermopiezoelectric elastodynamics , and can fully characterizethe initial-boundary-value problem in linear thermopiezoelectric elastodynamics.

  15. Politeness Principle and Intercultural Communication

    Institute of Scientific and Technical Information of China (English)

    周宇岚

    2007-01-01

    There are many potential problems in intercultural communications.Politeness principle is very important in helping improving intercultural communications.But different cultures have various standard of politeness principle.This essay discusses the very different points of view on politeness principle between Chinese people and westerners,and studies how the context and settings affect the practice of politeness principle.At the ending of the essay,the guiding significance of politeness principle is pointed out.And it also points out seeking common understanding of various cultures.In some aspects,this paper is useful for effective intercultural communications.

  16. Applications of Bohr's correspondence principle

    Science.gov (United States)

    Crawford, Frank S.

    1989-07-01

    The Bohr correspondence-principle (cp) formula dE/dn=ℏω is presented (ω is the classical angular frequency) and its predicted energy levels En are compared to those given by the stationary state solutions of the Schrödinger equation, first for several examples in one dimension (1D), including the ``quantum bouncer,'' and then for several examples in three dimensions (3D), including the hydrogen atom and the isotropic harmonic oscillator. For the 3-D cases, the cp predictions based on classical circular orbits are compared with the ``circlelike'' Schrödinger solutions (those with the lowest energy eigenvalue for a given l) and the cp predictions based on classical ``needle'' orbits (having zero angular momentum) with the Schrödinger l=0 solutions. For the H atom and the isotropic oscillator, the cp prediction does not depend on the classical orbit chosen because of a ``degeneracy'': the fact that for these systems ω is independent of the orbit. As a more stringent test of the cp, analogous nondegenerate systems V=-k/r3/2 in place of the H-atom potential V=-e2/r and V=kr4 in place of the oscillator potential V=(1/2)mω2r2 are therefore considered. An interesting anomaly that occurs for the harmonic oscillator and its nondegenerate analog V=kr4 is encountered (but not for the H atom nor its nondegenerate analog V=-k/r3/2), wherein half of the states predicted by application of the cp to the needle orbits are ``spurious'' in that there are no corresponding Schrödinger l=0 states. The assumption that generated the spurious cp states is uncovered—a plausible, but erroneous factor of 2 in calculating the classical frequency—and thus the spurious states are eliminated.

  17. Recent Advances in Compressed Sensing: Discrete Uncertainty Principles and Fast Hyperspectral Imaging

    Science.gov (United States)

    2015-03-26

    Recent Advances in Compressed Sensing : Discrete Uncertainty Principles and Fast Hyperspectral Imaging THESIS MARCH 2015 Megan E. Lewis, Second...IN COMPRESSED SENSING : DISCRETE UNCERTAINTY PRINCIPLES AND FAST HYPERSPECTRAL IMAGING THESIS Presented to the Faculty Department of Mathematics and...MARCH 2015 DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. AFIT-ENC–MS-15-M-002 RECENT ADVANCES IN COMPRESSED SENSING

  18. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2015-01-01

    This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.  Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...

  19. Stochastic Gauss Equations

    CERN Document Server

    Frédéric, Pierret

    2014-01-01

    The equations of celestial mechanics that govern the variation of the orbital elements are completely derived for stochastic perturbation which generalized the classic perturbation equations which are used since Gauss, starting from Newton's equation and it's solution. The six most understandable orbital element, the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle and the mean motion are express in term of the angular momentum vector $\\textbf{H}$ per unit of mass and the energy $E$ per unit of mass. We differentiate those expressions using It\\^o's theory of differential equations due to the stochastic nature of the perturbing force. The result is applied to the two-body problem perturbed by a stochastic dust cloud and also perturbed by a stochastic dynamical oblateness of the central body.

  20. Kinetic equations: computation

    CERN Document Server

    Pareschi, Lorenzo

    2013-01-01

    Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity.

  1. Modern nonlinear equations

    CERN Document Server

    Saaty, Thomas L

    1981-01-01

    Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.

  2. Geometry of differential equations

    CERN Document Server

    Khovanskiĭ, A; Vassiliev, V

    1998-01-01

    This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.

  3. Regularized Structural Equation Modeling.

    Science.gov (United States)

    Jacobucci, Ross; Grimm, Kevin J; McArdle, John J

    A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM's utility.

  4. Complex Maxwell's equations

    Institute of Scientific and Technical Information of China (English)

    A.I.Arbab

    2013-01-01

    A unified complex model of Maxwell's equations is presented.The wave nature of the electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities.A new vacuum solution is obtained,and a new transformation under which Maxwell's equations are invariant is proposed.This transformation extends ordinary gauge transformation to include charge-current as well as scalar-vector potential.An electric dipole moment is found to be related to the magnetic charges,and Dirac's quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges.We generalize Maxwell's equations to include longitudinal waves.A formal analogy between this formulation and Dirac's equation is also discussed.

  5. Applied partial differential equations

    CERN Document Server

    DuChateau, Paul

    2012-01-01

    Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.

  6. Singular Renormalization Group Equations

    OpenAIRE

    Minoru, HIRAYAMA; Department of Physics, Toyama University

    1984-01-01

    The possible behaviour of the effective charge is discussed in Oehme and Zimmermann's scheme of the renormalization group equation. The effective charge in an example considered oscillates so violently in the ultraviolet limit that the bare charge becomes indefinable.

  7. Problems in differential equations

    CERN Document Server

    Brenner, J L

    2013-01-01

    More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.

  8. Principle of Spacetime and Black Hole Equivalence

    Science.gov (United States)

    Zhang, Tianxi

    2016-06-01

    Modelling the universe without relying on a set of hypothetical entities (HEs) to explain observations and overcome problems and difficulties is essential to developing a physical cosmology. The well-known big bang cosmology, widely accepted as the standard model, stands on two fundamentals, which are Einstein’s general relativity (GR) that describes the effect of matter on spacetime and the cosmological principle (CP) of spacetime isotropy and homogeneity. The field equation of GR along with the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric of spacetime derived from CP generates the Friedmann equation (FE) that governs the development and dynamics of the universe. The big bang theory has made impressive successes in explaining the universe, but still has problems and solutions of them rely on an increasing number of HEs such as inflation, dark matter, dark energy, and so on. Recently, the author has developed a new cosmological model called black hole universe, which, instead of making many those hypotheses, only includes a new single postulate (or a new principle) to the cosmology - Principle of Spacetime and Black Hole Equivalence (SBHEP) - to explain all the existing observations of the universe and overcome all the existing problems in conventional cosmologies. This study thoroughly demonstrates how this newly developed black hole universe model, which therefore stands on the three fundamentals (GR, CP, and SBHEP), can fully explain the universe as well as easily conquer the difficulties according to the well-developed physics, thus, neither needing any other hypotheses nor existing any unsolved difficulties. This work was supported by NSF/REU (Grant #: PHY-1263253) at Alabama A & M University.

  9. Relativistic Guiding Center Equations

    Energy Technology Data Exchange (ETDEWEB)

    White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association

    2014-10-01

    In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.

  10. Topological and non-topological soliton solutions to some time-fractional differential equations

    Indian Academy of Sciences (India)

    M Mirzazadeh

    2015-07-01

    This paper investigates, for the first time, the applicability and effectiveness of He’s semi-inverse variational principle method and the ansatz method on systems of nonlinear fractional partial differential equations. He’s semi-inverse variational principle method and the ansatz method are used to construct exact solutions of nonlinear fractional Klein–Gordon equation and generalized Hirota–Satsuma coupled KdV system. These equations have been widely applied in many branches of nonlinear sciences such as nonlinear optics, plasma physics, superconductivity and quantum mechanics. So, finding exact solutions of such equations are very helpful in the theoretical and numerical studies.

  11. Asymptotics for dissipative nonlinear equations

    CERN Document Server

    Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A

    2006-01-01

    Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.

  12. THE EQUALITY PRINCIPLE REQUIREMENTS

    Directory of Open Access Journals (Sweden)

    CLAUDIA ANDRIŢOI

    2013-05-01

    Full Text Available The problem premises and the objectives followed: the idea of inserting the equality principle between the freedom and the justice principles is manifested in positive law in two stages, as a general idea of all judicial norms and as requirement of the owner of a subjective right of the applicants of an objective law. Equality in face of the law and of public authorities can not involve the idea of standardization, of uniformity, of enlisting of all citizens under the mark of the same judicial regime, regardless of their natural or socio-professional situation. Through the Beijing Platform and the position documents of the European Commission we have defined the integrative approach of equality as representing an active and visible integration of the gender perspective in all sectors and at all levels. The research methods used are: the conceptualist method, the logical method and the intuitive method necessary as means of reasoning in order to argue our demonstration. We have to underline the fact that the system analysis of the research methods of the judicial phenomenon doesn’t agree with “value ranking”, because one value cannot be generalized in rapport to another. At the same time, we must fight against a methodological extremism. The final purpose of this study is represented by the reaching of the perfecting/excellence stage by all individuals through the promotion of equality and freedom. This supposes the fact that the existence of a non-discrimination favourable frame (fairness represents a means and a condition of self-determination, and the state of perfection/excellency is a result of this self-determination, the condition necessary for the obtaining of this nondiscrimination frame for all of us and in conditions of freedom for all individuals, represents the same condition that promotes the state of perfection/excellency. In conclusion we may state the fact that the equality principle represents a true catalyst of the

  13. A unified multicomponent stress-diffusion model of drug release from non-biodegradable polymeric matrix tablets.

    Science.gov (United States)

    Salehi, Ali; Zhao, Jin; Cabelka, Tim D; Larson, Ronald G

    2016-02-28

    We propose a new transport model of drug release from hydrophilic polymeric matrices, based on Stefan-Maxwell flux laws for multicomponent transport. Polymer stress is incorporated in the total mixing free energy, which contributes directly to the diffusion driving force while leading to time-dependent boundary conditions at the tablet interface. Given that hydrated matrix tablets are dense multicomponent systems, extended Stefan-Maxwell (ESM) flux laws are adopted to ensure consistency with the Onsager reciprocity principle and the Gibbs-Duhem thermodynamic constraint. The ESM flux law for any given component takes into account the friction exerted by all other species and is invariant with respect to reference velocity, thus satisfying Galilean translational invariance. Our model demonstrates that penetrant-induced plasticization of polymer chains partially or even entirely offsets the steady decline of chemical potential gradients at the tablet-medium interface that drive drug release. Utilizing a Flory-Huggins thermodynamic model, a modified form of the upper convected Maxwell constitutive equation for polymer stress and a Fujita-type dependence of mutual diffusivities on composition, depending on parameters, Fickian, anomalous or case II drug transport arises naturally from the model, which are characterized by quasi-power-law release profiles with exponents ranging from 0.5 to 1, respectively. A necessary requirement for non-Fickian release in our model is that the matrix stress relaxation time is comparable to the time scale for water diffusion. Mutual diffusivities and their composition dependence are the most decisive factors in controlling drug release characteristics in our model. Regression of the experimental polymer dissolution and drug release profiles in a system of Theophylline/cellulose (K15M) demonstrate that API-water mutual diffusivity in the presence of excipient cannot generally be taken as a constant.

  14. Functional Equations and Fourier Analysis

    OpenAIRE

    2010-01-01

    By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation, on compact groups.

  15. Principles of Bioenergetics

    CERN Document Server

    Skulachev, Vladimir P; Kasparinsky, Felix O

    2013-01-01

    Principles of Bioenergetics summarizes one of the quickly growing branches of modern biochemistry. Bioenergetics concerns energy transductions occurring in living systems and this book pays special attention to molecular mechanisms of these processes. The main subject of the book is the "energy coupling membrane" which refers to inner membranes of intracellular organelles, for example, mitochondria and chloroplasts. Cellular cytoplasmic membranes where respiratory and photosynthetic energy transducers, as well as ion-transporting ATP-synthases (ATPases) are also part of this membrane. Significant attention is paid to the alternative function of mitochondria as generators of reactive oxygen species (ROS) that mediate programmed death of cells (apoptosis and necrosis) and organisms (phenoptosis). The latter process is considered as a key mechanism of aging which may be suppressed by mitochondria-targeted antioxidants.

  16. Emulsion Science Basic Principles

    CERN Document Server

    Leal-Calderon, Fernando; Schmitt, Véronique

    2007-01-01

    Emulsions are generally made out of two immiscible fluids like oil and water, one being dispersed in the second in the presence of surface-active compounds.They are used as intermediate or end products in a huge range of areas including the food, chemical, cosmetic, pharmaceutical, paint, and coating industries. Besides the broad domain of technological interest, emulsions are raising a variety of fundamental questions at the frontier between physics and chemistry. This book aims to give an overview of the most recent advances in emulsion science. The basic principles, covering aspects of emulsions from their preparation to their destruction, are presented in close relation to both the fundamental physics and the applications of these materials. The book is intended to help scientists and engineers in formulating new materials by giving them the basics of emulsion science.

  17. Neuronavigation. Principles. Surgical technique.

    Science.gov (United States)

    Ivanov, Marcel; Ciurea, Alexandru Vlad

    2009-01-01

    Neuronavigation and stereotaxy are techniques designed to help neurosurgeons precisely localize different intracerebral pathological processes by using a set of preoperative images (CT, MRI, fMRI, PET, SPECT etc.). The development of computer assisted surgery was possible only after a significant technological progress, especially in the area of informatics and imagistics. The main indications of neuronavigation are represented by the targeting of small and deep intracerebral lesions and choosing the best way to treat them, in order to preserve the neurological function. Stereotaxis also allows lesioning or stimulation of basal ganglia for the treatment of movement disorders. These techniques can bring an important amount of confort both to the patient and to the neurosurgeon. Neuronavigation was introduced in Romania around 2003, in four neurosurgical centers. We present our five-years experience in neuronavigation and describe the main principles and surgical techniques.

  18. Mirror Principle, 1

    CERN Document Server

    Lian Bong H; Yau, S T

    1997-01-01

    We propose and study the following Mirror Principle: certain sequences of multiplicative equivariant characteristic classes on Kontsevich's stable map moduli spaces can be computed in terms of certain hypergeometric type classes. As applications, we compute the equivariant Euler classes of obstruction bundles induced by any concavex bundles -- including any direct sum of line bundles -- on $\\P^n$. This includes proving the formula of Candelas-de la Ossa-Green-Parkes hence completing the program of Candelas et al, Kontesevich, Manin, and Givental, to compute rigorously the instanton prepotential function for the quintic in $\\P^4$. We derive, among many other examples, the multiple cover formula for Gromov-Witten invariants of $\\P^1$, computed earlier by Morrison-Aspinwall and by Manin in different approaches. We also prove a formula for enumerating Euler classes which arise in the so-called local mirror symmetry for some noncompact Calabi-Yau manifolds. At the end we interprete an infinite dimensional transfor...

  19. Principles of Lasers

    CERN Document Server

    Svelto, Orazio

    2010-01-01

    This new Fifth Edition of Principles of Lasers incorporates corrections to the previous edition. The text’s essential mission remains the same: to provide a wide-ranging yet unified description of laser behavior, physics, technology, and current applications. Dr. Svelto emphasizes the physical rather than the mathematical aspects of lasers, and presents the subject in the simplest terms compatible with a correct physical understanding. Praise for earlier editions: "Professor Svelto is himself a longtime laser pioneer and his text shows the breadth of his broad acquaintance with all aspects of the field … Anyone mastering the contents of this book will be well prepared to understand advanced treatises and research papers in laser science and technology." (Arthur L. Schawlow, 1981 Nobel Laureate in Physics) "Already well established as a self-contained introduction to the physics and technology of lasers … Professor Svelto’s book, in this lucid translation by David Hanna, can be strongly recommended for...

  20. Principles & practice of physics

    CERN Document Server

    Mazur, Eric; Dourmashkin, Peter A; Pedigo, Daryl; Bieniek, Ronald J

    2015-01-01

    Putting physics first Based on his storied research and teaching, Eric Mazur's Principles & Practice of Physics builds an understanding of physics that is both thorough and accessible. Unique organization and pedagogy allow you to develop a true conceptual understanding of physics alongside the quantitative skills needed in the course. *New learning architecture: The book is structured to help you learn physics in an organized way that encourages comprehension and reduces distraction.*Physics on a contemporary foundation: Traditional texts delay the introduction of ideas that we now see as unifying and foundational. This text builds physics on those unifying foundations, helping you to develop an understanding that is stronger, deeper, and fundamentally simpler.*Research-based instruction: This text uses a range of research-based instructional techniques to teach physics in the most effective manner possible. The result is a groundbreaking book that puts physics first, thereby making it more accessible to...

  1. Release the Body, Release the Mind.

    Science.gov (United States)

    Stoner, Martha Goff

    1998-01-01

    A college English teacher describes the anxiety and resentment of students during in-class writing assignments and the successful classroom use of meditation and body movement. Movement seemed to relax the students, change their attitudes, and release their creative impulses to write. Implications related to the body-mind connection are pondered.…

  2. Fault Management Guiding Principles

    Science.gov (United States)

    Newhouse, Marilyn E.; Friberg, Kenneth H.; Fesq, Lorraine; Barley, Bryan

    2011-01-01

    Regardless of the mission type: deep space or low Earth orbit, robotic or human spaceflight, Fault Management (FM) is a critical aspect of NASA space missions. As the complexity of space missions grows, the complexity of supporting FM systems increase in turn. Data on recent NASA missions show that development of FM capabilities is a common driver for significant cost overruns late in the project development cycle. Efforts to understand the drivers behind these cost overruns, spearheaded by NASA's Science Mission Directorate (SMD), indicate that they are primarily caused by the growing complexity of FM systems and the lack of maturity of FM as an engineering discipline. NASA can and does develop FM systems that effectively protect mission functionality and assets. The cost growth results from a lack of FM planning and emphasis by project management, as well the maturity of FM as an engineering discipline, which lags behind the maturity of other engineering disciplines. As a step towards controlling the cost growth associated with FM development, SMD has commissioned a multi-institution team to develop a practitioner's handbook representing best practices for the end-to-end processes involved in engineering FM systems. While currently concentrating primarily on FM for science missions, the expectation is that this handbook will grow into a NASA-wide handbook, serving as a companion to the NASA Systems Engineering Handbook. This paper presents a snapshot of the principles that have been identified to guide FM development from cradle to grave. The principles range from considerations for integrating FM into the project and SE organizational structure, the relationship between FM designs and mission risk, and the use of the various tools of FM (e.g., redundancy) to meet the FM goal of protecting mission functionality and assets.

  3. Principles of rockbolting design

    Directory of Open Access Journals (Sweden)

    Charlie C. Li

    2017-06-01

    Full Text Available This article introduces the principles of underground rockbolting design. The items discussed include underground loading conditions, natural pressure zone around an underground opening, design methodologies, selection of rockbolt types, determination of bolt length and spacing, factor of safety, and compatibility between support elements. Different types of rockbolting used in engineering practise are also presented. The traditional principle of selecting strong rockbolts is valid only in conditions of low in situ stresses in the rock mass. Energy-absorbing rockbolts are preferred in the case of high in situ stresses. A natural pressure arch is formed in the rock at a certain distance behind the tunnel wall. Rockbolts should be long enough to reach the natural pressure arch when the failure zone is small. The bolt length should be at least 1 m beyond the failure zone. In the case of a vast failure zone, tightly spaced short rockbolts are installed to establish an artificial pressure arch within the failure zone and long cables are anchored on the natural pressure arch. In this case, the rockbolts are usually less than 3 m long in mine drifts, but can be up to 7 m in large-scale rock caverns. Bolt spacing is more important than bolt length in the case of establishing an artificial pressure arch. In addition to the factor of safety, the maximum allowable displacement in the tunnel and the ultimate displacement capacity of rockbolts must be also taken into account in the design. Finally, rockbolts should be compatible with other support elements in the same support system in terms of displacement and energy absorption capacities.

  4. Fault Management Guiding Principles

    Science.gov (United States)

    Newhouse, Marilyn E.; Friberg, Kenneth H.; Fesq, Lorraine; Barley, Bryan

    2011-01-01

    Regardless of the mission type: deep space or low Earth orbit, robotic or human spaceflight, Fault Management (FM) is a critical aspect of NASA space missions. As the complexity of space missions grows, the complexity of supporting FM systems increase in turn. Data on recent NASA missions show that development of FM capabilities is a common driver for significant cost overruns late in the project development cycle. Efforts to understand the drivers behind these cost overruns, spearheaded by NASA's Science Mission Directorate (SMD), indicate that they are primarily caused by the growing complexity of FM systems and the lack of maturity of FM as an engineering discipline. NASA can and does develop FM systems that effectively protect mission functionality and assets. The cost growth results from a lack of FM planning and emphasis by project management, as well the maturity of FM as an engineering discipline, which lags behind the maturity of other engineering disciplines. As a step towards controlling the cost growth associated with FM development, SMD has commissioned a multi-institution team to develop a practitioner's handbook representing best practices for the end-to-end processes involved in engineering FM systems. While currently concentrating primarily on FM for science missions, the expectation is that this handbook will grow into a NASA-wide handbook, serving as a companion to the NASA Systems Engineering Handbook. This paper presents a snapshot of the principles that have been identified to guide FM development from cradle to grave. The principles range from considerations for integrating FM into the project and SE organizational structure, the relationship between FM designs and mission risk, and the use of the various tools of FM (e.g., redundancy) to meet the FM goal of protecting mission functionality and assets.

  5. Almost Automorphic Solutions to Nonautonomous Stochastic Functional Integrodifferential Equations

    Directory of Open Access Journals (Sweden)

    Li Xi-liang

    2013-01-01

    Full Text Available This paper concerns the square-mean almost automorphic solutions to a class of abstract semilinear nonautonomous functional integrodifferential stochastic evolution equations in real separable Hilbert spaces. Using the so-called “Acquistapace-Terreni” conditions and Banach contraction principle, the existence, uniqueness, and asymptotical stability results of square-mean almost automorphic mild solutions to such stochastic equations are established. As an application, square-mean almost automorphic solution to a concrete nonautonomous integro-differential stochastic evolution equation is analyzed to illustrate our abstract results.

  6. From hyperbolic regularization to exact hydrodynamics for linearized Grad's equations.

    Science.gov (United States)

    Colangeli, Matteo; Karlin, Iliya V; Kröger, Martin

    2007-05-01

    Inspired by a recent hyperbolic regularization of Burnett's hydrodynamic equations [A. Bobylev, J. Stat. Phys. 124, 371 (2006)], we introduce a method to derive hyperbolic equations of linear hydrodynamics to any desired accuracy in Knudsen number. The approach is based on a dynamic invariance principle which derives exact constitutive relations for the stress tensor and heat flux, and a transformation which renders the exact equations of hydrodynamics hyperbolic and stable. The method is described in detail for a simple kinetic model -- a 13 moment Grad system.

  7. SUSTAINED RELEASE ITOPRIDE HYDROCHLORIDE MATRIX TABLET

    Directory of Open Access Journals (Sweden)

    BHUPENDRA, PRAJAPATI, NIKLESH PATEL, HITESH

    2013-09-01

    Full Text Available Oral route gets the highest priority for thedelivery of the drug as well as better patient compliance incase of self delivery dosage formulation. The aim ofpresent investigation was undertaken with the objective offormulating sustain release formulation of Itopridehydrochloride for oral drug delivery. Itopride hydrochlorideis highly water soluble prokinetic drug.Hydroxypropylmethylcellulose K4M (lower viscositygrade and K100M (higher viscosity grade were used as amatrix forming agents to control the release of drug. HPMCK4M and HPMC K100M were used individually as well asin combination with different proportion in the preparationof the Sustained release formulation. 32 factorial designswere applied to the polymer concentration that affects thedrug release profile. Reduced equation for drug release at2hr,6hr,and10hrwere22 1 2 1 Q 37.644 5.41X 3.25X 2.017X ,26 1 2 1 Q 72.367 8.05X 4.4X 3.75X ,and10 1 1 2 90.844 5.8 2.633 2.8 2 Q X X X Xrespectively. Optimized batch F019 shows good tabletproperties like hardness(7-9kg/cm2, thickness(4.48mm,friability(0.024%,assay(99.3% and nearly similar drugrelease profile to the targeted reference drug release profileand it was indicated by similarity factor (f2=86.04.

  8. Microencapsulation of Bioactive Principles with an Airless Spray-Gun Suitable for Processing High Viscous Solutions

    Directory of Open Access Journals (Sweden)

    Moreno Cocchietto

    2013-11-01

    Full Text Available Purpose: to design, assemble and test a prototype of a novel production plant, suitable for producing microparticles (MPs by processing highly viscous feed solutions (FSs. Methods: the prototype has been built using a commercial air compressor, a piston pump, an airless spray-gun, a customized air-treatment section, a timer, a rotating base, and a filtration section. Preliminary prototype parameter setting was carried out to individuate the best performing nozzle’s dimension, the nebulization timing, and the CaCl2 concentration in the gelation fluid. In addition, prototype throughput (1 L to 5 L and the range of practicable feed solution (FS viscosities were assayed. A set of four batches was prepared in order to characterize the MPs, in terms of mean particle size and distribution, flow properties, swelling, encapsulation efficiency and release. Results: according to a qualitative scoring, the large nozzle was suitable to nebulize FSs at a higher alginate concentration. Conversely, the small nozzle performed better in the processing of FSs with an alginate concentration up to 2% w/v. Only at the highest degree of viscosity, corresponding to 5% w/v of alginate, the FS processing was not technically possible. Among the CaCl2 concentrations considered, 15% w/v was recognized as the most versatile. The prototype appears to be convenient and suitable to grant a high yield starting from 2 L of FS. The flow behavior of the FSs assayed can be satisfactorily described with the Carreau-Yasuda equation and the throughput begins to slightly decrease for FSs at alginate concentrations exceeding 3% w/v. MP morphology was irregular with crumpled shape. The angle of repose indicates a good flowability and the release studies showed gastro-resistance and potential prolonged release applications. Conclusions: the novel prototype of production plant is suitable to process large amounts (2 L or more of FSs, characterized by a high viscosity, to produce MPs

  9. RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅴ)-POLAR THERMOMECHANICAL CONTINUA

    Institute of Scientific and Technical Information of China (English)

    戴天民

    2003-01-01

    The purpose is to reestablish rather complete basic balance equations and boundary conditions for polar thermomechanical continua based on the restudy of the traditional theories of micropolar thermoelasticity and thermopiezoelectricity. The equations of motion and the local balance equation of energy rate for micropolar thermoelasticity are derived from the rather complete principle of virtual power. The equations of motion, the balance equation of entropy and all boundary conditions are derived from the rather complete Hamilton principle. The new balance equations of momentum and energy rate which are essentially different from the existing results are presented. The corresponding results of micromorphic thermoelasticity and couple stress elastodynamics may be naturally obtained by the transition and the reduction from the micropolar case, respectively. Finally, the results of micropolar thermopiezoelectricity are directly given.

  10. Existence and uniqueness of solutions for nonlinear hyperbolic fractional differential equation with integral boundary conditions

    OpenAIRE

    Brahim Tellab; Kamel Haouam

    2016-01-01

    In this paper, we investigate the existence and uniqueness of solutions for second order nonlinear fractional differential equation with integral boundary conditions. Our result is an application of the Banach contraction principle and the Krasnoselskii fixed point theorem.

  11. Symmetric waves are traveling waves for a shallow water equation for surface waves of moderate amplitude

    OpenAIRE

    Geyer, Anna

    2016-01-01

    Following a general principle introduced by Ehrnstr\\"{o}m et.al. we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves.

  12. Symmetric waves are traveling waves for a shallow water equation for surface waves of moderate amplitude

    OpenAIRE

    Geyer, Anna

    2016-01-01

    Following a general principle introduced by Ehrnstr\\"{o}m et.al. we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves.

  13. An introduction to the Boltzmann equation and transport processes in gases

    CERN Document Server

    Kremer, Gilberto M; Colton, David

    2010-01-01

    This book covers classical kinetic theory of gases, presenting basic principles in a self-contained framework and from a more rigorous approach based on the Boltzmann equation. Uses methods in kinetic theory for determining the transport coefficients of gases.

  14. NUMERICAL SIMULATION OF SEDIMENT RELEASE FROM RESERVOIRS

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    For the computation of the sediment quantity released from reservoirs, a vertical two-dimensional hydrodynamic model is combined with a sediment transport model. The hydrodynamic model is based on the equations of mass and momentum conservation along with a k - ε model for closure of the Reynolds stresses. The sediment transport model is based on the convection-diffusion equation of sediment concentration and the sediment continuity equation. Both the hydrodynamic and sediment transport models are developed in a boundary-fitted curvilinear co-ordinate system. Comparison of the predicted mean velocity field with laboratory results indicates that the present model captures most experimental trends with reasonable accuracy. Also good agreement is found in comparison of the sediment transport results for the numerical model and the experimental model.

  15. STABILITY RESULTS OF RANDOM IMPULSIVE SEMILINEAR DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    M.GOWRISANKAR; P.MOHANKUMAR; A.VINODKUMAR

    2014-01-01

    In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilinear differential equations un-der sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.

  16. Random Perturbation of Forward-Backward Stochastic Differential Equations

    CERN Document Server

    Zhang, Liangquan

    2012-01-01

    In this paper, we consider a kind of coupled Forward-Backward Stochastic Differential Equations (FBSDEs in short) with parameter $\\varepsilon >0.$%. We study the convergence of distributions of $(X^{\\varepsilon,t,x},Y^{\\varepsilon,t,x}),$ as $\\varepsilon \\rightarrow 0,$ and prove the Freidlin-Wentzell's large deviation principle as well.

  17. ON SOLUTIONS TO SEMILINEAR INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper, using the theory of resolvent operators, Banach,s contraction prin-ciple and Schauder,s fixed point theorem, we study the existence of integral solutions to semilinear integrodifferential equations under nonlocal conditions in Banach space. An example is provided to illustrate the results obtained.

  18. MACHINE MOTION EQUATIONS

    Directory of Open Access Journals (Sweden)

    Florian Ion Tiberiu Petrescu

    2015-09-01

    Full Text Available This paper presents the dynamic, original, machine motion equations. The equation of motion of the machine that generates angular speed of the shaft (which varies with position and rotation speed is deduced by conservation kinetic energy of the machine. An additional variation of angular speed is added by multiplying by the coefficient dynamic D (generated by the forces out of mechanism and or by the forces generated by the elasticity of the system. Kinetic energy conservation shows angular speed variation (from the shaft with inertial masses, while the dynamic coefficient introduces the variation of w with forces acting in the mechanism. Deriving the first equation of motion of the machine one can obtain the second equation of motion dynamic. From the second equation of motion of the machine it determines the angular acceleration of the shaft. It shows the distribution of the forces on the mechanism to the internal combustion heat engines. Dynamic, the velocities can be distributed in the same way as forces. Practically, in the dynamic regimes, the velocities have the same timing as the forces. Calculations should be made for an engine with a single cylinder. Originally exemplification is done for a classic distribution mechanism, and then even the module B distribution mechanism of an Otto engine type.

  19. Introduction to partial differential equations

    CERN Document Server

    Greenspan, Donald

    2000-01-01

    Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.

  20. The Distorted Wheeler-DeWitt Equation

    CERN Document Server

    Garattini, Remo

    2015-01-01

    The Wheeler-DeWitt Equation represents a tool to study Quantum Gravity and Quantum Cosmology. Its solution in a very general context is, of course, impossible. To this purpose we consider some distortions of General Relativity like Gravity's Rainbow, Varying Speed of Light Cosmology, Generalized Uncertainty Principle deformations and Ho\\v{r}ava-Lifshitz gravity which could allow the calculation of some observables like the cosmological constant. For simplicity we consider only the Mini-Superspace approach related to a Friedmann-Lema\\^itre-Robertson-Walker space-time.