Softened gravity and the extension of the standard model up to infinite energy

NASA Astrophysics Data System (ADS)

Giudice, Gian F.; Isidori, Gino; Salvio, Alberto; Strumia, Alessandro

2015-02-01

Attempts to solve naturalness by having the weak scale as the only breaking of classical scale invariance have to deal with two severe difficulties: gravity and the absence of Landau poles. We show that solutions to the first problem require premature modifications of gravity at scales no larger than 1011 GeV, while the second problem calls for many new particles at the weak scale. To build models that fulfill these properties, we classify 4- dimensional Quantum Field Theories that satisfy Total Asymptotic Freedom (TAF): the theory holds up to infinite energy, where all coupling constants flow to zero. We develop a technique to identify such theories and determine their low-energy predictions. Since the Standard Model turns out to be asymptotically free only under the unphysical conditions g 1 = 0, M t = 186 GeV, M τ = 0, M h = 163 GeV, we explore some of its weak-scale extensions that satisfy the requirements for TAF.

Soliton, rational, and periodic solutions for the infinite hierarchy of defocusing nonlinear Schrödinger equations.

PubMed

Ankiewicz, Adrian

2016-07-01

Analysis of short-pulse propagation in positive dispersion media, e.g., in optical fibers and in shallow water, requires assorted high-order derivative terms. We present an infinite-order "dark" hierarchy of equations, starting from the basic defocusing nonlinear Schrödinger equation. We present generalized soliton solutions, plane-wave solutions, and periodic solutions of all orders. We find that "even"-order equations in the set affect phase and "stretching factors" in the solutions, while "odd"-order equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are complex. There are various applications in optics and water waves.

Spinning solutions in general relativity with infinite central density

NASA Astrophysics Data System (ADS)

Flammer, P. D.

2018-05-01

This paper presents general relativistic numerical simulations of uniformly rotating polytropes. Equations are developed using MSQI coordinates, but taking a logarithm of the radial coordinate. The result is relatively simple elliptical differential equations. Due to the logarithmic scale, we can resolve solutions with near-singular mass distributions near their center, while the solution domain extends many orders of magnitude larger than the radius of the distribution (to connect with flat space-time). Rotating solutions are found with very high central energy densities for a range of adiabatic exponents. Analytically, assuming the pressure is proportional to the energy density (which is true for polytropes in the limit of large energy density), we determine the small radius behavior of the metric potentials and energy density. This small radius behavior agrees well with the small radius behavior of large central density numerical results, lending confidence to our numerical approach. We compare results with rotating solutions available in the literature, which show good agreement. We study the stability of spherical solutions: instability sets in at the first maximum in mass versus central energy density; this is also consistent with results in the literature, and further lends confidence to the numerical approach.

Infinite derivative gravity: non-singular cosmology & blackhole solutions

NASA Astrophysics Data System (ADS)

Mazumdar, A.

Both Einstein’s theory of General Relativity and Newton’s theory of gravity possess a short distance and small time scale catastrophe. The blackhole singularity and cosmological Big Bang singularity problems highlight that current theories of gravity are incomplete description at early times and small distances. I will discuss how one can potentially resolve these fundamental problems at a classical level and quantum level. In particular, I will discuss infinite derivative theories of gravity, where gravitational interactions become weaker in the ultraviolet, and therefore resolving some of the classical singularities, such as Big Bang and Schwarzschild singularity for compact non-singular objects with mass up to 1025 grams. In this lecture, I will discuss quantum aspects of infinite derivative gravity and discuss few aspects which can make the theory asymptotically free in the UV.

Introduction to the theory of infinite systems. Theory and practices

NASA Astrophysics Data System (ADS)

Fedorov, Foma M.

2017-11-01

A review of the author's work is given, which formed the basis for a new theory of general infinite systems. The Gaussian elimination and Cramer's rule have been extended to infinite systems. A special particular solution is obtained, it is called a strictly particular solution. Necessary and sufficient conditions for existence of the nontrivial solutions of homogeneous systems are given.

Solutions of Boltzmann`s Equation for Mono-energetic Neutrons in an Infinite Homogeneous Medium

DOE R&D Accomplishments Database

Wigner, E. P.

1943-11-30

Boltzman's equation is solved for the case of monoenergetic neutrons created by a plane or point source in an infinite medium which has spherically symmetric scattering. The customary solution of the diffusion equation appears to be multiplied by a constant factor which is smaller than 1. In addition to this term the total neutron density contains another term which is important in the neighborhood of the source. It varies as 1/r{sup 2} in the neighborhood of a point source. (auth)

The passage of an infinite swept airfoil through an oblique gust. [approximate solution for aerodynamic response

NASA Technical Reports Server (NTRS)

Adamczyk, J. L.

1974-01-01

An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.

Lyapunov exponents for infinite dimensional dynamical systems

NASA Technical Reports Server (NTRS)

Mhuiris, Nessan Mac Giolla

1987-01-01

Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.

A Reduced Basis Method with Exact-Solution Certificates for Symmetric Coercive Equations

DTIC Science & Technology

2013-11-06

the energy associated with the infinite - dimensional weak solution of parametrized symmetric coercive partial differential equations with piecewise...builds bounds with respect to the infinite - dimensional weak solution, aims to entirely remove the issue of the “truth” within the certified reduced basis...framework. We in particular introduce a reduced basis method that provides rigorous upper and lower bounds

Infinite Conservation Laws, Continuous Symmetries and Invariant Solutions of Some Discrete Integrable Equations

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Zhang, Xiang-Zhi; Dong, Huan-He

2017-12-01

Two new shift operators are introduced for which a few differential-difference equations are generated by applying the R-matrix method. These equations can be reduced to the standard Toda lattice equation and (1+1)-dimensional and (2+1)-dimensional Toda-type equations which have important applications in hydrodynamics, plasma physics, and so on. Based on these consequences, we deduce the Hamiltonian structures of two discrete systems. Finally, we obtain some new infinite conservation laws of two discrete equations and employ Lie-point transformation group to obtain some continuous symmetries and part of invariant solutions for the (1+1) and (2+1)-dimensional Toda-type equations. Supported by the Fundamental Research Funds for the Central University under Grant No. 2017XKZD11

Infinite variance in fermion quantum Monte Carlo calculations.

PubMed

Shi, Hao; Zhang, Shiwei

2016-03-01

For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.

Electronic excitations in finite and infinite polyenes

NASA Astrophysics Data System (ADS)

Tavan, Paul; Schulten, Klaus

1987-09-01

We study electronic excitations in long polyenes, i.e., in one-dimensional strongly correlated electron systems which are neither infinite nor small. The excitations are described within Hubbard and Pariser-Parr-Pople (PPP) models by means of a multiple-reference double-excitation expansion [P. Tavan and K. Schulten, J. Chem. Phys. 85, 6602 (1986)]. We find that quantized ``transition'' momenta can be assigned to electronic excitations in finite chains. These momenta link excitation energies of finite chains to dispersion relations of infinite chains, i.e., they bridge the gap between finite and infinite systems. A key result is the following: Excitation energies E in polyenes with N carbon atoms are described very accurately by the formula Eβ=ΔEβ0+αβk(N)q, q=1,2,..., where β denotes the excitation class, ΔEβ0 the energy gap in the infinite system [αβk(N)>0], and k(N) the elementary transition momentum. The parameters ΔEβ0 and αβ are determined for covalent and ionic excitations in alternating and nonalternating polyenes. The covalent excitations are combinations of triplet excitations T, i.e., T, TT, TTT, . . . . The lowest singlet excitations in the infinite polyene, e.g., in polyacetylene or polydiacetylene, are TT states. Available evidence proves that these states can dissociate into separate triplets. The bond structure of TT states is that of a neutral soliton-antisoliton pair. The level density of TT states in long polyenes is high enough to allow dissociation into separate solitons.

Observation of a Relaxed Plasma State in a Quasi-Infinite Cylinder

NASA Astrophysics Data System (ADS)

Gray, T.; Brown, M. R.; Dandurand, D.

2013-02-01

A helical relaxed plasma state is observed in a long cylindrical volume. The cylinder is long enough so that the predicted minimum energy state is a close approximation to the infinite cylinder solution. The plasma is injected at v≥50km/s by a coaxial magnetized plasma gun located at one end of the cylindrical volume. The relaxed state is rapidly attained in 1-2 axial Alfvén times after initiation of the plasma. Magnetic data are favorably compared with an analytical model. Magnetic data exhibit broadband fluctuations of the measured axial modes during the formation period. The broadband activity rapidly decays as the energy condenses into the lowest energy mode, which is in agreement with the minimum energy eigenstate of ∇×B=λB.

Infinite time interval backward stochastic differential equations with continuous coefficients.

PubMed

Zong, Zhaojun; Hu, Feng

2016-01-01

In this paper, we study the existence theorem for [Formula: see text] [Formula: see text] solutions to a class of 1-dimensional infinite time interval backward stochastic differential equations (BSDEs) under the conditions that the coefficients are continuous and have linear growths. We also obtain the existence of a minimal solution. Furthermore, we study the existence and uniqueness theorem for [Formula: see text] [Formula: see text] solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients. It should be pointed out that the assumptions of this result is weaker than that of Theorem 3.1 in Zong (Turkish J Math 37:704-718, 2013).

Robust Consumption-Investment Problem on Infinite Horizon

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

Zawisza, Dariusz, E-mail: dariusz.zawisza@im.uj.edu.pl

In our paper we consider an infinite horizon consumption-investment problem under a model misspecification in a general stochastic factor model. We formulate the problem as a stochastic game and finally characterize the saddle point and the value function of that game using an ODE of semilinear type, for which we provide a proof of an existence and uniqueness theorem for its solution. Such equation is interested on its own right, since it generalizes many other equations arising in various infinite horizon optimization problems.

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

USGS Publications Warehouse

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

2004-01-01

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

Observation of a relaxed plasma state in a quasi-infinite cylinder.

PubMed

Gray, T; Brown, M R; Dandurand, D

2013-02-22

A helical relaxed plasma state is observed in a long cylindrical volume. The cylinder is long enough so that the predicted minimum energy state is a close approximation to the infinite cylinder solution. The plasma is injected at v ≥ 50 km/s by a coaxial magnetized plasma gun located at one end of the cylindrical volume. The relaxed state is rapidly attained in 1-2 axial Alfvén times after initiation of the plasma. Magnetic data are favorably compared with an analytical model. Magnetic data exhibit broadband fluctuations of the measured axial modes during the formation period. The broadband activity rapidly decays as the energy condenses into the lowest energy mode, which is in agreement with the minimum energy eigenstate of [Symbol: see text] × B = λB.

Identities of Finitely Generated Algebras Over AN Infinite Field

NASA Astrophysics Data System (ADS)

Kemer, A. R.

1991-02-01

It is proved that for each finitely generated associative PI-algebra U over an infinite field F, there is a finite-dimensional F-algebra C such that the ideals of identities of the algebras U and C coincide. This yields a positive solution to the local problem of Specht for algebras over an infinite field: A finitely generated free associative algebra satisfies the maximum condition for T-ideals.

Infinite Multiplets

DOE R&D Accomplishments Database

Nambu, Y.

1967-01-01

The main ingredients of the method of infinite multiplets consist of: 1) the use of wave functions with an infinite number of components for describing an infinite tower of discrete states of an isolated system (such as an atom, a nucleus, or a hadron), 2) the use of group theory, instead of dynamical considerations, in determining the properties of the wave functions.

Numerical Solution of the Flow of a Perfect Gas Over A Circular Cylinder at Infinite Mach Number

NASA Technical Reports Server (NTRS)

Hamaker, Frank M.

1959-01-01

A solution for the two-dimensional flow of an inviscid perfect gas over a circular cylinder at infinite Mach number is obtained by numerical methods of analysis. Nonisentropic conditions of curved shock waves and vorticity are included in the solution. The analysis is divided into two distinct regions, the subsonic region which is analyzed by the relaxation method of Southwell and the supersonic region which was treated by the method of characteristics. Both these methods of analysis are inapplicable on the sonic line which is therefore considered separately. The shapes of the sonic line and the shock wave are obtained by iteration techniques. The striking result of the solution is the strong curvature of the sonic line and of the other lines of constant Mach number. Because of this the influence of the supersonic flow on the sonic line is negligible. On comparison with Newtonian flow methods, it is found that the approximate methods show a larger variation of surface pressure than is given by the present solution.

A reference-modified density functional theory: An application to solvation free-energy calculations for a Lennard-Jones solution.

PubMed

Sumi, Tomonari; Maruyama, Yutaka; Mitsutake, Ayori; Koga, Kenichiro

2016-06-14

In the conventional classical density functional theory (DFT) for simple fluids, an ideal gas is usually chosen as the reference system because there is a one-to-one correspondence between the external field and the density distribution function, and the exact intrinsic free-energy functional is available for the ideal gas. In this case, the second-order density functional Taylor series expansion of the excess intrinsic free-energy functional provides the hypernetted-chain (HNC) approximation. Recently, it has been shown that the HNC approximation significantly overestimates the solvation free energy (SFE) for an infinitely dilute Lennard-Jones (LJ) solution, especially when the solute particles are several times larger than the solvent particles [T. Miyata and J. Thapa, Chem. Phys. Lett. 604, 122 (2014)]. In the present study, we propose a reference-modified density functional theory as a systematic approach to improve the SFE functional as well as the pair distribution functions. The second-order density functional Taylor series expansion for the excess part of the intrinsic free-energy functional in which a hard-sphere fluid is introduced as the reference system instead of an ideal gas is applied to the LJ pure and infinitely dilute solution systems and is proved to remarkably improve the drawbacks of the HNC approximation. Furthermore, the third-order density functional expansion approximation in which a factorization approximation is applied to the triplet direct correlation function is examined for the LJ systems. We also show that the third-order contribution can yield further refinements for both the pair distribution function and the excess chemical potential for the pure LJ liquids.

Boundary effect on the elastic field of a semi-infinite solid containing inhomogeneities

PubMed Central

Liu, Y. J.; Song, G.; Yin, H. M.

2015-01-01

The boundary effect of one inhomogeneity embedded in a semi-infinite solid at different depths has firstly been investigated using the fundamental solution for Mindlin's problem. Expanding the eigenstrain in a polynomial form and using the Eshelby's equivalent inclusion method, one can calculate the eigenstrain and thus obtain the elastic field. When the inhomogeneity is far from the boundary, the solution recovers Eshelby's solution. The method has been extended to a many-particle system in a semi-infinite solid, which is first demonstrated by the cases of two spheres. The comparison of the asymptotic form solution with the finite-element results shows the accuracy and capability of this method. The solution has been used to illustrate the boundary effects on its effective material behaviour of a semi-infinite simple cubic lattice particulate composite. The local field of a semi-infinite composite has been calculated at different volume fractions. A representative unit cell has been taken with different depths to the surface. The average stress and strain of the unit cell have been calculated under uniform loading conditions of normal or shear force on the surface, respectively. The effective elastic moduli of the unit cell not only depend on the material proportion, but also on its distance to the surface. The present model can be extended to other types of particle distribution and ellipsoidal particles. PMID:26345084

Boundary effect on the elastic field of a semi-infinite solid containing inhomogeneities.

PubMed

Liu, Y J; Song, G; Yin, H M

2015-07-08

The boundary effect of one inhomogeneity embedded in a semi-infinite solid at different depths has firstly been investigated using the fundamental solution for Mindlin's problem. Expanding the eigenstrain in a polynomial form and using the Eshelby's equivalent inclusion method, one can calculate the eigenstrain and thus obtain the elastic field. When the inhomogeneity is far from the boundary, the solution recovers Eshelby's solution. The method has been extended to a many-particle system in a semi-infinite solid, which is first demonstrated by the cases of two spheres. The comparison of the asymptotic form solution with the finite-element results shows the accuracy and capability of this method. The solution has been used to illustrate the boundary effects on its effective material behaviour of a semi-infinite simple cubic lattice particulate composite. The local field of a semi-infinite composite has been calculated at different volume fractions. A representative unit cell has been taken with different depths to the surface. The average stress and strain of the unit cell have been calculated under uniform loading conditions of normal or shear force on the surface, respectively. The effective elastic moduli of the unit cell not only depend on the material proportion, but also on its distance to the surface. The present model can be extended to other types of particle distribution and ellipsoidal particles.

Comparison principle for impulsive functional differential equations with infinite delays and applications

NASA Astrophysics Data System (ADS)

Li, Xiaodi; Shen, Jianhua; Akca, Haydar; Rakkiyappan, R.

2018-04-01

We introduce the Razumikhin technique to comparison principle and establish some comparison results for impulsive functional differential equations (IFDEs) with infinite delays, where the infinite delays may be infinite time-varying delays or infinite distributed delays. The idea is, under the help of Razumikhin technique, to reduce the study of IFDEs with infinite delays to the study of scalar impulsive differential equations (IDEs) in which the solutions are easy to deal with. Based on the comparison principle, we study the qualitative properties of IFDEs with infinite delays , which include stability, asymptotic stability, exponential stability, practical stability, boundedness, etc. It should be mentioned that the developed results in this paper can be applied to IFDEs with not only infinite delays but also persistent impulsive perturbations. Moreover, even for the special cases of non-impulsive effects or/and finite delays, the criteria prove to be simpler and less conservative than some existing results. Finally, two examples are given to illustrate the effectiveness and advantages of the proposed results.

An analytic solution for periodic thermally-driven flows over an infinite slope

NASA Astrophysics Data System (ADS)

Zardi, Dino; Serafin, Stefano

2013-04-01

The flow generated along an infinite slope in an unperturbed stably stratified atmosphere at rest by a time periodic surface temperature forcing is examined. Following Defant (1949), a set of equations is derived which extends Prandtl's (1942) theory to allow for nonstationary conditions. Uniform boundary conditions are conducive to an along-slope parallel flow, governed by a periodically reversing local imbalance between along-slope advection and slope-normal fluxes of momentum and heat. Solutions include both a transient part and a subsequent periodic regime. The former can only be expressed in an integral form, whereas the latter is a combination of exponential and sine or cosine functions of time and height normal to the slope. Key parameters are the quantity Nα = N sinα (where α is the slope angle, and N is the Brunt-Väisälä frequency of the unperturbed atmosphere) and the angular frequency of the driving surface temperature cycle, ?. Three different flow regimes may occur, namely subcritical (Nα < ?), critical (Nα = ?) and supercritical (Nα > ?). The properties of the solutions in each regime are examined and discussed. The relationship between the present solutions and the earlier time-dependent slope flow model by Defant (1949) is also discussed. References Defant, F., 1949: Zur Theorie der Hangwinde, nebst Bemerkungen zur Theorie der Berg- und Talwinde. [A theory of slope winds, along with remarks on the theory of mountain winds and valley winds]. Arch. Meteor. Geophys. Bioclimatol., Ser. A, 1, 421-450 (Theoretical and Applied Climatology). [English translation: Whiteman, C.D., and E. Dreiseitl, 1984: Alpine meteorology: Translations of classic contributions by A. Wagner, E. Ekhart and F. Defant. PNL-5141 / ASCOT-84-3. Pacific Northwest Laboratory, Richland, Washington, 121 pp]. Prandtl, L., 1942: Strömungslehre [Flow Studies]. Vieweg und Sohn, Braunschweig, 382 pp.

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS

PubMed Central

OTT, WILLIAM; RIVAS, MAURICIO A.; WEST, JAMES

2016-01-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝN using a ‘typical’ nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence). PMID:28066028

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.

PubMed

Ott, William; Rivas, Mauricio A; West, James

2015-12-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).

Analytical solution for the transient wave propagation of a buried cylindrical P-wave line source in a semi-infinite elastic medium with a fluid surface layer

NASA Astrophysics Data System (ADS)

Shan, Zhendong; Ling, Daosheng

2018-02-01

This article develops an analytical solution for the transient wave propagation of a cylindrical P-wave line source in a semi-infinite elastic solid with a fluid layer. The analytical solution is presented in a simple closed form in which each term represents a transient physical wave. The Scholte equation is derived, through which the Scholte wave velocity can be determined. The Scholte wave is the wave that propagates along the interface between the fluid and solid. To develop the analytical solution, the wave fields in the fluid and solid are defined, their analytical solutions in the Laplace domain are derived using the boundary and interface conditions, and the solutions are then decomposed into series form according to the power series expansion method. Each item of the series solution has a clear physical meaning and represents a transient wave path. Finally, by applying Cagniard's method and the convolution theorem, the analytical solutions are transformed into the time domain. Numerical examples are provided to illustrate some interesting features in the fluid layer, the interface and the semi-infinite solid. When the P-wave velocity in the fluid is higher than that in the solid, two head waves in the solid, one head wave in the fluid and a Scholte wave at the interface are observed for the cylindrical P-wave line source.

Interplay between gravity and quintessence: a set of new GR solutions

NASA Astrophysics Data System (ADS)

Chernin, Arthur D.; Santiago, David I.; Silbergleit, Alexander S.

2002-02-01

A set of new exact analytical general relativity (GR) solutions with time-dependent and spatially inhomogeneous quintessence demonstrate (1) a static non-empty space-time with a horizon-type singular surface; (2) time-dependent spatially homogeneous `spheres' which are completely different in geometry from the Friedmann isotropic models; (3) infinitely strong anti-gravity at a `true' singularity where the density is infinitely large. It is also found that (4) the GR solutions allow for an extreme `density-free' form of energy that can generate regular space-time geometries.

Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

NASA Astrophysics Data System (ADS)

Chakrabarti, Aloknath; Mohapatra, Smrutiranjan

2013-09-01

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates, separated by a gap of finite width, floating horizontally on water of finite depth, are investigated in the present work for a two-dimensional time-harmonic case. Within the frame of linear water wave theory, the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions. Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem. In both the problems, the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates. Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations. The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration. The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

II. Comment on “Critique and correction of the currently accepted solution of the infinite spherical well in quantum mechanics” by Huang Young-Sea and Thomann Hans-Rudolph

NASA Astrophysics Data System (ADS)

Prados, Antonio; Plata, Carlos A.

2016-12-01

We comment on the paper "Critique and correction of the currently accepted solution of the infinite spherical well in quantum mechanics" by Huang Young-Sea and Thomann Hans-Rudolph, EPL 115, 60001 (2016) .

Wronskian solutions of the T-, Q- and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl (M | N)

NASA Astrophysics Data System (ADS)

Tsuboi, Zengo

2013-05-01

In [1] (Z. Tsuboi, Nucl. Phys. B 826 (2010) 399, arxiv:arXiv:0906.2039), we proposed Wronskian-like solutions of the T-system for [ M , N ]-hook of the general linear superalgebra gl (M | N). We have generalized these Wronskian-like solutions to the ones for the general T-hook, which is a union of [M1 ,N1 ]-hook and [M2 ,N2 ]-hook (M =M1 +M2, N =N1 +N2). These solutions are related to Weyl-type supercharacter formulas of infinite dimensional unitarizable modules of gl (M | N). Our solutions also include a Wronskian-like solution discussed in [2] (N. Gromov, V. Kazakov, S. Leurent, Z. Tsuboi, JHEP 1101 (2011) 155, arxiv:arXiv:1010.2720) in relation to the AdS5 /CFT4 spectral problem.

Regular and singular pulse and front solutions and possible isochronous behavior in the short-pulse equation: Phase-plane, multi-infinite series and variational approaches

NASA Astrophysics Data System (ADS)

Gambino, G.; Tanriver, U.; Guha, P.; Choudhury, A. Ghose; Choudhury, S. Roy

2015-02-01

In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane analysis is first employed to show the existence of breaking kink wave solutions in certain parameter regimes. Secondly, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic (heteroclinic) orbits of the traveling-wave equations for the SPE equation, as well as for its generalized version with arbitrary coefficients. These correspond to pulse (kink or shock) solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddle equilibrium points of the corresponding traveling-wave equations, as well as ensure simultaneous convergence and continuity of the multi-infinite series solutions for the homoclinic/heteroclinic orbits anchored by these saddle points. Unlike the majority of unaccelerated convergent series, high accuracy is attained with relatively few terms. And finally, variational methods are employed to generate families of both regular and embedded solitary wave solutions for the SPE PDE. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and it is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in analytical form (within the assumed ansatz for the trial functions). Thus, a direct error analysis is performed, showing the accuracy of the resulting solitary waves. Given the importance of solitary wave solutions in wave dynamics and information propagation in nonlinear PDEs, as well as the fact that not much is known about solutions of the family of generalized SPE equations considered here, the results obtained are both new and timely.

The Gauss-Bonnet operator of an infinite graph

NASA Astrophysics Data System (ADS)

Anné, Colette; Torki-Hamza, Nabila

2015-06-01

We propose a general condition, to ensure essential self-adjointness for the Gauss-Bonnet operator , based on a notion of completeness as Chernoff. This gives essential self-adjointness of the Laplace operator both for functions and 1-forms on infinite graphs. This is used to extend Flanders result concerning solutions of Kirchhoff's laws.

Mass predictions of atomic nuclei in the infinite nuclear matter model

NASA Astrophysics Data System (ADS)

Nayak, R. C.; Satpathy, L.

2012-07-01

We present here the mass excesses, binding energies, one- and two-neutron, one- and two-proton and α-particle separation energies of 6727 nuclei in the ranges 4≤Z≤120 and 8≤A≤303 calculated in the infinite nuclear matter model. Compared to our predictions of 1999 mass table, the present ones are obtained using larger data base of 2003 mass table of Wapstra and Audi and resorting to higher accuracy in the solutions of the η-differential equations of the INM model. The local energy η's supposed to carry signature of the characteristic properties of nuclei are found to possess the predictive capability. In fact η-systematics reveal new magic numbers in the drip-line regions giving rise to new islands of stability supported by relativistic mean field theoretic calculations. This is a manifestation of a new phenomenon where shell-effect overcomes the instability due to repulsive components of the nucleon-nucleon force broadening the stability peninsula. The two-neutron separation energy-systematics derived from the present mass predictions reveal a general new feature for the existence of islands of inversion in the exotic neutron-rich regions of nuclear landscape, apart from supporting the presently known islands around 31Na and 62Ti. The five global parameters representing the properties of infinite nuclear matter, the surface, the Coulomb and the pairing terms are retained as per our 1999 mass table. The root-mean-square deviation of the present mass-fit to 2198 known masses is 342 keV, while the mean deviation is 1.3 keV, reminiscent of no left-over systematic effects. This is a substantive improvement over our 1999 mass table having rms deviation of 401 keV and mean deviation of 9 keV for 1884 data nuclei.

Mass predictions of atomic nuclei in the infinite nuclear matter model

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

Nayak, R.C., E-mail: rcnayak00@yahoo.com; Satpathy, L., E-mail: satpathy@iopb.res.in

We present here the mass excesses, binding energies, one- and two-neutron, one- and two-proton and {alpha}-particle separation energies of 6727 nuclei in the ranges 4{<=}Z{<=}120 and 8{<=}A{<=}303 calculated in the infinite nuclear matter model. Compared to our predictions of 1999 mass table, the present ones are obtained using larger data base of 2003 mass table of Wapstra and Audi and resorting to higher accuracy in the solutions of the {eta}-differential equations of the INM model. The local energy {eta}'s supposed to carry signature of the characteristic properties of nuclei are found to possess the predictive capability. In fact {eta}-systematics revealmore » new magic numbers in the drip-line regions giving rise to new islands of stability supported by relativistic mean field theoretic calculations. This is a manifestation of a new phenomenon where shell-effect overcomes the instability due to repulsive components of the nucleon-nucleon force broadening the stability peninsula. The two-neutron separation energy-systematics derived from the present mass predictions reveal a general new feature for the existence of islands of inversion in the exotic neutron-rich regions of nuclear landscape, apart from supporting the presently known islands around {sup 31}Na and {sup 62}Ti. The five global parameters representing the properties of infinite nuclear matter, the surface, the Coulomb and the pairing terms are retained as per our 1999 mass table. The root-mean-square deviation of the present mass-fit to 2198 known masses is 342 keV, while the mean deviation is 1.3 keV, reminiscent of no left-over systematic effects. This is a substantive improvement over our 1999 mass table having rms deviation of 401 keV and mean deviation of 9 keV for 1884 data nuclei.« less

Controllability of semi-infinite rod heating by a point source

NASA Astrophysics Data System (ADS)

Khurshudyan, A.

2018-04-01

The possibility of control over heating of a semi-infinite thin rod by a point source concentrated at an inner point of the rod, is studied. Quadratic and piecewise constant solutions of the problem are derived, and the possibilities of solving appropriate problems of optimal control are indicated. Determining of the parameters of the piecewise constant solution is reduced to a problem of nonlinear programming. Numerical examples are considered.

Infinite slope stability under steady unsaturated seepage conditions

USGS Publications Warehouse

Lu, Ning; Godt, Jonathan W.

2008-01-01

We present a generalized framework for the stability of infinite slopes under steady unsaturated seepage conditions. The analytical framework allows the water table to be located at any depth below the ground surface and variation of soil suction and moisture content above the water table under steady infiltration conditions. The framework also explicitly considers the effect of weathering and porosity increase near the ground surface on changes in the friction angle of the soil. The factor of safety is conceptualized as a function of the depth within the vadose zone and can be reduced to the classical analytical solution for subaerial infinite slopes in the saturated zone. Slope stability analyses with hypothetical sandy and silty soils are conducted to illustrate the effectiveness of the framework. These analyses indicate that for hillslopes of both sandy and silty soils, failure can occur above the water table under steady infiltration conditions, which is consistent with some field observations that cannot be predicted by the classical infinite slope theory. A case study of shallow slope failures of sandy colluvium on steep coastal hillslopes near Seattle, Washington, is presented to examine the predictive utility of the proposed framework.

Do massive compact objects without event horizon exist in infinite derivative gravity?

NASA Astrophysics Data System (ADS)

Koshelev, Alexey S.; Mazumdar, Anupam

2017-10-01

Einstein's general theory of relativity is plagued by cosmological and black-hole type singularities Recently, it has been shown that infinite derivative, ghost free, gravity can yield nonsingular cosmological and mini-black hole solutions. In particular, the theory possesses a mass-gap determined by the scale of new physics. This paper provides a plausible argument, not a no-go theorem, based on the Area-law of gravitational entropy that within infinite derivative, ghost free, gravity nonsingular compact objects in the static limit need not have horizons.

Quark ensembles with the infinite correlation length

NASA Astrophysics Data System (ADS)

Zinov'ev, G. M.; Molodtsov, S. V.

2015-01-01

A number of exactly integrable (quark) models of quantum field theory with the infinite correlation length have been considered. It has been shown that the standard vacuum quark ensemble—Dirac sea (in the case of the space-time dimension higher than three)—is unstable because of the strong degeneracy of a state, which is due to the character of the energy distribution. When the momentum cutoff parameter tends to infinity, the distribution becomes infinitely narrow, leading to large (unlimited) fluctuations. Various vacuum ensembles—Dirac sea, neutral ensemble, color superconductor, and BCS state—have been compared. In the case of the color interaction between quarks, the BCS state has been certainly chosen as the ground state of the quark ensemble.

Propagation and radiation of sound from flanged circular ducts with circumferentially varying wall admittances. I Semi-infinite ducts. II - Finite ducts with sources

NASA Technical Reports Server (NTRS)

Fuller, C. R.

1984-01-01

Sound propagation in infinite, semiinfinite, and finite circular ducts with circumferentially varying wall admittances is investigated analytically. The infinite case is considered, and an example demonstrates the effects of wall-admittance distribution on dispersion characteristics and mode shapes. An exact solution is obtained for the semiinfinite case, a circular duct with a flanged opening: sidelobe suppression and circumferential-mode energy scattering leading to radiated-field asymmetry are found. A finite duct system with specified hard-walled pressure sources is examined in detail, evaluating reflection coefficients, transmission losses, and radiated-field directivity. Graphs and diagrams are provided, and the implications of the results obtained for the design of aircraft-turbofan inlet liners are discussed.

Study of the convective fluid flows with evaporation on the basis of the exact solution in a three-dimensional infinite channel

NASA Astrophysics Data System (ADS)

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

2017-09-01

The solution of special type of the Boussinesq approximation of the Navier - Stokes equations is used to simulate the two-layer evaporative fluid flows. This solution is the 3D generalization of the Ostroumov - Birikh solution of the equations of free convection. Modeling of the 3D fluid flows is performed in an infinite channel of the rectangular cross section without assumption of the axis-symmetrical character of the flows. Influence of gravity and evaporation on the dynamic and thermal phenomena in the system is studied. The fluid flow patterns are determined by various thermal, mechanical and structural effects. Numerical investigations are performed for the liquid - gas system like ethanol - nitrogen and HFE-7100 - nitrogen under conditions of normal and low gravity. The solution allows one to describe a formation of the thermocapillary rolls and multi-vortex structures in the system. Alteration of topology and character of the flows takes place with change of the intensity of the applied thermal load, thermophysical properties of working media and gravity action. Flows with translational, translational-rotational or partially reverse motion can be formed in the system.

Dynamics with infinitely many time derivatives in Friedmann-Robertson-Walker background and rolling tachyons

NASA Astrophysics Data System (ADS)

Joukovskaya, Liudmila

2009-02-01

Dynamics with infinitely many time derivatives has place in string field theory and have been profoundly investigated there. Recently there has been considerable interest in theories with infinitely many derivatives in the cosmological context in view of new features which these theories might accommodate owing to nonlocal interaction. In present work we continue investigation of such models, as a concrete example we study the dynamics of unstable D-brane in the open string theory in the Friedmann-Robertson-Walker background. We construct numerical solutions describing dynamical interpolation between the perturbative and non-perturbative vacua. The obtained solutions have several interesting properties and might be of interest from the cosmological points of view.

New compacton soliton solutions and solitary patterns solutions of nonlinearly dispersive Boussinesq equations

NASA Astrophysics Data System (ADS)

Yan, Zhenya; Bluman, George

2002-11-01

The special exact solutions of nonlinearly dispersive Boussinesq equations (called B( m, n) equations), utt- uxx- a( un) xx+ b( um) xxxx=0, is investigated by using four direct ansatze. As a result, abundant new compactons: solitons with the absence of infinite wings, solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions of these two equations are obtained. The variant is extended to include linear dispersion to support compactons and solitary patterns in the linearly dispersive Boussinesq equations with m=1. Moreover, another new compacton solution of the special case, B(2,2) equation, is also found.

Scalable L-infinite coding of meshes.

PubMed

Munteanu, Adrian; Cernea, Dan C; Alecu, Alin; Cornelis, Jan; Schelkens, Peter

2010-01-01

The paper investigates the novel concept of local-error control in mesh geometry encoding. In contrast to traditional mesh-coding systems that use the mean-square error as target distortion metric, this paper proposes a new L-infinite mesh-coding approach, for which the target distortion metric is the L-infinite distortion. In this context, a novel wavelet-based L-infinite-constrained coding approach for meshes is proposed, which ensures that the maximum error between the vertex positions in the original and decoded meshes is lower than a given upper bound. Furthermore, the proposed system achieves scalability in L-infinite sense, that is, any decoding of the input stream will correspond to a perfectly predictable L-infinite distortion upper bound. An instantiation of the proposed L-infinite-coding approach is demonstrated for MESHGRID, which is a scalable 3D object encoding system, part of MPEG-4 AFX. In this context, the advantages of scalable L-infinite coding over L-2-oriented coding are experimentally demonstrated. One concludes that the proposed L-infinite mesh-coding approach guarantees an upper bound on the local error in the decoded mesh, it enables a fast real-time implementation of the rate allocation, and it preserves all the scalability features and animation capabilities of the employed scalable mesh codec.

Solute atmospheres at dislocations

DOE PAGES

Hirth, John P.; Barnett, David M.; Hoagland, Richard G.

2017-06-01

In this study, a two-dimensional plane strain elastic solution is determined for the Cottrell solute atmosphere around an edge dislocation in an infinitely long cylinder of finite radius (the matrix), in which rows of solutes are represented by cylindrical rods with in-plane hydrostatic misfit (axial misfit is also considered). The periphery of the matrix is traction-free, thus introducing an image solute field which generates a solute-solute interaction energy that has not been considered previously. The relevant energy for the field of any distribution of solutes coexistent with a single edge dislocation along the (matrix) cylinder axis is determined, and coherencymore » effects are discussed and studied. Monte Carlo simulations accounting for all pertinent interactions over a range of temperatures are found to yield solute distributions different from classical results, namely, (1) Fermi-Dirac condensations at low temperatures at the free surface, (2) the majority of the atmosphere lying within an unexpectedly large non-linear interaction region near the dislocation core, and (3) temperature-dependent asymmetrical solute arrangements that promote bending. The solute distributions at intermediate temperatures show a 1/r dependence in agreement with previous linearized approximations. With a standard state of solute corresponding to a mean concentration, c 0, the relevant interaction energy expression presented in this work is valid when extended to large concentrations for which Henry's Law and Vegard's Law do not apply.« less

Solute atmospheres at dislocations

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

Hirth, John P.; Barnett, David M.; Hoagland, Richard G.

In this study, a two-dimensional plane strain elastic solution is determined for the Cottrell solute atmosphere around an edge dislocation in an infinitely long cylinder of finite radius (the matrix), in which rows of solutes are represented by cylindrical rods with in-plane hydrostatic misfit (axial misfit is also considered). The periphery of the matrix is traction-free, thus introducing an image solute field which generates a solute-solute interaction energy that has not been considered previously. The relevant energy for the field of any distribution of solutes coexistent with a single edge dislocation along the (matrix) cylinder axis is determined, and coherencymore » effects are discussed and studied. Monte Carlo simulations accounting for all pertinent interactions over a range of temperatures are found to yield solute distributions different from classical results, namely, (1) Fermi-Dirac condensations at low temperatures at the free surface, (2) the majority of the atmosphere lying within an unexpectedly large non-linear interaction region near the dislocation core, and (3) temperature-dependent asymmetrical solute arrangements that promote bending. The solute distributions at intermediate temperatures show a 1/r dependence in agreement with previous linearized approximations. With a standard state of solute corresponding to a mean concentration, c 0, the relevant interaction energy expression presented in this work is valid when extended to large concentrations for which Henry's Law and Vegard's Law do not apply.« less

Clean Energy Solutions Center: Assisting Countries with Clean Energy Policy

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Energy Solutions Center: Assisting Countries with Clean Energy Policy NREL helps developing countries and adapting to climate change impacts, developing countries are looking for clean energy solutions supports clean energy scale-up in the developing world are knowledge, capacity, and cost. The Clean Energy

Infinitely Dilute Partial Molar Properties of Proteins from Computer Simulation

PubMed Central

2015-01-01

A detailed understanding of temperature and pressure effects on an infinitely dilute protein’s conformational equilibrium requires knowledge of the corresponding infinitely dilute partial molar properties. Established molecular dynamics methodologies generally have not provided a way to calculate these properties without either a loss of thermodynamic rigor, the introduction of nonunique parameters, or a loss of information about which solute conformations specifically contributed to the output values. Here we implement a simple method that is thermodynamically rigorous and possesses none of the above disadvantages, and we report on the method’s feasibility and computational demands. We calculate infinitely dilute partial molar properties for two proteins and attempt to distinguish the thermodynamic differences between a native and a denatured conformation of a designed miniprotein. We conclude that simple ensemble average properties can be calculated with very reasonable amounts of computational power. In contrast, properties corresponding to fluctuating quantities are computationally demanding to calculate precisely, although they can be obtained more easily by following the temperature and/or pressure dependence of the corresponding ensemble averages. PMID:25325571

Infinitely dilute partial molar properties of proteins from computer simulation.

PubMed

Ploetz, Elizabeth A; Smith, Paul E

2014-11-13

A detailed understanding of temperature and pressure effects on an infinitely dilute protein's conformational equilibrium requires knowledge of the corresponding infinitely dilute partial molar properties. Established molecular dynamics methodologies generally have not provided a way to calculate these properties without either a loss of thermodynamic rigor, the introduction of nonunique parameters, or a loss of information about which solute conformations specifically contributed to the output values. Here we implement a simple method that is thermodynamically rigorous and possesses none of the above disadvantages, and we report on the method's feasibility and computational demands. We calculate infinitely dilute partial molar properties for two proteins and attempt to distinguish the thermodynamic differences between a native and a denatured conformation of a designed miniprotein. We conclude that simple ensemble average properties can be calculated with very reasonable amounts of computational power. In contrast, properties corresponding to fluctuating quantities are computationally demanding to calculate precisely, although they can be obtained more easily by following the temperature and/or pressure dependence of the corresponding ensemble averages.

Infinite lattices of vortex molecules in Rabi-coupled condensates

NASA Astrophysics Data System (ADS)

Mencia Uranga, B.; Lamacraft, Austen

2018-04-01

Vortex molecules can form in a two-component superfluid when a Rabi field drives transitions between the two components. We study the ground state of an infinite system of vortex molecules in two dimensions, using a numerical scheme which makes no use of the lowest Landau level approximation. We find the ground state lattice geometry for different values of intercomponent interactions and strength of the Rabi field. In the limit of large field when molecules are tightly bound, we develop a complementary analytical description. The energy governing the alignment of molecules on a triangular lattice is found to correspond to that of an infinite system of two-dimensional quadrupoles, which may be written in terms of an elliptic function Q (zi j;ω1,ω2) . This allows for a numerical evaluation of the energy which enables us to find the ground state configuration of the molecules.

Boundary Conditions for Infinite Conservation Laws

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

On the contact interaction of two identical stringers with an elastic semi-infinite continuous or vertically cracked plate

NASA Astrophysics Data System (ADS)

Grigoryan, M. S.

2018-04-01

This paper considers two connected contact problems on the interaction of stringers with an elastic semi-infinite plate. In the first problem, an elastic half-infinite continuous plate is reinforced on its boundary by two identical stringers exposed to a tensile external force. In the second problem, in the presence of the same stringers, the plate contains a collinear system of cracks on its vertical axis. The solution of both problems is reduced to the solution of singular integral equations (SIE) that are solved by a known numerical-analytical method.

Particlelike solutions of the Einstein-Dirac equations

NASA Astrophysics Data System (ADS)

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

1999-05-01

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

Infinite order sudden approximation for rotational energy transfer in gaseous mixtures

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

Goldflam, R.; Green, S.; Kouri, D.J.

1977-11-01

Rotational energy transfer in gaseous mixtures has been considered within the framework of the infinite order sudden (IOS) approximation. A new derivation of the IOS from the coupled states Lippmann--Schwinger equation is given. This approach shows the relation between the IOS and CS T matrices and also shows in a rather transparent fashion Sencrest's result that the IOS method does not truncate closed channels but rather employs a closure relation to sum over all rotor states. The general CS effective cross section formula for relaxation processes is used, along with the IOS approximation to the CS T matrix, to derivemore » the general IOS effctive cross section.Factorization permits one to calculate other types of cross sections if any one type of cross section has been obtained by some procedure. The functional form can also be used to compact data. This formalism has been applied to calculate pressure broadening for the systems HD--He, HCl--He, CO--He, HCN--He, HCl--Ar, and CO/sub 2/--Ar. To test the IOS approximation, comparisons have been made to the CS results, which are known to be accurate for all these systems. The IOS approximation is found to be very accurate whenever the rotor spacings are small compared to the kinetic energy, provided closed channels do not play too great a role. For the systems CO--He, HCN--He, and CO/sub 2/--Ar, these conditions are well satisfied and the IOS is found to yield results accurate to within 10%--15%.« less

An isotherm-based thermodynamic model of multicomponent aqueous solutions, applicable over the entire concentration range.

PubMed

Dutcher, Cari S; Ge, Xinlei; Wexler, Anthony S; Clegg, Simon L

2013-04-18

In previous studies (Dutcher et al. J. Phys. Chem. C 2011, 115, 16474-16487; 2012, 116, 1850-1864), we derived equations for the Gibbs energy, solvent and solute activities, and solute concentrations in multicomponent liquid mixtures, based upon expressions for adsorption isotherms that include arbitrary numbers of hydration layers on each solute. In this work, the long-range electrostatic interactions that dominate in dilute solutions are added to the Gibbs energy expression, thus extending the range of concentrations for which the model can be used from pure liquid solute(s) to infinite dilution in the solvent, water. An equation for the conversion of the reference state for solute activity coefficients to infinite dilution in water has been derived. A number of simplifications are identified, notably the equivalence of the sorption site parameters r and the stoichiometric coefficients of the solutes, resulting in a reduction in the number of model parameters. Solute concentrations in mixtures conform to a modified Zdanovskii-Stokes-Robinson mixing rule, and solute activity coefficients to a modified McKay-Perring relation, when the effects of the long-range (Debye-Hückel) term in the equations are taken into account. Practical applications of the equations to osmotic and activity coefficients of pure aqueous electrolyte solutions and mixtures show both satisfactory accuracy from low to high concentrations, together with a thermodynamically reasonable extrapolation (beyond the range of measurements) to extreme concentration and to the pure liquid solute(s).

Acoustic plane wave diffraction from a truncated semi-infinite cone in axial irradiation

NASA Astrophysics Data System (ADS)

Kuryliak, Dozyslav; Lysechko, Victor

2017-11-01

The diffraction problem of the plane acoustic wave on the semi-infinite truncated soft and rigid cones in the case of axial incidence is solved. The problem is formulated as a boundary-value problem in terms of Helmholtz equation, with Dirichlet and Neumann boundary conditions, for scattered velocity potential. The incident field is taken to be the total field of semi-infinite cone, the expression of which is obtained by solving the auxiliary diffraction problem by the use of Kontorovich-Lebedev integral transformation. The diffracted field is sought via the expansion in series of the eigenfunctions for subdomains of the Helmholtz equation taking into account the edge condition. The corresponding diffraction problem is reduced to infinite system of linear algebraic equations (ISLAE) making use of mode matching technique and orthogonality properties of the Legendre functions. The method of analytical regularization is applied in order to extract the singular part in ISLAE, invert it exactly and reduce the problem to ISLAE of the second kind, which is readily amenable to calculation. The numerical solution of this system relies on the reduction method; and its accuracy depends on the truncation order. The case of degeneration of the truncated semi-infinite cone into an aperture in infinite plane is considered. Characteristic features of diffracted field in near and far fields as functions of cone's parameters are examined.

Nonexistence of compressible irrotational inviscid flows along infinite protruding corners

NASA Astrophysics Data System (ADS)

Elling, Volker

2018-06-01

We consider inviscid flow with isentropic coefficient greater than one. For flow along smooth infinite protruding corners, we attempt to impose a nonzero limit for velocity at infinity at the upstream wall. We prove that the problem does not have any irrotational uniformly subsonic solutions, whereas rotational flows do exist. This can be considered a case of a slip-condition solid "generating" vorticity in inviscid flow.

Decay of Solutions of the Wave Equation in the Kerr Geometry

NASA Astrophysics Data System (ADS)

Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T.

2006-06-01

We consider the Cauchy problem for the massless scalar wave equation in the Kerr geometry for smooth initial data compactly supported outside the event horizon. We prove that the solutions decay in time in L ∞ loc. The proof is based on a representation of the solution as an infinite sum over the angular momentum modes, each of which is an integral of the energy variable ω on the real line. This integral representation involves solutions of the radial and angular ODEs which arise in the separation of variables.

Solution of the radiative transfer equation for Rayleigh scattering using the infinite medium Green's function

NASA Astrophysics Data System (ADS)

Biçer, M.; Kaşkaş, A.

2018-03-01

The infinite medium Green's function is used to solve the half-space albedo, slab albedo and Milne problems for the unpolarized Rayleigh scattering case; these problems are the most classical problems of radiative transfer theory. The numerical results are obtained and are compared with previous ones.

A new scheme of the time-domain fluorescence tomography for a semi-infinite turbid medium

NASA Astrophysics Data System (ADS)

Prieto, Kernel; Nishimura, Goro

2017-04-01

A new scheme for reconstruction of a fluorophore target embedded in a semi-infinite medium was proposed and evaluated. In this scheme, we neglected the presence of the fluorophore target for the excitation light and used an analytical solution of the time-dependent radiative transfer equation (RTE) for the excitation light in a homogeneous semi-infinite media instead of solving the RTE numerically in the forward calculation. The inverse problem for imaging the fluorophore target was solved using the Landweber-Kaczmarz method with the concept of the adjoint fields. Numerical experiments show that the proposed scheme provides acceptable results of the reconstructed shape and location of the target. The computation times of the solution of the forward problem and the whole reconstruction process were reduced by about 40 and 15%, respectively.

The effects of magnetohydrodynamic and radiation on flow of second grade fluid past an infinite inclined plate in porous medium

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

Ismail, Zulkhibri; Khan, Ilyas; Nasir, Nadirah Mohd

2015-02-03

An analysis of the exact solutions of second grade fluid problem for unsteady magnetohydrodynamic (MHD) flows past an infinite inclined plate in a porous medium is presented. It is assumed that the bounding infinite inclined plate has a constant temperature with radiation effects. Based on Boussinesq approximation the expressions for dimensionless velocity, temperature and concentration are obtained by using Laplace transform method. The derived solutions satisfying the involved differential equations, and all the boundary and initial conditions. The influence of various parameters on the velocity has been illustrated graphically and analyzed.

Determination of diffusion coefficients of various livestock antibiotics in water at infinite dilution

NASA Astrophysics Data System (ADS)

Soriano, Allan N.; Adamos, Kristoni G.; Bonifacio, Pauline B.; Adornado, Adonis P.; Bungay, Vergel C.; Vairavan, Rajendaran

2017-11-01

The fate of antibiotics entering the environment raised concerns on the possible effect of antimicrobial resistance bacteria. Prediction of the fate and transport of these particles are needed to be determined, significantly the diffusion coefficient of antibiotic in water at infinite dilution. A systematic determination of diffusion coefficient of antibiotic in water at infinite dilution of five different kinds of livestock antibiotics namely: Amtyl, Ciprotyl, Doxylak Forte, Trisullak, and Vetracin Gold in the 293.15 to 313.15 K temperature range are reported through the use of the method involving the electrolytic conductivity measurements. A continuous stirred tank reactor is utilized to measure the electrolytic conductivities of the considered systems. These conductivities are correlated by using the Nernst-Haskell equation to determine the infinite dilution diffusion coefficient. Determined diffusion coefficients are based on the assumption that in dilute solution, these antibiotics behave as strong electrolyte from which H+ cation dissociate from the antibiotic's anion.

75 FR 76962 - Application To Export Electric Energy; MAG Energy Solutions, Inc.

Federal Register 2010, 2011, 2012, 2013, 2014

2010-12-10

... DEPARTMENT OF ENERGY [OE Docket No. EA-306-A] Application To Export Electric Energy; MAG Energy Solutions, Inc. AGENCY: Office of Electricity Delivery and Energy Reliability, DOE. ACTION: Notice of Application. SUMMARY: MAG Energy Solutions, Inc. (MAG E.S.) has applied to renew its authority to transmit...

Simulation of water solutions of Ni 2+ at infinite dilution

NASA Astrophysics Data System (ADS)

Natália, M.; Cordeiro, D. S.; Ignaczak, Anna; Gomes, José A. N. F.

1993-10-01

A new ab initio pair potential is developed to describe the nickel—water interactions in Ni(II) aqueous solutions. Results of Monte Carlo simulations for the Ni(II)(H 2O) 200 system are presented for this pair potential with and without three-body classical polarization terms (the water—water interaction is described by the ab initio MCY potential). The structure of the solution around Ni(II) is discussed in terms of radial distribution functions, coordination numbers and thermal ellipsoids. The results show that the three-body terms have a non-negligible effect on the simulated solution. In fact, the experimental coordination number of six is reproduced with the full potential while a higher value is predicted when the simple pairwise-additive potential is used. The equilibrium NiO distance for the first hydration shell is also dependent on the use of the three-body terms. Comparison of our distribution functions with those obtained by neutron-diffraction experiments shows a reasonable quantitative agreement. Statistical pattern recognition analysis has also been applied to our simulations in order to better understand the local thermal motion of the water molecules around the metal ion. In this way, thermal ellipsoids have been computed (and graphically displayed) for each atom of the water molecules belonging to the Ni(II) first hydration shell. This analysis revealed that the twisting and bending motions are greater than the radial motion, and that the hydrogens have a higher mobility than the oxygens. In addition, a thermodynamic perturbation method has been incorporated in our Monte Carlo procedure in order to compute the free energy of hydration for the Ni(II) ion. Agreement between these results and the experimental ones is also sufficiently reasonable to demonstrate the feasibility of this new potential for the nickel—water interactions.

Clean Energy Solutions Center Services (Chinese Translation)

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

2016-03-01

This is a Mandarin translation of the Clean Energy Solutions Center fact sheet. The Solutions Center offers no-cost expert policy assistance, webinars and training forums, clean energy policy reports, data, and tools provided in partnership with more than 35 leading international and regional clean energy organizations.

Clean Energy Solutions Center Services (Vietnamese Translation)

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

2016-03-01

This is a Vietnamese translation of the Clean Energy Solutions Center fact sheet. The Solutions Center offers no-cost expert policy assistance, webinars and training forums, clean energy policy reports, data, and tools provided in partnership with more than 35 leading international and regional clean energy organizations.

Clean Energy Solutions Center Services (French Translation)

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

This is a French translation of the Clean Energy Solutions Center fact sheet. The Solutions Center offers no-cost expert policy assistance, webinars and training forums, clean energy policy reports, data, and tools provided in partnership with more than 35 leading international and regional clean energy organizations.

Clean Energy Solutions Center Services (Arabic Translation)

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

2016-03-01

This is an Arabic translation of the Clean Energy Solutions Center fact sheet. The Solutions Center offers no-cost expert policy assistance, webinars and training forums, clean energy policy reports, data, and tools provided in partnership with more than 35 leading international and regional clean energy organizations.

Edge effect on a vacancy state in semi-infinite graphene

NASA Astrophysics Data System (ADS)

Deng, Hai-Yao; Wakabayashi, Katsunori

2014-09-01

The edge effect on a single vacancy state of semi-infinite graphene (SIG) has been studied using Green's function method within the tight-binding model. In the case of infinite graphene, it is known that a vacancy induces a zero-energy resonance state, whose wave function decays inversely with distance (R) from the vacancy and is not normalizable. However, for SIG with an armchair edge, we find that the corresponding wave function decays as R-2 and hence becomes normalizable owing to the intervalley interference caused by the armchair edge. For SIG with a zigzag edge, the vacancy state depends on the sublattice of the vacancy. When the vacancy and the edge belong to different sublattices, the vacancy has no effect on the zero-energy vacancy state. In contrast, when the vacancy is located on the same sublattice as the edge, the resonance state disappears but the wave function at zero energy is strongly distorted near the vacancy. Our results reveal that the presence of edges crucially changes the vacancy state in graphene, and thus such a state can be used to probe the edge structure.

Clean Energy Solutions Center Services (Portuguese Translation)

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

This is a Portuguese translation of the Clean Energy Solutions Center Services fact sheet. The Solutions Center offers no-cost expert policy assistance, webinars and training forums, clean energy policy reports, data, and tools provided in partnership with more than 35 leading international and regional clean energy organizations.

Students' Conception of Infinite Series

ERIC Educational Resources Information Center

Martinez-Planell, Rafael; Gonzalez, Ana Carmen; DiCristina, Gladys; Acevedo, Vanessa

2012-01-01

This is a report of a study of students' understanding of infinite series. It has a three-fold purpose: to show that students may construct two essentially different notions of infinite series, to show that one of the constructions is particularly difficult for students, and to examine the way in which these two different constructions may be…

Clean Energy Solutions Center Services (Arabic Translation) (Fact Sheet)

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

Not Available

2014-06-01

This is the Arabic translation of the Clean Energy Solutions Center Services fact sheet. The Clean Energy Solutions Center (Solutions Center) helps governments, advisors and analysts create policies and programs that advance the deployment of clean energy technologies. The Solutions Center partners with international organizations to provide online training, expert assistance, and technical resources on clean energy policy.

Precise calculation of quasienergies of a driven two-level atom based on the Guo-Wu-Van Woerkom solution

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

Wang Yi; Zhang Jingtao; Xu Zhizhan

2010-07-15

The exact algebraic solution recently obtained by Guo, Wu, and Van Woerkom (Phys. Rev. A 73 (2006) 023419) made possible accurate calculations of quasienergies of a driven two-level atom with an arbitrary original energy spacing and laser intensity. Due to the complication of the analytic solutions that involves an infinite number of infinite determinants, many mathematical difficulties must be overcome to obtain precise values of quasienergies. In this paper, with a further developed algebraic method, we show how to solve the computational problem completely and results are presented in a data table. With this table, one can easily obtain allmore » quasienergies of a driven two-level atom with an arbitrary original energy spacing and arbitrary intensity and frequency of the driving laser. The numerical solution technique developed here can be applied to the calculation of Freeman resonances in photoelectron energy spectra. As an example for applications, we show how to use the data table to calculate the peak laser intensity at which a Freeman resonance occurs in the transition between the ground Xe 5p P{sub 3/2} state and the Rydberg state Xe 8p P{sub 3/2}.« less

Analytical energy gradient based on spin-free infinite-order Douglas-Kroll-Hess method with local unitary transformation

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

Nakajima, Yuya; Seino, Junji; Nakai, Hiromi, E-mail: nakai@waseda.jp

In this study, the analytical energy gradient for the spin-free infinite-order Douglas-Kroll-Hess (IODKH) method at the levels of the Hartree-Fock (HF), density functional theory (DFT), and second-order Møller-Plesset perturbation theory (MP2) is developed. Furthermore, adopting the local unitary transformation (LUT) scheme for the IODKH method improves the efficiency in computation of the analytical energy gradient. Numerical assessments of the present gradient method are performed at the HF, DFT, and MP2 levels for the IODKH with and without the LUT scheme. The accuracies are examined for diatomic molecules such as hydrogen halides, halogen dimers, coinage metal (Cu, Ag, and Au) halides,more » and coinage metal dimers, and 20 metal complexes, including the fourth–sixth row transition metals. In addition, the efficiencies are investigated for one-, two-, and three-dimensional silver clusters. The numerical results confirm the accuracy and efficiency of the present method.« less

Piezoelectric Energy Harvesting Solutions

PubMed Central

Caliò, Renato; Rongala, Udaya Bhaskar; Camboni, Domenico; Milazzo, Mario; Stefanini, Cesare; de Petris, Gianluca; Oddo, Calogero Maria

2014-01-01

This paper reviews the state of the art in piezoelectric energy harvesting. It presents the basics of piezoelectricity and discusses materials choice. The work places emphasis on material operating modes and device configurations, from resonant to non-resonant devices and also to rotational solutions. The reviewed literature is compared based on power density and bandwidth. Lastly, the question of power conversion is addressed by reviewing various circuit solutions. PMID:24618725

General Solutions for Hydromagnetic Free Convection Flow over an Infinite Plate with Newtonian Heating, Mass Diffusion and Chemical Reaction

NASA Astrophysics Data System (ADS)

Fetecau, Constatin; Shah, Nehad Ali; Vieru, Dumitru

2017-12-01

The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined. Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration, three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution (the steady-state), for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.

On Kronecker-Capelli type theorems for infinite systems

NASA Astrophysics Data System (ADS)

Fedorov, Foma M.; Potapova, Sargylana V.

2017-11-01

On the basis of the new concept of the decrement of an infinite matrices and determinants, we studied the inconsistency of a general infinite systems of linear algebraic equations. We proved the theorem on inconsistency of a infinite system when the decrement of its matrix is nonzero.

Black Plane Solutions and Localized Gravitational Energy

PubMed Central

Roberts, Jennifer

2015-01-01

We explore the issue of gravitational energy localization for static plane-symmetric solutions of the Einstein-Maxwell equations in 3+1 dimensions with asymptotic anti-de Sitter behavior. We apply three different energy-momentum complexes, the Einstein, Landau-Lifshitz, and Møller prescriptions, to the metric representing this category of solutions and determine the energy distribution for each. We find that the three prescriptions offer identical energy distributions, suggesting their utility for this type of model. PMID:27347499

Clean Energy Solutions Center Services (Vietnamese Translation) (Fact Sheet)

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

Not Available

2014-11-01

This is the Vietnamese language translation of the Clean Energy Solutions Center (Solutions Center) fact sheet. The Solutions Center helps governments, advisors and analysts create policies and programs that advance the deployment of clean energy technologies. The Solutions Center partners with international organizations to provide online training, expert assistance, and technical resources on clean energy policy.

Clean Energy Solutions Center Services (Chinese Translation) (Fact Sheet)

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

Not Available

2014-04-01

This is the Chinese language translation of the Clean Energy Solutions Center (Solutions Center) fact sheet. The Solutions Center helps governments, advisors and analysts create policies and programs that advance the deployment of clean energy technologies. The Solutions Center partners with international organizations to provide online training, expert assistance, and technical resources on clean energy policy.

Improving the Instruction of Infinite Series

ERIC Educational Resources Information Center

Lindaman, Brian; Gay, A. Susan

2012-01-01

Calculus instructors struggle to teach infinite series, and students have difficulty understanding series and related concepts. Four instructional strategies, prominently used during the calculus reform movement, were implemented during a 3-week unit on infinite series in one class of second-semester calculus students. A description of each…

On infinite-dimensional state spaces

NASA Astrophysics Data System (ADS)

Fritz, Tobias

2013-05-01

It is well known that the canonical commutation relation [x, p] = i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p] = i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V-1U2V = U3, then finite-dimensionality entails the relation UV-1UV = V-1UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V-1U2V = U3 holds only up to ɛ and then yields a lower bound on the dimension.

The virtual infinite capacitor

NASA Astrophysics Data System (ADS)

Yona, Guy; Weiss, George

2017-01-01

We define the virtual infinite capacitor (VIC) as a nonlinear capacitor that has the property that for an interval of the charge Q (the operating range), the voltage V remains constant. We propose a lossless approximate realisation for the VIC as a simple circuit with two controllers: a voltage controller acts fast to maintain the desired terminal voltage, while a charge controller acts more slowly and maintains the charge Q in the desired operating range by influencing the incoming current. The VIC is useful as a filter capacitor for various applications, for example, power factor compensators (PFC), as we describe. In spite of using small capacitors, the VIC can replace a very large capacitor in applications that do not require substantial energy storage. We give simulation results for a PFC working in critical conduction mode with a VIC for output voltage filtering.

Heuristic Green's function of the time dependent radiative transfer equation for a semi-infinite medium.

PubMed

Martelli, Fabrizio; Sassaroli, Angelo; Pifferi, Antonio; Torricelli, Alessandro; Spinelli, Lorenzo; Zaccanti, Giovanni

2007-12-24

The Green's function of the time dependent radiative transfer equation for the semi-infinite medium is derived for the first time by a heuristic approach based on the extrapolated boundary condition and on an almost exact solution for the infinite medium. Monte Carlo simulations performed both in the simple case of isotropic scattering and of an isotropic point-like source, and in the more realistic case of anisotropic scattering and pencil beam source, are used to validate the heuristic Green's function. Except for the very early times, the proposed solution has an excellent accuracy (> 98 % for the isotropic case, and > 97 % for the anisotropic case) significantly better than the diffusion equation. The use of this solution could be extremely useful in the biomedical optics field where it can be directly employed in conditions where the use of the diffusion equation is limited, e.g. small volume samples, high absorption and/or low scattering media, short source-receiver distances and early times. Also it represents a first step to derive tools for other geometries (e.g. slab and slab with inhomogeneities inside) of practical interest for noninvasive spectroscopy and diffuse optical imaging. Moreover the proposed solution can be useful to several research fields where the study of a transport process is fundamental.

Hydrogen: A Promising Fuel and Energy Storage Solution - Continuum

Science.gov Websites

Magazine | NREL Hydrogen: A Promising Fuel and Energy Storage Solution Fuel cell electric Ainscough, NREL Hydrogen: A Promising Fuel and Energy Storage Solution Electrolysis-generated hydrogen may provide a solution to fluctuations in renewable-sourced energy. As electricity from renewable resources

Improved phase shift approach to the energy correction of the infinite order sudden approximation

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

Chang, B.; Eno, L.; Rabitz, H.

1980-07-15

A new method is presented for obtaining energy corrections to the infinite order sudden (IOS) approximation by incorporating the effect of the internal molecular Hamiltonian into the IOS wave function. This is done by utilizing the JWKB approximation to transform the Schroedinger equation into a differential equation for the phase. It is found that the internal Hamiltonian generates an effective potential from which a new improved phase shift is obtained. This phase shift is then used in place of the IOS phase shift to generate new transition probabilities. As an illustration the resulting improved phase shift (IPS) method is appliedmore » to the Secrest--Johnson model for the collinear collision of an atom and diatom. In the vicinity of the sudden limit, the IPS method gives results for transition probabilities, P/sub n/..-->..n+..delta..n, in significantly better agreement with the 'exact' close coupling calculations than the IOS method, particularly for large ..delta..n. However, when the IOS results are not even qualitatively correct, the IPS method is unable to satisfactorily provide improvements.« less

On infinite-dimensional state spaces

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

Fritz, Tobias

It is well known that the canonical commutation relation [x, p]=i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p]=i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context frommore » which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V{sup -1}U{sup 2}V=U{sup 3}, then finite-dimensionality entails the relation UV{sup -1}UV=V{sup -1}UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V{sup -1}U{sup 2}V=U{sup 3} holds only up to {epsilon} and then yields a lower bound on the dimension.« less

ALESEP. Part 2: A computer program for the analysis of leading edge separation bubbles on infinite swept wings

NASA Technical Reports Server (NTRS)

Davis, R. L.

1986-01-01

A program called ALESEP is presented for the analysis of the inviscid-viscous interaction which occurs due to the presence of a closed laminar-transitional separation bubble on an airfoil or infinite swept wing. The ALESEP code provides an iterative solution of the boundary layer equations expressed in an inverse formulation coupled to a Cauchy integral representation of the inviscid flow. This interaction analysis is treated as a local perturbation to a known solution obtained from a global airfoil analysis; hence, part of the required input to the ALESEP code are the reference displacement thickness and tangential velocity distributions. Special windward differencing may be used in the reversed flow regions of the separation bubble to accurately account for the flow direction in the discretization of the streamwise convection of momentum. The ALESEP code contains a forced transition model based on a streamwise intermittency function, a natural transition model based on a solution of the integral form of the turbulent kinetic energy equation, and an empirical natural transition model.

Free Convection from a Semi-Infinite Vertical Plate with Discontinuous Blowing or Suction.

DTIC Science & Technology

1981-03-01

SCHIESSR UNCLASSIFIED; EhEllllEllEE EE[E]hEEEIllIEllhlEEIl EEEEEIIIEEEEI EEEIIIIIIIIII EIIIEIIEEEEII EEEIIIIIIIIIIE LVEL NAVAL POSTGRADUATE SCHOOL Monterey...the unsteady free convective flow past a simi-infinite porous plate with constant suction were studied through mathematical analysis by Soundalgekar...boundary-layers and; therefore, will often indicate a preferred method of analytical solution. Although there are several possible mathematical techniques

Energy Access Solutions Advance Gender Mainstreaming in West African States

Science.gov Websites

| Integrated Energy Solutions | NREL Energy Access Solutions Advance Gender Mainstreaming in West African States Energy Access Solutions Advance Gender Mainstreaming in West African States Under a expertise to an innovative policy that not only supports women in energy, but also helps bring clean energy

Analytic solution of the Spencer-Lewis angular-spatial moments equations

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

Filippone, W.L.

A closed-form solution for the angular-spatial moments of the Spencer-Lewis equation is presented that is valid for infinite homogeneous media. From the moments, the electron density distribution as a function of position and path length (energy) is reconstructed for several sample problems involving plane isotropic sources of electrons in aluminium. The results are in excellent agreement with those determined numerically using the streaming ray method. The primary use of the closed form solution will most likely be to generate accurate electron transport benchmark solutions. In principle, the electron density as a function of space, path length, and direction can bemore » determined for planar sources of arbitrary angular distribution.« less

Necessary optimality conditions for infinite dimensional state constrained control problems

NASA Astrophysics Data System (ADS)

Frankowska, H.; Marchini, E. M.; Mazzola, M.

2018-06-01

This paper is concerned with first order necessary optimality conditions for state constrained control problems in separable Banach spaces. Assuming inward pointing conditions on the constraint, we give a simple proof of Pontryagin maximum principle, relying on infinite dimensional neighboring feasible trajectories theorems proved in [20]. Further, we provide sufficient conditions guaranteeing normality of the maximum principle. We work in the abstract semigroup setting, but nevertheless we apply our results to several concrete models involving controlled PDEs. Pointwise state constraints (as positivity of the solutions) are allowed.

Global existence of weak solutions to dissipative transport equations with nonlocal velocity

NASA Astrophysics Data System (ADS)

Bae, Hantaek; Granero-Belinchón, Rafael; Lazar, Omar

2018-04-01

We consider 1D dissipative transport equations with nonlocal velocity field: where is a nonlocal operator given by a Fourier multiplier. We especially consider two types of nonlocal operators: (1) , the Hilbert transform, (2) . In this paper, we show several global existence of weak solutions depending on the range of γ, δ and α. When , we take initial data having finite energy, while we take initial data in weighted function spaces (in the real variables or in the Fourier variables), which have infinite energy, when .

Global Well-Posedness of the NLS System for Infinitely Many Fermions

NASA Astrophysics Data System (ADS)

Chen, Thomas; Hong, Younghun; Pavlović, Nataša

2017-04-01

In this paper, we study the mean field quantum fluctuation dynamics for a system of infinitely many fermions with delta pair interactions in the vicinity of an equilibrium solution (the Fermi sea) at zero temperature, in dimensions d = 2, 3, and prove global well-posedness of the corresponding Cauchy problem. Our work extends some of the recent important results obtained by Lewin and Sabin in [33,34], who addressed this problem for more regular pair interactions.

Solar Energy - Solution or Pipedream?

ERIC Educational Resources Information Center

Polk, Joyce

This series of lessons and class activities is designed for presentation in a sequence of nine class days. The collection is intended to provide the student in advanced science classes with awareness of the possibilities and limitations of solar energy as a potential solution to the energy crisis. Included are discussion of the following: (1)…

Propagation of SH waves in an infinite/semi-infinite piezoelectric/piezomagnetic periodically layered structure.

PubMed

Pang, Yu; Liu, Yu-Shan; Liu, Jin-Xi; Feng, Wen-Jie

2016-04-01

In this paper, SH bulk/surface waves propagating in the corresponding infinite/semi-infinite piezoelectric (PE)/piezomagnetic (PM) and PM/PE periodically layered composites are investigated by two methods, the stiffness matrix method and the transfer matrix method. For a semi-infinite PE/PM or PM/PE medium, the free surface is parallel to the layer interface. Both PE and PM materials are assumed to be transversely isotropic solids. Dispersion equations are derived by the stiffness/transfer matrix methods, respectively. The effects of electric-magnetic (ME) boundary conditions at the free surface and the layer thickness ratios on dispersion curves are considered in detail. Numerical examples show that the results calculated by the two methods are the same. The dispersion curves of SH surface waves are below the bulk bands or inside the frequency gaps. The ratio of the layer thickness has an important effect not only on the bulk bands but also on the dispersion curves of SH surface waves. Electric and magnetic boundary conditions, respectively, determine the dispersion curves of SH surface waves for the PE/PM and PM/PE semi-infinite structures. The band structures of SH bulk waves are consistent for the PE/PM and PM/PE structures, however, the dispersive behaviors of SH surface waves are indeed different for the two composites. The realization of the above-mentioned characteristics of SH waves will make it possible to design PE/PM acoustic wave devices with periodical structures and achieve the better performance. Copyright © 2016 Elsevier B.V. All rights reserved.

Convergence of Asymptotic Systems of Non-autonomous Neural Network Models with Infinite Distributed Delays

NASA Astrophysics Data System (ADS)

Oliveira, José J.

2017-10-01

In this paper, we investigate the global convergence of solutions of non-autonomous Hopfield neural network models with discrete time-varying delays, infinite distributed delays, and possible unbounded coefficient functions. Instead of using Lyapunov functionals, we explore intrinsic features between the non-autonomous systems and their asymptotic systems to ensure the boundedness and global convergence of the solutions of the studied models. Our results are new and complement known results in the literature. The theoretical analysis is illustrated with some examples and numerical simulations.

Solute-solvent interactions in 2,4-dihydroxyacetophenone isonicotinoylhydrazone solutions in N, N-dimethylformamide and dimethyl sulfoxide at 298-313 K on ultrasonic and viscometric data

NASA Astrophysics Data System (ADS)

Dikkar, A. B.; Pethe, G. B.; Aswar, A. S.

2016-02-01

The speed of sound ( u), density (ρ), and viscosity (η) of 2,4-dihydroxyacetophenone isonicotinoylhydrazone (DHAIH) have been measured in N, N-dimethyl formamide and dimethyl sulfoxide at equidistance temperatures 298.15, 303.15, 308.15, and 313.15 K. These data were used to calculate some important ultrasonic and thermodynamic parameters such as apparent molar volume ( V ϕ s st ), apparent molar compressibility ( K ϕ), partial molar volume ( V ϕ 0 ) and partial molar compressibility ( K ϕ 0 ), were estimated by using the values of ( V ϕ 0 ) and ( K ϕ), at infinite dilution. Partial molar expansion at infinite dilution, (ϕ E 0 ) has also been calculated from temperature dependence of partial molar volume V ϕ 0 . The viscosity data have been analyzed using the Jones-Dole equation, and the viscosity, B coefficients are calculated. The activation free energy has been calculated from B coefficients and partial molar volume data. The results have been discussed in the term of solute-solvent interaction occurring in solutions and it was found that DHAIH acts as a structure maker in present systems.

Asymptotics of the monomer-dimer model on two-dimensional semi-infinite lattices

NASA Astrophysics Data System (ADS)

Kong, Yong

2007-05-01

By using the asymptotic theory of Pemantle and Wilson [R. Pemantle and M. C. Wilson, J. Comb. Theory, Ser. AJCBTA70097-316510.1006/jcta.2001.3201 97, 129 (2002)], asymptotic expansions of the free energy of the monomer-dimer model on two-dimensional semi-infinite ∞×n lattices in terms of dimer density are obtained for small values of n , at both high- and low-dimer-density limits. In the high-dimer-density limit, the theoretical results confirm the dependence of the free energy on the parity of n , a result obtained previously by computational methods by Y. Kong [Y. Kong, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.74.061102 74, 061102 (2006); Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.73.016106 73, 016106 (2006);Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.74.011102 74, 011102 (2006)]. In the low-dimer-density limit, the free energy on a cylinder ∞×n lattice strip has exactly the same first n terms in the series expansion as that of an infinite ∞×∞ lattice.

Finite-floe wave reflection and transmission coefficients from a semi-infinite model

NASA Astrophysics Data System (ADS)

Meylan, Michael; Squire, Vernon A.

1993-07-01

A model to describe the reflection and transmission of ocean waves by a single ice floe is developed from the semi-infinite model of Fox and Squire (1990, 1991). This is done by considering the coefficients for the transition from ice to water in the semi-infinite case in terms of those from water to ice. Finite-floe reflection and transmission coefficients, R and T, respectively, are then found as the solution of a set of four simple simultaneous equations. The properties of R and T are investigated, and examples of their absolute values are given for several geometries. |R| compares well with the predictions of a precise model in the case of deep water. These results suggest that the analytical model described has applications to defining the sea state within marginal ice zones, given the floe size and ice thickness distributions and the incoming sea wave spectrum.

Integrated Solutions for a Complex Energy World - Continuum Magazine |

Science.gov Websites

NREL Integrated Solutions for a Complex Energy World Integrated Solutions for a Complex Energy World Energy systems integration optimizes electrical, thermal, fuel, and data technologies design and performance. An array of clean energy technologies, including wind, solar, and electric vehicle batteries, is

Truly self-consistent solution of Kohn-Sham equations for extended systems with inhomogeneous electron gas

NASA Astrophysics Data System (ADS)

Shul'man, A. Ya; Posvyanskii, D. V.

2014-05-01

The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistent solution method for infinite systems involves iterations with alternate solutions of the Poisson and Schrödinger equations. One of problems with such an approach is that the charge distribution, updated by solving the Schrodinger equation, may be incompatible with the boundary conditions of the Poisson equation for Coulomb potential. The resulting instability or divergence manifests itself most appreciably in the case of infinitely extended systems because the corresponding boundary-value problem becomes singular. In this work the stable iterative scheme for solving the Kohn-Sham equations for infinite systems with inhomogeneous electron gas is described based on eliminating the long-range character of the Coulomb interaction, which causes the tight coupling of the charge distribution with the boundary conditions. This algorithm has been previously successfully implemented in the calculation of work function and surface energy of simple metals in the jellium model. Here it is used to calculate the energy spectrum of quasi-two-dimensional electron gas in the accumulation layer at the semiconductor surface n-InAs. The electrons in such a structure occupy states that belong to both discrete and continuous parts of the energy spectrum. This causes the problems of convergence in the usually used approaches, which do not exist in our case. Because of the narrow bandgap of InAs, it is necessary to take the nonparabolicity of the conduction band into account; this is done by means of a new effective mass method. The calculated quasi-two-dimensional energy bands correspond well to experimental data measured by the angle resolved photoelectron spectroscopy technique.

An improved technique for determining reflection from semi-infinite atmospheres with linearly anisotropic phase functions. [radiative transfer

NASA Technical Reports Server (NTRS)

Fricke, C. L.

1975-01-01

A solution to the problem of reflection from a semi-infinite atmosphere is presented, based upon Chandrasekhar's H-function method for linearly anisotropic phase functions. A modification to the Gauss quadrature formula which gives about the same accuracy with 10 points as the conventional Gauss quadrature does with 100 points was developed. A computer program achieving this solution is described and results are presented for several illustrative cases.

Analytical solution for multi-species contaminant transport in finite media with time-varying boundary conditions

USDA-ARS?s Scientific Manuscript database

Most analytical solutions available for the equations governing the advective-dispersive transport of multiple solutes undergoing sequential first-order decay reactions have been developed for infinite or semi-infinite spatial domains and steady-state boundary conditions. In this work we present an ...

Envisioning the Infinite by Projecting Finite Properties

ERIC Educational Resources Information Center

Ely, Robert

2011-01-01

We analyze interviews with 24 post-secondary students as they reason about infinite processes in the context of the tricky Tennis Ball Problem. By metaphorically projecting various properties from the finite states such as counting and indexing, participants envisioned widely varying final states for the infinite process. Depending on which…

Understanding the Behaviour of Infinite Ladder Circuits

ERIC Educational Resources Information Center

Ucak, C.; Yegin, K.

2008-01-01

Infinite ladder circuits are often encountered in undergraduate electrical engineering and physics curricula when dealing with series and parallel combination of impedances, as a part of filter design or wave propagation on transmission lines. The input impedance of such infinite ladder circuits is derived by assuming that the input impedance does…

Partial molar volume of n-alcohols at infinite dilution in water calculated by means of scaled particle theory.

PubMed

Graziano, Giuseppe

2006-04-07

The partial molar volume of n-alcohols at infinite dilution in water is smaller than the molar volume in the neat liquid phase. It is shown that the formula for the partial molar volume at infinite dilution obtained from the scaled particle theory equation of state for binary hard sphere mixtures is able to reproduce in a satisfactory manner the experimental data over a large temperature range. This finding implies that the packing effects play the fundamental role in determining the partial molar volume at infinite dilution in water also for solutes, such as n-alcohols, forming H bonds with water molecules. Since the packing effects in water are largely related to the small size of its molecules, the latter feature is the ultimate cause of the decrease in partial molar volume associated with the hydrophobic effect.

Three-dimensional elasticity solution of an infinite plate with a circular hole

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1982-01-01

The elasticity problem for a thick plate with a circular hole is formulated in a systematic fashion by using the z-component of the Galerkin vector and that of Muki's harmonic vector function. The problem was originally solved by Alblas. The reasons for reconsidering it are to develop a technique which may be used in solving the elasticity problem for a multilayered plate and to verify and extend the results given by Alblas. The problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Various stress components are tabulated as functions of a/h, z/h, r/a, and nu, a and 2h being the radius of the hole and the plate thickness and nu, the Poisson's ratio. The significant effect of the Poisson's ratio on the behavior and the magnitude of the stresses is discussed.

Asymptotically Exact Solution of the Problem of Harmonic Vibrations of an Elastic Parallelepiped

NASA Astrophysics Data System (ADS)

Papkov, S. O.

2017-11-01

An asymptotically exact solution of the classical problem of elasticity about the steadystate forced vibrations of an elastic rectangular parallelepiped is constructed. The general solution of the vibration equations is constructed in the form of double Fourier series with undetermined coefficients, and an infinite system of linear algebraic equations is obtained for determining these coefficients. An analysis of the infinite system permits determining the asymptotics of the unknowns which are used to convolve the double series in both equations of the infinite systems and the displacement and stress components. The efficiency of this approach is illustrated by numerical examples and comparison with known solutions. The spectrum of the parallelepiped symmetric vibrations is studied for various ratios of its sides.

Density functional theory study of the conformational space of an infinitely long polypeptide chain

NASA Astrophysics Data System (ADS)

Ireta, Joel; Scheffler, Matthias

2009-08-01

The backbone conformational space of infinitely long polyalanine is investigated with density-functional theory and mapping the potential energy surface in terms of (L, θ) cylindrical coordinates. A comparison of the obtained (L, θ) Ramachandran-like plot with results from an extended set of protein structures shows excellent conformity, with the exception of the polyproline II region. It is demonstrated the usefulness of infinitely long polypeptide models for investigating the influence of hydrogen bonding and its cooperative effect on the backbone conformations. The results imply that hydrogen bonding together with long-range electrostatics is the main actuator for most of the structures assumed by protein residues.

Orthogonality preserving infinite dimensional quadratic stochastic operators

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

Akın, Hasan; Mukhamedov, Farrukh

In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

Inspiring Examples in Rearrangements of Infinite Products

ERIC Educational Resources Information Center

Ramasinghe, W.

2007-01-01

It is well known that simple examples are really encouraging in the understanding of rearrangements of infinite series. In this paper a similar role is played by simple examples in the case of infinite products. Iterated products of double products seem to have a similar spirit of rearrangements of products, although they are not the same.…

Sn ion energy distributions of ns- and ps-laser produced plasmas

NASA Astrophysics Data System (ADS)

Bayerle, A.; Deuzeman, M. J.; van der Heijden, S.; Kurilovich, D.; de Faria Pinto, T.; Stodolna, A.; Witte, S.; Eikema, K. S. E.; Ubachs, W.; Hoekstra, R.; Versolato, O. O.

2018-04-01

Ion energy distributions arising from laser-produced plasmas of Sn are measured over a wide laser parameter space. Planar-solid and liquid-droplet targets are exposed to infrared laser pulses with energy densities between 1 J cm‑2 and 4 kJ cm‑2 and durations spanning 0.5 ps to 6 ns. The measured ion energy distributions are compared to two self-similar solutions of a hydrodynamic approach assuming isothermal expansion of the plasma plume into vacuum. For planar and droplet targets exposed to ps-long pulses, we find good agreement between the experimental results and the self-similar solution of a semi-infinite simple planar plasma configuration with an exponential density profile. The ion energy distributions resulting from solid Sn exposed to ns-pulses agrees with solutions of a limited-mass model that assumes a Gaussian-shaped initial density profile.

Effect of capillary forces on the nonstationary fall of a drop in an infinite fluid

NASA Astrophysics Data System (ADS)

Antanovskii, L. K.

1991-12-01

An explicit solution is presented for the linear problem concerning the motion of a drop in an infinite fluid in the presence of any number of surfactants (chemical reactions are not considered in the first approximation). It is shown that the behavior of the system considered is consistent with the Le Chatelier principle. The reactivity of the capillary forces is directly related to the fundamental principles of thermodynamics, which makes it possible to write equations of surfactant thermodiffusion in symmetric form and obtain a relatively simple solution to the linearized problem.

The Infinite Hotel

ERIC Educational Resources Information Center

Wanko, Jeffrey J.

2009-01-01

This article provides a historical context for the debate between Georg Cantor and Leopold Kronecker regarding the cardinality of different infinities and incorporates the short story "Welcome to the Hotel Infinity," which uses the analogy of a hotel with an infinite number of rooms to help explain this concept. Wanko makes use of this history and…

IMSF: Infinite Methodology Set Framework

NASA Astrophysics Data System (ADS)

Ota, Martin; Jelínek, Ivan

Software development is usually an integration task in enterprise environment - few software applications work autonomously now. It is usually a collaboration of heterogeneous and unstable teams. One serious problem is lack of resources, a popular result being outsourcing, ‘body shopping’, and indirectly team and team member fluctuation. Outsourced sub-deliveries easily become black boxes with no clear development method used, which has a negative impact on supportability. Such environments then often face the problems of quality assurance and enterprise know-how management. The used methodology is one of the key factors. Each methodology was created as a generalization of a number of solved projects, and each methodology is thus more or less connected with a set of task types. When the task type is not suitable, it causes problems that usually result in an undocumented ad-hoc solution. This was the motivation behind formalizing a simple process for collaborative software engineering. Infinite Methodology Set Framework (IMSF) defines the ICT business process of adaptive use of methods for classified types of tasks. The article introduces IMSF and briefly comments its meta-model.

Behavior of a semi-infinite ice cover under periodic dynamic impact

NASA Astrophysics Data System (ADS)

Tkacheva, L. A.

2017-07-01

Oscillations of a semi-infinite ice cover in an ideal incompressible liquid of finite depth under local time-periodic axisymmetric load are considered. The ice cover is simulated by a thin elastic plate of constant thickness. An analytical solution of the problem is obtained using the Wiener-Hopf method. The asymptotic behavior of the amplitudes of oscillations of the plate and the liquid in the far field is studied. It is shown that the propagation of waves in the far field is uneven: in some directions, the waves propagate with a significantly greater amplitude.

Slicing the vacuum: New accelerating mirror solutions of the dynamical Casimir effect

NASA Astrophysics Data System (ADS)

Good, Michael R. R.; Linder, Eric V.

2017-12-01

Radiation from accelerating mirrors in a Minkowski spacetime provides insights into the nature of horizons, black holes, and entanglement entropy. We introduce new, simple, symmetric and analytic moving mirror solutions and study their particle, energy, and entropy production. This includes an asymptotically static case with finite emission that is the black hole analog of complete evaporation. The total energy, total entropy, total particles, and spectrum are the same on both sides of the mirror. We also study its asymptotically inertial, drifting analog (which gives a black hole remnant) to explore differences in finite and infinite production.

Infinite index extensions of local nets and defects

NASA Astrophysics Data System (ADS)

Del Vecchio, Simone; Giorgetti, Luca

The subfactor theory provides a tool to analyze and construct extensions of Quantum Field Theories, once the latter are formulated as local nets of von Neumann algebras. We generalize some of the results of [62] to the case of extensions with infinite Jones index. This case naturally arises in physics, the canonical examples are given by global gauge theories with respect to a compact (non-finite) group of internal symmetries. Building on the works of Izumi-Longo-Popa [44] and Fidaleo-Isola [30], we consider generalized Q-systems (of intertwiners) for a semidiscrete inclusion of properly infinite von Neumann algebras, which generalize ordinary Q-systems introduced by Longo [58] to the infinite index case. We characterize inclusions which admit generalized Q-systems of intertwiners and define a braided product among the latter, hence we construct examples of QFTs with defects (phase boundaries) of infinite index, extending the family of boundaries in the grasp of [7].

Viscous/potential flow about multi-element two-dimensional and infinite-span swept wings: Theory and experiment

NASA Technical Reports Server (NTRS)

Olson, L. E.; Dvorak, F. A.

1975-01-01

The viscous subsonic flow past two-dimensional and infinite-span swept multi-component airfoils is studied theoretically and experimentally. The computerized analysis is based on iteratively coupled boundary layer and potential flow analysis. The method, which is restricted to flows with only slight separation, gives surface pressure distribution, chordwise and spanwise boundary layer characteristics, lift, drag, and pitching moment for airfoil configurations with up to four elements. Merging confluent boundary layers are treated. Theoretical predictions are compared with an exact theoretical potential flow solution and with experimental measures made in the Ames 40- by 80-Foot Wind Tunnel for both two-dimensional and infinite-span swept wing configurations. Section lift characteristics are accurately predicted for zero and moderate sweep angles where flow separation effects are negligible.

Charged Vaidya solution satisfies weak energy condition

NASA Astrophysics Data System (ADS)

Chatterjee, Soumyabrata; Ganguli, Suman; Virmani, Amitabh

2016-07-01

The external matter stress-tensor supporting charged Vaidya solution appears to violate weak energy condition in certain region of the spacetime. Motivated by this, a new interpretation of charged Vaidya solution was proposed by Ori (Class Quant Grav 8:1559, 1991) in which the energy condition continues to be satisfied. In this construction, one glues an outgoing Vaidya solution to the original ingoing Vaidya solution provided the surface where the external stress-tensor vanishes is spacelike. We revisit this study and extend it to higher-dimensions, to AdS settings, and to higher-derivative f( R) theories. In asymptotically flat space context, we explore in detail the case when the mass function m( v) is proportional to the charge function q( v). When the proportionality constant ν = q(v)/m(v) lies in between zero and one, we show that the surface where the external stress-tensor vanishes is spacelike and lies in between the inner and outer apparent horizons.

Physicochemical characterization of D-mannitol polymorphs: the challenging surface energy determination by inverse gas chromatography in the infinite dilution region.

PubMed

Cares-Pacheco, M G; Vaca-Medina, G; Calvet, R; Espitalier, F; Letourneau, J-J; Rouilly, A; Rodier, E

2014-11-20

Nowadays, it is well known that surface interactions play a preponderant role in mechanical operations, which are fundamental in pharmaceutical processing and formulation. Nevertheless, it is difficult to correlate surface behaviour in processes to physical properties measurement. Indeed, most pharmaceutical solids have multiple surface energies because of varying forms, crystal faces and impurities contents or physical defects, among others. In this paper, D-mannitol polymorphs (α, β and δ) were studied through different characterization techniques highlighting bulk and surface behaviour differences. Due to the low adsorption behaviour of β and δ polymorphs, special emphasis has been paid to surface energy analysis by inverse gas chromatography, IGC. Surface energy behaviour has been studied in Henry's domain showing that, for some organic solids, the classical IGC infinite dilution zone is never reached. IGC studies highlighted, without precedent in literature, dispersive surface energy differences between α and β mannitol, with a most energetically active α form with a γ(s)(d) of 74.9 mJ·m⁻². Surface heterogeneity studies showed a highly heterogeneous α mannitol with a more homogeneous β (40.0 mJ·m⁻²) and δ mannitol (40.3 mJ·m⁻²). Moreover, these last two forms behaved similarly considering surface energy at different probe concentrations. Copyright © 2014 Elsevier B.V. All rights reserved.

Spring back of infinite honeycomb sheets beyond plastic deformation

NASA Astrophysics Data System (ADS)

Bonfanti, A.; Bhaskar, A.

2015-02-01

Cellular structures are promising for applications where high stiffness and strength are required with the minimal use of material. They are often used in applications where the plastic deformation plays an important role, such as those involving crashworthiness, energy absorption, and stents. The elastic analysis of a honeycomb sheet has been carried out in the past [1]. The present analysis extends this classical work in the elasto-plastic regime. Recoil analysis due to elastic recovery is absent from the published literature. This work aims to develop an analytical model to calculate the spring back for a simplified case, that of an infinite honeycomb sheet. An elastic-perfectly plastic material model is assumed. The recoil for a clamped beam with a load and moment applied at the free edge is analytically calculated first. This is carried out by relating the stress distribution of the cross section to the final deformed shape. The part corresponding to the elastic contribution is subsequently subtracted in order to obtain the final configuration after the external load is removed. This simple elasto-plastic analysis is then incorporated into the analysis of an infinite sheet made of uniform hexagonal cells. The translational symmetry of the lattice is exploited along with the analysis of a beam under tip loading through to plastic stage and recoil. The final shape of the struts upon the removal of the remote stress is completely determined by the plastic deformation which cannot be recovered. The expression for the beam thus obtained is then used to build an analytical model for an infinite honeycomb sheet loaded in both directions.

Effect of zone size on the convergence of exact solutions for diffusion in single phase systems with planar, cylindrical or spherical geometry

NASA Technical Reports Server (NTRS)

Unnam, J.; Tenney, D. R.

1981-01-01

Exact solutions for diffusion in single phase binary alloy systems with constant diffusion coefficient and zero-flux boundary condition have been evaluated to establish the optimum zone size of applicability. Planar, cylindrical and spherical interface geometry, and finite, singly infinite, and doubly infinite systems are treated. Two solutions are presented for each geometry, one well suited to short diffusion times, and one to long times. The effect of zone-size on the convergence of these solutions is discussed. A generalized form of the diffusion solution for doubly infinite systems is proposed.

The infinite limit as an eliminable approximation for phase transitions

NASA Astrophysics Data System (ADS)

Ardourel, Vincent

2018-05-01

It is generally claimed that infinite idealizations are required for explaining phase transitions within statistical mechanics (e.g. Batterman 2011). Nevertheless, Menon and Callender (2013) have outlined theoretical approaches that describe phase transitions without using the infinite limit. This paper closely investigates one of these approaches, which consists of studying the complex zeros of the partition function (Borrmann et al., 2000). Based on this theory, I argue for the plausibility for eliminating the infinite limit for studying phase transitions. I offer a new account for phase transitions in finite systems, and I argue for the use of the infinite limit as an approximation for studying phase transitions in large systems.

Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients.

PubMed

Kedziora, D J; Ankiewicz, A; Chowdury, A; Akhmediev, N

2015-10-01

We present an infinite nonlinear Schrödinger equation hierarchy of integrable equations, together with the recurrence relations defining it. To demonstrate integrability, we present the Lax pairs for the whole hierarchy, specify its Darboux transformations and provide several examples of solutions. These resulting wavefunctions are given in exact analytical form. We then show that the Lax pair and Darboux transformation formalisms still apply in this scheme when the coefficients in the hierarchy depend on the propagation variable (e.g., time). This extension thus allows for the construction of complicated solutions within a greatly diversified domain of generalised nonlinear systems.

Phosphorescence and Energy Transfer in Rigid Solutions.

ERIC Educational Resources Information Center

Enciso, E.; Cabello, A.

1980-01-01

Describes an experiment which illustrates the general aspects of intermolecular energy transfer between triplet states in rigid solutions of organic compounds solved in an ethanol-ether mixture. Measurements of quenching and energy transfer processes are made using the chemicals of benzophenone and naphthalene. (CS)

NREL's Impact Grows Through the Clean Energy Solutions Center and the New

Science.gov Websites

Clean Energy Design Studio - Continuum Magazine | NREL NREL's Impact Grows Through the Clean Energy Solutions Center and the New Clean Energy Design Studio The Clean Energy Solutions Center (Solutions Center) helps governments design and adopt policies and programs that support the deployment of

Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations

NASA Astrophysics Data System (ADS)

Chiodaroli, Elisabetta; Michálek, Martin

2017-08-01

We consider the initial value problem for the inviscid Primitive and Boussinesq equations in three spatial dimensions. We recast both systems as an abstract Euler-type system and apply the methods of convex integration of De Lellis and Székelyhidi to show the existence of infinitely many global weak solutions of the studied equations for general initial data. We also introduce an appropriate notion of dissipative solutions and show the existence of suitable initial data which generate infinitely many dissipative solutions.

One-dimensional gravity in infinite point distributions.

PubMed

Gabrielli, A; Joyce, M; Sicard, F

2009-10-01

The dynamics of infinite asymptotically uniform distributions of purely self-gravitating particles in one spatial dimension provides a simple and interesting toy model for the analogous three dimensional problem treated in cosmology. In this paper we focus on a limitation of such models as they have been treated so far in the literature: the force, as it has been specified, is well defined in infinite point distributions only if there is a centre of symmetry (i.e., the definition requires explicitly the breaking of statistical translational invariance). The problem arises because naive background subtraction (due to expansion, or by "Jeans swindle" for the static case), applied as in three dimensions, leaves an unregulated contribution to the force due to surface mass fluctuations. Following a discussion by Kiessling of the Jeans swindle in three dimensions, we show that the problem may be resolved by defining the force in infinite point distributions as the limit of an exponentially screened pair interaction. We show explicitly that this prescription gives a well defined (finite) force acting on particles in a class of perturbed infinite lattices, which are the point processes relevant to cosmological N -body simulations. For identical particles the dynamics of the simplest toy model (without expansion) is equivalent to that of an infinite set of points with inverted harmonic oscillator potentials which bounce elastically when they collide. We discuss and compare with previous results in the literature and present new results for the specific case of this simplest (static) model starting from "shuffled lattice" initial conditions. These show qualitative properties of the evolution (notably its "self-similarity") like those in the analogous simulations in three dimensions, which in turn resemble those in the expanding universe.

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.

Electronic orbital response of regular extended and infinite periodic systems to magnetic fields. I. Theoretical foundations for static case

NASA Astrophysics Data System (ADS)

Springborg, Michael; Molayem, Mohammad; Kirtman, Bernard

2017-09-01

A theoretical treatment for the orbital response of an infinite, periodic system to a static, homogeneous, magnetic field is presented. It is assumed that the system of interest has an energy gap separating occupied and unoccupied orbitals and a zero Chern number. In contrast to earlier studies, we do not utilize a perturbation expansion, although we do assume the field is sufficiently weak that the occurrence of Landau levels can be ignored. The theory is developed by analyzing results for large, finite systems and also by comparing with the analogous treatment of an electrostatic field. The resulting many-electron Hamilton operator is forced to be hermitian, but hermiticity is not preserved, in general, for the subsequently derived single-particle operators that determine the electronic orbitals. However, we demonstrate that when focusing on the canonical solutions to the single-particle equations, hermiticity is preserved. The issue of gauge-origin dependence of approximate solutions is addressed. Our approach is compared with several previously proposed treatments, whereby limitations in some of the latter are identified.

Infinite charge mobility in muscovite at 300 K

NASA Astrophysics Data System (ADS)

Russell, F. Michael; Archilla, Juan F. R.; Frutos, Fabian; Medina-Carrasco, Santiago

2017-11-01

Evidence is presented for infinite charge mobility in natural crystals of muscovite mica at room temperature. Muscovite has a basic layered structure containing a flat monatomic sheet of potassium sandwiched between mirror silicate layers. It is an excellent electrical insulator. Studies of defects in muscovite crystals indicated that positive charge could propagate over great distances along atomic chains in the potassium sheets in the absence of an applied electric potential. The charge moved in association with anharmonic lattice excitations that moved at about sonic speed and created by nuclear recoil of the radioactive isotope 40K. This was verified by measuring currents passing through crystals when irradiated with energetic alpha particles at room temperature. The charge propagated more than 1000 times the range of the alpha particles of average energy and 250 times the range of channelling particles of maximum energy. The range is limited only by size of the crystal.

Second cluster integral from the spectrum of an infinite XXZ spin chain

NASA Astrophysics Data System (ADS)

Bibikov, P. N.

2015-03-01

First and second terms of the low-temperature cluster expansion for the free energy density of a magnetically polarized XXZ spin chain is obtained within the propagator approach suggested by E.W. Montroll and J.C. Ward. All the calculations employ only one- and two-magnon infinite-chain spectrums. In the XXX-point the result reproduces the well known S. Katsura's formula obtained 50 years ago by finite-chain calculations.

Solution behavior of metoclopramide in aqueous-alcoholic solutions at 30°C

NASA Astrophysics Data System (ADS)

Deosarkar, S. D.; Sawale, R. T.; Tawde, P. D.; Kalyankar, T. M.

2016-07-01

Densities (ρ) and refractive indices ( n D) of solutions of antiemetic drug metoclopramide (4-amino-5-chloro- N-(2-(diethylamino)ethyl)-2-methoxybenzamide hydrochloride hydrate) in methanolwater and ethanol-water mixtures of different compositions were measured at 30°C. Apparent molar volume (φv) of the drug was calculated from density data and partial molar volumes (φ v 0 ) were determined from Massons relation. Concentration dependence of nD has been studied to determine refractive indices of solution at infinite dilution ( n D 0 ). Results have been interpreted in terms of solute-solvent interactions.

Diffusiophoresis in one-dimensional solute gradients

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

Ault, Jesse T.; Warren, Patrick B.; Shin, Sangwoo

Here, the diffusiophoretic motion of suspended colloidal particles under one-dimensional solute gradients is solved using numerical and analytical techniques. Similarity solutions are developed for the injection and withdrawal dynamics of particles into semi-infinite pores. Furthermore, a method of characteristics formulation of the diffusion-free particle transport model is presented and integrated to realize particle trajectories. Analytical solutions are presented for the limit of small particle diffusiophoretic mobility Γ p relative to the solute diffusivity D s for particle motions in both semi-infinite and finite domains. Results confirm the build up of local maxima and minima in the propagating particle front dynamics.more » The method of characteristics is shown to successfully predict particle motions and the position of the particle front, although it fails to accurately predict suspended particle concentrations in the vicinity of sharp gradients, such as at the particle front peak seen in some injection cases, where particle diffusion inevitably plays an important role. Results inform the design of applications in which the use of applied solute gradients can greatly enhance particle injection into and withdrawal from pores.« less

Survey of Thermoelectric and Solar Technologies as Alternative Energy Solutions

DTIC Science & Technology

2012-02-01

Survey of Thermoelectric and Solar Technologies as Alternative Energy Solutions by Kendall Bianchi, Jay R. Maddux, Kimberly Sablon-Ramsey...Research Laboratory Adelphi, MD 20783-1197 ARL-TR-5920 February 2012 Survey of Thermoelectric and Solar Technologies as Alternative Energy...Final 3. DATES COVERED (From - To) 4. TITLE AND SUBTITLE Survey of Thermoelectric and Solar Technologies as Alternative Energy Solutions 5a

VERTPAK1. Code Verification Analytic Solution

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

Golis, M.J.

1983-04-01

VERTPAK1 is a package of analytical solutions used in verification of numerical codes that simulate fluid flow, rock deformation, and solute transport in fractured and unfractured porous media. VERTPAK1 contains the following: BAREN, an analytical solution developed by Barenblatt, Zhelton and Kochina (1960) for describing transient flow to a well penetrating a (double porosity) confined aquifer; GIBMAC, an analytical solution developed by McNamee and Gibson (1960) for describing consolidation of a semi-infinite soil medium subject to a strip (plane strain) or cylindrical (axisymmetric) loading; GRINRH, an analytical solution developed by Gringarten (1971) for describing transient flow to a partially penetratingmore » well in a confined aquifer containing a single horizontal fracture; GRINRV, an analytical solution developed by Gringarten, Ramey, and Raghavan (1974) for describing transient flow to a fully penetrating well in a confined aquifer containing a single vertical fracture; HART, an analytical solution given by Nowacki (1962) and implemented by HART (1981) for describing the elastic behavior of an infinite solid subject to a line heat source; LESTER, an analytical solution presented by Lester, Jansen, and Burkholder (1975) for describing one-dimensional transport of radionuclide chains through an adsorbing medium; STRELT, an analytical solution presented by Streltsova-Adams (1978) for describing transient flow to a fully penetrating well in a (double porosity) confined aquifer; and TANG, an analytical solution developed by Tang, Frind, and Sudicky (1981) for describing solute transport in a porous medium containing a single fracture.« less

A high frequency analysis of electromagnetic plane wave scattering by perfectly-conducting semi-infinite parallel plate and rectangular waveguides with absorber coated inner walls

NASA Technical Reports Server (NTRS)

Noh, H. M.; Pathak, P. H.

1986-01-01

An approximate but sufficiently accurate high frequency solution which combines the uniform geometrical theory of diffraction (UTD) and the aperture integration (AI) method is developed for analyzing the problem of electromagnetic (EM) plane wave scattering by an open-ended, perfectly-conducting, semi-infinite hollow rectangular waveguide (or duct) with a thin, uniform layer of lossy or absorbing material on its inner wall, and with a planar termination inside. In addition, a high frequency solution for the EM scattering by a two dimensional (2-D), semi-infinite parallel plate waveguide with a absorber coating on the inner walls is also developed as a first step before analyzing the open-ended semi-infinite three dimensional (3-D) rectangular waveguide geometry. The total field scattered by the semi-infinite waveguide consists firstly of the fields scattered from the edges of the aperture at the open-end, and secondly of the fields which are coupled into the waveguide from the open-end and then reflected back from the interior termination to radiate out of the open-end. The first contribution to the scattered field can be found directly via the UTD ray method. The second contribution is found via the AI method which employs rays to describe the fields in the aperture that arrive there after reflecting from the interior termination. It is assumed that the direction of the incident plane wave and the direction of observation lie well inside the forward half space tht exists outside the half space containing the semi-infinite waveguide geometry. Also, the medium exterior to the waveguide is assumed to be free space.

Celestial mechanics solutions that escape

NASA Astrophysics Data System (ADS)

Gingold, Harry; Solomon, Daniel

2017-08-01

We establish the existence of an open set of initial conditions through which pass solutions without singularities to Newton's gravitational equations in R3 on a semi-infinite interval in forward time, for which every pair of particles separates like At , A > 0, as t → ∞. The solutions are constructable as series with rapid uniform convergence and their asymptotic behavior to any order is prescribed. We show that this family of solutions depends on 6N parameters subject to certain constraints.

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

NASA Astrophysics Data System (ADS)

Blas, Harold; Callisaya, Hector Flores

2018-02-01

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

Conformally-flat, non-singular static metric in infinite derivative gravity

NASA Astrophysics Data System (ADS)

Buoninfante, Luca; Koshelev, Alexey S.; Lambiase, Gaetano; Marto, João; Mazumdar, Anupam

2018-06-01

In Einstein's theory of general relativity the vacuum solution yields a blackhole with a curvature singularity, where there exists a point-like source with a Dirac delta distribution which is introduced as a boundary condition in the static case. It has been known for a while that ghost-free infinite derivative theory of gravity can ameliorate such a singularity at least at the level of linear perturbation around the Minkowski background. In this paper, we will show that the Schwarzschild metric does not satisfy the boundary condition at the origin within infinite derivative theory of gravity, since a Dirac delta source is smeared out by non-local gravitational interaction. We will also show that the spacetime metric becomes conformally-flat and singularity-free within the non-local region, which can be also made devoid of an event horizon. Furthermore, the scale of non-locality ought to be as large as that of the Schwarzschild radius, in such a way that the gravitational potential in any metric has to be always bounded by one, implying that gravity remains weak from the infrared all the way up to the ultraviolet regime, in concurrence with the results obtained in [arXiv:1707.00273]. The singular Schwarzschild blackhole can now be potentially replaced by a non-singular compact object, whose core is governed by the mass and the effective scale of non-locality.

Combined effects on MHD flow of Newtonian fluid past infinite vertical porous plate

NASA Astrophysics Data System (ADS)

Subbanna, K.; Mohiddin, S. Gouse; Vijaya, R. Bhuvana

2018-05-01

In this paper, we discussed free convective flow of a viscous fluid past an infinite vertical porous plate under the influence of uniform transverse magnetic field. Time dependent permeability and oscillatory suction is considered. The equations of the flow field are solved by a routine perturbation method for small amplitude of the permeability. The solutions for the velocity, temperature and concentration have been derived analytically and also its behavior is computationally discussed with the help of profiles. The shear stress, the Nusselt number and Sherwood number are also obtained and their behavior discussed computationally

Modality, Infinitives, and Finite Bare Verbs in Dutch and English Child Language

ERIC Educational Resources Information Center

Blom, Elma

2007-01-01

This article focuses on the meaning of nonfinite clauses ("root infinitives") in Dutch and English child language. I present experimental and naturalistic data confirming the claim that Dutch root infinitives are more often modal than English root infinitives. This cross-linguistic difference is significantly smaller than previously assumed,…

Exact Solutions for Stationary and Unsteady Layered Convection of a Viscous Incompressible Fluid with the Specified Velocities at the Bottom

NASA Astrophysics Data System (ADS)

Prosviryakov, E. Yu; Spevak, L. F.

2017-06-01

The layered convective flow of a viscous incompressible fluid is considered with the specified velocities at the bottom of an infinite layer. A new exact stationary and nonstationary solution of the Oberbeck-Boussinesq system is presented. The account of fluid velocity at the bottom is characterized by the presence of two stagnant points, this being indicative of the nonmonotonic kinetic energy profile with two local extrema.

A motif for infinite metal atom wires.

PubMed

Yin, Xi; Warren, Steven A; Pan, Yung-Tin; Tsao, Kai-Chieh; Gray, Danielle L; Bertke, Jeffery; Yang, Hong

2014-12-15

A new motif for infinite metal atom wires with tunable compositions and properties is developed based on the connection between metal paddlewheel and square planar complex moieties. Two infinite Pd chain compounds, [Pd4(CO)4(OAc)4Pd(acac)2] 1 and [Pd4(CO)4(TFA)4Pd(acac)2] 2, and an infinite Pd-Pt heterometallic chain compound, [Pd4(CO)4(OAc)4Pt(acac)2] 3, are identified by single-crystal X-ray diffraction analysis. In these new structures, the paddlewheel moiety is a Pd four-membered ring coordinated by bridging carboxylic ligands and μ2 carbonyl ligands. The planar moiety is either Pd(acac)2 or Pt(acac)2 (acac = acetylacetonate). These moieties are connected by metallophilic interactions. The results showed that these one-dimensional metal wire compounds have photoluminescent properties that are tunable by changing ligands and metal ions. 3 can also serve as a single source precursor for making Pd4Pt bimetallic nanostructures with precise control of metal composition. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Electromagnetic pulse excitation of finite- and infinitely-long lossy conductors over a lossy ground plane

DOE PAGES

Campione, Salvatore; Warne, Larry K.; Basilio, Lorena I.; ...

2017-01-13

This study details a model for the response of a finite- or an infinite-length wire interacting with a conducting ground to an electromagnetic pulse excitation. We develop a frequency–domain method based on transmission line theory that we name ATLOG – Analytic Transmission Line Over Ground. This method is developed as an alternative to full-wave methods, as it delivers a fast and reliable solution. It allows for the treatment of finite or infinite lossy, coated wires, and lossy grounds. The cases of wire above ground, as well as resting on the ground and buried beneath the ground are treated. The reportedmore » method is general and the time response of the induced current is obtained using an inverse Fourier transform of the current in the frequency domain. The focus is on the characteristics and propagation of the transmission line mode. Comparisons with full-wave simulations strengthen the validity of the proposed method.« less

Electromagnetic pulse excitation of finite- and infinitely-long lossy conductors over a lossy ground plane

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

Campione, Salvatore; Warne, Larry K.; Basilio, Lorena I.

This study details a model for the response of a finite- or an infinite-length wire interacting with a conducting ground to an electromagnetic pulse excitation. We develop a frequency–domain method based on transmission line theory that we name ATLOG – Analytic Transmission Line Over Ground. This method is developed as an alternative to full-wave methods, as it delivers a fast and reliable solution. It allows for the treatment of finite or infinite lossy, coated wires, and lossy grounds. The cases of wire above ground, as well as resting on the ground and buried beneath the ground are treated. The reportedmore » method is general and the time response of the induced current is obtained using an inverse Fourier transform of the current in the frequency domain. The focus is on the characteristics and propagation of the transmission line mode. Comparisons with full-wave simulations strengthen the validity of the proposed method.« less

Effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

NASA Astrophysics Data System (ADS)

Saunders, B. V.; Murray, B. T.; McFadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1991-10-01

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress free boundaries is studied using Floquet theory for the linear stability analysis. Situations are considered for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double diffusive convection. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency.

On Landauer's Principle and Bound for Infinite Systems

NASA Astrophysics Data System (ADS)

Longo, Roberto

2018-04-01

Landauer's principle provides a link between Shannon's information entropy and Clausius' thermodynamical entropy. Here we set up a basic formula for the incremental free energy of a quantum channel, possibly relative to infinite systems, naturally arising by an Operator Algebraic point of view. By the Tomita-Takesaki modular theory, we can indeed describe a canonical evolution associated with a quantum channel state transfer. Such evolution is implemented both by a modular Hamiltonian and a physical Hamiltonian, the latter being determined by its functoriality properties. This allows us to make an intrinsic analysis, extending our QFT index formula, but without any a priori given dynamics; the associated incremental free energy is related to the logarithm of the Jones index and is thus quantised. This leads to a general lower bound for the incremental free energy of an irreversible quantum channel which is half of the Landauer bound, and to further bounds corresponding to the discrete series of the Jones index. In the finite dimensional context, or in the case of DHR charges in QFT, where the dimension is a positive integer, our lower bound agrees with Landauer's bound.

Elastic Solutions in a Semi-Infinite Solid with an Ellipsoidal Inclusion

DTIC Science & Technology

1990-01-25

the free surface has been solved for a spherical inclusion with pure dilatational eigenstrain ( stress free transformation strain ) ( Mindlin and Cheng...1950B ), an ellipsoidal inclusion with pure dilatational eigenstrains ( Seo and Mura, 1979 ) and a cuboidal inclusion with uniform eigenstrains ...solution of a half-space under normal surface traction on the full space solution due to a cuboidal inclusion and its image with the uniform eigenstrains

Broadband computation of the scattering coefficients of infinite arbitrary cylinders.

PubMed

Blanchard, Cédric; Guizal, Brahim; Felbacq, Didier

2012-07-01

We employ a time-domain method to compute the near field on a contour enclosing infinitely long cylinders of arbitrary cross section and constitution. We therefore recover the cylindrical Hankel coefficients of the expansion of the field outside the circumscribed circle of the structure. The recovered coefficients enable the wideband analysis of complex systems, e.g., the determination of the radar cross section becomes straightforward. The prescription for constructing such a numerical tool is provided in great detail. The method is validated by computing the scattering coefficients for a homogeneous circular cylinder illuminated by a plane wave, a problem for which an analytical solution exists. Finally, some radiation properties of an optical antenna are examined by employing the proposed technique.

Infinite-disorder critical points of models with stretched exponential interactions

NASA Astrophysics Data System (ADS)

Juhász, Róbert

2014-09-01

We show that an interaction decaying as a stretched exponential function of distance, J(l)˜ e-cl^a , is able to alter the universality class of short-range systems having an infinite-disorder critical point. To do so, we study the low-energy properties of the random transverse-field Ising chain with the above form of interaction by a strong-disorder renormalization group (SDRG) approach. We find that the critical behavior of the model is controlled by infinite-disorder fixed points different from those of the short-range model if 0 < a < 1/2. In this range, the critical exponents calculated analytically by a simplified SDRG scheme are found to vary with a, while, for a > 1/2, the model belongs to the same universality class as its short-range variant. The entanglement entropy of a block of size L increases logarithmically with L at the critical point but, unlike the short-range model, the prefactor is dependent on disorder in the range 0 < a < 1/2. Numerical results obtained by an improved SDRG scheme are found to be in agreement with the analytical predictions. The same fixed points are expected to describe the critical behavior of, among others, the random contact process with stretched exponentially decaying activation rates.

Free vibration analysis of elastic structures submerged in an infinite or semi-infinite fluid domain by means of a coupled FE-BE solver

NASA Astrophysics Data System (ADS)

Zheng, Chang-Jun; Bi, Chuan-Xing; Zhang, Chuanzeng; Gao, Hai-Feng; Chen, Hai-Bo

2018-04-01

The vibration behavior of thin elastic structures can be noticeably influenced by the surrounding water, which represents a kind of heavy fluid. Since the feedback of the acoustic pressure onto the structure cannot be neglected in this case, a strong coupled scheme between the structural and fluid domains is usually required. In this work, a coupled finite element and boundary element (FE-BE) solver is developed for the free vibration analysis of structures submerged in an infinite fluid domain or a semi-infinite fluid domain with a free water surface. The structure is modeled by the finite element method (FEM). The compressibility of the fluid is taken into account, and hence the Helmholtz equation serves as the governing equation of the fluid domain. The boundary element method (BEM) is employed to model the fluid domain, and a boundary integral formulation with a half-space fundamental solution is used to satisfy the Dirichlet boundary condition on the free water surface exactly. The resulting nonlinear eigenvalue problem (NEVP) is converted into a small linear one by using a contour integral method. Adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenfrequencies of interest. The Burton-Miller method is used to filter out the fictitious eigenfrequencies of the boundary integral formulations. Numerical examples are given to demonstrate the accuracy and applicability of the developed eigensolver, and also show that the fluid-loading effect strongly depends on both the water depth and the mode shapes.

Infinite tension limit of the pure spinor superstring

NASA Astrophysics Data System (ADS)

Berkovits, Nathan

2014-03-01

Mason and Skinner recently constructed a chiral infinite tension limit of the Ramond-Neveu-Schwarz superstring which was shown to compute the Cachazo-He-Yuan formulae for tree-level d = 10 Yang-Mills amplitudes and the NS-NS sector of tree-level d = 10 supergravity amplitudes. In this letter, their chiral infinite tension limit is generalized to the pure spinor superstring which computes a d = 10 superspace version of the Cachazo-He-Yuan formulae for tree-level d = 10 super-Yang-Mills and supergravity amplitudes.

Solute-solvent cavity and bridge functions. I. Varying size of the solute

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

Vyalov, I., E-mail: ivan.vyalov@iit.it; Chuev, G., E-mail: genchuev@rambler.ru; Georgi, N., E-mail: georgi@mis.mpg.de

2014-08-21

In this work we present the results of the extensive molecular simulations of solute-solvent cavity and bridge functions. The mixtures of Lennard-Jones solvent with Lennard-Jones solute at infinite dilution are considered for different solute-solvent size ratios—up to 4:1. The Percus-Yevick and hypernetted chain closures deviate substantially from simulation results in the investigated temperature and density ranges. We also find that the behavior of the indirect and cavity correlation functions is non-monotonous within the hard-core region, but the latter can be successfully approximated by mean-field theory if the solute-solvent interaction energy is divided into repulsive and attractive contribution, according to Weeks-Chandler-Andersenmore » theory. Furthermore, in spite of the non-monotonous behavior of logarithm of the cavity function and the indirect correlation function, their difference, i.e., the bridge function remains constant within the hard-core region. Such behavior of the bridge and indirect correlation functions at small distances and for small values of indirect correlation function is well known from the Duh-Haymet plots, where the non-unique relationship results in loops of the bridge function vs. indirect correlation function graphs. We show that the same pathological behavior appears also when distance is small and indirect correlation function is large. We further show that the unique functional behavior of the bridge function can be established when bridge is represented as a function of the renormalized, repulsive indirect correlation function.« less

Non-singular spacetimes with a negative cosmological constant: IV. Stationary black hole solutions with matter fields

NASA Astrophysics Data System (ADS)

Chruściel, Piotr T.; Delay, Erwann; Klinger, Paul

2018-02-01

We use an elliptic system of equations with complex coefficients for a set of complex-valued tensor fields as a tool to construct infinite-dimensional families of non-singular stationary black holes, real-valued Lorentzian solutions of the Einstein–Maxwell-dilaton-scalar fields-Yang–Mills–Higgs–Chern–Simons-f(R) equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.

Research Staff | Integrated Energy Solutions | NREL

Science.gov Websites

Ricardo.Castillo@nrel.gov 303-384-7452 Chamberlain, Kyle Post Graduate Researcher Kyle.Chamberlain@nrel.gov 303-275 Researcher-Land Reuse & Arctic Energy Solutions Gail.Mosey@nrel.gov 303-384-7356 Mow, Benjamin Post Peterson, Zachary Post Graduate Researcher - Grid Modernization Zachary.Peterson@nrel.gov 303-275-4949

The global existence and large time behavior of smooth compressible fluid in an infinitely expanding ball, III: The 3-D Boltzmann equation

NASA Astrophysics Data System (ADS)

Yin, Huicheng; Zhao, Wenbin

2018-01-01

This paper is a continuation of the works in [35] and [37], where the authors have established the global existence of smooth compressible flows in infinitely expanding balls for inviscid gases and viscid gases, respectively. In this paper, we are concerned with the global existence and large time behavior of compressible Boltzmann gases in an infinitely expanding ball. Such a problem is one of the interesting models in studying the theory of global smooth solutions to multidimensional compressible gases with time dependent boundaries and vacuum states at infinite time. Due to the conservation of mass, the fluid in the expanding ball becomes rarefied and eventually tends to a vacuum state meanwhile there are no appearances of vacuum domains in any part of the expansive ball, which is easily observed in finite time. In the present paper, we will confirm this physical phenomenon for the Boltzmann equation by obtaining the exact lower and upper bound on the macroscopic density function.

On the convergence of an iterative formulation of the electromagnetic scattering from an infinite grating of thin wires

NASA Technical Reports Server (NTRS)

Brand, J. C.

1985-01-01

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. The mathematical background for formulating an iterative equation is covered using straightforward single variable examples including an extension to vector spaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.

A COMPARISON OF TRANSIENT INFINITE ELEMENTS AND TRANSIENT KIRCHHOFF INTEGRAL METHODS FOR FAR FIELD ACOUSTIC ANALYSIS

DOE PAGES

WALSH, TIMOTHY F.; JONES, ANDREA; BHARDWAJ, MANOJ; ...

2013-04-01

Finite element analysis of transient acoustic phenomena on unbounded exterior domains is very common in engineering analysis. In these problems there is a common need to compute the acoustic pressure at points outside of the acoustic mesh, since meshing to points of interest is impractical in many scenarios. In aeroacoustic calculations, for example, the acoustic pressure may be required at tens or hundreds of meters from the structure. In these cases, a method is needed for post-processing the acoustic results to compute the response at far-field points. In this paper, we compare two methods for computing far-field acoustic pressures, onemore » derived directly from the infinite element solution, and the other from the transient version of the Kirchhoff integral. Here, we show that the infinite element approach alleviates the large storage requirements that are typical of Kirchhoff integral and related procedures, and also does not suffer from loss of accuracy that is an inherent part of computing numerical derivatives in the Kirchhoff integral. In order to further speed up and streamline the process of computing the acoustic response at points outside of the mesh, we also address the nonlinear iterative procedure needed for locating parametric coordinates within the host infinite element of far-field points, the parallelization of the overall process, linear solver requirements, and system stability considerations.« less

Conical intersections of free energy surfaces in solution: Effect of electron correlation on a protonated Schiff base in methanol solution

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

Mori, Toshifumi; Nakano, Katsuhiro; Kato, Shigeki

2010-08-14

The minimum energy conical intersection (MECI) optimization method with taking account of the dynamic electron correlation effect [T. Mori and S. Kato, Chem. Phys. Lett. 476, 97 (2009)] is extended to locate the MECI of nonequilibrium free energy surfaces in solution. A multistate electronic perturbation theory is introduced into the nonequilibrium free energy formula, which is defined as a function of solute and solvation coordinates. The analytical free energy gradient and interstate coupling vectors are derived, and are applied to locate MECIs in solution. The present method is applied to study the cis-trans photoisomerization reaction of a protonated Schiff basemore » molecule (PSB3) in methanol (MeOH) solution. It is found that the effect of dynamic electron correlation largely lowers the energy of S{sub 1} state. We also show that the solvation effect strongly stabilizes the MECI obtained by twisting the terminal C=N bond to become accessible in MeOH solution, whereas the conical intersection is found to be unstable in gas phase. The present study indicates that both electron correlation and solvation effects are important in the photoisomerization reaction of PSB3. The effect of counterion is also examined, and seems to be rather small in solution. The structures of free energy surfaces around MECIs are also discussed.« less

The study of the behaviour of a disturbed semi-infinite liquid jet using a spatial instability method

NASA Astrophysics Data System (ADS)

Basu (‧nee De), Shukla

2001-11-01

A study has been made of the behaviour of a disturbed semi-infinite liquid jet using a spatial instability method. A sinusoidal disturbance in the axial component of jet velocity at the nozzle is considered which resulted in an elliptic free surface boundary value problem with two non-linear boundary conditions. The system is linearised using perturbation techniques and the first order solution resulted in the dispersion relation. The jet stability is found to depend explicitly on the frequency of the disturbance and the Weber number. The second and third order solutions have been derived analytically which are used to predict on jet break-up and satellite formation.

Interaction and charge transfer between dielectric spheres: Exact and approximate analytical solutions.

PubMed

Lindén, Fredrik; Cederquist, Henrik; Zettergren, Henning

2016-11-21

We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones.

Concurrent Solution and Adsorption of Hydrocarbons in Gas Chromatographic Columns Packed with Different Loadings of 3-Methylsydnone on Chromosorb P

PubMed

Castells; Romero; Nardillo

1997-08-01

Thermodynamic properties of solution in 3-methylsydnone (3MS) and of adsorption at the nitrogen/3MS interface were gas chromatographically measured for a group of fifteen hydrocarbons at infinite dilution conditions. Retention volumes were measured at five temperatures within the range 37-52°C in six columns containing different loadings of 3MS on Chromosorb P AW. Partition and adsorption coefficients were calculated and from their temperature dependence the corresponding enthalpies were obtained, although with considerable error; infinite dilution activity coefficients of the hydrocarbons in the bulk and in the surface phases demonstrated a strong correlation. Bulk activity coefficients in 3MS were very much smaller than those previously measured for the same solutes in formamide (FA) and in ethyleneglycol (EG), and were also smaller than what could be predicted on account of 3MS cohesive energy density as estimated from the quotient sigma/v1/3 (sigma, surface tension; v, molar volume). There was not such a large difference between the surface activity coefficients in the three solvents; furthermore, the quotients (surface activity coefficient/bulk activity coefficient) for a given solute in 3MS were twice as large as in FA and about three times larger than in EG. These results make evident the difficulties inherent in the prediction of surface phase properties from those in the bulk and cast doubts on the pertinency of employing the surface tension to compare cohesive energy densities of polar solvents with important chemical differences.

Solution synthesis of metal oxides for electrochemical energy storage applications.

PubMed

Xia, Xinhui; Zhang, Yongqi; Chao, Dongliang; Guan, Cao; Zhang, Yijun; Li, Lu; Ge, Xiang; Bacho, Ignacio Mínguez; Tu, Jiangping; Fan, Hong Jin

2014-05-21

This article provides an overview of solution-based methods for the controllable synthesis of metal oxides and their applications for electrochemical energy storage. Typical solution synthesis strategies are summarized and the detailed chemical reactions are elaborated for several common nanostructured transition metal oxides and their composites. The merits and demerits of these synthesis methods and some important considerations are discussed in association with their electrochemical performance. We also propose the basic guideline for designing advanced nanostructure electrode materials, and the future research trend in the development of high power and energy density electrochemical energy storage devices.

On multisoliton solutions of the constant astigmatism equation

NASA Astrophysics Data System (ADS)

Hlaváč, Adam

2015-09-01

We introduce an algebraic formula producing infinitely many exact solutions of the constant astigmatism equation {z}{yy}+{(1/z)}{xx}+2=0 from a given seed. A construction of corresponding surfaces of constant astigmatism is then a matter of routine. As a special case, we consider multisoliton solutions of the constant astigmatism equation defined as counterparts of famous multisoliton solutions of the sine-Gordon equation. A few particular examples are surveyed as well.

Modeling the free energy surfaces of electron transfer in condensed phases

NASA Astrophysics Data System (ADS)

Matyushov, Dmitry V.; Voth, Gregory A.

2000-10-01

We develop a three-parameter model of electron transfer (ET) in condensed phases based on the Hamiltonian of a two-state solute linearly coupled to a harmonic, classical solvent mode with different force constants in the initial and final states (a classical limit of the quantum Kubo-Toyozawa model). The exact analytical solution for the ET free energy surfaces demonstrates the following features: (i) the range of ET reaction coordinates is limited by a one-sided fluctuation band, (ii) the ET free energies are infinite outside the band, and (iii) the free energy surfaces are parabolic close to their minima and linear far from the minima positions. The model provides an analytical framework to map physical phenomena conflicting with the Marcus-Hush two-parameter model of ET. Nonlinear solvation, ET in polarizable charge-transfer complexes, and configurational flexibility of donor-acceptor complexes are successfully mapped onto the model. The present theory leads to a significant modification of the energy gap law for ET reactions.

Dynamic Infinite Mixed-Membership Stochastic Blockmodel.

PubMed

Fan, Xuhui; Cao, Longbing; Xu, Richard Yi Da

2015-09-01

Directional and pairwise measurements are often used to model interactions in a social network setting. The mixed-membership stochastic blockmodel (MMSB) was a seminal work in this area, and its ability has been extended. However, models such as MMSB face particular challenges in modeling dynamic networks, for example, with the unknown number of communities. Accordingly, this paper proposes a dynamic infinite mixed-membership stochastic blockmodel, a generalized framework that extends the existing work to potentially infinite communities inside a network in dynamic settings (i.e., networks are observed over time). Additional model parameters are introduced to reflect the degree of persistence among one's memberships at consecutive time stamps. Under this framework, two specific models, namely mixture time variant and mixture time invariant models, are proposed to depict two different time correlation structures. Two effective posterior sampling strategies and their results are presented, respectively, using synthetic and real-world data.

Criteria for resolving the cosmological singularity in infinite derivative gravity around expanding backgrounds

NASA Astrophysics Data System (ADS)

Edholm, James; Conroy, Aindriú

2017-12-01

We derive the conditions whereby null rays "defocus" within infinite derivative gravity for perturbations around an (A)dS background, and show that it is therefore possible to avoid singularities within this framework. This is in contrast to Einstein's theory of general relativity, where singularities are generated unless the null energy condition is violated. We further extend this to an (A)dS-Bianchi I background metric, and also give an example of a specific perturbation where defocusing is possible given certain conditions.

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

NASA Astrophysics Data System (ADS)

Nutku, Y.

1985-06-01

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

Eisenstein series for infinite-dimensional U-duality groups

NASA Astrophysics Data System (ADS)

Fleig, Philipp; Kleinschmidt, Axel

2012-06-01

We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E 9, E 10 and E 11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D < 3 space-time dimensions.

Classical and quantum production of cornucopions at energies below 1018 GeV

NASA Astrophysics Data System (ADS)

Banks, T.; O'loughlin, M.

1993-01-01

We argue that the paradoxes associated with infinitely degenerate states, which plague relic particle scenarios for the end point of black hole evaporation, may be absent when the relics are horned particles. Most of our arguments are based on simple observations about the classical geometry of extremal dilaton black holes, but at a crucial point we are forced to speculate about classical solutions to string theory in which the infinite coupling singularity of the extremal dilaton solution is shielded by a condensate of massless modes propagating in its infinite horn. We use the nonsingular c=1 solution of (1+1)-dimensional string theory as a crude model for the properties of the condensate. We also present a brief discussion of more general relic scenarios based on large relics of low mass.

Clean Energy Solutions Center and SE4All: Partnering to Support Country Actions

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

2016-05-01

Since 2012, the Clean Energy Solutions Center (Solutions Center) and Sustainable Energy for All (SE4All) have partnered to deliver information, knowledge and expert assistance to policymakers and practitioners in countries actively working to achieve SE4All objectives. Through SE4All efforts, national governments are implementing integrated country actions to strategically transform their energy markets. This fact sheet details the Solutions Center and SE4All partnership and available areas of technical assistance.

Infinite-range Heisenberg model and high-temperature superconductivity

NASA Astrophysics Data System (ADS)

Tahir-Kheli, Jamil; Goddard, William A., III

1993-11-01

A strongly coupled variational wave function, the doublet spin-projected Néel state (DSPN), is proposed for oxygen holes in three-band models of high-temperature superconductors. This wave function has the three-spin system of the oxygen hole plus the two neighboring copper atoms coupled in a spin-1/2 doublet. The copper spins in the neighborhood of a hole are in an eigenstate of the infinite-range Heisenberg antiferromagnet (SPN state). The doublet three-spin magnetic polaron or hopping polaron (HP) is stabilized by the hopping terms tσ and tτ, rather than by the copper-oxygen antiferromagnetic coupling Jpd. Although, the HP has a large projection onto the Emery (Dg) polaron, a non-negligible amount of doublet-u (Du) character is required for optimal hopping stabilization. This is due to Jdd, the copper-copper antiferromagnetic coupling. For the copper spins near an oxygen hole, the copper-copper antiferromagnetic coupling can be considered to be almost infinite ranged, since the copper-spin-correlation length in the superconducting phase (0.06-0.25 holes per in-plane copper) is approximately equal to the mean separation of the holes (between 2 and 4 lattice spacings). The general DSPN wave function is constructed for the motion of a single quasiparticle in an antiferromagnetic background. The SPN state allows simple calculations of various couplings of the oxygen hole with the copper spins. The energy minimum is found at symmetry (π/2,π/2) and the bandwidth scales with Jdd. These results are in agreement with exact computations on a lattice. The coupling of the quasiparticles leads to an attraction of holes and its magnitude is estimated.

Soliton stability in some knot soliton models

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

Adam, C.; Sanchez-Guillen, J.; Wereszczynski, A.

2007-02-15

We study the issue of stability of static solitonlike solutions in some nonlinear field theories which allow for knotted field configurations. Concretely, we investigate the Aratyn-Ferreira-Zimerman model [Phys. Lett. B 456, 162 (1999); Phys. Rev. Lett. 83, 1723 (1999)], based on a Lagrangian quartic in first derivatives with infinitely many conserved currents, for which infinitely many soliton solutions are known analytically. For this model we find that sectors with different (integer) topological charges (Hopf index) are not separated by an infinite energy barrier. Further, if variations which change the topological charge are allowed, then the static solutions are not evenmore » critical points of the energy functional. We also explain why soliton solutions can exist at all, in spite of these facts. In addition, we briefly discuss the Nicole model [J. Phys. G 4, 1363 (1978)], which is based on a sigma-model-type Lagrangian. For the Nicole model we find that different topological sectors are separated by an infinite energy barrier.« less

Electromagnetic Scattering by Multiple Cavities Embedded in the Infinite 2D Ground Plane

DTIC Science & Technology

2014-07-01

Electromagnetic Scattering by Multiple Cavities Embedded in the Infinite 2D Ground Plane Peijun Li 1 and Aihua W. Wood 2 1 Department of...of the electromagnetic wave scattering by multiple open cavities, which are embedded in an infinite two-dimensional ground plane . By introducing a...equation, variational formulation. I. INTRODUCTION A cavity is referred to as a local perturbation of the infinite ground plane . Given the cavity

Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping

NASA Astrophysics Data System (ADS)

Lu, Jianfeng; Zhou, Zhennan

2018-02-01

To accelerate the thermal equilibrium sampling of multi-level quantum systems, the infinite swapping limit of a recently proposed multi-level ring polymer representation is investigated. In the infinite swapping limit, the ring polymer evolves according to an averaged Hamiltonian with respect to all possible surface index configurations of the ring polymer and thus connects the surface hopping approach to the mean-field path-integral molecular dynamics. A multiscale integrator for the infinite swapping limit is also proposed to enable efficient sampling based on the limiting dynamics. Numerical results demonstrate the huge improvement of sampling efficiency of the infinite swapping compared with the direct simulation of path-integral molecular dynamics with surface hopping.

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

NASA Technical Reports Server (NTRS)

Banks, H. T.; Wang, C.

1989-01-01

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

Asymptotic expansions of solutions of the heat conduction equation in internally bounded cylindrical geometry

USGS Publications Warehouse

Ritchie, R.H.; Sakakura, A.Y.

1956-01-01

The formal solutions of problems involving transient heat conduction in infinite internally bounded cylindrical solids may be obtained by the Laplace transform method. Asymptotic series representing the solutions for large values of time are given in terms of functions related to the derivatives of the reciprocal gamma function. The results are applied to the case of the internally bounded infinite cylindrical medium with, (a) the boundary held at constant temperature; (b) with constant heat flow over the boundary; and (c) with the "radiation" boundary condition. A problem in the flow of gas through a porous medium is considered in detail.

Flowing partially penetrating well: solution to a mixed-type boundary value problem

NASA Astrophysics Data System (ADS)

Cassiani, G.; Kabala, Z. J.; Medina, M. A.

A new semi-analytic solution to the mixed-type boundary value problem for a flowing partially penetrating well with infinitesimal skin situated in an anisotropic aquifer is developed. The solution is suited to aquifers having a semi-infinite vertical extent or to packer tests with aquifer horizontal boundaries far enough from the tested area. The problem reduces to a system of dual integral equations (DE) and further to a deconvolution problem. Unlike the analogous Dagan's steady-state solution [Water Resour. Res. 1978; 14:929-34], our DE solution does not suffer from numerical oscillations. The new solution is validated by matching the corresponding finite-difference solution and is computationally much more efficient. An automated (Newton-Raphson) parameter identification algorithm is proposed for field test inversion, utilizing the DE solution for the forward model. The procedure is computationally efficient and converges to correct parameter values. A solution for the partially penetrating flowing well with no skin and a drawdown-drawdown discontinuous boundary condition, analogous to that by Novakowski [Can. Geotech. J. 1993; 30:600-6], is compared to the DE solution. The D-D solution leads to physically inconsistent infinite total flow rate to the well, when no skin effect is considered. The DE solution, on the other hand, produces accurate results.

The University as an Infinite Game: Revitalising Activism in the Academy

ERIC Educational Resources Information Center

Harré, Niki; Grant, Barbara M.; Locke, Kirsten; Sturm, Sean

2017-01-01

We offer here a metaphor of the university as an "infinite game" in which we bring to life insight, imagination, and radical inclusion; and resist the "finite games" that can lead us astray. We suggest that keeping the infinite game alive within universities is a much-needed form of academic activism. We offer four vignettes…

Dependence of Interaction Free Energy between Solutes on an External Electrostatic Field

PubMed Central

Yang, Pei-Kun

2013-01-01

To explore the athermal effect of an external electrostatic field on the stabilities of protein conformations and the binding affinities of protein-protein/ligand interactions, the dependences of the polar and hydrophobic interactions on the external electrostatic field, −Eext, were studied using molecular dynamics (MD) simulations. By decomposing Eext into, along, and perpendicular to the direction formed by the two solutes, the effect of Eext on the interactions between these two solutes can be estimated based on the effects from these two components. Eext was applied along the direction of the electric dipole formed by two solutes with opposite charges. The attractive interaction free energy between these two solutes decreased for solutes treated as point charges. In contrast, the attractive interaction free energy between these two solutes increased, as observed by MD simulations, for Eext = 40 or 60 MV/cm. Eext was applied perpendicular to the direction of the electric dipole formed by these two solutes. The attractive interaction free energy was increased for Eext = 100 MV/cm as a result of dielectric saturation. The force on the solutes along the direction of Eext computed from MD simulations was greater than that estimated from a continuum solvent in which the solutes were treated as point charges. To explore the hydrophobic interactions, Eext was applied to a water cluster containing two neutral solutes. The repulsive force between these solutes was decreased/increased for Eext along/perpendicular to the direction of the electric dipole formed by these two solutes. PMID:23852018

Loss of Energy Concentration in Nonlinear Evolution Beam Equations

NASA Astrophysics Data System (ADS)

Garrione, Maurizio; Gazzola, Filippo

2017-12-01

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

Finite-action solutions of Yang-Mills equations on de Sitter dS4 and anti-de Sitter AdS4 spaces

NASA Astrophysics Data System (ADS)

Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.

2017-11-01

We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter dS4 and anti-de Sitter AdS4 spaces and construct various solutions to the Yang-Mills equations. On de Sitter space we reduce the Yang-Mills equations via an SU(2)-equivariant ansatz to Newtonian mechanics of a particle moving in R^3 under the influence of a quartic potential. Then we describe magnetic and electric-magnetic solutions, both Abelian and non-Abelian, all having finite energy and finite action. A similar reduction on anti-de Sitter space also yields Yang-Mills solutions with finite energy and action. We propose a lower bound for the action on both backgrounds. Employing another metric on AdS4, the SU(2) Yang-Mills equations are reduced to an analytic continuation of the above particle mechanics from R^3 to R^{2,1} . We discuss analytical solutions to these equations, which produce infinite-action configurations. After a Euclidean continuation of dS4 and AdS4 we also present self-dual (instanton-type) Yang-Mills solutions on these backgrounds.

Quantum transverse-field Ising model on an infinite tree from matrix product states

NASA Astrophysics Data System (ADS)

Nagaj, Daniel; Farhi, Edward; Goldstone, Jeffrey; Shor, Peter; Sylvester, Igor

2008-06-01

We give a generalization to an infinite tree geometry of Vidal’s infinite time-evolving block decimation (iTEBD) algorithm [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)] for simulating an infinite line of quantum spins. We numerically investigate the quantum Ising model in a transverse field on the Bethe lattice using the matrix product state ansatz. We observe a second order phase transition, with certain key differences from the transverse field Ising model on an infinite spin chain. We also investigate a transverse field Ising model with a specific longitudinal field. When the transverse field is turned off, this model has a highly degenerate ground state as opposed to the pure Ising model whose ground state is only doubly degenerate.

Intertwining solutions for magnetic relativistic Hartree type equations

NASA Astrophysics Data System (ADS)

Cingolani, Silvia; Secchi, Simone

2018-05-01

We consider the magnetic pseudo-relativistic Schrödinger equation where , m  >  0, is an external continuous scalar potential, is a continuous vector potential and is a convolution kernel, is a constant, , . We assume that A and V are symmetric with respect to a closed subgroup G of the group of orthogonal linear transformations of . If for any , the cardinality of the G-orbit of x is infinite, then we prove the existence of infinitely many intertwining solutions assuming that is either linear in x or uniformly bounded. The results are proved by means of a new local realization of the square root of the magnetic laplacian to a local elliptic operator with Neumann boundary condition on a half-space. Moreover we derive an existence result of a ground state intertwining solution for bounded vector potentials, if G admits a finite orbit.

Effect of ion concentration, solution and membrane permittivity on electric energy storage and capacitance.

PubMed

Tajparast, Mohammad; Glavinović, Mladen I

2018-06-06

Bio-membranes as capacitors store electric energy, but their permittivity is low whereas the permittivity of surrounding solution is high. To evaluate the effective capacitance of the membrane/solution system and determine the electric energy stored within the membrane and in the solution, we estimated their electric variables using Poisson-Nernst-Planck simulations. We calculated membrane and solution capacitances from stored electric energy. The effective capacitance was calculated by fitting a six-capacitance model to charges (fixed and ion) and associated potentials, because it cannot be considered as a result of membrane and solution capacitance in series. The electric energy stored within the membrane (typically much smaller than that in the solution), depends on the membrane permittivity, but also on the external electric field, surface charge density, water permittivity and ion concentration. The effect on capacitances is more specific. Solution capacitance rises with greater solution permittivity or ion concentration, but the membrane capacitance (much smaller than solution capacitance) is only influenced by its permittivity. Interestingly, the effective capacitance is independent of membrane or solution permittivity, but rises as the ion concentration increases and surface charge becomes positive. Experimental estimates of membrane capacitance are thus not necessarily a reliable index of its surface area. Copyright © 2018. Published by Elsevier B.V.

Work with Us | Integrated Energy Solutions | NREL

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Work with Us Work with Us NREL offers industry, academia, and government agencies opportunities to work with us and leverage our research, facilities, and expertise. Contact Us Photo of Adam Warren with Us We're making an impact on advancing integrated energy solutions in the United States and abroad

Gini estimation under infinite variance

NASA Astrophysics Data System (ADS)

Fontanari, Andrea; Taleb, Nassim Nicholas; Cirillo, Pasquale

2018-07-01

We study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index α ∈(1 , 2)). We show that, in such a case, the Gini coefficient cannot be reliably estimated using conventional nonparametric methods, because of a downward bias that emerges under fat tails. This has important implications for the ongoing discussion about economic inequality. We start by discussing how the nonparametric estimator of the Gini index undergoes a phase transition in the symmetry structure of its asymptotic distribution, as the data distribution shifts from the domain of attraction of a light-tailed distribution to that of a fat-tailed one, especially in the case of infinite variance. We also show how the nonparametric Gini bias increases with lower values of α. We then prove that maximum likelihood estimation outperforms nonparametric methods, requiring a much smaller sample size to reach efficiency. Finally, for fat-tailed data, we provide a simple correction mechanism to the small sample bias of the nonparametric estimator based on the distance between the mode and the mean of its asymptotic distribution.

Infinite densities for Lévy walks.

PubMed

Rebenshtok, A; Denisov, S; Hänggi, P; Barkai, E

2014-12-01

Motion of particles in many systems exhibits a mixture between periods of random diffusive-like events and ballistic-like motion. In many cases, such systems exhibit strong anomalous diffusion, where low-order moments 〈|x(t)|(q)〉 with q below a critical value q(c) exhibit diffusive scaling while for q>q(c) a ballistic scaling emerges. The mixed dynamics constitutes a theoretical challenge since it does not fall into a unique category of motion, e.g., the known diffusion equations and central limit theorems fail to describe both aspects. In this paper we resolve this problem by resorting to the concept of infinite density. Using the widely applicable Lévy walk model, we find a general expression for the corresponding non-normalized density which is fully determined by the particles velocity distribution, the anomalous diffusion exponent α, and the diffusion coefficient K(α). We explain how infinite densities play a central role in the description of dynamics of a large class of physical processes and discuss how they can be evaluated from experimental or numerical data.

NREL, LiquidCool Solutions Partner on Energy-Efficient Cooling for

Science.gov Websites

denser and generate more heat. Liquid cooling, including the LiquidCool Solutions technology, offers a more energy-efficient solution that also allows for effective reuse of the heat rejected by the water, depending on the coolant temperature and heat exchanger specifications. These water temperatures

Geometry of quantum dynamics in infinite-dimensional Hilbert space

NASA Astrophysics Data System (ADS)

Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana

2018-04-01

We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.

Steps in Solution Growth: Revised Gibbs-Thomson Law, Turbulence and Morphological Stability

NASA Technical Reports Server (NTRS)

Chernov, A. A.; Rashkovich, L. N.; Vekilov, P. G.

2004-01-01

Two groups of new phenomena revealed by AFM and high resolution optical interferometry on crystal faces growing from solutions will be discussed. 1. Spacing between strongly polygonized spiral steps with low less than 10(exp -2) kink density on lysozyme and K- biphtalate do not follow the Burton-cabrera-Frank theory. The critical length of the yet immobile first Short step segment adjacent to a pinning defect (dislocation, stacking fault) is many times longer than that following from the step free energy. The low-kink density steps are typical of many growth conditions and materials, including low temperature gas phase epitaxy and MBE. 2. The step bunching pattern on the approx. 1 cm long { 110) KDP face growing from the turbulent solution flow (Re (triple bonds) 10(exp 4), solution flow rate approx. 1 m/s) suggests that the step bunch height does not increase infinitely as the bunch path on the crystal face rises, as is usually observed on large KDP crystals. The mechanism controlling the maximal bunch width and height is based on the drag of the solution depleted by the step bunch down thc solution stream. It includes splitting, coagulation and interlacing of bunches

Numerical and theoretical evaluations of AC losses for single and infinite numbers of superconductor strips with direct and alternating transport currents in external AC magnetic field

NASA Astrophysics Data System (ADS)

Kajikawa, K.; Funaki, K.; Shikimachi, K.; Hirano, N.; Nagaya, S.

2010-11-01

AC losses in a superconductor strip are numerically evaluated by means of a finite element method formulated with a current vector potential. The expressions of AC losses in an infinite slab that corresponds to a simple model of infinitely stacked strips are also derived theoretically. It is assumed that the voltage-current characteristics of the superconductors are represented by Bean's critical state model. The typical operation pattern of a Superconducting Magnetic Energy Storage (SMES) coil with direct and alternating transport currents in an external AC magnetic field is taken into account as the electromagnetic environment for both the single strip and the infinite slab. By using the obtained results of AC losses, the influences of the transport currents on the total losses are discussed quantitatively.

Functors of White Noise Associated to Characters of the Infinite Symmetric Group

NASA Astrophysics Data System (ADS)

Bożejko, Marek; Guţă, Mădălin

The characters of the infinite symmetric group are extended to multiplicative positive definite functions on pair partitions by using an explicit representation due to Veršik and Kerov. The von Neumann algebra generated by the fields with f in an infinite dimensional real Hilbert space is infinite and the vacuum vector is not separating. For a family depending on an integer N< - 1 an ``exclusion principle'' is found allowing at most ``identical particles'' on the same state: The algebras are type factors. Functors of white noise are constructed and proved to be non-equivalent for different values of N.

NREL Incubator Alliance Helps Entrepreneurs Build Clean Energy Solutions

Science.gov Websites

Incubator Alliance Helps Entrepreneurs Build Clean Energy Solutions For more information contact alliance. "We can do that by helping companies succeed." The incubators' objective is to build

Geometric MCMC for infinite-dimensional inverse problems

NASA Astrophysics Data System (ADS)

Beskos, Alexandros; Girolami, Mark; Lan, Shiwei; Farrell, Patrick E.; Stuart, Andrew M.

2017-04-01

Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned Crank-Nicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method.

Generalized analytical solutions to sequentially coupled multi-species advective-dispersive transport equations in a finite domain subject to an arbitrary time-dependent source boundary condition

NASA Astrophysics Data System (ADS)

Chen, Jui-Sheng; Liu, Chen-Wuing; Liang, Ching-Ping; Lai, Keng-Hsin

2012-08-01

SummaryMulti-species advective-dispersive transport equations sequentially coupled with first-order decay reactions are widely used to describe the transport and fate of the decay chain contaminants such as radionuclide, chlorinated solvents, and nitrogen. Although researchers attempted to present various types of methods for analytically solving this transport equation system, the currently available solutions are mostly limited to an infinite or a semi-infinite domain. A generalized analytical solution for the coupled multi-species transport problem in a finite domain associated with an arbitrary time-dependent source boundary is not available in the published literature. In this study, we first derive generalized analytical solutions for this transport problem in a finite domain involving arbitrary number of species subject to an arbitrary time-dependent source boundary. Subsequently, we adopt these derived generalized analytical solutions to obtain explicit analytical solutions for a special-case transport scenario involving an exponentially decaying Bateman type time-dependent source boundary. We test the derived special-case solutions against the previously published coupled 4-species transport solution and the corresponding numerical solution with coupled 10-species transport to conduct the solution verification. Finally, we compare the new analytical solutions derived for a finite domain against the published analytical solutions derived for a semi-infinite domain to illustrate the effect of the exit boundary condition on coupled multi-species transport with an exponential decaying source boundary. The results show noticeable discrepancies between the breakthrough curves of all the species in the immediate vicinity of the exit boundary obtained from the analytical solutions for a finite domain and a semi-infinite domain for the dispersion-dominated condition.

Common misconceptions about the dynamical theory of crystal lattices: Cauchy relations, lattice potentials and infinite crystals

NASA Astrophysics Data System (ADS)

Elcoro, Luis; Etxebarria, Jesús

2011-01-01

The requirement of rotational invariance for lattice potential energies is investigated. Starting from this condition, it is shown that the Cauchy relations for the elastic constants are fulfilled if the lattice potential is built from pair interactions or when the first-neighbour approximation is adopted. This is seldom recognized in widely used solid-state textbooks. Frequently, pair interaction is even considered to be the most general situation. In addition, it is shown that the demand of rotational invariance in an infinite crystal leads to inconsistencies in the symmetry of the elastic tensor. However, for finite crystals, no problems arise, and the Huang conditions are deduced using exclusively a microscopic approach for the elasticity theory, without making any reference to macroscopic parameters. This work may be useful in both undergraduate and graduate level courses to point out the crudeness of the pair-potential interaction and to explore the limits of the infinite-crystal approximation.

Resilience in Remote Communities | Integrated Energy Solutions | NREL

Science.gov Websites

community stakeholders, we develop and implement comprehensive road maps for resilience through: Strategic issues Experience developing and deploying integrated energy solutions Specialized facilities and expert Affordable Power in the Developing World Study Shows Philippine Power System Can Achieve 30% and 50

The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

NASA Astrophysics Data System (ADS)

Saunders, B. V.; Murray, B. T.; McFadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1992-06-01

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.

The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

NASA Technical Reports Server (NTRS)

Saunders, B. V.; Murray, B. T.; Mcfadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1992-01-01

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.

77 FR 20019 - FirstEnergy Solutions Corp., Allegheny Energy Supply Company, LLC v. PJM Interconnection, L.L.C...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-04-03

... DEPARTMENT OF ENERGY Federal Energy Regulatory Commission [Docket No. EL12-50-000] FirstEnergy Solutions Corp., Allegheny Energy Supply Company, LLC v. PJM Interconnection, L.L.C.; Notice of Complaint... 206 of the Federal Energy Regulatory Commission's Rules of Practice and Procedure, 18 CFR 385.206 and...

The exact solution of the monoenergetic transport equation for critical cylinders

NASA Technical Reports Server (NTRS)

Westfall, R. M.; Metcalf, D. R.

1972-01-01

An analytic solution for the critical, monoenergetic, bare, infinite cylinder is presented. The solution is obtained by modifying a previous development based on a neutron density transform and Case's singular eigenfunction method. Numerical results for critical radii and the neutron density as a function of position are included and compared with the results of other methods.

Multi-cut solutions in Chern-Simons matrix models

NASA Astrophysics Data System (ADS)

Morita, Takeshi; Sugiyama, Kento

2018-04-01

We elaborate the Chern-Simons (CS) matrix models at large N. The saddle point equations of these matrix models have a curious structure which cannot be seen in the ordinary one matrix models. Thanks to this structure, an infinite number of multi-cut solutions exist in the CS matrix models. Particularly we exactly derive the two-cut solutions at finite 't Hooft coupling in the pure CS matrix model. In the ABJM matrix model, we argue that some of multi-cut solutions might be interpreted as a condensation of the D2-brane instantons.

Solution of a cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula

NASA Astrophysics Data System (ADS)

Remizov, I. D.

2012-07-01

The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is proved that the Cauchy problem in well posed in the class of uniform limits of infinitely smooth bounded cylindrical functions on the Hilbert space, and the solution is presented in the form of the so-called Feynman formula, i.e., a limit of multiple integrals against a gaussian measure as the multiplicity tends to infinity. It is also proved that the solution of the Cauchy problem depends continuously on the diffusion coefficient. A process reducing an approximate solution of an infinite-dimensional diffusion equation to finding a multiple integral of a real function of finitely many real variables is indicated.

Infinite non-causality in active cancellation of random noise

NASA Astrophysics Data System (ADS)

Friot, Emmanuel

2006-03-01

Active cancellation of broadband random noise requires the detection of the incoming noise with some time advance. In an duct for example this advance must be larger than the delays in the secondary path from the control source to the error sensor. In this paper it is shown that, in some cases, the advance required for perfect noise cancellation is theoretically infinite because the inverse of the secondary path, which is required for control, can include an infinite non-causal response. This is shown to be the result of two mechanisms: in the single-channel case (one control source and one error sensor), this can arise because of strong echoes in the control path. In the multi-channel case this can arise even in free field simply because of an unfortunate placing of sensors and actuators. In the present paper optimal feedforward control is derived through analytical and numerical computations, in the time and frequency domains. It is shown that, in practice, the advance required for significant noise attenuation can be much larger than the secondary path delays. Practical rules are also suggested in order to prevent infinite non-causality from appearing.

Single file diffusion into a semi-infinite tube.

PubMed

Farrell, Spencer G; Brown, Aidan I; Rutenberg, Andrew D

2015-11-23

We investigate single file diffusion (SFD) of large particles entering a semi-infinite tube, such as luminal diffusion of proteins into microtubules or flagella. While single-file effects have no impact on the evolution of particle density, we report significant single-file effects for individually tracked tracer particle motion. Both exact and approximate ordering statistics of particles entering semi-infinite tubes agree well with our stochastic simulations. Considering initially empty semi-infinite tubes, with particles entering at one end starting from an initial time t = 0, tracked particles are initially super-diffusive after entering the system, but asymptotically diffusive at later times. For finite time intervals, the ratio of the net displacement of individual single-file particles to the average displacement of untracked particles is reduced at early times and enhanced at later times. When each particle is numbered, from the first to enter (n = 1) to the most recent (n = N), we find good scaling collapse of this distance ratio for all n. Experimental techniques that track individual particles, or local groups of particles, such as photo-activation or photobleaching of fluorescently tagged proteins, should be able to observe these single-file effects. However, biological phenomena that depend on local concentration, such as flagellar extension or luminal enzymatic activity, should not exhibit single-file effects.

Certain approximation problems for functions on the infinite-dimensional torus: Lipschitz spaces

NASA Astrophysics Data System (ADS)

Platonov, S. S.

2018-02-01

We consider some questions about the approximation of functions on the infinite-dimensional torus by trigonometric polynomials. Our main results are analogues of the direct and inverse theorems in the classical theory of approximation of periodic functions and a description of the Lipschitz spaces on the infinite-dimensional torus in terms of the best approximation.

A path-independent integral for the characterization of solute concentration and flux at biofilm detachments

USGS Publications Warehouse

Moran, B.; Kulkarni, S.S.; Reeves, H.W.

2007-01-01

A path-independent (conservation) integral is developed for the characterization of solute concentration and flux in a biofilm in the vicinity of a detachment or other flux limiting boundary condition. Steady state conditions of solute diffusion are considered and biofilm kinetics are described by an uptake term which can be expressed in terms of a potential (Michaelis-Menten kinetics). An asymptotic solution for solute concentration at the tip of the detachment is obtained and shown to be analogous to that of antiplane crack problems in linear elasticity. It is shown that the amplitude of the asymptotic solution can be calculated by evaluating a path-independent integral. The special case of a semi-infinite detachment in an infinite strip is considered and the amplitude of the asymptotic field is related to the boundary conditions and problem parameters in closed form for zeroth and first order kinetics and numerically for Michaelis-Menten kinetics. ?? Springer Science+Business Media, Inc. 2007.

Classical simulation of infinite-size quantum lattice systems in two spatial dimensions.

PubMed

Jordan, J; Orús, R; Vidal, G; Verstraete, F; Cirac, J I

2008-12-19

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)10.1103/PhysRevLett.98.070201]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.

An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation.

PubMed

Ilias, Miroslav; Saue, Trond

2007-02-14

The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra. They apply the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom. The results are compared to corresponding calculations using identical basis sets and based on the four-component Dirac-Coulomb Hamiltonian as well as Douglas-Kroll-Hess and zeroth-order regular approximation Hamiltonians, all implemented in the DIRAC program package, thus allowing a comprehensive comparison of relativistic Hamiltonians within the finite basis approximation.

Predictive Rate-Distortion for Infinite-Order Markov Processes

NASA Astrophysics Data System (ADS)

Marzen, Sarah E.; Crutchfield, James P.

2016-06-01

Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on finite sequences cannot capture all of their past dependencies. Spectral arguments confirm a popular intuition: algorithms that cluster finite-length sequences fail dramatically when the underlying process has long-range temporal correlations and can fail even for processes generated by finite-memory hidden Markov models. We circumvent the curse of dimensionality in rate-distortion analysis of finite- and infinite-order processes by casting predictive rate-distortion objective functions in terms of the forward- and reverse-time causal states of computational mechanics. Examples demonstrate that the resulting algorithms yield substantial improvements.

Entanglement entropy at infinite-randomness fixed points in higher dimensions.

PubMed

Lin, Yu-Cheng; Iglói, Ferenc; Rieger, Heiko

2007-10-05

The entanglement entropy of the two-dimensional random transverse Ising model is studied with a numerical implementation of the strong-disorder renormalization group. The asymptotic behavior of the entropy per surface area diverges at, and only at, the quantum phase transition that is governed by an infinite-randomness fixed point. Here we identify a double-logarithmic multiplicative correction to the area law for the entanglement entropy. This contrasts with the pure area law valid at the infinite-randomness fixed point in the diluted transverse Ising model in higher dimensions.

A High Frequency Analysis of Electromagnetic Plane Wave Scattering by a Fully Illuminated Perfectly Conducting Semi-Infinite Cone.

DTIC Science & Technology

1986-01-01

mn, 5] sin OdOd (B.39) 98 V Due to the orthogonality of the Legendre polynomials (shown in Appendix D), there is only a value when v = v’. This yields... some of his unpublished results. These results were for the special case of axial incidence on the semi- infinite cone, and were useful in verifying my... general solution. I express gratitude to Mr.(Ph.D. Candidate) Ming Cheng Liang for our many hours of discussion, and to my office mate Mr.(Ph.D

A Planar Calculus for Infinite Index Subfactors

NASA Astrophysics Data System (ADS)

Penneys, David

2013-05-01

We develop an analog of Jones' planar calculus for II 1-factor bimodules with arbitrary left and right von Neumann dimension. We generalize to bimodules Burns' results on rotations and extremality for infinite index subfactors. These results are obtained without Jones' basic construction and the resulting Jones projections.

DIFFUSED SOLUTE-SOLVENT INTERFACE WITH POISSON-BOLTZMANN ELECTROSTATICS: FREE-ENERGY VARIATION AND SHARP-INTERFACE LIMIT.

PubMed

Li, B O; Liu, Yuan

A phase-field free-energy functional for the solvation of charged molecules (e.g., proteins) in aqueous solvent (i.e., water or salted water) is constructed. The functional consists of the solute volumetric and solute-solvent interfacial energies, the solute-solvent van der Waals interaction energy, and the continuum electrostatic free energy described by the Poisson-Boltzmann theory. All these are expressed in terms of phase fields that, for low free-energy conformations, are close to one value in the solute phase and another in the solvent phase. A key property of the model is that the phase-field interpolation of dielectric coefficient has the vanishing derivative at both solute and solvent phases. The first variation of such an effective free-energy functional is derived. Matched asymptotic analysis is carried out for the resulting relaxation dynamics of the diffused solute-solvent interface. It is shown that the sharp-interface limit is exactly the variational implicit-solvent model that has successfully captured capillary evaporation in hydrophobic confinement and corresponding multiple equilibrium states of underlying biomolecular systems as found in experiment and molecular dynamics simulations. Our phase-field approach and analysis can be used to possibly couple the description of interfacial fluctuations for efficient numerical computations of biomolecular interactions.

On multiple solutions of non-Newtonian Carreau fluid flow over an inclined shrinking sheet

NASA Astrophysics Data System (ADS)

Khan, Masood; Sardar, Humara; Gulzar, M. Mudassar; Alshomrani, Ali Saleh

2018-03-01

This paper presents the multiple solutions of a non-Newtonian Carreau fluid flow over a nonlinear inclined shrinking surface in presence of infinite shear rate viscosity. The governing boundary layer equations are derived for the Carreau fluid with infinite shear rate viscosity. The suitable transformations are employed to alter the leading partial differential equations to a set of ordinary differential equations. The consequential non-linear ODEs are solved numerically by an active numerical approach namely Runge-Kutta Fehlberg fourth-fifth order method accompanied by shooting technique. Multiple solutions are presented graphically and results are shown for various physical parameters. It is important to state that the velocity and momentum boundary layer thickness reduce with increasing viscosity ratio parameter in shear thickening fluid while opposite trend is observed for shear thinning fluid. Another important observation is that the wall shear stress is significantly decreased by the viscosity ratio parameter β∗ for the first solution and opposite trend is observed for the second solution.

Comparison of Energy and Nutrient Contents of Commercial and Noncommercial Enteral Nutrition Solutions

PubMed Central

Jolfaie, Nahid Ramezani; Rouhani, Mohammad Hossein; Mirlohi, Maryam; Babashahi, Mina; Abbasi, Saeid; Adibi, Peiman; Esmaillzadeh, Ahmad; Azadbakht, Leila

2017-01-01

Background: Nutritional support plays a major role in the management of critically ill patients. This study aimed to compare the nutritional quality of enteral nutrition solutions (noncommercial vs. commercial) and the amount of energy and nutrients delivered and required in patients receiving these solutions. Materials and Methods: This cross-sectional study was conducted among 270 enterally fed patients. Demographic and clinical data in addition to values of nutritional needs and intakes were collected. Moreover, enteral nutrition solutions were analyzed in a food laboratory. Results: There were 150 patients who fed noncommercial enteral nutrition solutions (NCENS) and 120 patients who fed commercial enteral nutrition solutions (CENSs). Although energy and nutrients contents in CENSs were more than in NCENSs, these differences regarding energy, protein, carbohydrates, phosphorus, and calcium were not statistically significant. The values of energy and macronutrients delivered in patients who fed CENSs were higher (P < 0.001). Energy, carbohydrate, and fat required in patients receiving CENSs were provided, but protein intake was less than the required amount. In patients who fed NCENSs, only the values of fat requirement and intake were not significantly different, but other nutrition delivered was less than required amounts (P < 0.001). CENSs provided the nutritional needs of higher numbers of patients (P < 0.001). In patients receiving CENSs, nutrient adequacy ratio and also mean adequacy ratio were significantly higher than the other group (P < 0.001). Conclusion: CENSs contain more energy and nutrients compared with NCENSs. They are more effective to meet the nutritional requirements of entirely fed patients. PMID:29142894

An organic jelly made fractal logic gate with an infinite truth table

PubMed Central

Ghosh, Subrata; Fujita, Daisuke; Bandyopadhyay, Anirban

2015-01-01

Widely varying logic gates invented over a century are all finite. As data deluge problem looms large on the information processing and communication industry, the thrust to explore radical concepts is increasing rapidly. Here, we design and synthesis a molecule, wherein, the input energy transmits in a cycle inside the molecular system, just like an oscillator, then, we use the molecule to make a jelly that acts as chain of oscillators with a fractal like resonance band. Hence, with the increasing detection resolution, in the vacant space between two energy levels of a given resonance band, a new band appears, due to fractal nature, generation of newer energy levels never stops. This is natural property of a linear chain oscillator. As we correlate each energy level of the resonance band of organic jelly, as a function of pH and density of the jelly, we realize a logic gate, whose truth table is finite, but if we zoom any small part, a new truth table appears. In principle, zooming of truth table would continue forever. Thus, we invent a new class of infinite logic gate for the first time. PMID:26086417

Momentum Probabilities for a Single Quantum Particle in Three-Dimensional Regular "Infinite" Wells: One Way of Promoting Understanding of Probability Densities

ERIC Educational Resources Information Center

Riggs, Peter J.

2013-01-01

Students often wrestle unsuccessfully with the task of correctly calculating momentum probability densities and have difficulty in understanding their interpretation. In the case of a particle in an "infinite" potential well, its momentum can take values that are not just those corresponding to the particle's quantised energies but…

Local quantum transformations requiring infinite rounds of classical communication.

PubMed

Chitambar, Eric

2011-11-04

In this Letter, we investigate the number of measurement and communication rounds needed to implement certain tasks by local quantum operations and classical communication (LOCC), a relatively unexplored topic. To demonstrate the possible strong dependence on the round number, we consider the problem of converting three-qubit entanglement into two-qubit form, specifically in the random distillation setting of [Phys. Rev. Lett. 98, 260501 (2007)]. We find that the number of LOCC rounds needed for a transformation can depend on the amount of entanglement distilled. In fact, for a wide range of transformations, the required number of rounds is infinite (unbounded). This represents the first concrete example of a task needing an infinite number of rounds to implement.

Approximation of Optimal Infinite Dimensional Compensators for Flexible Structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.; Adamian, A.; Jabbari, F.

1985-01-01

The infinite dimensional compensator for a large class of flexible structures, modeled as distributed systems are discussed, as well as an approximation scheme for designing finite dimensional compensators to approximate the infinite dimensional compensator. The approximation scheme is applied to develop a compensator for a space antenna model based on wrap-rib antennas being built currently. While the present model has been simplified, it retains the salient features of rigid body modes and several distributed components of different characteristics. The control and estimator gains are represented by functional gains, which provide graphical representations of the control and estimator laws. These functional gains also indicate the convergence of the finite dimensional compensators and show which modes the optimal compensator ignores.

Inspiring Examples in Rearrangements of Infinite Series

ERIC Educational Resources Information Center

Ramasinghe, W.

2002-01-01

Simple examples are really encouraging in the understanding of rearrangements of infinite series, since many texts and teachers provide only existence theorems. In the absence of examples, an existence theorem is just a statement and lends little confidence to understanding. Iterated sums of double series seem to have a similar spirit of…

Analytical and numerical analyses for a penny-shaped crack embedded in an infinite transversely isotropic multi-ferroic composite medium: semi-permeable electro-magnetic boundary condition

NASA Astrophysics Data System (ADS)

Zheng, R.-F.; Wu, T.-H.; Li, X.-Y.; Chen, W.-Q.

2018-06-01

The problem of a penny-shaped crack embedded in an infinite space of transversely isotropic multi-ferroic composite medium is investigated. The crack is assumed to be subjected to uniformly distributed mechanical, electric and magnetic loads applied symmetrically on the upper and lower crack surfaces. The semi-permeable (limited-permeable) electro-magnetic boundary condition is adopted. By virtue of the generalized method of potential theory and the general solutions, the boundary integro-differential equations governing the mode I crack problem, which are of nonlinear nature, are established and solved analytically. Exact and complete coupling magneto-electro-elastic field is obtained in terms of elementary functions. Important parameters in fracture mechanics on the crack plane, e.g., the generalized crack surface displacements, the distributions of generalized stresses at the crack tip, the generalized stress intensity factors and the energy release rate, are explicitly presented. To validate the present solutions, a numerical code by virtue of finite element method is established for 3D crack problems in the framework of magneto-electro-elasticity. To evaluate conveniently the effect of the medium inside the crack, several empirical formulae are developed, based on the numerical results.

Note on the eigensolution of a homogeneous equation with semi-infinite domain

NASA Technical Reports Server (NTRS)

Wadia, A. R.

1980-01-01

The 'variation-iteration' method using Green's functions to find the eigenvalues and the corresponding eigenfunctions of a homogeneous Fredholm integral equation is employed for the stability analysis of fluid hydromechanics problems with a semiinfinite (infinite) domain of application. The objective of the study is to develop a suitable numerical approach to the solution of such equations in order to better understand the full set of equations for 'real-world' flow models. The study involves a search for a suitable value of the length of the domain which is a fair finite approximation to infinity, which makes the eigensolution an approximation dependent on the length of the interval chosen. In the examples investigated y = 1 = a seems to be the best approximation of infinity; for y greater than unity this method fails due to the polynomial nature of Green's functions.

Physicochemical Behavior of Some Amino Acids/Glycylglycine in Aqueous D-Galactose Solutions at Different Temperatures

NASA Astrophysics Data System (ADS)

Ali, Anwar; Patel, Rajan; Shahjahan; Ansari, Nizamul Haque

2010-03-01

The apparent molar volumes {(overline{V_2})} for glycine (Gly), l-alanine (Ala), phenylalanine (Phe), and glycylglycine (Gly-Gly) in 0.10 m aqueous d-galactose solutions have been determined from density measurements at (298.15, 303.15, 308.15, and 313.15) K. The data for {(overline{V_2})} were utilized to estimate the partial molar volume at infinite dilution {(overline{V_2^0})} , and experimental slope {(S_v^ast)} . The transfer volume, {(overline{V2^0}_(tr))} , and hydration number, ( n H) were also evaluated. The viscosity data were used to evaluate A- and B-coefficients of the Jones-Dole equation, the free energy of activation of viscous flow per mole of the solvent {left(Δ μ1^{0ast} right)} and the solute {left(Δ μ 2^{0ast} right)} . The molar refractivity ( R D) was calculated from refractive index data. The results were discussed in terms of hydrophilic-ionic, hydrophilic-hydrophobic, and hydrophobic-hydrophobic interactions, and structure-making/-breaking ability of the solute (AAs/peptide) in aqueous d-galactose solutions.

Boundary control for a flexible manipulator based on infinite dimensional disturbance observer

NASA Astrophysics Data System (ADS)

Jiang, Tingting; Liu, Jinkun; He, Wei

2015-07-01

This paper focuses on disturbance observer and boundary control design for the flexible manipulator in presence of both boundary disturbance and spatially distributed disturbance. Taking the infinite-dimensionality of the flexural dynamics into account, this study proposes a partial differential equation (PDE) model. Since the spatially distributed disturbance is infinite dimensional, it cannot be compensated by the typical disturbance observer, which is designed by finite dimensional approach. To estimate the spatially distributed disturbance, we propose a novel infinite dimensional disturbance observer (IDDO). Applying the IDDO as a feedforward compensator, a boundary control scheme is designed to regulate the joint position and eliminate the elastic vibration simultaneously. Theoretical analysis validates the stability of both the proposed disturbance observer and the boundary controller. The performance of the closed-loop system is demonstrated by numerical simulations.

Global, decaying solutions of a focusing energy-critical heat equation in R4

NASA Astrophysics Data System (ADS)

Gustafson, Stephen; Roxanas, Dimitrios

2018-05-01

We study solutions of the focusing energy-critical nonlinear heat equation ut = Δu - | u|2 u in R4. We show that solutions emanating from initial data with energy and H˙1-norm below those of the stationary solution W are global and decay to zero, via the "concentration-compactness plus rigidity" strategy of Kenig-Merle [33,34]. First, global such solutions are shown to dissipate to zero, using a refinement of the small data theory and the L2-dissipation relation. Finite-time blow-up is then ruled out using the backwards-uniqueness of Escauriaza-Seregin-Sverak [17,18] in an argument similar to that of Kenig-Koch [32] for the Navier-Stokes equations.

A notable difference between ideal gas and infinite molar volume limit of van der Waals gas

NASA Astrophysics Data System (ADS)

Liu, Q. H.; Shen, Y.; Bai, R. L.; Wang, X.

2010-05-01

The van der Waals equation of state does not sufficiently represent a gas unless a thermodynamic potential with two proper and independent variables is simultaneously determined. The limiting procedures under which the behaviour of the van der Waals gas approaches that of an ideal gas are letting two van der Waals coefficients be zero rather than letting the molar volume become infinitely large; otherwise, the partial derivative of internal energy with respect to pressure at a fixed temperature does not vanish.

Determination of partial molar volumes from free energy perturbation theory.

PubMed

Vilseck, Jonah Z; Tirado-Rives, Julian; Jorgensen, William L

2015-04-07

Partial molar volume is an important thermodynamic property that gives insights into molecular size and intermolecular interactions in solution. Theoretical frameworks for determining the partial molar volume (V°) of a solvated molecule generally apply Scaled Particle Theory or Kirkwood-Buff theory. With the current abilities to perform long molecular dynamics and Monte Carlo simulations, more direct methods are gaining popularity, such as computing V° directly as the difference in computed volume from two simulations, one with a solute present and another without. Thermodynamically, V° can also be determined as the pressure derivative of the free energy of solvation in the limit of infinite dilution. Both approaches are considered herein with the use of free energy perturbation (FEP) calculations to compute the necessary free energies of solvation at elevated pressures. Absolute and relative partial molar volumes are computed for benzene and benzene derivatives using the OPLS-AA force field. The mean unsigned error for all molecules is 2.8 cm(3) mol(-1). The present methodology should find use in many contexts such as the development and testing of force fields for use in computer simulations of organic and biomolecular systems, as a complement to related experimental studies, and to develop a deeper understanding of solute-solvent interactions.

Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II

NASA Astrophysics Data System (ADS)

Kazeykina, Anna; Muñoz, Claudio

2018-04-01

We continue our study on the Cauchy problem for the two-dimensional Novikov-Veselov (NV) equation, integrable via the inverse scattering transform for the two dimensional Schrödinger operator at a fixed energy parameter. This work is concerned with the more involved case of a positive energy parameter. For the solution of the linearized equation we derive smoothing and Strichartz estimates by combining new estimates for two different frequency regimes, extending our previous results for the negative energy case [18]. The low frequency regime, which our previous result was not able to treat, is studied in detail. At non-low frequencies we also derive improved smoothing estimates with gain of almost one derivative. Then we combine the linear estimates with a Fourier decomposition method and Xs,b spaces to obtain local well-posedness of NV at positive energy in Hs, s > 1/2. Our result implies, in particular, that at least for s > 1/2, NV does not change its behavior from semilinear to quasilinear as energy changes sign, in contrast to the closely related Kadomtsev-Petviashvili equations. As a complement to our LWP results, we also provide some new explicit solutions of NV at zero energy, generalizations of the lumps solutions, which exhibit new and nonstandard long time behavior. In particular, these solutions blow up in infinite time in L2.

Technology Solutions Case Study: Southern Energy Homes, First DOE Zero Energy Ready Manufactured Home

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

None

The country’s first Zero Energy Ready manufactured home that is certified by the U.S. Department of Energy (DOE) is up and running in Russellville, Alabama. The manufactured home was built by a partnership between Southern Energy Homes and the Advanced Residential Integrated Energy Solutions Collaborative (ARIES), which is a DOE Building America team. The effort was part of a three-home study including a standard-code manufactured home and an ENERGY STAR® manufactured home. Cooling-season results showed that the building used half the space-conditioning energy of a manufactured home built to the U.S. Department of Housing and Urban Development’s (HUD’s) Manufactured Homemore » Construction and Safety Standards. These standards are known collectively as the HUD Code, which is the building standard for all U.S. manufactured housing.« less

On some properties of force-free magnetic fields in infinite regions of space

NASA Technical Reports Server (NTRS)

Aly, J. J.

1984-01-01

Techniques for solving boundary value problems (BVP) for a force free magnetic field (FFF) in infinite space are presented. A priori inequalities are defined which must be satisfied by the force-free equations. It is shown that upper bounds may be calculated for the magnetic energy of the region provided the value of the magnetic normal component at the boundary of the region can be shown to decay sufficiently fast at infinity. The results are employed to prove a nonexistence theorem for the BVP for the FFF in the spatial region. The implications of the theory for modeling the origins of solar flares are discussed.

Newtonian potential and geodesic completeness in infinite derivative gravity

NASA Astrophysics Data System (ADS)

Edholm, James; Conroy, Aindriú

2017-08-01

Recent study has shown that a nonsingular oscillating potential—a feature of infinite derivative gravity theories—matches current experimental data better than the standard General Relativity potential. In this work, we show that this nonsingular oscillating potential can be given by a wider class of theories which allows the defocusing of null rays and therefore geodesic completeness. We consolidate the conditions whereby null geodesic congruences may be made past complete, via the Raychaudhuri equation, with the requirement of a nonsingular Newtonian potential in an infinite derivative gravity theory. In doing so, we examine a class of Newtonian potentials characterized by an additional degree of freedom in the scalar propagator, which returns the familiar potential of General Relativity at large distances.

Exploring the Free Energy Landscape of Solutes Embedded in Lipid Bilayers.

PubMed

Jämbeck, Joakim P M; Lyubartsev, Alexander P

2013-06-06

Free energy calculations are vital for our understanding of biological processes on an atomistic scale and can offer insight to various mechanisms. However, in some cases, degrees of freedom (DOFs) orthogonal to the reaction coordinate have high energy barriers and/or long equilibration times, which prohibit proper sampling. Here we identify these orthogonal DOFs when studying the transfer of a solute from water to a model membrane. Important DOFs are identified in bulk liquids of different dielectric nature with metadynamics simulations and are used as reaction coordinates for the translocation process, resulting in two- and three-dimensional space of reaction coordinates. The results are in good agreement with experiments and elucidate the pitfalls of using one-dimensional reaction coordinates. The calculations performed here offer the most detailed free energy landscape of solutes embedded in lipid bilayers to date and show that free energy calculations can be used to study complex membrane translocation phenomena.

Rare events in finite and infinite dimensions

NASA Astrophysics Data System (ADS)

Reznikoff, Maria G.

Thermal noise introduces stochasticity into deterministic equations and makes possible events which are never seen in the zero temperature setting. The driving force behind the thesis work is a desire to bring analysis and probability to bear on a class of relevant and intriguing physical problems, and in so doing, to allow applications to drive the development of new mathematical theory. The unifying theme is the study of rare events under the influence of small, random perturbations, and the manifold mathematical problems which ensue. In the first part, we apply large deviation theory and prefactor estimates to a coherent rotation micromagnetic model in order to analyze thermally activated magnetic switching. We consider recent physical experiments and the mathematical questions "asked" by them. A stochastic resonance type phenomenon is discovered, leading to the definition of finite temperature astroids. Non-Arrhenius behavior is discussed. The analysis is extended to ramped astroids. In addition, we discover that for low damping and ultrashort pulses, deterministic effects can override thermal effects, in accord with very recent ultrashort pulse experiments. Even more interesting, perhaps, is the study of large deviations in the infinite dimensional context, i.e. in spatially extended systems. Inspired by recent numerical investigations, we study the stochastically perturbed Allen Cahn and Cahn Hilliard equations. For the Allen Cahn equation, we study the action minimization problem (a deterministic variational problem) and prove the action scaling in four parameter regimes, via upper and lower bounds. The sharp interface limit is studied. We formally derive a reduced action functional which lends insight into the connection between action minimization and curvature flow. For the Cahn Hilliard equation, we prove upper and lower bounds for the scaling of the energy barrier in the nucleation and growth regime. Finally, we consider rare events in large or infinite

A DPL model of photo-thermal interaction in an infinite semiconductor material containing a spherical hole

NASA Astrophysics Data System (ADS)

Hobiny, Aatef D.; Abbas, Ibrahim A.

2018-01-01

The dual phase lag (DPL) heat transfer model is applied to study the photo-thermal interaction in an infinite semiconductor medium containing a spherical hole. The inner surface of the cavity was traction free and loaded thermally by pulse heat flux. By using the eigenvalue approach methodology and Laplace's transform, the physical variable solutions are obtained analytically. The numerical computations for the silicon-like semiconductor material are obtained. The comparison among the theories, i.e., dual phase lag (DPL), Lord and Shulman's (LS) and the classically coupled thermoelastic (CT) theory is presented graphically. The results further show that the analytical scheme can overcome mathematical problems by analyzing these problems.

Predicting chaos for infinite dimensional dynamical systems: The Kuramoto-Sivashinsky equation, a case study

NASA Technical Reports Server (NTRS)

Smyrlis, Yiorgos S.; Papageorgiou, Demetrios T.

1991-01-01

The results of extensive computations are presented in order to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular, the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos is followed. As many as thirteen period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable, for the first time, an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a fractal behavior which is demonstrated and used to compute a universal scaling factor that enables the self-similar continuation of the solution into a chaotic regime.

Symbolic Dynamics, Flower Automata and Infinite Traces

NASA Astrophysics Data System (ADS)

Foryś, Wit; Oprocha, Piotr; Bakalarski, Slawomir

Considering a finite alphabet as a set of allowed instructions, we can identify finite words with basic actions or programs. Hence infinite paths on a flower automaton can represent order in which these programs are executed and a flower shift related with it represents list of instructions to be executed at some mid-point of the computation.

Effects of Shapes of Solute Molecules on Diffusion: A Study of Dependences on Solute Size, Solvent, and Temperature.

PubMed

Chan, T C; Li, H T; Li, K Y

2015-12-24

Diffusivities of basically linear, planar, and spherical solutes at infinite dilution in various solvents are studied to unravel the effects of solute shapes on diffusion. On the basis of the relationship between the reciprocal of diffusivity and the molecular volume of solute molecules with similar shape in a given solvent at constant temperature, the diffusivities of solutes of equal molecular volume but different shapes are evaluated and the effects due to different shapes of two equal-sized solute molecules on diffusion are determined. It is found that the effects are dependent on the size of the solute pairs studied. Evidence of the dependence of the solute-shape effects on solvent properties is also demonstrated and discussed. Here, some new diffusion data of aromatic compounds in methanol at different temperatures are reported. The result for methanol in this study indicates that the effects of solute shape on diffusivity are only weakly dependent on temperature.

Validation of the SINDA/FLUINT code using several analytical solutions

NASA Technical Reports Server (NTRS)

Keller, John R.

1995-01-01

The Systems Improved Numerical Differencing Analyzer and Fluid Integrator (SINDA/FLUINT) code has often been used to determine the transient and steady-state response of various thermal and fluid flow networks. While this code is an often used design and analysis tool, the validation of this program has been limited to a few simple studies. For the current study, the SINDA/FLUINT code was compared to four different analytical solutions. The thermal analyzer portion of the code (conduction and radiative heat transfer, SINDA portion) was first compared to two separate solutions. The first comparison examined a semi-infinite slab with a periodic surface temperature boundary condition. Next, a small, uniform temperature object (lumped capacitance) was allowed to radiate to a fixed temperature sink. The fluid portion of the code (FLUINT) was also compared to two different analytical solutions. The first study examined a tank filling process by an ideal gas in which there is both control volume work and heat transfer. The final comparison considered the flow in a pipe joining two infinite reservoirs of pressure. The results of all these studies showed that for the situations examined here, the SINDA/FLUINT code was able to match the results of the analytical solutions.

Verifying the Simulation Hypothesis via Infinite Nested Universe Simulacrum Loops

NASA Astrophysics Data System (ADS)

Sharma, Vikrant

2017-01-01

The simulation hypothesis proposes that local reality exists as a simulacrum within a hypothetical computer's dimension. More specifically, Bostrom's trilemma proposes that the number of simulations an advanced 'posthuman' civilization could produce makes the proposition very likely. In this paper a hypothetical method to verify the simulation hypothesis is discussed using infinite regression applied to a new type of infinite loop. Assign dimension n to any computer in our present reality, where dimension signifies the hierarchical level in nested simulations our reality exists in. A computer simulating known reality would be dimension (n-1), and likewise a computer simulating an artificial reality, such as a video game, would be dimension (n +1). In this method, among others, four key assumptions are made about the nature of the original computer dimension n. Summations show that regressing such a reality infinitely will create convergence, implying that the verification of whether local reality is a grand simulation is feasible to detect with adequate compute capability. The action of reaching said convergence point halts the simulation of local reality. Sensitivities to the four assumptions and implications are discussed.

Multigrid one shot methods for optimal control problems: Infinite dimensional control

NASA Technical Reports Server (NTRS)

Arian, Eyal; Taasan, Shlomo

1994-01-01

The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

Energy Literacy: A Natural and Essential Part of a Solutions-Based Approach to Climate Literacy

NASA Astrophysics Data System (ADS)

Inman, M. M.

2011-12-01

As with climate science topics, many Americans have misconceptions or gaps in understanding related to energy topics. Recent literacy efforts are geared to address these gaps in understanding. The U.S. Global Change Research Program's recently published "Energy Literacy: Essential Principles and Fundamental Concepts for Energy Education" offers a welcome complement to the Climate Literacy Essential Principles released in 2008. Research and experience suggest that education, communication and outreach about global climate change and related topics is best done using a solutions-based approach. Energy is a natural and effective topic to frame these solutions around. Used as a framework for designing curricula, Energy Literacy naturally leads to solutions-based approaches to Climate Change education. An inherently interdisciplinary topic, energy education must happen in the context of both the natural and social sciences. The Energy Literacy Essential Principles reflect this and open the door to curriculum that integrates the two.

Analysis of transitional separation bubbles on infinite swept wings

NASA Technical Reports Server (NTRS)

Davis, R. L.; Carter, J. E.

1986-01-01

A previously developed two-dimensional local inviscid-viscous interaction technique for the analysis of airfoil transitional separation bubbles, ALESEP (Airfoil Leading Edge Separation), has been extended for the calculation of transitional separation bubbles over infinite swept wings. As part of this effort, Roberts' empirical correlation, which is interpreted as a separated flow empirical extension of Mack's stability theory for attached flows, has been incorporated into the ALESEP procedure for the prediction of the transition location within the separation bubble. In addition, the viscous procedure used in the ALESEP techniques has been modified to allow for wall suction. A series of two-dimensional calculations is presented as a verification of the prediction capability of the interaction techniques with the Roberts' transition model. Numerical tests have shown that this two-dimensional natural transition correlation may also be applied to transitional separation bubbles over infinite swept wings. Results of the interaction procedure are compared with Horton's detailed experimental data for separated flow over a swept plate which demonstrates the accuracy of the present technique. Wall suction has been applied to a similar interaction calculation to demonstrate its effect on the separation bubble. The principal conclusion of this paper is that the prediction of transitional separation bubbles over two-dimensional or infinite swept geometries is now possible using the present interacting boundary layer approach.

Quasi-periodic solutions of the Belov-Chaltikian lattice hierarchy

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Zeng, Xin

Utilizing the characteristic polynomial of Lax matrix for the Belov-Chaltikian (BC) lattice hierarchy associated with a 3 × 3 discrete matrix spectral problem, we introduce a trigonal curve with three infinite points, from which we establish the associated Dubrovin-type equations. The essential properties of the Baker-Akhiezer function and the meromorphic function are discussed, that include their asymptotic behavior near three infinite points on the trigonal curve and the divisor of the meromorphic function. The Abel map is introduced to straighten out the continuous flow and the discrete flow in the Jacobian variety, from which the quasi-periodic solutions of the entire BC lattice hierarchy are obtained in terms of the Riemann theta function.

Wave vector modification of the infinite order sudden approximation

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

Sachs, J.G.; Bowman, J.M.

1980-10-15

A simple method is proposed to modify the infinite order sudden approximation (IOS) in order to extend its region of quantitative validity. The method involves modifying the phase of the IOS scattering matrix to include a part calculated at the outgoing relative kinetic energy as well as a part calculated at the incoming kinetic energy. An immediate advantage of this modification is that the resulting S matrix is symmetric. We also present a closely related method in which the relative kinetic energies used in the calculation of the phase are determined from quasiclassical trajectory calculations. A set of trajectories ismore » run with the initial state being the incoming state, and another set is run with the initial state being the outgoing state, and the average final relative kinetic energy of each set is obtained. One part of the S-operator phase is then calculated at each of these kinetic energies. We apply these methods to vibrationally inelastic collinear collisions of an atom and a harmonic oscillator, and calculate transition probabilities P/sub n/1..-->..nf for three model systems. For systems which are sudden, or nearly so, the agreement with exact quantum close-coupling calculations is substantially improved over standard IOS ones when ..delta..n=such thatub f/-n/sub i/ is large, and the corresponding transition probability is small, i.e., less than 0.1. However, the modifications we propose will not improve the accuracy of the IOS transition probabilities for any collisional system unless the standard form of IOS already gives at least qualitative agreement with exact quantal calculations. We also suggest comparisons between some classical quantities and sudden predictions which should help in determining the validity of the sudden approximation. This is useful when exact quantal data is not available for comparison.« less

Wave vector modification of the infinite order sudden approximation

NASA Astrophysics Data System (ADS)

Sachs, Judith Grobe; Bowman, Joel M.

1980-10-01

A simple method is proposed to modify the infinite order sudden approximation (IOS) in order to extend its region of quantitative validity. The method involves modifying the phase of the IOS scattering matrix to include a part calculated at the outgoing relative kinetic energy as well as a part calculated at the incoming kinetic energy. An immediate advantage of this modification is that the resulting S matrix is symmetric. We also present a closely related method in which the relative kinetic energies used in the calculation of the phase are determined from quasiclassical trajectory calculations. A set of trajectories is run with the initial state being the incoming state, and another set is run with the initial state being the outgoing state, and the average final relative kinetic energy of each set is obtained. One part of the S-operator phase is then calculated at each of these kinetic energies. We apply these methods to vibrationally inelastic collinear collisions of an atom and a harmonic oscillator, and calculate transition probabilities Pn1→nf for three model systems. For systems which are sudden, or nearly so, the agreement with exact quantum close-coupling calculations is substantially improved over standard IOS ones when Δn=‖nf-ni‖ is large, and the corresponding transition probability is small, i.e., less than 0.1. However, the modifications we propose will not improve the accuracy of the IOS transition probabilities for any collisional system unless the standard form of IOS already gives at least qualitative agreement with exact quantal calculations. We also suggest comparisons between some classical quantities and sudden predictions which should help in determining the validity of the sudden approximation. This is useful when exact quantal data is not available for comparison.

Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials

NASA Astrophysics Data System (ADS)

Antonelli, Paolo; Michelangeli, Alessandro; Scandone, Raffaele

2018-04-01

We prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

Revealing plant cryptotypes: defining meaningful phenotypes among infinite traits.

PubMed

Chitwood, Daniel H; Topp, Christopher N

2015-04-01

The plant phenotype is infinite. Plants vary morphologically and molecularly over developmental time, in response to the environment, and genetically. Exhaustive phenotyping remains not only out of reach, but is also the limiting factor to interpreting the wealth of genetic information currently available. Although phenotyping methods are always improving, an impasse remains: even if we could measure the entirety of phenotype, how would we interpret it? We propose the concept of cryptotype to describe latent, multivariate phenotypes that maximize the separation of a priori classes. Whether the infinite points comprising a leaf outline or shape descriptors defining root architecture, statistical methods to discern the quantitative essence of an organism will be required as we approach measuring the totality of phenotype. Copyright © 2015 Elsevier Ltd. All rights reserved.

Dynamic stability of vortex solutions of Ginzburg-Landau and nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Weinstein, M. I.; Xin, J.

1996-10-01

The dynamic stability of vortex solutions to the Ginzburg-Landau and nonlinear Schrödinger equations is the basic assumption of the asymptotic particle plus field description of interacting vortices. For the Ginzburg-Landau dynamics we prove that all vortices are asymptotically nonlinearly stable relative to small radial perturbations. Initially finite energy perturbations of vortices decay to zero in L p (ℝ2) spaces with an algebraic rate as time tends to infinity. We also prove that under general (nonradial) perturbations, the plus and minus one-vortices are linearly dynamically stable in L 2; the linearized operator has spectrum equal to (-∞, 0] and generates a C 0 semigroup of contractions on L 2(ℝ2). The nature of the zero energy point is clarified; it is resonance, a property related to the infinite energy of planar vortices. Our results on the linearized operator are also used to show that the plus and minus one-vortices for the Schrödinger (Hamiltonian) dynamics are spectrally stable, i.e. the linearized operator about these vortices has ( L 2) spectrum equal to the imaginary axis. The key ingredients of our analysis are the Nash-Aronson estimates for obtaining Gaussian upper bounds for fundamental solutions of parabolic operator, and a combination of variational and maximum principles.

Reactive silica transport in fractured porous media: Analytical solutions for a system of parallel fractures

NASA Astrophysics Data System (ADS)

Yang, Jianwen

2012-04-01

A general analytical solution is derived by using the Laplace transformation to describe transient reactive silica transport in a conceptualized 2-D system involving a set of parallel fractures embedded in an impermeable host rock matrix, taking into account of hydrodynamic dispersion and advection of silica transport along the fractures, molecular diffusion from each fracture to the intervening rock matrix, and dissolution of quartz. A special analytical solution is also developed by ignoring the longitudinal hydrodynamic dispersion term but remaining other conditions the same. The general and special solutions are in the form of a double infinite integral and a single infinite integral, respectively, and can be evaluated using Gauss-Legendre quadrature technique. A simple criterion is developed to determine under what conditions the general analytical solution can be approximated by the special analytical solution. It is proved analytically that the general solution always lags behind the special solution, unless a dimensionless parameter is less than a critical value. Several illustrative calculations are undertaken to demonstrate the effect of fracture spacing, fracture aperture and fluid flow rate on silica transport. The analytical solutions developed here can serve as a benchmark to validate numerical models that simulate reactive mass transport in fractured porous media.

On optimal infinite impulse response edge detection filters

NASA Technical Reports Server (NTRS)

Sarkar, Sudeep; Boyer, Kim L.

1991-01-01

The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions. The implementation is very simple and computationally efficient, has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation.

Energy dissipation in Ni-containing concentrated solid solutions.

NASA Astrophysics Data System (ADS)

Samolyuk, German; Mu, Sai; Jin, Ke; Bei, Hongbin; Stocks, G. Malcolm

Due to high disorder the diffusion processes are noticeably suppressed concentrated solid solution, so called high entropy alloys. It makes these alloys promising candidate for energy application under extreme conditions. Understanding of the energy dissipation in these alloys during the irradiation or interaction with laser bean is extremely important. In the metals and alloys the main channel of energy dissipation is provided by the electronic subsystem. The first principles approach was used to investigate the electronic structure properties of the alloys. The obtained results were used to calculate the electronic part of thermal resistivity caused by scattering of electrons on atomic disorder, magnetic and phonon excitations The contribution of last two excitations to the temperature dependence of thermal resistivity is discussed. The importance of magnetism in 3d transition metals based alloy was demonstrated. In particular, it was shown that antiferromagnetic ordering of chromium or manganese leads to significant increase of electron scattering in alloy containing these elements. It results in significant reduction of conductivity in chromium or manganese containing alloys. The comparison with the existing experimental data is discussed. This work was supported as part of the Energy Dissipation to Defect Evolution (EDDE), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences.

Estimation of Solvation Quantities from Experimental Thermodynamic Data: Development of the Comprehensive CompSol Databank for Pure and Mixed Solutes

NASA Astrophysics Data System (ADS)

Moine, Edouard; Privat, Romain; Sirjean, Baptiste; Jaubert, Jean-Noël

2017-09-01

The Gibbs energy of solvation measures the affinity of a solute for its solvent and is thus a key property for the selection of an appropriate solvent for a chemical synthesis or a separation process. More fundamentally, Gibbs energies of solvation are choice data for developing and benchmarking molecular models predicting solvation effects. The Comprehensive Solvation—CompSol—database was developed with the ambition to propose very large sets of new experimental solvation chemical-potential, solvation entropy, and solvation enthalpy data of pure and mixed components, covering extended temperature ranges. For mixed compounds, the solvation quantities were generated in infinite-dilution conditions by combining experimental values of pure-component and binary-mixture thermodynamic properties. Three types of binary-mixture properties were considered: partition coefficients, activity coefficients at infinite dilution, and Henry's-law constants. A rigorous methodology was implemented with the aim to select data at appropriate conditions of temperature, pressure, and concentration for the estimation of solvation data. Finally, our comprehensive CompSol database contains 21 671 data associated with 1969 pure species and 70 062 data associated with 14 102 binary mixtures (including 760 solvation data related to the ionic-liquid class of solvents). On the basis of the very large amount of experimental data contained in the CompSol database, it is finally discussed how solvation energies are influenced by hydrogen-bonding association effects.

Power series solutions of ordinary differential equations in MACSYMA

NASA Technical Reports Server (NTRS)

Lafferty, E. L.

1977-01-01

A program is described which extends the differential equation solving capability of MACSYMA to power series solutions and is available via the SHARE library. The program is directed toward those classes of equations with variable coefficients (in particular, those with singularities) and uses the method of Frobenius. Probably the most important distinction between this package and others currently available or being developed is that, wherever possible, this program will attempt to provide a complete solution to the equation rather than an approximation, i.e., a finite number of terms. This solution will take the form of a sum of infinite series.

Gas chromatographic measurements of activity coefficients at infinite dilution for refrigerants with a polyol ester oil as a stationary phase

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

Stryjek, R.; Bobbo, S.; Camporese, R.

1999-05-01

Activity coefficients at infinite dilution have been measured by gas chromatography for 14 refrigerants (R12, R22, R32, R124, R125, R134a, R142b, R143a, RE170, R236ea, R290, R600, R600a, and R236fa) as solutes, using a polyol ester oil (POE), EMKARATE by ICI, as a stationary phase (solvent). Instrumental analysis (NMR, IR) showed that the main components of the oil are pentaerithritol esters of carboxylic acids, and electrospray ionization spectrometry revealed an average molecular mass of the POE of 618 g/mol. The measurements were performed within a temperature range of 244 K to 313 K, but a specific temperature range for each refrigerantmore » was adopted depending on its retention data. The experimental findings are well-represented by the equation: ln {gamma}{sub i}{sup {infinity}} = a{sub i} {minus} b{sub i}/T. Some refrigerants, i.e., R22, R124, R125, R236ea, and R236fa, show quite a considerable positive temperature dependence of their activity coefficients at infinite dilution, which can be attributed to hydrogen bonding with the POE, unlike other refrigerants that show a small, either positive or negative temperature dependence. To the authors` knowledge, there are no data in the literature on activity coefficients at infinite dilution for refrigerant and oil (lubricant) systems, and details on the solubility of refrigerants in oils are also extremely scarce.« less

A New Kind of Shift Operators for Infinite Circular and Spherical Wells

DOE PAGES

Sun, Guo-Hua; Launey, K. D.; Dytrych, T.; ...

2014-01-01

A new kind of smore » hift operators for infinite circular and spherical wells is identified. These shift operators depend on all spatial variables of quantum systems and connect some eigenstates of confined systems of different radii R sharing energy levels with a common eigenvalue. In circular well, the momentum operators P ± = P x ± i P y play the role of shift operators. The P x and P y operators, the third projection of the orbital angular momentum operator L z , and the Hamiltonian H form a complete set of commuting operators with the SO(2) symmetry. In spherical well, the shift operators establish a novel relation between ψ l m ( r ) and ψ ( l ± 1 ) ( m ± 1 ) ( r ) .« less

Fredholm and Wronskian representations of solutions to the KPI equation and multi-rogue waves

NASA Astrophysics Data System (ADS)

Gaillard, Pierre

2016-06-01

We construct solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants. We deduce solutions written as a quotient of Wronskians of order 2N. These solutions, called solutions of order N, depend on 2N - 1 parameters. When one of these parameters tends to zero, we obtain N order rational solutions expressed as a quotient of two polynomials of degree 2N(N + 1) in x, y, and t depending on 2N - 2 parameters. So we get with this method an infinite hierarchy of solutions to the KPI equation.

Non-pairwise additivity of the leading-order dispersion energy

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

Hollett, Joshua W., E-mail: j.hollett@uwinnipeg.ca

2015-02-28

The leading-order (i.e., dipole-dipole) dispersion energy is calculated for one-dimensional (1D) and two-dimensional (2D) infinite lattices, and an infinite 1D array of infinitely long lines, of doubly occupied locally harmonic wells. The dispersion energy is decomposed into pairwise and non-pairwise additive components. By varying the force constant and separation of the wells, the non-pairwise additive contribution to the dispersion energy is shown to depend on the overlap of density between neighboring wells. As well separation is increased, the non-pairwise additivity of the dispersion energy decays. The different rates of decay for 1D and 2D lattices of wells is explained inmore » terms of a Jacobian effect that influences the number of nearest neighbors. For an array of infinitely long lines of wells spaced 5 bohrs apart, and an inter-well spacing of 3 bohrs within a line, the non-pairwise additive component of the leading-order dispersion energy is −0.11 kJ mol{sup −1} well{sup −1}, which is 7% of the total. The polarizability of the wells and the density overlap between them are small in comparison to that of the atomic densities that arise from the molecular density partitioning used in post-density-functional theory (DFT) damped dispersion corrections, or DFT-D methods. Therefore, the nonadditivity of the leading-order dispersion observed here is a conservative estimate of that in molecular clusters.« less

Analysis of an infinite array of rectangular microstrip patches with idealized probe feeds

NASA Technical Reports Server (NTRS)

Pozar, D. M.; Schaubert, D. H.

1984-01-01

A solution is presented to the problem of an infinite array of microstrip patches fed by idealized current probes. The input reflection coefficient is calculated versus scan angle in an arbitrary scan plane, and the effects of substrate parameters and grid spacing are considered. It is pointed out that even when a Galerkin method is used the impedance matrix is not symmetric due to phasing through a unit cell, as required for scanning. The mechanism by which scan blindness can occur is discussed. Measurement results are presented for the reflection coefficient magnitude variation with angle for E-plane, H-plane, and D-plane scans, for various substrate parameters. Measured results from waveguide simulators are also presented, and the scan blindness phenomenon is observed and discussed in terms of forced surface waves and a modified grating lobe diagram.

Device for adapting continuously variable transmissions to infinitely variable transmissions with forward-neutral-reverse capabilities

DOEpatents

Wilkes, Donald F.; Purvis, James W.; Miller, A. Keith

1997-01-01

An infinitely variable transmission is capable of operating between a maximum speed in one direction and a minimum speed in an opposite direction, including a zero output angular velocity, while being supplied with energy at a constant angular velocity. Input energy is divided between a first power path carrying an orbital set of elements and a second path that includes a variable speed adjustment mechanism. The second power path also connects with the orbital set of elements in such a way as to vary the rate of angular rotation thereof. The combined effects of power from the first and second power paths are combined and delivered to an output element by the orbital element set. The transmission can be designed to operate over a preselected ratio of forward to reverse output speeds.

Integrated Energy Solutions Research | Integrated Energy Solutions | NREL

Science.gov Websites

that spans the height and width of the wall they are facing. Decision Science and Informatics Enabling decision makers with rigorous, technology-neutral, data-backed decision support to maximize the impact of security in energy systems through analysis, decision support, advanced energy technology development, and

Social Institutions and Nuclear Energy

ERIC Educational Resources Information Center

Weinberg, Alvin M.

1972-01-01

Nuclear technologists can offer an all but infinite source of relatively cheap and clean energy" but society must decide whether the price of eternal vigilance needed to ensure proper and safe operation of its nuclear energy system" is worth the benefits. (Author/AL)

A Solution to the Fundamental Linear Fractional Order Differential Equation

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

Solutions-based climate change education for K-Gray: Renewable energy and energy efficiency

NASA Astrophysics Data System (ADS)

Petrone, C.

2017-12-01

Through the National Science Foundation-funded MADE CLEAR (www.madeclear.org) climate change education project's Informal Climate Change Education (ICCE) Community, funds were received to collaboratively train teachers, informal educators, students, and university docents in climate change basics and solutions, specifically renewable energy and energy efficiency. In all, 10 docents, 50 classroom teachers, over 600 K-16 students, and several hundred science-interested citizens participated in programs and workshops lasting between one and seven hours. Using commercially available kits and other DIY projects, program participants used science content and engineering to develop models of wind turbines, wind mills, solar cells, solar cookers, solar stills, and wind-powered cars. Using thermal imaging cameras, Kill-a-Watt meters, "Carbon Food Print" kit, "Energy Matters" kit, and other tools, program participants learned about energy efficiency as not only a global climate change mitigation strategy, but also a way to save money. ICCE Community members and external partners, such as local electric cooperative personnel, university researchers, and state-sponsored energy efficiency program personnel, provided content presentations, discussions, and hands-on activities to program participants.

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

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

Thapliyal, Kishore, E-mail: tkishore36@yahoo.com; Banerjee, Subhashish, E-mail: subhashish@iitj.ac.in; Pathak, Anirban, E-mail: anirban.pathak@gmail.com

Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained frommore » experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.« less

Expansions for infinite or finite plane circular time-reversal mirrors and acoustic curtains for wave-field-synthesis.

PubMed

Mellow, Tim; Kärkkäinen, Leo

2014-03-01

An acoustic curtain is an array of microphones used for recording sound which is subsequently reproduced through an array of loudspeakers in which each loudspeaker reproduces the signal from its corresponding microphone. Here the sound originates from a point source on the axis of symmetry of the circular array. The Kirchhoff-Helmholtz integral for a plane circular curtain is solved analytically as fast-converging expansions, assuming an ideal continuous array, to speed up computations and provide insight. By reversing the time sequence of the recording (or reversing the direction of propagation of the incident wave so that the point source becomes an "ideal" point sink), the curtain becomes a time reversal mirror and the analytical solution for this is given simultaneously. In the case of an infinite planar array, it is demonstrated that either a monopole or dipole curtain will reproduce the diverging sound field of the point source on the far side. However, although the real part of the sound field of the infinite time-reversal mirror is reproduced, the imaginary part is an approximation due to the missing singularity. It is shown that the approximation may be improved by using the appropriate combination of monopole and dipole sources in the mirror.

The solutions and thermodynamic dark energy in the accelerating universe

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

Demirel, E. C. Günay

Recently, Tachyonic matter expressed in terms of scalar field is suggested to be the reason of acceleration of the universe as dark energy [1]-[3]. In this study, dynamic solutions and thermodynamic properties of matters such as Tachyonic matters were investigated.

More on the holographic Ricci dark energy model: smoothing Rips through interaction effects?

PubMed

Bouhmadi-López, Mariam; Errahmani, Ahmed; Ouali, Taoufik; Tavakoli, Yaser

2018-01-01

The background cosmological dynamics of the late Universe is analysed on the framework of a dark energy model described by an holographic Ricci dark energy component. Several kind of interactions between the dark energy and the dark matter components are considered herein. We solve the background cosmological dynamics for the different choices of interactions with the aim to analyse not only the current evolution of the universe but also its asymptotic behaviour and, in particular, possible future singularities removal. We show that in most of the cases, the Big Rip singularity, a finger print of this model in absence of an interaction between the dark sectors, is substituted by a de Sitter or a Minkowski state. Most importantly, we found two new future bouncing solutions leading to two possible asymptotic behaviours, we named Little Bang and Little Sibling of the Big Bang. At a Little Bang, as the size of the universe shrinks to zero in an infinite cosmic time, the Hubble rate and its cosmic time derivative blow up. In addition, at a Little sibling of the Big Bang, as the size of the universe shrinks to zero in an infinite cosmic time, the Hubble rate blows up but its cosmic time derivative is finite. These two abrupt events can happen as well in the past.

More on the holographic Ricci dark energy model: smoothing Rips through interaction effects?

NASA Astrophysics Data System (ADS)

Bouhmadi-López, Mariam; Errahmani, Ahmed; Ouali, Taoufik; Tavakoli, Yaser

2018-04-01

The background cosmological dynamics of the late Universe is analysed on the framework of a dark energy model described by an holographic Ricci dark energy component. Several kind of interactions between the dark energy and the dark matter components are considered herein. We solve the background cosmological dynamics for the different choices of interactions with the aim to analyse not only the current evolution of the universe but also its asymptotic behaviour and, in particular, possible future singularities removal. We show that in most of the cases, the Big Rip singularity, a finger print of this model in absence of an interaction between the dark sectors, is substituted by a de Sitter or a Minkowski state. Most importantly, we found two new future bouncing solutions leading to two possible asymptotic behaviours, we named Little Bang and Little Sibling of the Big Bang. At a Little Bang, as the size of the universe shrinks to zero in an infinite cosmic time, the Hubble rate and its cosmic time derivative blow up. In addition, at a Little sibling of the Big Bang, as the size of the universe shrinks to zero in an infinite cosmic time, the Hubble rate blows up but its cosmic time derivative is finite. These two abrupt events can happen as well in the past.

Gacs quantum algorithmic entropy in infinite dimensional Hilbert spaces

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

Benatti, Fabio, E-mail: benatti@ts.infn.it; Oskouei, Samad Khabbazi, E-mail: kh.oskuei@ut.ac.ir; Deh Abad, Ahmad Shafiei, E-mail: shafiei@khayam.ut.ac.ir

We extend the notion of Gacs quantum algorithmic entropy, originally formulated for finitely many qubits, to infinite dimensional quantum spin chains and investigate the relation of this extension with two quantum dynamical entropies that have been proposed in recent years.

Critical Role of Surface Energy in Guiding Crystallization of Solution-Coated Conjugated Polymer Thin Films

DOE PAGES

Zhang, Fengjiao; Mohammadi, Erfan; Luo, Xuyi; ...

2017-10-02

It is well-known that substrate surface properties have a profound impact on morphology of thin films solution coated atop and the resulting solid-state properties. However, design rules for guiding the substrate selection have not yet been established. Such design rules are particularly important for solution coated semiconducting polymers, as the substratedirected thin film morphology can impact charge transport properties by orders of magnitude. We hypothesize that substrate surface energies dictate the thin film morphology by modulating the free energy barrier to heterogeneous nucleation. To test this hypothesis, we systematically vary the substrate surface energy via surface functionalization techniques. We performmore » in-depth morphology and device characterizations to establish the relationship between substrate surface energy, thin film morphology and charge transport properties, employing a donor-accepter (D-A) conjugated polymer. Here, we find that decreasing the substrate surface energy progressively increases thin film crystallinity, degree of molecular ordering and extent of domain alignment. Notably, the enhanced morphology on the lowest surface energy substrate lead to a 10-fold increase in the charge carrier mobility. We further develop a free energy model relating the substrate surface energy to the penalty of heterogeneous nucleation from solution in the thin film geometry. The model correctly predicts the experimental trend, thereby validating our hypothesis. This work is a significant step towards establishing design rules and understanding the critical role of substrates in determining morphology of solution coated thin films.« less

Critical Role of Surface Energy in Guiding Crystallization of Solution-Coated Conjugated Polymer Thin Films

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

Zhang, Fengjiao; Mohammadi, Erfan; Luo, Xuyi

It is well-known that substrate surface properties have a profound impact on morphology of thin films solution coated atop and the resulting solid-state properties. However, design rules for guiding the substrate selection have not yet been established. Such design rules are particularly important for solution coated semiconducting polymers, as the substratedirected thin film morphology can impact charge transport properties by orders of magnitude. We hypothesize that substrate surface energies dictate the thin film morphology by modulating the free energy barrier to heterogeneous nucleation. To test this hypothesis, we systematically vary the substrate surface energy via surface functionalization techniques. We performmore » in-depth morphology and device characterizations to establish the relationship between substrate surface energy, thin film morphology and charge transport properties, employing a donor-accepter (D-A) conjugated polymer. Here, we find that decreasing the substrate surface energy progressively increases thin film crystallinity, degree of molecular ordering and extent of domain alignment. Notably, the enhanced morphology on the lowest surface energy substrate lead to a 10-fold increase in the charge carrier mobility. We further develop a free energy model relating the substrate surface energy to the penalty of heterogeneous nucleation from solution in the thin film geometry. The model correctly predicts the experimental trend, thereby validating our hypothesis. This work is a significant step towards establishing design rules and understanding the critical role of substrates in determining morphology of solution coated thin films.« less

When is a product of finite order qubit gates of infinite order?

NASA Astrophysics Data System (ADS)

Karnas, Katarzyna; Sawicki, Adam

2018-02-01

We consider a product of two finite order quantum SU(2) -gates U 1, U 2 and ask when U_1\\cdot U2 has an infinite order. Using the fact that SU(2) is a double cover of SO(3) we actually study the product O(γ, k12) of two rotations O(φ, k_1)\\in SO(3) and O(φ, k_2)\\in SO(3) about axes k1 , k_2\\in {R}3 . In particular, we focus on the case when k_1\\cdotk_2=0 , and φ_1=φ=φ2 are rational multiples of π and show that γ is not a rational multiple of π unless φ\\in\\{\\frac{kπ}{2}:k\\in{Z}\\} . The proof presented in this paper boils down to finding all pairs γ, φ\\in \\{aπ : a\\in{Q}\\} that are solutions of \\cos\\fracγ{2}=\\cos^2\\fracφ{2} .

Examining the accuracy of the infinite order sudden approximation using sensitivity analysis

NASA Astrophysics Data System (ADS)

Eno, Larry; Rabitz, Herschel

1981-08-01

A method is developed for assessing the accuracy of scattering observables calculated within the framework of the infinite order sudden (IOS) approximation. In particular, we focus on the energy sudden assumption of the IOS method and our approach involves the determination of the sensitivity of the IOS scattering matrix SIOS with respect to a parameter which reintroduces the internal energy operator ?0 into the IOS Hamiltonian. This procedure is an example of sensitivity analysis of missing model components (?0 in this case) in the reference Hamiltonian. In contrast to simple first-order perturbation theory a finite result is obtained for the effect of ?0 on SIOS. As an illustration, our method of analysis is applied to integral state-to-state cross sections for the scattering of an atom and rigid rotor. Results are generated within the He+H2 system and a comparison is made between IOS and coupled states cross sections and the corresponding IOS sensitivities. It is found that the sensitivity coefficients are very useful indicators of the accuracy of the IOS results. Finally, further developments and applications are discussed.

Quantum solution for the one-dimensional Coulomb problem

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

Nunez-Yepez, H. N.; Salas-Brito, A. L.; Solis, Didier A.

2011-06-15

The one-dimensional hydrogen atom has been a much studied system with a wide range of applications. Since the pioneering work of Loudon [R. Loudon, Am. J. Phys. 27, 649 (1959).], a number of different features related to the nature of the eigenfunctions have been found. However, many of the claims made throughout the years in this regard are not correct--such as the existence of only odd eigenstates or of an infinite binding-energy ground state. We explicitly show that the one-dimensional hydrogen atom does not admit a ground state of infinite binding energy and that the one-dimensional Coulomb potential is notmore » its own supersymmetric partner. Furthermore, we argue that at the root of many such false claims lies the omission of a superselection rule that effectively separates the right side from the left side of the singularity of the Coulomb potential.« less

Coherent scattering from semi-infinite non-Hermitian potentials

NASA Astrophysics Data System (ADS)

Ahmed, Zafar; Ghosh, Dona; Kumar, Sachin

2018-02-01

When two identical (coherent) beams are injected at a semi-infinite non-Hermitian medium from left and right, we show that both reflection (rL,rR) and transmission (tL,tR) amplitudes are nonreciprocal. In a parametric domain, there exists spectral singularity (SS) at a real energy E =E*=k*2 and the determinant of the time-reversed two port scattering matrix, i.e., |det(S (-k ) ) |=| tL(-k ) tR(-k ) -rL(-k ) rR(-k ) | , vanishes sharply at k =k* , displaying the phenomenon of coherent perfect absorption (CPA). In the complementary parametric domain, the potential becomes either left or right reflectionless at E =Ez . We rule out the existence of invisibility despite rR(Ei) =0 and tR(Ei) =1 but T (Ei)≠1 , in this avenue. We present two simple exactly solvable models where expressions for E*, Ez, Ei, and parametric conditions on the potential have been obtained in explicit and simple forms. Earlier, the phenomena of SS and CPA have been found to occur only in the scattering complex potentials which are spatially localized (vanish asymptotically) and have tL=tR .

Rational solutions to the KPI equation and multi rogue waves

NASA Astrophysics Data System (ADS)

Gaillard, Pierre

2016-04-01

We construct here rational solutions to the Kadomtsev-Petviashvili equation (KPI) as a quotient of two polynomials in x, y and t depending on several real parameters. This method provides an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2 N(N + 1) in x, y and t depending on 2 N - 2 real parameters for each positive integer N. We give explicit expressions of the solutions in the simplest cases N = 1 and N = 2 and we study the patterns of their modulus in the (x , y) plane for different values of time t and parameters.

Functional DNA: Teaching Infinite Series through Genetic Analogy

ERIC Educational Resources Information Center

Kowalski, R. Travis

2011-01-01

This article presents an extended analogy that connects infinite sequences and series to the science of genetics, by identifying power series as "DNA for a function." This analogy allows standard topics such as convergence tests or Taylor approximations to be recast in a "forensic" light as mathematical analogs of genetic concepts such as DNA…

Explaining Infinite Series--An Exploration of Students' Images

ERIC Educational Resources Information Center

Champney, Danielle Dawn

2013-01-01

This study uses self-generated representations (SGR)--images produced in the act of explaining--as a means of uncovering what university calculus students understand about infinite series convergence. It makes use of student teaching episodes, in which students were asked to explain to a peer what that student might have missed had they been…

On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales

NASA Astrophysics Data System (ADS)

Sergeyev, Yaroslav D.; Kvasov, Dmitri E.; Mukhametzhanov, Marat S.

2018-06-01

The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is strong homogeneity meaning that a method produces the same sequences of points where the objective function is evaluated independently both of multiplication of the function by a scaling constant and of adding a shifting constant. In this paper, several aspects of global optimization using strongly homogeneous methods are considered. First, it is shown that even if a method possesses this property theoretically, numerically very small and large scaling constants can lead to ill-conditioning of the scaled problem. Second, a new class of global optimization problems where the objective function can have not only finite but also infinite or infinitesimal Lipschitz constants is introduced. Third, the strong homogeneity of several Lipschitz global optimization algorithms is studied in the framework of the Infinity Computing paradigm allowing one to work numerically with a variety of infinities and infinitesimals. Fourth, it is proved that a class of efficient univariate methods enjoys this property for finite, infinite and infinitesimal scaling and shifting constants. Finally, it is shown that in certain cases the usage of numerical infinities and infinitesimals can avoid ill-conditioning produced by scaling. Numerical experiments illustrating theoretical results are described.

A Computer Simulation Study of Vntr Population Genetics: Constrained Recombination Rules Out the Infinite Alleles Model

PubMed Central

Harding, R. M.; Boyce, A. J.; Martinson, J. J.; Flint, J.; Clegg, J. B.

1993-01-01

Extensive allelic diversity in variable numbers of tandem repeats (VNTRs) has been discovered in the human genome. For population genetic studies of VNTRs, such as forensic applications, it is important to know whether a neutral mutation-drift balance of VNTR polymorphism can be represented by the infinite alleles model. The assumption of the infinite alleles model that each new mutant is unique is very likely to be violated by unequal sister chromatid exchange (USCE), the primary process believed to generate VNTR mutants. We show that increasing both mutation rates and misalignment constraint for intrachromosomal recombination in a computer simulation model reduces simulated VNTR diversity below the expectations of the infinite alleles model. Maximal constraint, represented as slippage of single repeats, reduces simulated VNTR diversity to levels expected from the stepwise mutation model. Although misalignment rule is the more important variable, mutation rate also has an effect. At moderate rates of USCE, simulated VNTR diversity fluctuates around infinite alleles expectation. However, if rates of USCE are high, as for hypervariable VNTRs, simulated VNTR diversity is consistently lower than predicted by the infinite alleles model. This has been observed for many VNTRs and accounted for by technical problems in distinguishing alleles of neighboring size classes. We use sampling theory to confirm the intrinsically poor fit to the infinite alleles model of both simulated VNTR diversity and observed VNTR polymorphisms sampled from two Papua New Guinean populations. PMID:8293988

A computer simulation study of VNTR population genetics: constrained recombination rules out the infinite alleles model.

PubMed

Harding, R M; Boyce, A J; Martinson, J J; Flint, J; Clegg, J B

1993-11-01

Extensive allelic diversity in variable numbers of tandem repeats (VNTRs) has been discovered in the human genome. For population genetic studies of VNTRs, such as forensic applications, it is important to know whether a neutral mutation-drift balance of VNTR polymorphism can be represented by the infinite alleles model. The assumption of the infinite alleles model that each new mutant is unique is very likely to be violated by unequal sister chromatid exchange (USCE), the primary process believed to generate VNTR mutants. We show that increasing both mutation rates and misalignment constraint for intrachromosomal recombination in a computer simulation model reduces simulated VNTR diversity below the expectations of the infinite alleles model. Maximal constraint, represented as slippage of single repeats, reduces simulated VNTR diversity to levels expected from the stepwise mutation model. Although misalignment rule is the more important variable, mutation rate also has an effect. At moderate rates of USCE, simulated VNTR diversity fluctuates around infinite alleles expectation. However, if rates of USCE are high, as for hypervariable VNTRs, simulated VNTR diversity is consistently lower than predicted by the infinite alleles model. This has been observed for many VNTRs and accounted for by technical problems in distinguishing alleles of neighboring size classes. We use sampling theory to confirm the intrinsically poor fit to the infinite alleles model of both simulated VNTR diversity and observed VNTR polymorphisms sampled from two Papua New Guinean populations.

A computer simulation study of VNTR population genetics: Constrained recombination rules out the infinite alleles model

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

Harding, R.M.; Martinson, J.J.; Flint, J.

1993-11-01

Extensive allelic diversity in variable numbers of tandem repeats (VNTRs) has been discovered in the human genome. For population genetic studies of VNTRs, such as forensic applications, it is important to know whether a neutral mutation-drift balance of VNTR polymorphism can be represented by the infinite alleles model. The assumption of the infinite alleles model that each new mutant is unique is very likely to be violated by unequal sister chromatid exchange (USCE), the primary process believed to generate VNTR mutants. The authors show that increasing both mutation rates and misalignment constraint for intrachromosomal recombination in a computer simulation modelmore » reduces simulated VNTR diversity below the expectations of the infinite alleles model. Maximal constraint, represented as slippage of single repeats, reduces simulated VNTR diversity to levels expected from the stepwise mutation model. Although misalignment rule is the more important variable, mutation rate also has an effect. At moderate rates of USCE, simulated VNTR diversity fluctuates around infinite alleles expectation. However, if rates of USCE are high, as for hypervariable VNTRs, simulated VNTR diversity is consistently lower than predicted by the infinite alleles model. This has been observed for many VNTRs and accounted for by technical problems in distinguishing alleles of neighboring size classes. The authors use sampling theory to confirm the intrinsically poor fit to the infinite model of both simulated VNTR diversity and observed VNTR polymorphisms sampled from two Papua New Guinean populations. 25 refs., 20 figs., 4 tabs.« less

Transient Infiltration Analysis for Infinite Slopes using the Modified Function of Unsaturated Hydraulic Conductivity

NASA Astrophysics Data System (ADS)

Oh, Seboong; Achmad Zaky, Fauzi; Mog Park, Young

2016-04-01

The hydraulic behaviors in the soil layer are crucial to the transient infiltration analysis into natural slopes, in which unsaturated hydraulic conductivity (HC) can be evaluated theoretically from soil water retention curves (SWRC) by Mualem's equation. In the nonlinear infiltration analysis, the solution by some of smooth SWRCs is not converge for heavy rainfall condition, since the gradient of HCs is extremely steep near saturation. The van Genuchten's SWRC model has been modified near saturation and subsequently an analytical HC function was proposed to improve the van Genuchten-Mualem HC. Using the examples on 1-D infiltration analysis by the modified HC model, it is validated that any solutions can be converged for various rainfall conditions to keep numerical stability. Stability analysis based on unsaturated effective stress could simulate the infinite slope failure by the proposed HC model. The pore water pressure and the ratio of saturation increased from the surface to shallow depth (˜1m) and the factor of safety decreased gradually due to infiltration. Acknowledgements This research is supported by grants from Korean NRF (2012M3A2A1050974 and 2015R1A2A2A01), which are greatly appreciated.

Analytical solutions for tomato peeling with combined heat flux and convective boundary conditions

NASA Astrophysics Data System (ADS)

Cuccurullo, G.; Giordano, L.; Metallo, A.

2017-11-01

Peeling of tomatoes by radiative heating is a valid alternative to steam or lye, which are expensive and pollutant methods. Suitable energy densities are required in order to realize short time operations, thus involving only a thin layer under the tomato surface. This paper aims to predict the temperature field in rotating tomatoes exposed to the source irradiation. Therefore, a 1D unsteady analytical model is presented, which involves a semi-infinite slab subjected to time dependent heating while convective heat transfer takes place on the exposed surface. In order to account for the tomato rotation, the heat source is described as the positive half-wave of a sinusoidal function. The problem being linear, the solution is derived following the Laplace Transform Method. In addition, an easy-to-handle solution for the problem at hand is presented, which assumes a differentiable function for approximating the source while neglecting convective cooling, the latter contribution turning out to be negligible for the context at hand. A satisfying agreement between the two analytical solutions is found, therefore, an easy procedure for a proper design of the dry heating system can be set up avoiding the use of numerical simulations.

2.5D Finite/infinite Element Approach for Simulating Train-Induced Ground Vibrations

NASA Astrophysics Data System (ADS)

Yang, Y. B.; Hung, H. H.; Kao, J. C.

2010-05-01

The 2.5D finite/infinite element approach for simulating the ground vibrations by surface or underground moving trains will be briefly summarized in this paper. By assuming the soils to be uniform along the direction of the railway, only a two-dimensional profile of the soil perpendicular to the railway need be considered in the modeling. Besides the two in-plane degrees of freedom (DOFs) per node conventionally used for plane strain elements, an extra DOF is introduced to account for the out-of-plane wave transmission. The profile of the half-space is divided into a near field and a semi-infinite far field. The near field containing the train loads and irregular structures is simulated by the finite elements, while the far field covering the soils with infinite boundary by the infinite elements, by which due account is taken of the radiation effects for the moving loads. Enhanced by the automated mesh expansion procedure proposed previously by the writers, the far field impedances for all the lower frequencies are generated repetitively from the mesh created for the highest frequency considered. Finally, incorporated with a proposed load generation mechanism that takes the rail irregularity and dynamic properties of trains into account, an illustrative case study was performed. This paper investigates the vibration isolation effect of the elastic foundation that separates the concrete slab track from the underlying soil or tunnel structure. In addition, the advantage of the 2.5D approach was clearly demonstrated in that the three-dimensional wave propagation effect can be virtually captured using a two-dimensional finite/infinite element mesh. Compared with the conventional 3D approach, the present approach appears to be simple, efficient and generally accurate.

The Transition from Comparison of Finite to the Comparison of Infinite Sets: Teaching Prospective Teachers.

ERIC Educational Resources Information Center

Tsamir, Pessia

1999-01-01

Describes a course in Cantorian Set Theory relating to prospective secondary mathematics teachers' tendencies to overgeneralize from finite to infinite sets. Indicates that when comparing the number of elements in infinite sets, teachers who took the course were more successful and more consistent in their use of single method than those who…

Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices

NASA Astrophysics Data System (ADS)

Jahromi, Saeed S.; Orús, Román; Kargarian, Mehdi; Langari, Abdollah

2018-03-01

The infinite projected entangled-pair state (iPEPS) algorithm is one of the most efficient techniques for studying the ground-state properties of two-dimensional quantum lattice Hamiltonians in the thermodynamic limit. Here, we show how the algorithm can be adapted to explore nearest-neighbor local Hamiltonians on the ruby and triangle-honeycomb lattices, using the corner transfer matrix (CTM) renormalization group for 2D tensor network contraction. Additionally, we show how the CTM method can be used to calculate the ground-state fidelity per lattice site and the boundary density operator and entanglement entropy (EE) on an infinite cylinder. As a benchmark, we apply the iPEPS method to the ruby model with anisotropic interactions and explore the ground-state properties of the system. We further extract the phase diagram of the model in different regimes of the couplings by measuring two-point correlators, ground-state fidelity, and EE on an infinite cylinder. Our phase diagram is in agreement with previous studies of the model by exact diagonalization.

Infinitely divisible cascades to model the statistics of natural images.

PubMed

Chainais, Pierre

2007-12-01

We propose to model the statistics of natural images thanks to the large class of stochastic processes called Infinitely Divisible Cascades (IDC). IDC were first introduced in one dimension to provide multifractal time series to model the so-called intermittency phenomenon in hydrodynamical turbulence. We have extended the definition of scalar infinitely divisible cascades from 1 to N dimensions and commented on the relevance of such a model in fully developed turbulence in [1]. In this article, we focus on the particular 2 dimensional case. IDC appear as good candidates to model the statistics of natural images. They share most of their usual properties and appear to be consistent with several independent theoretical and experimental approaches of the literature. We point out the interest of IDC for applications to procedural texture synthesis.

Ultrasonic speed, densities and viscosities of xylitol in water and in aqueous tyrosine and phenylalanine solutions at different temperatures

NASA Astrophysics Data System (ADS)

Ali, A.; Bidhuri, P.; Uzair, S.

2014-07-01

Ultrasonic speed u, densities ρ and viscosities η of xylitol in water and in 0.001 m aqueous l-tyrosine (Tyr) and l-phenylalanine (Phe) have been measured at different temperatures. From the density and ultrasonic speed measurements apparent molar isentropic compression κ_{φ}, apparent molar isentropic compressions at infinite dilution κ_{{S,φ}}0 , experimental slope S K , hydration number n H , transfer partial molar isentropic compressibility Δ_{tr} κ_{{S,φ}}0 of xylitol from water to aqueous Tyr and Phe have been obtained. From the viscosity data, B-coefficient and B-coefficient of transfer Δ tr B of xylitol from water to aqueous Phe and Tyr at different temperatures have also been estimated. Gibbs free energies of activation of viscous flow per mole of solvent Δ μ 1 0# and per mole of solute Δ μ 2 0# have been calculated by using Feakins transition state theory for the studied systems. The calculated parameters have been interpreted in terms of solute-solute and solute-solvent interactions and hydration behavior of xylitol.

Is the tautochrone curve unique?

NASA Astrophysics Data System (ADS)

Terra, Pedro; de Melo e Souza, Reinaldo; Farina, C.

2016-12-01

We show that there are an infinite number of tautochrone curves in addition to the cycloid solution first obtained by Christiaan Huygens in 1658. We begin by reviewing the inverse problem of finding the possible potential energy functions that lead to periodic motions of a particle whose period is a given function of its mechanical energy. There are infinitely many such solutions, called "sheared" potentials. As an interesting example, we show that a Pöschl-Teller potential and the one-dimensional Morse potentials are sheared relative to one another for negative energies, clarifying why they share the same oscillation periods for their bounded solutions. We then consider periodic motions of a particle sliding without friction over a track around its minimum under the influence of a constant gravitational field. After a brief historical survey of the tautochrone problem we show that, given the oscillation period, there is an infinity of tracks that lead to the same period. As a bonus, we show that there are infinitely many tautochrones.

Energy Solutions

ERIC Educational Resources Information Center

Sobieski, Jeff

2010-01-01

Education facilities managers are faced with a daunting set of challenges: They must find new ways to reduce energy consumption and carry out greener energy policies. HVAC typically accounts for more than 30% of a building's electricity costs, so there is a clear incentive to eliminate unnecessary heating and cooling of unoccupied rooms. With more…

Confusing Aspects in the Calculation of the Electrostatic Potential of an Infinite Line of Charge

ERIC Educational Resources Information Center

Jimenez, J. L.; Campos, I.; Roa-Neri, J. A. E.

2012-01-01

In this work we discuss the trick of eliminating infinite potential of reference arguing that it corresponds to a constant of integration, in the problem of determining the electrostatic potential of an infinite line of charge with uniform density, and show how the problem must be tackled properly. The usual procedure is confusing for most…

On power series representing solutions of the one-dimensional time-independent Schrödinger equation

NASA Astrophysics Data System (ADS)

Trotsenko, N. P.

2017-06-01

For the equation χ″( x) = u( x)χ( x) with infinitely smooth u( x), the general solution χ( x) is found in the form of a power series. The coefficients of the series are expressed via all derivatives u ( m)( y) of the function u( x) at a fixed point y. Examples of solutions for particular functions u( x) are considered.

Dark matter and dark energy from the solution of the strong CP problem.

PubMed

Mainini, Roberto; Bonometto, Silvio A

2004-09-17

The Peccei-Quinn (PQ) solution of the strong CP problem requires the existence of axions, which are viable candidates for dark matter. If the Nambu-Goldstone potential of the PQ model is replaced by a potential V(|Phi|) admitting a tracker solution, the scalar field |Phi| can account for dark energy, while the phase of Phi yields axion dark matter. If V is a supergravity (SUGRA) potential, the model essentially depends on a single parameter, the energy scale Lambda. Once we set Lambda approximately equal to 10(10) GeV at the quark-hadron transition, |Phi| naturally passes through values suitable to solve the strong CP problem, later growing to values providing fair amounts of dark matter and dark energy.

An analytical model for solute transport in an infiltration tracer test in soil with a shallow groundwater table

NASA Astrophysics Data System (ADS)

Liang, Ching-Ping; Hsu, Shao-Yiu; Chen, Jui-Sheng

2016-09-01

It is recommended that an in-situ infiltration tracer test is considered for simultaneously determining the longitudinal and transverse dispersion coefficients in soil. Analytical solutions have been derived for two-dimensional advective-dispersive transport in a radial geometry in the literature which can be used for interpreting the result of such a tracer test. However, these solutions were developed for a transport domain with an unbounded-radial extent and an infinite thickness of vadose zone which might not be realistically manifested in the actual solute transport during a field infiltration tracer test. Especially, the assumption of infinite thickness of vadose zone should be invalid for infiltration tracer tests conducted in soil with a shallow groundwater table. This paper describes an analytical model for interpreting the results of an infiltration tracer test based on improving the transport domain with a bounded-radial extent and a finite thickness of vadose zone. The analytical model is obtained with the successive application of appropriate integral transforms and their corresponding inverse transforms. A comparison of the newly derived analytical solution against the previous analytical solutions in which two distinct sets of radial extent and thickness of vadose zone are considered is conducted to determine the influence of the radial and exit boundary conditions on the solute transport. The results shows that both the radial and exit boundary conditions substantially affect the trailing segment of the breakthrough curves for a soil medium with large dispersion coefficients. Previous solutions derived for a transport domain with an unbounded-radial and an infinite thickness of vadose zone boundary conditions give lower concentration predictions compared with the proposed solution at late times. Moreover, the differences between two solutions are amplified when the observation positions are near the groundwater table. In addition, we compare our

Verification assessment of piston boundary conditions for Lagrangian simulation of compressible flow similarity solutions

DOE PAGES

Ramsey, Scott D.; Ivancic, Philip R.; Lilieholm, Jennifer F.

2015-12-10

This work is concerned with the use of similarity solutions of the compressible flow equations as benchmarks or verification test problems for finite-volume compressible flow simulation software. In practice, this effort can be complicated by the infinite spatial/temporal extent of many candidate solutions or “test problems.” Methods can be devised with the intention of ameliorating this inconsistency with the finite nature of computational simulation; the exact strategy will depend on the code and problem archetypes under investigation. For example, self-similar shock wave propagation can be represented in Lagrangian compressible flow simulations as rigid boundary-driven flow, even if no such “piston”more » is present in the counterpart mathematical similarity solution. The purpose of this work is to investigate in detail the methodology of representing self-similar shock wave propagation as a piston-driven flow in the context of various test problems featuring simple closed-form solutions of infinite spatial/temporal extent. The closed-form solutions allow for the derivation of similarly closed-form piston boundary conditions (BCs) for use in Lagrangian compressible flow solvers. Finally, the consequences of utilizing these BCs (as opposed to directly initializing the self-similar solution in a computational spatial grid) are investigated in terms of common code verification analysis metrics (e.g., shock strength/position errors and global convergence rates).« less

Verification assessment of piston boundary conditions for Lagrangian simulation of compressible flow similarity solutions

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

Ramsey, Scott D.; Ivancic, Philip R.; Lilieholm, Jennifer F.

This work is concerned with the use of similarity solutions of the compressible flow equations as benchmarks or verification test problems for finite-volume compressible flow simulation software. In practice, this effort can be complicated by the infinite spatial/temporal extent of many candidate solutions or “test problems.” Methods can be devised with the intention of ameliorating this inconsistency with the finite nature of computational simulation; the exact strategy will depend on the code and problem archetypes under investigation. For example, self-similar shock wave propagation can be represented in Lagrangian compressible flow simulations as rigid boundary-driven flow, even if no such “piston”more » is present in the counterpart mathematical similarity solution. The purpose of this work is to investigate in detail the methodology of representing self-similar shock wave propagation as a piston-driven flow in the context of various test problems featuring simple closed-form solutions of infinite spatial/temporal extent. The closed-form solutions allow for the derivation of similarly closed-form piston boundary conditions (BCs) for use in Lagrangian compressible flow solvers. Finally, the consequences of utilizing these BCs (as opposed to directly initializing the self-similar solution in a computational spatial grid) are investigated in terms of common code verification analysis metrics (e.g., shock strength/position errors and global convergence rates).« less

Some examples of exact and approximate solutions in small particle scattering - A progress report

NASA Technical Reports Server (NTRS)

Greenberg, J. M.

1974-01-01

The formulation of basic equations from which the scattering of radiation by a localized variation in a medium is discussed. These equations are developed in both the differential and the integral form. Primary interest is in the scattering of electromagnetic waves for which the solution of the vector wave equation with appropriate boundary conditions must be considered. Scalar scattering by an infinite homogeneous isotropic circular cylinder, and scattering of electromagnetic waves by infinite circular cylinders are treated, and the case of the finite circular cylinder is considered. A procedure is given for obtaining angular scattering distributions from spheroids.

Stress and strain concentration at a circular hole in an infinite plate

NASA Technical Reports Server (NTRS)

Stowell, Elbridge Z

1950-01-01

The theory of elasticity shows that the maximum stress at a circular hole in an infinite plate in tension is three times the applied stress when the material remains elastic. The effect of plasticity of the material is to lower this ratio. This paper considers the theoretical problem of the stress distribution in an infinitely large sheet with a circular hole for the general case where the material may have any stress-strain curve. The plate is assumed to be under uniform tension at a large distance from the hole. The material is taken to be isotropic and incompressible. (author)

One-loop β-function for an infinite-parameter family of gauge theories

NASA Astrophysics Data System (ADS)

Krasnov, Kirill

2015-03-01

We continue to study an infinite-parametric family of gauge theories with an arbitrary function of the self-dual part of the field strength as the Lagrangian. The arising one-loop divergences are computed using the background field method. We show that they can all be absorbed by a local redefinition of the gauge field, as well as multiplicative renormalisations of the couplings. Thus, this family of theories is one-loop renormalisable. The infinite set of β-functions for the couplings is compactly stored in a renormalisation group flow for a single function of the curvature. The flow is obtained explicitly.

Finding Limit Cycles in self-excited oscillators with infinite-series damping functions

NASA Astrophysics Data System (ADS)

Das, Debapriya; Banerjee, Dhruba; Bhattacharjee, Jayanta K.

2015-03-01

In this paper we present a simple method for finding the location of limit cycles of self excited oscillators whose damping functions can be represented by some infinite convergent series. We have used standard results of first-order perturbation theory to arrive at amplitude equations. The approach has been kept pedagogic by first working out the cases of finite polynomials using elementary algebra. Then the method has been extended to various infinite polynomials, where the fixed points of the corresponding amplitude equations cannot be found out. Hopf bifurcations for systems with nonlinear powers in velocities have also been discussed.

Relativistic density functional theory with picture-change corrected electron density based on infinite-order Douglas-Kroll-Hess method

NASA Astrophysics Data System (ADS)

Oyama, Takuro; Ikabata, Yasuhiro; Seino, Junji; Nakai, Hiromi

2017-07-01

This Letter proposes a density functional treatment based on the two-component relativistic scheme at the infinite-order Douglas-Kroll-Hess (IODKH) level. The exchange-correlation energy and potential are calculated using the electron density based on the picture-change corrected density operator transformed by the IODKH method. Numerical assessments indicated that the picture-change uncorrected density functional terms generate significant errors, on the order of hartree for heavy atoms. The present scheme was found to reproduce the energetics in the four-component treatment with high accuracy.

Silicon carbide at nanoscale: Finite single-walled to "infinite" multi-walled tubes

NASA Astrophysics Data System (ADS)

Adhikari, Kapil

A systematic ab initio study of silicon carbide (SiC) nanostructures, especially finite single-walled, infinite double- and multi-walled nanotubes and nanocones is presented. Electronic and structural properties of all these nanostructures have been calculated using hybrid density functionals (B3LYP and PBE0) as implemented in the GAUSSIAN 03/09 suite of software. The unusual dependence of band gap of silicon carbide nanotubes (SiCNT) has been explained as a direct consequence of curvature effect on the ionicity of the bonds. The study of fullerene hemisphere capped, finite SiC nanotubes indicates that the carbon-capped SiC nanotubes are energetically more preferred than silicon-capped finite or hydrogen terminated infinite nanotubes. Capping a nanotube by fullerene hemisphere reduces its band gap. SiC nanocones have also been investigated as possible cap structures of nanotubes. Electronic properties of the nanocones are found to be strongly dependent upon their tip and edge structures, with possible interesting applications in surface science. Three types of double-walled SiCNTs (n, n)@(m, m) (3 ≤ n ≤ 6 ; 7 ≤ m ≤ 12) have been studied using the finite cluster approximation. The stabilities of these nanotubes are of the same order as those of the single-walled SiC nanotubes and it should be experimentally possible to synthesize both single-walled and double-walled SiC nanotubes. The binding energy per atom or the cohesive energy of the double-walled nanotubes depends not only on the number of atoms but also on the coupling of the constituent single-walled nanotubes and their types. A study of binding energies, Mulliken charges, density of states and HOMO-LUMO gaps has been performed for all nanotubes from (n, n)@(n+3,n+3) to (n, n)@(n+6, n+6) (n=3-6). Evolution of band gaps of the SiCNTs with increase in the number of walls has also been investigated. The nature of interaction between transition metal atoms and silicon carbide nanotubes with different

Rotating metric in nonsingular infinite derivative theories of gravity

NASA Astrophysics Data System (ADS)

Cornell, Alan S.; Harmsen, Gerhard; Lambiase, Gaetano; Mazumdar, Anupam

2018-05-01

In this paper, we will provide a nonsingular rotating spacetime metric for a ghost-free infinite derivative theory of gravity in a linearized limit. We will provide the predictions for the Lense-Thirring effect for a slowly rotating system, and how it is compared with that from general relativity.

Asymptotic solution of Fokker-Planck equation for plasma in Paul traps

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

Shah, Kushal

2010-05-15

An exact analytic solution of the Vlasov equation for the plasma distribution in a Paul trap is known to be a Maxwellian and thus, immune to collisions under the assumption of infinitely fast relaxation [K. Shah and H. S. Ramachandran, Phys. Plasmas 15, 062303 (2008)]. In this paper, it is shown that even for a more realistic situation of finite time relaxation, solutions of the Fokker-Planck equation lead to an equilibrium solution of the form of a Maxwellian with oscillatory temperature. This shows that the rf heating observed in Paul traps cannot be caused due to collisional effects alone.

Phantom energy: dark energy with w <--1 causes a cosmic doomsday.

PubMed

Caldwell, Robert R; Kamionkowski, Marc; Weinberg, Nevin N

2003-08-15

We explore the consequences that follow if the dark energy is phantom energy, in which the sum of the pressure and energy density is negative. The positive phantom-energy density becomes infinite in finite time, overcoming all other forms of matter, such that the gravitational repulsion rapidly brings our brief epoch of cosmic structure to a close. The phantom energy rips apart the Milky Way, solar system, Earth, and ultimately the molecules, atoms, nuclei, and nucleons of which we are composed, before the death of the Universe in a "big rip."

Effect of debond growth on stress-intensity factors in a cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet

NASA Technical Reports Server (NTRS)

Bigelow, C. A.

1986-01-01

Stress-intensity factors are determined for a cracked infinite sheet adhesively bonded to a stringer, and debonding of the adhesive layer is predicted. The stringer is modeled as a semi-infinite sheet. Adhesive nonlinearity is also included. Both the sheet and stringer are treated as homogeneous, orthotropic materials. A set of integral equations is formulated and solved to obtain the adhesive shear stresses and crack-tip stress-intensity factors. Adhesive debonding is predicted using a rupture criterion based on the combined adhesive stresses. When the crack is not under the stringer, the debond extends along the edge of the stringer. When the crack tip is beneath the stringer, the debond grows to the end of the crack, then along the edge of the stringer. Stress levels required for debond initiation decrease as the crack tip is moved beneath the stringer. With a nonlinear adhesive, the debond initiates at higher applied stress levels than in linear adhesive cases. Compared with the linear adhesive solution, modeling a nonlinear adhesive causes the stress-intensity factor to increase when the bond is assumed to remain intact but causes the stress-intensity factor to decrease when debonding is included.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result

NASA Astrophysics Data System (ADS)

Wu, Yang; Kelly, Damien P.

2014-12-01

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of ? and ? type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of ? and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by ?, where ? is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

Guided wave propagation in single and double layer hollow cylinders embedded in infinite media.

PubMed

Jia, Hua; Jing, Mu; Joseph, L Rose

2011-02-01

Millions of miles of pipes are being used for the transportation, distribution, and local use of petroleum products, gas, water, and chemicals. Most of the pipes are buried in soil, leading to the significance of the study on the subject of guided wave propagation in pipes with soil influence. Previous investigations of ultrasonic guided wave propagation in an elastic hollow cylinder and in an elastic hollow cylinder coated with a viscoelastic material have led to the development of inspection techniques for bare and coated pipes. However, the lack of investigation on guided wave propagation in hollow cylinders embedded in infinite media like soil has hindered the development of pipe inspection methods. Therefore the influence of infinite media on wave propagation is explored in this paper. Dispersion curves and wave structures of both axisymmetric and nonaxisymmetric wave modes are developed. Due to the importance of the convergence of numerical calculations, the requirements of thickness and element number of the finite soil layer between hollow cylinder and infinite element layer are discussed, and an optimal combination is obtained in this paper. Wave structures are used for the mode identification in the non-monotonic region caused by the viscoelastic properties of coating and infinite media.

Infinite family of three-dimensional Floquet topological paramagnets

NASA Astrophysics Data System (ADS)

Potter, Andrew C.; Vishwanath, Ashvin; Fidkowski, Lukasz

2018-06-01

We uncover an infinite family of time-reversal symmetric 3 d interacting topological insulators of bosons or spins, in time-periodically driven systems, which we term Floquet topological paramagnets (FTPMs). These FTPM phases exhibit intrinsically dynamical properties that could not occur in thermal equilibrium and are governed by an infinite set of Z2-valued topological invariants, one for each prime number. The topological invariants are physically characterized by surface magnetic domain walls that act as unidirectional quantum channels, transferring quantized packets of information during each driving period. We construct exactly solvable models realizing each of these phases, and discuss the anomalous dynamics of their topologically protected surface states. Unlike previous encountered examples of Floquet SPT phases, these 3 d FTPMs are not captured by group cohomology methods and cannot be obtained from equilibrium classifications simply by treating the discrete time translation as an ordinary symmetry. The simplest such FTPM phase can feature anomalous Z2 (toric code) surface topological order, in which the gauge electric and magnetic excitations are exchanged in each Floquet period, which cannot occur in a pure 2 d system without breaking time reversal symmetry.

What Causes Adverbial Infinitives to Spread? Evidence from Romance

ERIC Educational Resources Information Center

Schulte, K.

2007-01-01

It is cross-linguistically common for languages to undergo a diachronic increase in the range of adverbial notions that can be expressed by means of infinitival constructions, and the Romance languages are a good example of this process. Examining the development of adverbial "prepositional infinitive" constructions in Spanish, Portuguese and…

Determination of thermodynamic properties of isotactic poly(1-butene) at infinite dilution using density and inverse gas chromatography.

PubMed

Kozłowska, Marta Karolina; Domańska, Urszula; Lempert, Małgorzata; Rogalski, Marek

2005-03-18

The partial molar volumes, V1(M), and the molar volume of isotactic crystalline low-molecular-weight poly(1-butene), iPBu-1, V1, have been calculated from the measured density of {iPBu-1 + solvent (n-hexane, n-heptane, n-nonane, n-decane, p-xylene, cyclohexane and chloroform)} systems. Some of the thermodynamic quantities were also obtained for the iPBu-1 with eight hydrocarbons (n-octane, n-decane, n-undecane, n-dodecane, n-tridecane, o-xylene, m-xylene, p-xylene) by the method of inverse gas chromatography at various temperatures. The weight fraction activity coefficients of the solvent at infinite dilution, omega2(infinity) and the Flory-Huggins thermodynamic interaction parameters, chi21(infinity), between polymer and solvents were determined. The partial molar free energy, deltaG2(infinity), the partial molar heat of mixing, deltaH2(infinity), at infinite dilution and the polymer solubility parameter, delta1, were calculated. Additionally, the (solid + liquid) binary mixtures equilibria, SLE, of iPBu-1 with three hydrocarbons (n-octane, n-decane and m-xylene) were studied by a dynamic method. By performing these experiments over a large concentration range, the T-x phase diagrams of the polymer-solvent systems were constructed. The excess Gibbs energy models were used to describe the nonideal behaviour of the liquid phase. The omega2(infinity) were determined from the solubility measurements and were predicted by using the UNIFAC FV model.

Inverse-scattering-theory approach to the exact n→∞ solutions of O(n) ϕ⁴ models on films and semi-infinite systems bounded by free surfaces.

PubMed

Rutkevich, Sergei B; Diehl, H W

2015-06-01

The O(n) ϕ(4) model on a strip bounded by a pair of planar free surfaces at separation L can be solved exactly in the large-n limit in terms of the eigenvalues and eigenfunctions of a self-consistent one-dimensional Schrödinger equation. The scaling limit of a continuum version of this model is considered. It is shown that the self-consistent potential can be eliminated in favor of scattering data by means of appropriately extended methods of inverse scattering theory. The scattering data (Jost function) associated with the self-consistent potential are determined for the L=∞ semi-infinite case in the scaling regime for all values of the temperature scaling field t=(T-T(c))/T(c) above and below the bulk critical temperature T(c). These results are used in conjunction with semiclassical and boundary-operator expansions and a trace formula to derive exact analytical results for a number of quantities such as two-point functions, universal amplitudes of two excess surface quantities, the universal amplitude difference associated with the thermal singularity of the surface free energy, and potential coefficients. The asymptotic behaviors of the scaled eigenenergies and eigenfunctions of the self-consistent Schrödinger equation as function of x=t(L/ξ(+))(1/ν) are determined for x→-∞. In addition, the asymptotic x→-∞ forms of the universal finite-size scaling functions Θ(x) and ϑ(x) of the residual free energy and the Casimir force are computed exactly to order 1/x, including their x(-1)ln|x| anomalies.

Solution-Processed Two-Dimensional Metal Dichalcogenide-Based Nanomaterials for Energy Storage and Conversion.

PubMed

Cao, Xiehong; Tan, Chaoliang; Zhang, Xiao; Zhao, Wei; Zhang, Hua

2016-08-01

The development of renewable energy storage and conversion devices is one of the most promising ways to address the current energy crisis, along with the global environmental concern. The exploration of suitable active materials is the key factor for the construction of highly efficient, highly stable, low-cost and environmentally friendly energy storage and conversion devices. The ability to prepare two-dimensional (2D) metal dichalcogenide (MDC) nanosheets and their functional composites in high yield and large scale via various solution-based methods in recent years has inspired great research interests in their utilization for renewable energy storage and conversion applications. Here, we will summarize the recent advances of solution-processed 2D MDCs and their hybrid nanomaterials for energy storage and conversion applications, including rechargeable batteries, supercapacitors, electrocatalytic hydrogen generation and solar cells. Moreover, based on the current progress, we will also give some personal insights on the existing challenges and future research directions in this promising field. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Determination of partial molar volumes from free energy perturbation theory†

PubMed Central

Vilseck, Jonah Z.; Tirado-Rives, Julian

2016-01-01

Partial molar volume is an important thermodynamic property that gives insights into molecular size and intermolecular interactions in solution. Theoretical frameworks for determining the partial molar volume (V°) of a solvated molecule generally apply Scaled Particle Theory or Kirkwood–Buff theory. With the current abilities to perform long molecular dynamics and Monte Carlo simulations, more direct methods are gaining popularity, such as computing V° directly as the difference in computed volume from two simulations, one with a solute present and another without. Thermodynamically, V° can also be determined as the pressure derivative of the free energy of solvation in the limit of infinite dilution. Both approaches are considered herein with the use of free energy perturbation (FEP) calculations to compute the necessary free energies of solvation at elevated pressures. Absolute and relative partial molar volumes are computed for benzene and benzene derivatives using the OPLS-AA force field. The mean unsigned error for all molecules is 2.8 cm3 mol−1. The present methodology should find use in many contexts such as the development and testing of force fields for use in computer simulations of organic and biomolecular systems, as a complement to related experimental studies, and to develop a deeper understanding of solute–solvent interactions. PMID:25589343

A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo in Natural Waters

EPA Science Inventory

Several numerical and analytical solutions of the radiative transfer equation (RTE) for plane albedo were compared for solar light reflection by sea water. The study incorporated the simplest case, that being a semi-infinite one-dimensional plane-parallel absorbing and scattering...

A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo of Natural Waters

EPA Science Inventory

Three numerical algorithms were compared to provide a solution of a radiative transfer equation (RTE) for plane albedo (hemispherical reflectance) in semi-infinite one-dimensional plane-parallel layer. Algorithms were based on the invariant imbedding method and two different var...

Wormhole at the core of an infinite cosmic string

NASA Astrophysics Data System (ADS)

Aros, Rodrigo O.; Zamorano, Nelson

1997-11-01

We study a solution of Einstein's equations that describes a straight cosmic string with a variable angular deficit, starting with a 2π deficit at the core. We show that the coordinate singularity associated with this defect can be interpreted as a traversable wormhole lodging at the core of the string. A negative energy density gradually decreases the angular deficit as the distance from the core increases, ending, at radial infinity, in a Minkowski spacetime. The negative energy density can be confined to a small transversal section of the string by gluing to it an exterior Gott-like solution that freezes the angular deficit existing at the matching border. The equation of state of the string is such that any massive particle may stay at rest anywhere in this spacetime. In this sense this is a 2+1 spacetime solution. A generalization that includes the existence of two interacting parallel wormholes is displayed. These wormholes are not traversable. Finally, we point out that a similar result, flat at infinity and with a 2π defect (or excess) at the core, has been recently published by Dyer and Marleau. Even though theirs is a local string fully coupled to gravity, our toy model captures important aspects of this solution.

Examining the accuracy of the infinite order sudden approximation using sensitivity analysis

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

Eno, L.; Rabitz, H.

1981-08-15

A method is developed for assessing the accuracy of scattering observables calculated within the framework of the infinite order sudden (IOS) approximation. In particular, we focus on the energy sudden assumption of the IOS method and our approach involves the determination of the sensitivity of the IOS scattering matrix S/sup IOS/ with respect to a parameter which reintroduces the internal energy operator h/sub 0/ into the IOS Hamiltonian. This procedure is an example of sensitivity analysis of missing model components (h/sub 0/ in this case) in the reference Hamiltonian. In contrast to simple first-order perturbation theory a finite result ismore » obtained for the effect of h/sub 0/ on S/sup IOS/. As an illustration, our method of analysis is applied to integral state-to-state cross sections for the scattering of an atom and rigid rotor. Results are generated within the He+H/sub 2/ system and a comparison is made between IOS and coupled states cross sections and the corresponding IOS sensitivities. It is found that the sensitivity coefficients are very useful indicators of the accuracy of the IOS results. Finally, further developments and applications are discussed.« less

Quasineutral plasma expansion into infinite vacuum as a model for parallel ELM transport

NASA Astrophysics Data System (ADS)

Moulton, D.; Ghendrih, Ph; Fundamenski, W.; Manfredi, G.; Tskhakaya, D.

2013-08-01

An analytic solution for the expansion of a plasma into vacuum is assessed for its relevance to the parallel transport of edge localized mode (ELM) filaments along field lines. This solution solves the 1D1V Vlasov-Poisson equations for the adiabatic (instantaneous source), collisionless expansion of a Gaussian plasma bunch into an infinite space in the quasineutral limit. The quasineutral assumption is found to hold as long as λD0/σ0 ≲ 0.01 (where λD0 is the initial Debye length at peak density and σ0 is the parallel length of the Gaussian filament), a condition that is physically realistic. The inclusion of a boundary at x = L and consequent formation of a target sheath is found to have a negligible effect when L/σ0 ≳ 5, a condition that is physically plausible. Under the same condition, the target flux densities predicted by the analytic solution are well approximated by the ‘free-streaming’ equations used in previous experimental studies, strengthening the notion that these simple equations are physically reasonable. Importantly, the analytic solution predicts a zero heat flux density so that a fluid approach to the problem can be used equally well, at least when the source is instantaneous. It is found that, even for JET-like pedestal parameters, collisions can affect the expansion dynamics via electron temperature isotropization, although this is probably a secondary effect. Finally, the effect of a finite duration, τsrc, for the plasma source is investigated. As is found for an instantaneous source, when L/σ0 ≳ 5 the presence of a target sheath has a negligible effect, at least up to the explored range of τsrc = L/cs (where cs is the sound speed at the initial temperature).

Interval-parameter semi-infinite fuzzy-stochastic mixed-integer programming approach for environmental management under multiple uncertainties.

PubMed

Guo, P; Huang, G H

2010-03-01

In this study, an interval-parameter semi-infinite fuzzy-chance-constrained mixed-integer linear programming (ISIFCIP) approach is developed for supporting long-term planning of waste-management systems under multiple uncertainties in the City of Regina, Canada. The method improves upon the existing interval-parameter semi-infinite programming (ISIP) and fuzzy-chance-constrained programming (FCCP) by incorporating uncertainties expressed as dual uncertainties of functional intervals and multiple uncertainties of distributions with fuzzy-interval admissible probability of violating constraint within a general optimization framework. The binary-variable solutions represent the decisions of waste-management-facility expansion, and the continuous ones are related to decisions of waste-flow allocation. The interval solutions can help decision-makers to obtain multiple decision alternatives, as well as provide bases for further analyses of tradeoffs between waste-management cost and system-failure risk. In the application to the City of Regina, Canada, two scenarios are considered. In Scenario 1, the City's waste-management practices would be based on the existing policy over the next 25 years. The total diversion rate for the residential waste would be approximately 14%. Scenario 2 is associated with a policy for waste minimization and diversion, where 35% diversion of residential waste should be achieved within 15 years, and 50% diversion over 25 years. In this scenario, not only landfill would be expanded, but also CF and MRF would be expanded. Through the scenario analyses, useful decision support for the City's solid-waste managers and decision-makers has been generated. Three special characteristics of the proposed method make it unique compared with other optimization techniques that deal with uncertainties. Firstly, it is useful for tackling multiple uncertainties expressed as intervals, functional intervals, probability distributions, fuzzy sets, and their

Blow-up of solutions to a quasilinear wave equation for high initial energy

NASA Astrophysics Data System (ADS)

Li, Fang; Liu, Fang

2018-05-01

This paper deals with blow-up solutions to a nonlinear hyperbolic equation with variable exponent of nonlinearities. By constructing a new control function and using energy inequalities, the authors obtain the lower bound estimate of the L2 norm of the solution. Furthermore, the concavity arguments are used to prove the nonexistence of solutions; at the same time, an estimate of the upper bound of blow-up time is also obtained. This result extends and improves those of [1,2].

Thermodynamic analysis of energy density in pressure retarded osmosis: The impact of solution volumes and costs

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

Reimund, Kevin K.; McCutcheon, Jeffrey R.; Wilson, Aaron D.

A general method was developed for estimating the volumetric energy efficiency of pressure retarded osmosis via pressure-volume analysis of a membrane process. The resulting model requires only the osmotic pressure, π, and mass fraction, w, of water in the concentrated and dilute feed solutions to estimate the maximum achievable specific energy density, uu, as a function of operating pressure. The model is independent of any membrane or module properties. This method utilizes equilibrium analysis to specify the volumetric mixing fraction of concentrated and dilute solution as a function of operating pressure, and provides results for the total volumetric energy densitymore » of similar order to more complex models for the mixing of seawater and riverwater. Within the framework of this analysis, the total volumetric energy density is maximized, for an idealized case, when the operating pressure is π/(1+√w⁻¹), which is lower than the maximum power density operating pressure, Δπ/2, derived elsewhere, and is a function of the solute osmotic pressure at a given mass fraction. It was also found that a minimum 1.45 kmol of ideal solute is required to produce 1 kWh of energy while a system operating at “maximum power density operating pressure” requires at least 2.9 kmol. Utilizing this methodology, it is possible to examine the effects of volumetric solution cost, operation of a module at various pressure, and operation of a constant pressure module with various feed.« less

Energy in elastic fiber embedded in elastic matrix containing incident SH wave

NASA Technical Reports Server (NTRS)

Williams, James H., Jr.; Nagem, Raymond J.

1989-01-01

A single elastic fiber embedded in an infinite elastic matrix is considered. An incident plane SH wave is assumed in the infinite matrix, and an expression is derived for the total energy in the fiber due to the incident SH wave. A nondimensional form of the fiber energy is plotted as a function of the nondimensional wavenumber of the SH wave. It is shown that the fiber energy attains maximum values at specific values of the wavenumber of the incident wave. The results obtained here are interpreted in the context of phenomena observed in acousto-ultrasonic experiments on fiber reinforced composite materials.

Structural properties of aqueous metoprolol succinate solutions. Density, viscosity, and refractive index at 311 K

NASA Astrophysics Data System (ADS)

Deosarkar, S. D.; Kalyankar, T. M.

2013-06-01

Density, viscosity and refractive index of aqueous solutions of metoprolol succinate of different concentrations (0.005-0.05 mol dm-3) were measured at 38°C. Apparent molar volume of resultant solutions were calculated and fitted to the Masson's equation and apparent molar volume at infinite dilution was determined graphically. Viscosity data of solutions has been fitted to the Jone-Dole equation and viscosity A- and B-coefficients were determined graphically. Physicochemical data obtained were discussed in terms of molecular interactions.

Vector image method for the derivation of elastostatic solutions for point sources in a plane layered medium. Part 1: Derivation and simple examples

NASA Technical Reports Server (NTRS)

Fares, Nabil; Li, Victor C.

1986-01-01

An image method algorithm is presented for the derivation of elastostatic solutions for point sources in bonded halfspaces assuming the infinite space point source is known. Specific cases were worked out and shown to coincide with well known solutions in the literature.

Quasimonochromatic exact solutions to Maxwell's equations with finite total energy and arbitrary frequencies in the vacuum.

PubMed

Ma, Xiaolu; Thompson, Richard S

2017-12-01

We analyze a family of exact finite energy solutions to Maxwell's equations. These solutions are a subset of the modified-power-spectrum solutions found by Ziolkowski [Phys. Rev. A 39, 2005 (1989)10.1103/PhysRevA.39.2005]. There are three characteristic parameters in the solutions: q_{1},q_{2}, and k_{0}. q_{1} and q_{2} are related to the frequency bandwidth of the solution. In the parameter space of k_{0}q_{1}≫1 and k_{0}q_{2}≫1, they represent quasimonochromatic continuous wave fields with the main angular frequency k_{0}c and energy localized in the transverse directions. Under the restriction of q_{1}≪q_{2}, the beam propagates mainly in the +z direction with velocity c and limited diffraction.

Finding Sums for an Infinite Class of Alternating Series

ERIC Educational Resources Information Center

Chen, Zhibo; Wei, Sheng; Xiao, Xuerong

2012-01-01

Calculus II students know that many alternating series are convergent by the Alternating Series Test. However, they know few alternating series (except geometric series and some trivial ones) for which they can find the sum. In this article, we present a method that enables the students to find sums for infinitely many alternating series in the…

On scalar and vector fields coupled to the energy-momentum tensor

NASA Astrophysics Data System (ADS)

Jiménez, Jose Beltrán; Cembranos, Jose A. R.; Sánchez Velázquez, Jose M.

2018-05-01

We consider theories for scalar and vector fields coupled to the energy-momentum tensor. Since these fields also carry a non-trivial energy-momentum tensor, the coupling prescription generates self-interactions. In analogy with gravity theories, we build the action by means of an iterative process that leads to an infinite series, which can be resumed as the solution of a set of differential equations. We show that, in some particular cases, the equations become algebraic and that is also possible to find solutions in the form of polynomials. We briefly review the case of the scalar field that has already been studied in the literature and extend the analysis to the case of derivative (disformal) couplings. We then explore theories with vector fields, distinguishing between gauge-and non-gauge-invariant couplings. Interactions with matter are also considered, taking a scalar field as a proxy for the matter sector. We also discuss the ambiguity introduced by superpotential (boundary) terms in the definition of the energy-momentum tensor and use them to show that it is also possible to generate Galileon-like interactions with this procedure. We finally use collider and astrophysical observations to set constraints on the dimensionful coupling which characterises the phenomenology of these models.

Peculiarities of the electron energy spectrum in the Coulomb field of a superheavy nucleus

NASA Astrophysics Data System (ADS)

Voronov, B. L.; Gitman, D. M.; Levin, A. D.; Ferreira, R.

2016-05-01

We consider the peculiarities of the electron energy spectrum in the Coulomb field of a superheavy nucleus and discuss the long history of an incorrect interpretation of this problem in the case of a pointlike nucleus and its current correct solution. We consider the spectral problem in the case of a regularized Coulomb potential. For some special regularizations, we derive an exact equation for the point spectrum in the energy interval (-m,m) and find some of its solutions numerically. We also derive an exact equation for charges yielding bound states with the energy E = -m; some call them supercritical charges. We show the existence of an infinite number of such charges. Their existence does not mean that the oneparticle relativistic quantum mechanics based on the Dirac Hamiltonian with the Coulomb field of such charges is mathematically inconsistent, although it is physically unacceptable because the spectrum of the Hamiltonian is unbounded from below. The question of constructing a consistent nonperturbative second-quantized theory remains open, and the consequences of the existence of supercritical charges from the standpoint of the possibility of constructing such a theory also remain unclear.

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Energy efficient wireless sensor networks by using a fuzzy-based solution

NASA Astrophysics Data System (ADS)

Tirrito, Salvatore; Nicolosi, Giuseppina

2016-12-01

Wireless Sensor Networks are characterized by a distributed architecture realized by a set of autonomous electronic devices able to sense data from the surrounding environment and to communicate among them. These devices are battery powered since they may be used even to monitor hazardous events in inaccessible areas. As a consequence, it is preferable to assure the adoption of energy management solutions in order to extend the WSN lifetime, as far as possible. Moreover, it is crucial to guarantee that the nodes receive the transmitted data correctly. It is clear that trading off power optimization and quality of service has become one the most important concerns when dealing with modern systems based on WSNs. This paper introduces a solution based on a Fuzzy Logic Controller (FLC) focusing on the minimization of energy consumption of wireless sensor nodes. This is made possible because the sleeping time of these nodes is dynamically regulated by a FLC.

An analytical solution for modeling thermal energy transfer in a confined aquifer system

NASA Astrophysics Data System (ADS)

Shaw-Yang, Yang; Hund-der, Yeh

2008-12-01

A mathematical model is developed for simulating the thermal energy transfer in a confined aquifer with different geological properties in the underlying and overlying rocks. The solutions for temperature distributions in the aquifer, underlying rock, and overlying rock are derived by the Laplace transforms and their corresponding time-domain solutions are evaluated by the modified Crump method. Field data adopted from the literature are used as examples to demonstrate the applicability of the solutions in modeling the heat transfer in an aquifer thermal energy storage (ATES) system. The results show that the aquifer temperature increases with time, injection flow rate, and water temperature. However, the temperature decreases with increasing radial and vertical distances. The heat transfer in the rocks is slow and has an effect on the aquifer temperature only after a long period of injection time. The influence distance depends on the aquifer physical and thermal properties, injection flow rate, and injected water temperature. A larger value of thermal diffusivity or injection flow rate will result in a longer influence distance. The present solution can be used as a tool for designing the heat injection facilities for an ATES system.

GD Friend, Inc. d/b/a Everlast Home Energy Solutions Information Sheet

EPA Pesticide Factsheets

GD Friend, Inc. d/b/a Everlast Home Energy Solutions (the Company) is located in Anaheim, California. The settlement involves renovation activities conducted at properties constructed prior to 1978, located in Anaheim and La Verne, California.

Electronic transport close to semi-infinite 2D systems and their interfaces

NASA Astrophysics Data System (ADS)

Xia, Fanbing; Wang, Jian; Jian Wang's research Group Team

Transport properties of 2D materials especially close to their boundary has received much attention after the successful fabrication of Graphene. While most previous work is devoted to the conventional lead-device-lead setup with a finite size center area, this project investigates real space transport properties of infinite and semi-infinite 2D systems under the framework of Non-equilibrium Green's function. The commonly used method of calculating Green's function by inverting matrices in the real space can be unstable in dealing with large systems as sometimes it gives non-converging result. By transforming from the real space to momentum space, the author managed to replace the matrix inverting process by Brillouin Zone integral which can be greatly simplified by the application of contour integral. Combining this methodology with Dyson equations, we are able to calculate transport properties of semi-infinite graphene close to its zigzag boundary and its combination with other material including s-wave superconductor. Interference pattern of transmitted and reflected electrons, Graphene lensing effects and difference between Specular Andreev reflection and normal Andreev reflection are verified. We also generalize how to apply this method to a broad range of 2D materials. The University of Hong Kong.

The infinite sites model of genome evolution.

PubMed

Ma, Jian; Ratan, Aakrosh; Raney, Brian J; Suh, Bernard B; Miller, Webb; Haussler, David

2008-09-23

We formalize the problem of recovering the evolutionary history of a set of genomes that are related to an unseen common ancestor genome by operations of speciation, deletion, insertion, duplication, and rearrangement of segments of bases. The problem is examined in the limit as the number of bases in each genome goes to infinity. In this limit, the chromosomes are represented by continuous circles or line segments. For such an infinite-sites model, we present a polynomial-time algorithm to find the most parsimonious evolutionary history of any set of related present-day genomes.

EMERGING TECHNOLOGY BULLETIN: REMOVAL OF PHENOL FROM AQUEOUS SOLUTIONS USING HIGH ENERGY ELECTRON BEAM IRRADIATION

EPA Science Inventory

Irradiation of aqueous solutions with high-energy electrons results in the formation of the aqueous electron, hydrogen radical, H-, and the hydroxyl radical, OH-. These reactive transient species initiate chemical reactions capable of destroying organic compounds in aqueous solut...

Energy solutions, neo-liberalism, and social diversity in Toronto, Canada.

PubMed

Teelucksingh, Cheryl; Poland, Blake

2011-01-01

In response to the dominance of green capitalist discourses in Canada's environmental movement, in this paper, we argue that strategies to improve energy policy must also provide mechanisms to address social conflicts and social disparities. Environmental justice is proposed as an alternative to mainstream environmentalism, one that seeks to address systemic social and spatial exclusion encountered by many racialized immigrants in Toronto as a result of neo-liberal and green capitalist municipal policy and that seeks to position marginalized communities as valued contributors to energy solutions. We examine Toronto-based municipal state initiatives aimed at reducing energy use while concurrently stimulating growth (specifically, green economy/green jobs and 'smart growth'). By treating these as instruments of green capitalism, we illustrate the utility of environmental justice applied to energy-related problems and as a means to analyze stakeholders' positions in the context of neo-liberalism and green capitalism, and as opening possibilities for resistance.

Energy Solutions, Neo-Liberalism, and Social Diversity in Toronto, Canada

PubMed Central

Teelucksingh, Cheryl; Poland, Blake

2011-01-01

In response to the dominance of green capitalist discourses in Canada’s environmental movement, in this paper, we argue that strategies to improve energy policy must also provide mechanisms to address social conflicts and social disparities. Environmental justice is proposed as an alternative to mainstream environmentalism, one that seeks to address systemic social and spatial exclusion encountered by many racialized immigrants in Toronto as a result of neo-liberal and green capitalist municipal policy and that seeks to position marginalized communities as valued contributors to energy solutions. We examine Toronto-based municipal state initiatives aimed at reducing energy use while concurrently stimulating growth (specifically, green economy/green jobs and ‘smart growth’). By treating these as instruments of green capitalism, we illustrate the utility of environmental justice applied to energy-related problems and as a means to analyze stakeholders’ positions in the context of neo-liberalism and green capitalism, and as opening possibilities for resistance. PMID:21318023

Optimal control of coupled parabolic-hyperbolic non-autonomous PDEs: infinite-dimensional state-space approach

NASA Astrophysics Data System (ADS)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2018-04-01

This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.

Maximally reliable Markov chains under energy constraints.

PubMed

Escola, Sean; Eisele, Michael; Miller, Kenneth; Paninski, Liam

2009-07-01

Signal-to-noise ratios in physical systems can be significantly degraded if the outputs of the systems are highly variable. Biological processes for which highly stereotyped signal generations are necessary features appear to have reduced their signal variabilities by employing multiple processing steps. To better understand why this multistep cascade structure might be desirable, we prove that the reliability of a signal generated by a multistate system with no memory (i.e., a Markov chain) is maximal if and only if the system topology is such that the process steps irreversibly through each state, with transition rates chosen such that an equal fraction of the total signal is generated in each state. Furthermore, our result indicates that by increasing the number of states, it is possible to arbitrarily increase the reliability of the system. In a physical system, however, an energy cost is associated with maintaining irreversible transitions, and this cost increases with the number of such transitions (i.e., the number of states). Thus, an infinite-length chain, which would be perfectly reliable, is infeasible. To model the effects of energy demands on the maximally reliable solution, we numerically optimize the topology under two distinct energy functions that penalize either irreversible transitions or incommunicability between states, respectively. In both cases, the solutions are essentially irreversible linear chains, but with upper bounds on the number of states set by the amount of available energy. We therefore conclude that a physical system for which signal reliability is important should employ a linear architecture, with the number of states (and thus the reliability) determined by the intrinsic energy constraints of the system.

Graphene for energy solutions and its industrialization.

PubMed

Wei, Di; Kivioja, Jani

2013-11-07

Graphene attracts intensive interest globally across academia and industry since the award of the Nobel Prize in Physics 2010. Within the last half decade, there has been an explosion in the number of scientific publications, patents and industry projects involved in this topic. On the other hand, energy is one of the biggest challenges of this century and related to the global sustainable economy. There are many reviews on graphene and its applications in various devices, however, few of the review articles connect the intrinsic properties of graphene with its energy. The IUPAC definition of graphene refers to a single carbon layer of graphite structure and its related superlative properties. A lot of scientific results on graphene published to date are actually dealing with multi-layer graphenes or reduced graphenes from insulating graphene oxides (GO) which contain defects and contaminants from the reactions and do not possess some of the intrinsic physical properties of pristine graphene. In this review, the focus is on the most recent advances in the study of pure graphene properties and novel energy solutions based on these properties. It also includes graphene metrology and analysis of both intellectual property and the value chain for the existing and forthcoming graphene industry that may cause a new 'industry revolution' with the strong and determined support of governments and industries across the European Union, U. S., Asia and many other countries in the world.

[Infinite optical thickness of dentine porcelain of IPS E.max A color series].

PubMed

Sun, Ting; Shao, Long-quan; Yi, Yuan-fu; Deng, Bin; Wen, Ning; Zhang, Wei-wei

2011-02-01

To determine the infinite optical thickness of dentine porcelain of IPS E.max A color series. Cylindrical dentine porcelain specimens of the IPS E.max A color series were prepared with a diameter of 13 mm and thickness of 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, and 5.0 mm. The chromatic value of all the specimens was determined with CM-5 spectrometer against standard black and white background. The chromatic aberration (deltaE) was calculated by regression equation. The infinite optical thickness of dentine porcelain of the IPS E.max A color series ranged from 2.341 to 3.333 mm for a deltaE of 1.0, and from 2.064 to 2.904 mm for a deltaE of 1.5. As the chromaticity or thickness increased, the influence by the background color decreased, and the color of specimens became gradually close to the intrinsic color. The thickness of the background dentine porcelain specimens must exceed its infinite optical thickness to represent the intrinsic color and avoid the influence by the extrinsic color.

How Fragile Is Consolidated Knowledge? Ben's Comparisons of Infinite Sets

ERIC Educational Resources Information Center

Tsamir, Pessia; Dreyfus, Tommy

2005-01-01

This article builds on two previous ones in which we presented the processes of construction and consolidation of one student's knowledge structures about comparisons of infinite sets, according to a recently proposed theory of abstraction. In the present article, we show that under slight variations of context, knowledge structures that have…

Black hole solutions in mimetic Born-Infeld gravity

NASA Astrophysics Data System (ADS)

Chen, Che-Yu; Bouhmadi-López, Mariam; Chen, Pisin

2018-01-01

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularity is found to be infinite.

Black hole solutions in mimetic Born-Infeld gravity.

PubMed

Chen, Che-Yu; Bouhmadi-López, Mariam; Chen, Pisin

2018-01-01

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularity is found to be infinite.

Black hole solutions in mimetic Born-Infeld gravity

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

Chen, Che-Yu; Bouhmadi-López, Mariam; Chen, Pisin

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. Here, we find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularitymore » is found to be infinite.« less

Black hole solutions in mimetic Born-Infeld gravity

DOE PAGES

Chen, Che-Yu; Bouhmadi-López, Mariam; Chen, Pisin

2018-01-23

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. Here, we find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularitymore » is found to be infinite.« less

78 FR 31986 - In the Matter of Energy Solutions Inc.; Order Approving Indirect Transfer of Import and Export...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-05-28

... NUCLEAR REGULATORY COMMISSION [Docket Nos. 11005621, 11005896, 11005620, 11005897, 11006061, 11005840, 11005941; License Nos. IW017, IW029, XW010, XW018, XW020, XCOM1211, XSOU8825] In the Matter of Energy Solutions Inc.; Order Approving Indirect Transfer of Import and Export Licenses I EnergySolutions...

An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere

NASA Astrophysics Data System (ADS)

Swidinsky, Andrei; Liu, Lifei

2017-11-01

We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.

Deep Energy Retrofit Guidance for the Building America Solutions Center

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

Less, Brennan; Walker, Iain

2015-01-01

The U.S. DOE Building America program has established a research agenda targeting market-relevant strategies to achieve 40% reductions in existing home energy use by 2030. Deep Energy Retrofits (DERs) are part of the strategy to meet and exceed this goal. DERs are projects that create new, valuable assets from existing residences, by bringing homes into alignment with the expectations of the 21st century. Ideally, high energy using, dated homes that are failing to provide adequate modern services to their owners and occupants (e.g., comfortable temperatures, acceptable humidity, clean, healthy), are transformed through comprehensive upgrades to the building envelope, services andmore » miscellaneous loads into next generation high performance homes. These guidance documents provide information to aid in the broader market adoption of DERs. They are intended for inclusion in the online resource the Building America Solutions Center (BASC). This document is an assemblage of multiple entries in the BASC, each of which addresses a specific aspect of Deep Energy Retrofit best practices for projects targeting at least 50% energy reductions. The contents are based upon a review of actual DERs in the U.S., as well as a mixture of engineering judgment, published guidance from DOE research in technologies and DERs, simulations of cost-optimal DERs, Energy Star and Consortium for Energy Efficiency (CEE) product criteria, and energy codes.« less

Electrolyte solutions including a phosphoranimine compound, and energy storage devices including same

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

Klaehn, John R.; Dufek, Eric J.; Rollins, Harry W.

An electrolyte solution comprising at least one phosphoranimine compound and a metal salt. The at least one phosphoranimine compound comprises a compound of the chemical structure ##STR00001## where X is an organosilyl group or a tert-butyl group and each of R.sup.1, R.sup.2, and R.sup.3 is independently selected from the group consisting of an alkyl group, an aryl group, an alkoxy group, or an aryloxy group. An energy storage device including the electrolyte solution is also disclosed.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result.

PubMed

Wu, Yang; Kelly, Damien P

2014-12-12

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of [Formula: see text] and [Formula: see text] type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of [Formula: see text] and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by [Formula: see text], where [Formula: see text] is the replica order. These circular replicas are shown to be fundamentally

Compactified cosmological simulations of the infinite universe

NASA Astrophysics Data System (ADS)

Rácz, Gábor; Szapudi, István; Csabai, István; Dobos, László

2018-06-01

We present a novel N-body simulation method that compactifies the infinite spatial extent of the Universe into a finite sphere with isotropic boundary conditions to follow the evolution of the large-scale structure. Our approach eliminates the need for periodic boundary conditions, a mere numerical convenience which is not supported by observation and which modifies the law of force on large scales in an unrealistic fashion. We demonstrate that our method outclasses standard simulations executed on workstation-scale hardware in dynamic range, it is balanced in following a comparable number of high and low k modes and, its fundamental geometry and topology match observations. Our approach is also capable of simulating an expanding, infinite universe in static coordinates with Newtonian dynamics. The price of these achievements is that most of the simulated volume has smoothly varying mass and spatial resolution, an approximation that carries different systematics than periodic simulations. Our initial implementation of the method is called StePS which stands for Stereographically projected cosmological simulations. It uses stereographic projection for space compactification and naive O(N^2) force calculation which is nevertheless faster to arrive at a correlation function of the same quality than any standard (tree or P3M) algorithm with similar spatial and mass resolution. The N2 force calculation is easy to adapt to modern graphics cards, hence our code can function as a high-speed prediction tool for modern large-scale surveys. To learn about the limits of the respective methods, we compare StePS with GADGET-2 running matching initial conditions.

Chain of point-like potentials in Script R3 and infiniteness of the number of bound states

NASA Astrophysics Data System (ADS)

Boitsev, A. A.; Popov, I. Yu; Sokolov, O. V.

2014-10-01

Infinite chain of point-like potentials having the Hamiltonian with infinite number of eigenvalues below the continuous spectrum is constructed. The background of the model is the theory of self-adjoint extensions of symmetric operators in the Hilbert space. The analogous example of the Hamiltonian is obtained for the system of three-dimensional waveguides coupled through point-like windows.

Specific Language Impairment as a Period of Extended Optional Infinitive.

ERIC Educational Resources Information Center

Rice, Mabel L.; And Others

1995-01-01

This study evaluated an Extended Optional Infinitive theory of specific language impairment (SLI) in children, which suggests that SLI children omit finiteness markers longer than do normally developing children. Comparison of 18 SLI 5-year olds with 2 normally developing groups (ages 5 and 3) found that SLI subjects omitted finiteness markers…

Studies in nonlinear problems of energy. Final report

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

Matkowsky, B.J.

1998-12-01

The author completed a successful research program on Nonlinear Problems of Energy, with emphasis on combustion and flame propagation. A total of 183 papers associated with the grant has appeared in the literature, and the efforts have twice been recognized by DOE`s Basic Science Division for Top Accomplishment. In the research program the author concentrated on modeling, analysis and computation of combustion phenomena, with particular emphasis on the transition from laminar to turbulent combustion. Thus he investigated the nonlinear dynamics and pattern formation in the successive stages of transition. He described the stability of combustion waves, and transitions to wavesmore » exhibiting progressively higher degrees of spatio-temporal complexity. Combustion waves are characterized by large activation energies, so that chemical reactions are significant only in thin layers, termed reaction zones. In the limit of infinite activation energy, the zones shrink to moving surfaces, termed fronts, which must be found during the course of the analysis, so that the problems are moving free boundary problems. The analytical studies were carried out for the limiting case with fronts, while the numerical studies were carried out for the case of finite, though large, activation energy. Accurate resolution of the solution in the reaction zone(s) is essential, otherwise false predictions of dynamical behavior are possible. Since the reaction zones move, and their location is not known a-priori, the author has developed adaptive pseudo-spectral methods, which have proven to be very useful for the accurate, efficient computation of solutions of combustion, and other, problems. The approach is based on a combination of analytical and numerical methods. The numerical computations built on and extended the information obtained analytically. Furthermore, the solutions obtained analytically served as benchmarks for testing the accuracy of the solutions determined computationally

Spherically symmetric analysis on open FLRW solution in non-linear massive gravity

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

Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin, E-mail: chienichiang@berkeley.edu, E-mail: izumi@phys.ntu.edu.tw, E-mail: chen@slac.stanford.edu

2012-12-01

We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity frommore » general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.« less

Quantum field theory with infinite component local fields as an alternative to the string theories

NASA Astrophysics Data System (ADS)

Krasnikov, N. V.

1987-09-01

We show that the introduction of the infinite component local fields with higher-order derivatives in the interaction makes the theory completely ultraviolet finite. For the γ5-anomalous theories the introduction of the infinite component field makes the theory renormalizable or even superrenormalizable. I am indebted to J. Ambjōrn, P. Di Vecchia, H.B. Nielsen and L. Rozhansky for useful discussions. It is a pleasure to thank the Niels Bohr Institute (Copenhagen) where this work was completed for kind hospitality.

On exact solutions for some oscillating motions of a generalized Oldroyd-B fluid

NASA Astrophysics Data System (ADS)

Khan, M.; Anjum, Asia; Qi, Haitao; Fetecau, C.

2010-02-01

This paper deals with exact solutions for some oscillating motions of a generalized Oldroyd-B fluid. The fractional calculus approach is used in the constitutive relationship of fluid model. Analytical expressions for the velocity field and the corresponding shear stress for flows due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient are determined using Fourier sine and Laplace transforms. The obtained solutions are presented under integral and series forms in terms of the Mittag-Leffler functions. For α = β = 1, our solutions tend to the similar solutions for ordinary Oldroyd-B fluid. A comparison between generalized and ordinary Oldroyd-B fluids is shown by means of graphical illustrations.

The Hartree Equation for Infinitely Many Particles I. Well-Posedness Theory

NASA Astrophysics Data System (ADS)

Lewin, Mathieu; Sabin, Julien

2015-02-01

We show local and global well-posedness results for the Hartree equation where γ is a bounded self-adjoint operator on , ρ γ ( x) = γ( x, x) and w is a smooth short-range interaction potential. The initial datum γ(0) is assumed to be a perturbation of a translation-invariant state γ f = f(-Δ) which describes a quantum system with an infinite number of particles, such as the Fermi sea at zero temperature, or the Fermi-Dirac and Bose-Einstein gases at positive temperature. Global well-posedness follows from the conservation of the relative (free) energy of the state γ( t), counted relatively to the stationary state γ f . We indeed use a general notion of relative entropy, which allows us to treat a wide class of stationary states f(-Δ). Our results are based on a Lieb-Thirring inequality at positive density and on a recent Strichartz inequality for orthonormal functions, which are both due to Frank, Lieb, Seiringer and the first author of this article.

Comparative study of solute trapping and Gibbs free energy changes at the phase interface during alloy solidification under local nonequilibrium conditions

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

Sobolev, S. L., E-mail: sobolev@icp.ac.ru

An analytical model has been developed to describe the influence of solute trapping during rapid alloy solidification on the components of the Gibbs free energy change at the phase interface with emphasis on the solute drag energy. For relatively low interface velocity V < V{sub D}, where V{sub D} is the characteristic diffusion velocity, all the components, namely mixing part, local nonequilibrium part, and solute drag, significantly depend on solute diffusion and partitioning. When V ≥ V{sub D}, the local nonequilibrium effects lead to a sharp transition to diffusionless solidification. The transition is accompanied by complete solute trapping and vanishingmore » solute drag energy, i.e. partitionless and “dragless” solidification.« less

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice.

PubMed

Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

2016-10-10

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic-to-paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models.

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice

PubMed Central

Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

2016-01-01

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic–to–paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models. PMID:27721435

Bifurcating fronts for the Taylor-Couette problem in infinite cylinders

NASA Astrophysics Data System (ADS)

Hărăguş-Courcelle, M.; Schneider, G.

We show the existence of bifurcating fronts for the weakly unstable Taylor-Couette problem in an infinite cylinder. These fronts connect a stationary bifurcating pattern, here the Taylor vortices, with the trivial ground state, here the Couette flow. In order to show the existence result we improve a method which was already used in establishing the existence of bifurcating fronts for the Swift-Hohenberg equation by Collet and Eckmann, 1986, and by Eckmann and Wayne, 1991. The existence proof is based on spatial dynamics and center manifold theory. One of the difficulties in applying center manifold theory comes from an infinite number of eigenvalues on the imaginary axis for vanishing bifurcation parameter. But nevertheless, a finite dimensional reduction is possible, since the eigenvalues leave the imaginary axis with different velocities, if the bifurcation parameter is increased. In contrast to previous work we have to use normalform methods and a non-standard cut-off function to obtain a center manifold which is large enough to contain the bifurcating fronts.

Generalized thermoelastic problem of an infinite body with a spherical cavity under dual-phase-lags

NASA Astrophysics Data System (ADS)

Karmakar, R.; Sur, A.; Kanoria, M.

2016-07-01

The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord-Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the state-space approach. The expressions for the conductive temperature and elongation are obtained at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord-Shulman and dual-phase-lag models.

Global low-energy weak solution and large-time behavior for the compressible flow of liquid crystals

NASA Astrophysics Data System (ADS)

Wu, Guochun; Tan, Zhong

2018-06-01

In this paper, we consider the weak solution of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in R3. When the initial data are of small energy and initial density is positive and essentially bounded, we prove the existence of a global weak solution in R3. The large-time behavior of a global weak solution is also established.

Modifying Poisson equation for near-solute dielectric polarization and solvation free energy

NASA Astrophysics Data System (ADS)

Yang, Pei-Kun

2016-06-01

The dielectric polarization P is important for calculating the stability of protein conformation and the binding affinity of protein-protein/ligand interactions and for exploring the nonthermal effect of an external electric field on biomolecules. P was decomposed into the product of the electric dipole moment per molecule p; bulk solvent density Nbulk; and relative solvent molecular density g. For a molecular solute, 4πr2p(r) oscillates with the distance r to the solute, and g(r) has a large peak in the near-solute region, as observed in molecular dynamics (MD) simulations. Herein, the Poisson equation was modified for computing p based on the modified Gauss's law of Maxwell's equations, and the potential of the mean force was used for computing g. For one or two charged atoms in a water cluster, the solvation free energies of the solutes obtained by these equations were similar to those obtained from MD simulations.

Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c = m/2

NASA Astrophysics Data System (ADS)

Minami, Kazuhiko

2017-12-01

An infinite number of spin chains are solved and it is derived that the ground-state phase transitions belong to the universality classes with central charge c = m / 2, where m is an integer. The models are diagonalized by automatically obtained transformations, many of which are different from the Jordan-Wigner transformation. The free energies, correlation functions, string order parameters, exponents, central charges, and the phase diagram are obtained. Most of the examples consist of the stabilizers of the cluster state. A unified structure of the one-dimensional XY and cluster-type spin chains is revealed, and other series of solvable models can be obtained through this formula.

Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach

NASA Technical Reports Server (NTRS)

Balas, M. J.; Kaufman, H.; Wen, J.

1985-01-01

A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.

Development of deterministic transport methods for low energy neutrons for shielding in space

NASA Technical Reports Server (NTRS)

Ganapol, Barry

1993-01-01

Transport of low energy neutrons associated with the galactic cosmic ray cascade is analyzed in this dissertation. A benchmark quality analytical algorithm is demonstrated for use with BRYNTRN, a computer program written by the High Energy Physics Division of NASA Langley Research Center, which is used to design and analyze shielding against the radiation created by the cascade. BRYNTRN uses numerical methods to solve the integral transport equations for baryons with the straight-ahead approximation, and numerical and empirical methods to generate the interaction probabilities. The straight-ahead approximation is adequate for charged particles, but not for neutrons. As NASA Langley improves BRYNTRN to include low energy neutrons, a benchmark quality solution is needed for comparison. The neutron transport algorithm demonstrated in this dissertation uses the closed-form Green's function solution to the galactic cosmic ray cascade transport equations to generate a source of neutrons. A basis function expansion for finite heterogeneous and semi-infinite homogeneous slabs with multiple energy groups and isotropic scattering is used to generate neutron fluxes resulting from the cascade. This method, called the FN method, is used to solve the neutral particle linear Boltzmann transport equation. As a demonstration of the algorithm coded in the programs MGSLAB and MGSEMI, neutron and ion fluxes are shown for a beam of fluorine ions at 1000 MeV per nucleon incident on semi-infinite and finite aluminum slabs. Also, to demonstrate that the shielding effectiveness against the radiation from the galactic cosmic ray cascade is not directly proportional to shield thickness, a graph of transmitted total neutron scalar flux versus slab thickness is shown. A simple model based on the nuclear liquid drop assumption is used to generate cross sections for the galactic cosmic ray cascade. The ENDF/B V database is used to generate the total and scattering cross sections for neutrons in

On quasi-periodic solutions for generalized Boussinesq equation with quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Shi, Yanling; Xu, Junxiang; Xu, Xindong

2015-02-01

In this paper, one-dimensional generalized Boussinesq equation: utt - uxx + (u2 + uxx)xx = 0 with boundary conditions ux(0, t) = ux(π, t) = uxxx(0, t) = uxxx(π, t) = 0 is considered. It is proved that the equation admits a Whitney smooth family of small-amplitude quasi-periodic solutions with 2-dimensional Diophantine frequencies. The proof is based on an infinite dimensional Kolmogorov-Arnold-Moser theorem and Birkhoff normal form.

Computation of the free energy due to electron density fluctuation of a solute in solution: A QM/MM method with perturbation approach combined with a theory of solutions

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

Suzuoka, Daiki; Takahashi, Hideaki, E-mail: hideaki@m.tohoku.ac.jp; Morita, Akihiro

2014-04-07

We developed a perturbation approach to compute solvation free energy Δμ within the framework of QM (quantum mechanical)/MM (molecular mechanical) method combined with a theory of energy representation (QM/MM-ER). The energy shift η of the whole system due to the electronic polarization of the solute is evaluated using the second-order perturbation theory (PT2), where the electric field formed by surrounding solvent molecules is treated as the perturbation to the electronic Hamiltonian of the isolated solute. The point of our approach is that the energy shift η, thus obtained, is to be adopted for a novel energy coordinate of the distributionmore » functions which serve as fundamental variables in the free energy functional developed in our previous work. The most time-consuming part in the QM/MM-ER simulation can be, thus, avoided without serious loss of accuracy. For our benchmark set of molecules, it is demonstrated that the PT2 approach coupled with QM/MM-ER gives hydration free energies in excellent agreements with those given by the conventional method utilizing the Kohn-Sham SCF procedure except for a few molecules in the benchmark set. A variant of the approach is also proposed to deal with such difficulties associated with the problematic systems. The present approach is also advantageous to parallel implementations. We examined the parallel efficiency of our PT2 code on multi-core processors and found that the speedup increases almost linearly with respect to the number of cores. Thus, it was demonstrated that QM/MM-ER coupled with PT2 deserves practical applications to systems of interest.« less

Influence of chemical disorder on energy dissipation and defect evolution in concentrated solid solution alloys

PubMed Central

Zhang, Yanwen; Stocks, G. Malcolm; Jin, Ke; Lu, Chenyang; Bei, Hongbin; Sales, Brian C.; Wang, Lumin; Béland, Laurent K.; Stoller, Roger E.; Samolyuk, German D.; Caro, Magdalena; Caro, Alfredo; Weber, William J.

2015-01-01

A grand challenge in materials research is to understand complex electronic correlation and non-equilibrium atomic interactions, and how such intrinsic properties and dynamic processes affect energy transfer and defect evolution in irradiated materials. Here we report that chemical disorder, with an increasing number of principal elements and/or altered concentrations of specific elements, in single-phase concentrated solid solution alloys can lead to substantial reduction in electron mean free path and orders of magnitude decrease in electrical and thermal conductivity. The subsequently slow energy dissipation affects defect dynamics at the early stages, and consequentially may result in less deleterious defects. Suppressed damage accumulation with increasing chemical disorder from pure nickel to binary and to more complex quaternary solid solutions is observed. Understanding and controlling energy dissipation and defect dynamics by altering alloy complexity may pave the way for new design principles of radiation-tolerant structural alloys for energy applications. PMID:26507943

Assistance Focus: Asia/Pacific Region; Clean Energy Solutions Center (CESC)

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

None

The Clean Energy Solutions Center Ask an Expert service connects governments seeking policy information and advice with one of more than 30 global policy experts who can provide reliable and unbiased quick-response advice and information. The service is available at no cost to government agency representatives from any country and the technical institutes assisting them. This publication presents summaries of assistance provided to governments in the Asia/Pacific region, including the benefits of that assistance.

Infinite order quantum-gravitational correlations

NASA Astrophysics Data System (ADS)

Knorr, Benjamin

2018-06-01

A new approximation scheme for nonperturbative renormalisation group equations for quantum gravity is introduced. Correlation functions of arbitrarily high order can be studied by resolving the full dependence of the renormalisation group equations on the fluctuation field (graviton). This is reminiscent of a local potential approximation in O(N)-symmetric field theories. As a first proof of principle, we derive the flow equation for the ‘graviton potential’ induced by a conformal fluctuation and corrections induced by a gravitational wave fluctuation. Indications are found that quantum gravity might be in a non-metric phase in the deep ultraviolet. The present setup significantly improves the quality of previous fluctuation vertex studies by including infinitely many couplings, thereby testing the reliability of schemes to identify different couplings to close the equations, and represents an important step towards the resolution of the Nielsen identity. The setup further allows one, in principle, to address the question of putative gravitational condensates.

Flow adjustment inside large finite-size wind farms approaching the infinite wind farm regime

NASA Astrophysics Data System (ADS)

Wu, Ka Ling; Porté-Agel, Fernando

2017-04-01

Due to the increasing number and the growing size of wind farms, the distance among them continues to decrease. Thus, it is necessary to understand how these large finite-size wind farms and their wakes could interfere the atmospheric boundary layer (ABL) dynamics and adjacent wind farms. Fully-developed flow inside wind farms has been extensively studied through numerical simulations of infinite wind farms. The transportation of momentum and energy is only vertical and the advection of them is neglected in these infinite wind farms. However, less attention has been paid to examine the length of wind farms required to reach such asymptotic regime and the ABL dynamics in the leading and trailing edges of the large finite-size wind farms. Large eddy simulations are performed in this study to investigate the flow adjustment inside large finite-size wind farms in conventionally-neutral boundary layer with the effect of Coriolis force and free-atmosphere stratification from 1 to 5 K/km. For the large finite-size wind farms considered in the present work, when the potential temperature lapse rate is 5 K/km, the wind farms exceed the height of the ABL by two orders of magnitude for the incoming flow inside the farms to approach the fully-developed regime. An entrance fetch of approximately 40 times of the ABL height is also required for such flow adjustment. At the fully-developed flow regime of the large finite-size wind farms, the flow characteristics match those of infinite wind farms even though they have different adjustment length scales. The role of advection at the entrance and exit regions of the large finite-size wind farms is also examined. The interaction between the internal boundary layer developed above the large finite-size wind farms and the ABL under different potential temperature lapse rates are compared. It is shown that the potential temperature lapse rate plays a role in whether the flow inside the large finite-size wind farms adjusts to the fully

High-Capacity Hydrogen-Based Green-Energy Storage Solutions For The Grid Balancing

NASA Astrophysics Data System (ADS)

D'Errico, F.; Screnci, A.

One of the current main challenges in green-power storage and smart grids is the lack of effective solutions for accommodating the unbalance between renewable energy sources, that offer intermittent electricity supply, and a variable electricity demand. Energy management systems have to be foreseen for the near future, while they still represent a major challenge. Integrating intermittent renewable energy sources, by safe and cost-effective energy storage systems based on solid state hydrogen is today achievable thanks to recently some technology breakthroughs. Optimized solid storage method made of magnesium-based hydrides guarantees a very rapid absorption and desorption kinetics. Coupled with electrolyzer technology, high-capacity storage of green-hydrogen is therefore practicable. Besides these aspects, magnesium has been emerging as environmentally friend energy storage method to sustain integration, monitoring and control of large quantity of GWh from high capacity renewable generation in the EU.

High-Capacity Hydrogen-Based Green-Energy Storage Solutions for the Grid Balancing

NASA Astrophysics Data System (ADS)

D'Errico, F.; Screnci, A.

One of the current main challenges in green-power storage and smart grids is the lack of effective solutions for accommodating the unbalance between renewable energy sources, that offer intermittent electricity supply, and a variable electricity demand. Energy management systems have to be foreseen for the near future, while they still represent a major challenge. Integrating intermittent renewable energy sources, by safe and cost-effective energy storage systems based on solid state hydrogen is today achievable thanks to recently some technology breakthroughs. Optimized solid storage method made of magnesium-based hydrides guarantees a very rapid absorption and desorption kinetics. Coupled with electrolyzer technology, high-capacity storage of green-hydrogen is therefore practicable. Besides these aspects, magnesium has been emerging as environmentally friend energy storage method to sustain integration, monitoring and control of large quantity of GWh from high capacity renewable generation in the EU.

ASYMPTOTIC STEADY-STATE SOLUTION TO A BOW SHOCK WITH AN INFINITE MACH NUMBER

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

Yalinewich, Almog; Sari, Re’em

2016-08-01

The problem of a cold gas flowing past a stationary obstacle is considered. We study the bow shock that forms around the obstacle and show that at large distances from the obstacle the shock front forms a parabolic solid of revolution. The profiles of the hydrodynamic variables in the interior of the shock are obtained by solution of the hydrodynamic equations in parabolic coordinates. The results are verified with a hydrodynamic simulation. The drag force on the obstacle is also calculated. Finally, we use these results to model the bow shock around an isolated neutron star.

Reimagining Energy in the North: Developing Solutions for Improving Renewable Energy Security in Northern Communities

NASA Astrophysics Data System (ADS)

Creed, I. F.; Poelzer, G.; Noble, B.; Beatty, B.; Belcher, K.; Chung, T.; Loring, P. A.

2017-12-01

The global energy sector is at a crossroads. Efforts to reduce greenhouse gas emissions, volatile fossil fuel prices, the emergence of sustainability markets, and advances in renewable energy technologies are setting the foundation for what could be one of the most significant societal transitions since the industrial revolution. There is a growing movement to "re-energize" Canada, through embracing pathways to facilitate a societal transition a low-carbon future. For example, circumpolar jurisdictions are poised for a transition to renewable energy. There are more than 250 remote, off-grid communities across Canada's North, of which approximately 170 are Indigenous, that rely largely on diesel-fueled generators. Diesel-fueled generation is generally reliable when properly maintained; however, supply is limited, infrastructure is at capacity or in need of major upgrading, and the volatile price of fuel can mean significant social, community and economic opportunity loss. Renewable energy projects offer one possible opportunity to address these challenges. But, given the challenges of human capacity, limited fiscal resources, and regulatory barriers, how can Northern communities participate in the global energy transition and not be left behind? To answer this question, the University of Saskatchewan, together with partners from the circumpolar North, are leading an initiative to develop a cross-sectoral and multi-national consortium of communities, utilities, industries, governments, and academics engaged in renewable energy in the North. This consortium will reimagine energy security in the North by co-creating and brokering the knowledge and understanding to design renewable energy systems that enhance social and economic value. Northern communities and utilities will learn directly from other northern communities and utilities across Canada and internationally about what can be achieved in renewable energy development and the solutions to current and future

Energy Transitions | Integrated Energy Solutions | NREL

Science.gov Websites

clean energy access to remote populations across West Africa. NREL Supports Effort to Take Distributed develops and implements pilot projects to accelerate the development of distributed photovoltaics Renewable Energy into India's Electric Grid Volume 1 Volume 2 Designing Distributed Generation in Mexico

The Solutions Project: Educating the Public and Policy Makers About Solutions to Global Warming, Air Pollution, and Energy Security

NASA Astrophysics Data System (ADS)

Jacobson, M. Z.

2015-12-01

Three major global problems of our times are global warming, air pollution mortality and morbidity, and energy insecurity. Whereas, policy makers with the support of the public must implement solutions to these problems, it is scientists and engineers who are best equipped to evaluate technically sound, optimal, and efficient solutions. Yet, a disconnect exists between information provided by scientists and engineers and policies implemented. Part of the reason is that scientific information provided to policy makers and the public is swamped out by information provided by lobbyists and another part is the difficulty in providing information to the hundreds of millions of people who need it rather than to just a few thousand. What other ways are available, aside from issuing press releases on scientific papers, for scientists to disseminate information? Three growing methods are through social media, creative media, and storytelling. The Solutions Project is a non-profit non-governmental organization whose goal is to bring forth scientific information about 100% clean, renewable energy plans to the public, businesses, and policy makers using these and related tools. Through the use of social media, the development of engaging internet and video content, and storytelling, the group hopes to increase the dissemination of information for social good. This talk discusses the history and impacts to date of this group and its methods. Please see www.thesolutionsproject.org and 100.org for more information.

Exact solution for a non-Markovian dissipative quantum dynamics.

PubMed

Ferialdi, Luca; Bassi, Angelo

2012-04-27

We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.

Family Histories of Children with SLI Who Show Extended Optional Infinitives.

ERIC Educational Resources Information Center

Rice, Mabel L.; Haney, Karla R.; Wexler, Kenneth

1998-01-01

A study examined family histories of 31 children with specific language impairments who were known to have particular grammatical limitations in a core feature of grammatical acquisition, a stage known as Extended Optional Infinitives. The families had significantly more speech and language difficulties, as well as language-related difficulties,…

On predicting receptivity to surface roughness in a compressible infinite swept wing boundary layer

NASA Astrophysics Data System (ADS)

Thomas, Christian; Mughal, Shahid; Ashworth, Richard

2017-03-01

The receptivity of crossflow disturbances on an infinite swept wing is investigated using solutions of the adjoint linearised Navier-Stokes equations. The adjoint based method for predicting the magnitude of stationary disturbances generated by randomly distributed surface roughness is described, with the analysis extended to include both surface curvature and compressible flow effects. Receptivity is predicted for a broad spectrum of spanwise wavenumbers, variable freestream Reynolds numbers, and subsonic Mach numbers. Curvature is found to play a significant role in the receptivity calculations, while compressible flow effects are only found to marginally affect the initial size of the crossflow instability. A Monte Carlo type analysis is undertaken to establish the mean amplitude and variance of crossflow disturbances generated by the randomly distributed surface roughness. Mean amplitudes are determined for a range of flow parameters that are maximised for roughness distributions containing a broad spectrum of roughness wavelengths, including those that are most effective in generating stationary crossflow disturbances. A control mechanism is then developed where the short scale roughness wavelengths are damped, leading to significant reductions in the receptivity amplitude.

A table-top monochromator for tunable femtosecond XUV pulses generated in a semi-infinite gas cell: Experiment and simulations

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

Conta, A. von; Huppert, M.; Wörner, H. J.

2016-07-15

We present a new design of a time-preserving extreme-ultraviolet (XUV) monochromator using a semi-infinite gas cell as a source. The performance of this beamline in the photon-energy range of 20 eV–42 eV has been characterized. We have measured the order-dependent XUV pulse durations as well as the flux and the spectral contrast. XUV pulse durations of ≤40 fs using 32 fs, 800 nm driving pulses were measured on the target. The spectral contrast was better than 100 over the entire energy range. A simple model based on the strong-field approximation is presented to estimate different contributions to the measured XUVmore » pulse duration. On-axis phase-matching calculations are used to rationalize the variation of the photon flux with pressure and intensity.« less

Generalized essential energy space random walks to more effectively accelerate solute sampling in aqueous environment

NASA Astrophysics Data System (ADS)

Lv, Chao; Zheng, Lianqing; Yang, Wei

2012-01-01

Molecular dynamics sampling can be enhanced via the promoting of potential energy fluctuations, for instance, based on a Hamiltonian modified with the addition of a potential-energy-dependent biasing term. To overcome the diffusion sampling issue, which reveals the fact that enlargement of event-irrelevant energy fluctuations may abolish sampling efficiency, the essential energy space random walk (EESRW) approach was proposed earlier. To more effectively accelerate the sampling of solute conformations in aqueous environment, in the current work, we generalized the EESRW method to a two-dimension-EESRW (2D-EESRW) strategy. Specifically, the essential internal energy component of a focused region and the essential interaction energy component between the focused region and the environmental region are employed to define the two-dimensional essential energy space. This proposal is motivated by the general observation that in different conformational events, the two essential energy components have distinctive interplays. Model studies on the alanine dipeptide and the aspartate-arginine peptide demonstrate sampling improvement over the original one-dimension-EESRW strategy; with the same biasing level, the present generalization allows more effective acceleration of the sampling of conformational transitions in aqueous solution. The 2D-EESRW generalization is readily extended to higher dimension schemes and employed in more advanced enhanced-sampling schemes, such as the recent orthogonal space random walk method.

First-principles calculations for XAS of infinite-layer iron oxides

NASA Astrophysics Data System (ADS)

Kodera, Mitsuru; Shishidou, Tatsuya; Oguchi, Tamio

2011-03-01

The oxygen defect perovskite SrFe O3 - x shows various properties such as the giant magnetoresistance effect and the thermoelectric effect. It had been believed that the oxygen content in SrFe O3 - x changes up to x = 0.5 . Recently, Tsujimoto et al . have succeeded in synthesizing the infinite-layer iron oxide SrFe O2 . SrFe O2 has a square-planar oxygen coordination, while the iron oxides usually have the tetrahedral and octahedral coordination. CaFe O2 has also infinite layer structure and the same magnetic ordering as SrFe O2 . However, it is suggested that the oxygen coordination of CaFe O2 is different from that of SrFe O2 . In order to investigate the electronic structure of iron in (Ca, Sr) Fe O2 , the x-ray absorption spectroscopy (XAS) spectrum has been measured. In this work, we perform the calculation for XAS spectrum near the Fe-K edge of (Ca, Sr) Fe O2 using the first-principles calculations. We compare the results with the experiment and discuss the electronic structure of iron in (Ca, Sr) Fe O2 .

Private algebras in quantum information and infinite-dimensional complementarity

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

Crann, Jason, E-mail: jason-crann@carleton.ca; Laboratoire de Mathématiques Paul Painlevé–UMR CNRS 8524, UFR de Mathématiques, Université Lille 1–Sciences et Technologies, 59655 Villeneuve d’Ascq Cédex; Kribs, David W., E-mail: dkribs@uoguelph.ca

We introduce a generalized framework for private quantum codes using von Neumann algebras and the structure of commutants. This leads naturally to a more general notion of complementary channel, which we use to establish a generalized complementarity theorem between private and correctable subalgebras that applies to both the finite and infinite-dimensional settings. Linear bosonic channels are considered and specific examples of Gaussian quantum channels are given to illustrate the new framework together with the complementarity theorem.

Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies

NASA Astrophysics Data System (ADS)

Chang, Jing; Gao, Yixian; Li, Yong

2015-05-01

Consider the one dimensional nonlinear beam equation utt + uxxxx + mu + u3 = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form.

Determination of gas-liquid partition coefficients of several organic solutes in trihexyl(tetradecyl)phosphonium bromide using capillary gas chromatography columns.

PubMed

Ronco, Nicolás R; Menestrina, Fiorella; Romero, Lílian M; Castells, Cecilia B

2017-06-09

In this paper, we report gas-liquid partition constants for thirty-five volatile organic solutes in the room temperature ionic liquid trihexyl(tetradecyl)phosphonium bromide measured by gas-liquid chromatography using capillary columns. The relative contribution of gas-liquid partition and interfacial adsorption to retention was evaluated through the use of columns with different the phase ratio. Four capillary columns with exactly known phase ratios were constructed and employed to measure the solute retention factors at four temperatures between 313.15 and 343.15K. The partition coefficients were calculated from the slopes of the linear regression between solute retention factors and the reciprocal of phase ratio at a given temperature according to the gas-liquid chromatographic theory. Gas-liquid interfacial adsorption was detected for a few solutes and it has been considered for the calculations of partition coefficient. Reliable solute's infinite dilution activity coefficients can be obtained when retention data are determined by a unique partitioning mechanism. The partial molar excess enthalpies at infinite dilution have been estimated from the dependence of experimental values of solute activity coefficients with the column temperature. A thorough discussion of the uncertainties of the experimental measurements and the main advantages of the use of capillary columns to acquire the aforementioned relevant thermodynamic information was performed. Copyright © 2017 Elsevier B.V. All rights reserved.

The infinite range Heisenberg model and high temperature superconductivity

NASA Astrophysics Data System (ADS)

Tahir-Kheli, Jamil

1992-01-01

The thesis deals with the theory of high temperature superconductivity from the standpoint of three-band Hubbard models.Chapter 1 of the thesis proposes a strongly coupled variational wavefunction that has the three-spin system of an oxygen hole and its two neighboring copper spins in a doublet and the background Cu spins in an eigenstate of the infinite range antiferromagnet. This wavefunction is expected to be a good "zeroth order" wavefunction in the superconducting regime of dopings. The three-spin polaron is stabilized by the hopping terms rather than the copper-oxygen antiferromagnetic coupling Jpd. Considering the effect of the copper-copper antiferromagnetic coupling Jdd, we show that the three-spin polaron cannot be pure Emery (Dg), but must have a non-negligible amount of doublet-u (Du) character for hopping stabilization. Finally, an estimate is made for the magnitude of the attractive coupling of oxygen holes.Chapter 2 presents an exact solution to a strongly coupled Hamiltonian for the motion of oxygen holes in a 1-D Cu-O lattice. The Hamiltonian separates into two pieces: one for the spin degrees of freedom of the copper and oxygen holes, and the other for the charge degrees of freedom of the oxygen holes. The spinon part becomes the Heisenberg antiferromagnet in 1-D that is soluble by the Bethe Ansatz. The holon piece is also soluble by a Bethe Ansatz with simple algebraic relations for the phase shifts.Finally, we show that the nearest neighbor Cu-Cu spin correlation increases linearly with doping and becomes positive at x [...] 0.70.

Self-similar cosmological solutions with dark energy. I. Formulation and asymptotic analysis

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

Harada, Tomohiro; Maeda, Hideki; Centro de Estudios Cientificos

2008-01-15

Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=({gamma}-1){mu} with 0<{gamma}<2/3. This corresponds to a 'dark energy' fluid and the Friedmann solution is accelerated in this case due to antigravity. This extends the previous analysis of spherically symmetric self-similar solutions for fluids with positive pressure ({gamma}>1). However, in the latter case there is an additional parameter associated with the weak discontinuity at the sonic point and the solutions are only asymptotically 'quasi-Friedmann',more » in the sense that they exhibit an angle deficit at large distances. In the 0<{gamma}<2/3 case, there is no sonic point and there exists a one-parameter family of solutions which are genuinely asymptotically Friedmann at large distances. We find eight classes of asymptotic behavior: Friedmann or quasi-Friedmann or quasistatic or constant-velocity at large distances, quasi-Friedmann or positive-mass singular or negative-mass singular at small distances, and quasi-Kantowski-Sachs at intermediate distances. The self-similar asymptotically quasistatic and quasi-Kantowski-Sachs solutions are analytically extendible and of great cosmological interest. We also investigate their conformal diagrams. The results of the present analysis are utilized in an accompanying paper to obtain and physically interpret numerical solutions.« less

Using ‘particle in a box’ models to calculate energy levels in semiconductor quantum well structures

NASA Astrophysics Data System (ADS)

Ebbens, A. T.

2018-07-01

Although infinite potential ‘particle in a box’ models are widely used to introduce quantised energy levels their predictions cannot be quantitatively compared with atomic emission spectra. Here, this problem is overcome by describing how both infinite and finite potential well models can be used to calculate the confined energy levels of semiconductor quantum wells. This is done by using physics and mathematics concepts that are accessible to pre-university students. The results of the models are compared with experimental data and their accuracy discussed.

Revealing infinite derivative gravity's true potential: The weak-field limit around de Sitter backgrounds

NASA Astrophysics Data System (ADS)

Edholm, James

2018-03-01

General Relativity is known to produce singularities in the potential generated by a point source. Our universe can be modeled as a de Sitter (dS) metric and we show that ghost-free infinite derivative gravity (IDG) produces a nonsingular potential around a dS background, while returning to the GR prediction at large distances. We also show that although there are an apparently infinite number of coefficients in the theory, only a finite number actually affect the predictions. By writing the linearized equations of motion in a simplified form, we find that at distances below the Hubble length scale, the difference between the IDG potential around a flat background and around a de Sitter background is negligible.

On an adaptive preconditioned Crank-Nicolson MCMC algorithm for infinite dimensional Bayesian inference

NASA Astrophysics Data System (ADS)

Hu, Zixi; Yao, Zhewei; Li, Jinglai

2017-03-01

Many scientific and engineering problems require to perform Bayesian inference for unknowns of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary slow under the mesh refinement, which is referred to as being dimension dependent. To this end, a family of dimensional independent MCMC algorithms, known as the preconditioned Crank-Nicolson (pCN) methods, were proposed to sample the infinite dimensional parameters. In this work we develop an adaptive version of the pCN algorithm, where the covariance operator of the proposal distribution is adjusted based on sampling history to improve the simulation efficiency. We show that the proposed algorithm satisfies an important ergodicity condition under some mild assumptions. Finally we provide numerical examples to demonstrate the performance of the proposed method.

First Detected Arrival of a Quantum Walker on an Infinite Line

NASA Astrophysics Data System (ADS)

Thiel, Felix; Barkai, Eli; Kessler, David A.

2018-01-01

The first detection of a quantum particle on a graph is shown to depend sensitively on the distance ξ between the detector and initial location of the particle, and on the sampling time τ . Here, we use the recently introduced quantum renewal equation to investigate the statistics of first detection on an infinite line, using a tight-binding lattice Hamiltonian with nearest-neighbor hops. Universal features of the first detection probability are uncovered and simple limiting cases are analyzed. These include the large ξ limit, the small τ limit, and the power law decay with the attempt number of the detection probability over which quantum oscillations are superimposed. For large ξ the first detection probability assumes a scaling form and when the sampling time is equal to the inverse of the energy band width nonanalytical behaviors arise, accompanied by a transition in the statistics. The maximum total detection probability is found to occur for τ close to this transition point. When the initial location of the particle is far from the detection node we find that the total detection probability attains a finite value that is distance independent.

Nonexistence of global solutions of abstract wave equations with high energies.

PubMed

Esquivel-Avila, Jorge A

2017-01-01

We consider an undamped second order in time evolution equation. For any positive value of the initial energy, we give sufficient conditions to conclude nonexistence of global solutions. The analysis is based on a differential inequality. The success of our result is based in a detailed analysis which is different from the ones commonly used to prove blow-up. Several examples are given improving known results in the literature.

An Introduction to Differentials Based on Hyperreal Numbers and Infinite Microscopes

ERIC Educational Resources Information Center

Henry, Valerie

2010-01-01

In this article, we propose to introduce the differential of a function through a non-classical way, lying on hyperreals and infinite microscopes. This approach is based on the developments of nonstandard analysis, wants to be more intuitive than the classical one and tries to emphasize the functional and geometric aspects of the differential. In…

An infinite set of Ward identities for adiabatic modes in cosmology

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

Hinterbichler, Kurt; Hui, Lam; Khoury, Justin, E-mail: khinterbichler@perimeterinstitute.ca, E-mail: lh399@columbia.edu, E-mail: jkhoury@sas.upenn.edu

2014-01-01

We show that the correlation functions of any single-field cosmological model with constant growing-modes are constrained by an infinite number of novel consistency relations, which relate N+1-point correlation functions with a soft-momentum scalar or tensor mode to a symmetry transformation on N-point correlation functions of hard-momentum modes. We derive these consistency relations from Ward identities for an infinite tower of non-linearly realized global symmetries governing scalar and tensor perturbations. These symmetries can be labeled by an integer n. At each order n, the consistency relations constrain — completely for n = 0,1, and partially for n ≥ 2 — themore » q{sup n} behavior of the soft limits. The identities at n = 0 recover Maldacena's original consistency relations for a soft scalar and tensor mode, n = 1 gives the recently-discovered conformal consistency relations, and the identities for n ≥ 2 are new. As a check, we verify directly that the n = 2 identity is satisfied by known correlation functions in slow-roll inflation.« less

Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models

NASA Astrophysics Data System (ADS)

Luther, K.; Haitjema, H. M.

2000-04-01

We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.

System solution to improve energy efficiency of HVAC systems

NASA Astrophysics Data System (ADS)

Chretien, L.; Becerra, R.; Salts, N. P.; Groll, E. A.

2017-08-01

According to recent surveys, heating and air conditioning systems account for over 45% of the total energy usage in US households. Three main types of HVAC systems are available to homeowners: (1) fixed-speed systems, where the compressor cycles on and off to match the cooling load; (2) multi-speed (typically, two-speed) systems, where the compressor can operate at multiple cooling capacities, leading to reduced cycling; and (3) variable-speed systems, where the compressor speed is adjusted to match the cooling load of the household, thereby providing higher efficiency and comfort levels through better temperature and humidity control. While energy consumption could reduce significantly by adopting variable-speed compressor systems, the market penetration has been limited to less than 10% of the total HVAC units and a vast majority of systems installed in new construction remains single speed. A few reasons may explain this phenomenon such as the complexity of the electronic circuitry required to vary compressor speed as well as the associated system cost. This paper outlines a system solution to boost the Seasonal Energy Efficiency Rating (SEER) of a traditional single-speed unit through using a low power electronic converter that allows the compressor to operate at multiple low capacity settings and is disabled at high compressor speeds.

Determination of Gibbs energies of formation in aqueous solution using chemical engineering tools.

PubMed

Toure, Oumar; Dussap, Claude-Gilles

2016-08-01

Standard Gibbs energies of formation are of primary importance in the field of biothermodynamics. In the absence of any directly measured values, thermodynamic calculations are required to determine the missing data. For several biochemical species, this study shows that the knowledge of the standard Gibbs energy of formation of the pure compounds (in the gaseous, solid or liquid states) enables to determine the corresponding standard Gibbs energies of formation in aqueous solutions. To do so, using chemical engineering tools (thermodynamic tables and a model enabling to predict activity coefficients, solvation Gibbs energies and pKa data), it becomes possible to determine the partial chemical potential of neutral and charged components in real metabolic conditions, even in concentrated mixtures. Copyright © 2016 Elsevier Ltd. All rights reserved.

An input-to-state stability approach to verify almost global stability of a synchronous-machine-infinite-bus system.

PubMed

Schiffer, Johannes; Efimov, Denis; Ortega, Romeo; Barabanov, Nikita

2017-08-13

Conditions for almost global stability of an operating point of a realistic model of a synchronous generator with constant field current connected to an infinite bus are derived. The analysis is conducted by employing the recently proposed concept of input-to-state stability (ISS)-Leonov functions, which is an extension of the powerful cell structure principle developed by Leonov and Noldus to the ISS framework. Compared with the original ideas of Leonov and Noldus, the ISS-Leonov approach has the advantage of providing additional robustness guarantees. The efficiency of the derived sufficient conditions is illustrated via numerical experiments.This article is part of the themed issue 'Energy management: flexibility, risk and optimization'. © 2017 The Author(s).

Solution of Eshelby's inclusion problem with a bounded domain and Eshelby's tensor for a spherical inclusion in a finite spherical matrix based on a simplified strain gradient elasticity theory

NASA Astrophysics Data System (ADS)

Gao, X.-L.; Ma, H. M.

2010-05-01

A solution for Eshelby's inclusion problem of a finite homogeneous isotropic elastic body containing an inclusion prescribed with a uniform eigenstrain and a uniform eigenstrain gradient is derived in a general form using a simplified strain gradient elasticity theory (SSGET). An extended Betti's reciprocal theorem and an extended Somigliana's identity based on the SSGET are proposed and utilized to solve the finite-domain inclusion problem. The solution for the disturbed displacement field is expressed in terms of the Green's function for an infinite three-dimensional elastic body in the SSGET. It contains a volume integral term and a surface integral term. The former is the same as that for the infinite-domain inclusion problem based on the SSGET, while the latter represents the boundary effect. The solution reduces to that of the infinite-domain inclusion problem when the boundary effect is not considered. The problem of a spherical inclusion embedded concentrically in a finite spherical elastic body is analytically solved by applying the general solution, with the Eshelby tensor and its volume average obtained in closed forms. This Eshelby tensor depends on the position, inclusion size, matrix size, and material length scale parameter, and, as a result, can capture the inclusion size and boundary effects, unlike existing Eshelby tensors. It reduces to the classical Eshelby tensor for the spherical inclusion in an infinite matrix if both the strain gradient and boundary effects are suppressed. Numerical results quantitatively show that the inclusion size effect can be quite large when the inclusion is very small and that the boundary effect can dominate when the inclusion volume fraction is very high. However, the inclusion size effect is diminishing as the inclusion becomes large enough, and the boundary effect is vanishing as the inclusion volume fraction gets sufficiently low.

The Geometry of Quadratic Polynomial Differential Systems with a Finite and an Infinite Saddle-Node (C)

NASA Astrophysics Data System (ADS)

Artés, Joan C.; Rezende, Alex C.; Oliveira, Regilene D. S.

Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this family. Our goal is to make a global study of the family QsnSN of all real quadratic polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the collision of two infinite singular points. This family can be divided into three different subfamilies, all of them with the finite saddle-node in the origin of the plane with the eigenvectors on the axes and with the eigenvector associated with the zero eigenvalue on the horizontal axis and (A) with the infinite saddle-node in the horizontal axis, (B) with the infinite saddle-node in the vertical axis and (C) with the infinite saddle-node in the bisector of the first and third quadrants. These three subfamilies modulo the action of the affine group and time homotheties are three-dimensional and we give the bifurcation diagram of their closure with respect to specific normal forms, in the three-dimensional real projective space. The subfamilies (A) and (B) have already been studied [Artés et al., 2013b] and in this paper we provide the complete study of the geometry of the last family (C). The bifurcation diagram for the subfamily (C) yields 371 topologically distinct phase portraits with and without limit cycles for systems in the closure /line{QsnSN(C)} within the representatives of QsnSN(C) given by a chosen normal form. Algebraic invariants are used to construct the bifurcation set. The phase portraits are represented on the Poincaré disk. The bifurcation set of /line{QsnSN(C)} is not only algebraic due to the presence of some surfaces found numerically. All points in these surfaces correspond to either connections of separatrices, or the

Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise

PubMed Central

Zeng, Caibin; Yang, Qigui; Cao, Junfei

2014-01-01

This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient Φ: dX(t) = A(X(t))dt+Φ(t)dB H(t), where A is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system. Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalized p-Laplacian equation. PMID:24574903

Few-body resonances of unequal-mass systems with infinite interspecies two-body s-wave scattering length

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

Blume, D.; Daily, K. M.

Two-component Fermi and Bose gases with infinitely large interspecies s-wave scattering length a{sub s} exhibit a variety of intriguing properties. Among these are the scale invariance of two-component Fermi gases with equal masses, and the favorable scaling of Efimov features for two-component Bose gases and Bose-Fermi mixtures with unequal masses. This paper builds on our earlier work [Phys. Rev. Lett. 105, 170403 (2010)] and presents a detailed discussion of our studies of small unequal-mass two-component systems with infinite a{sub s} in the regime where three-body Efimov physics is absent. We report on nonuniversal few-body resonances. Just like with two-body systemsmore » on resonance, few-body systems have a zero-energy bound state in free space and a diverging generalized scattering length. Our calculations are performed within a nonperturbative microscopic framework and investigate the energetics and structural properties of small unequal-mass two-component systems as functions of the mass ratio {kappa}, and the numbers N{sub 1} and N{sub 2} of heavy and light atoms. For purely attractive Gaussian two-body interactions, we find that the (N{sub 1},N{sub 2})=(2,1) and (3,1) systems exhibit three-body and four-body resonances at mass ratios {kappa}=12.314(2) and 10.4(2), respectively. The three- and four-particle systems on resonance are found to be large. It seems feasible that the features discussed in this paper can be probed experimentally with present-day technology.« less

Analysis of the axisymmetric indentation of a semi-infinite piezoelectric material: The evaluation of the contact stiffness and the effective piezoelectric constant

NASA Astrophysics Data System (ADS)

Yang, Fuqian

2008-04-01

A general solution of the axisymmetric indentation is obtained in the closed form for a semi-infinite, transverse isotropic piezoelectric material by a rigid-conducting indenter of arbitrary-axisymmetric profile. Explicit relationships are derived for dependences of the indentation depth and the indentation-induced charge on indentation force and applied electrical potential. Simple formulas are obtained for contact stiffness and effective piezoelectric constant, which can be used in indentation test and piezoresponse force microscopy to analyze the elastic and piezoelectric responses of piezoelectric materials. Depending on the direction of electric field (the potential difference), the electric field can either increase or suppress indentation deformation. The corresponding results are given for cylindrical, conical, and paraboloidal indenters.

A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms

DOE PAGES

Doll, J.; Dupuis, P.; Nyquist, P.

2017-02-08

Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel simulations. From the perspective of large deviations it is optimal to let the swap rate tend to infinity and it is possible to construct a corresponding simulation scheme, known as infinite swapping. In this paper we propose a novel use of large deviations for empirical measures for a more detailed analysis of the infinite swapping limit in the setting of continuous time jump Markov processes. Usingmore » the large deviations rate function and associated stochastic control problems we consider a diagnostic based on temperature assignments, which can be easily computed during a simulation. We show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. The rate function is also used to investigate the impact of asymmetries in the underlying potential landscape, and where in the state space poor sampling is most likely to occur.« less

PML solution of longitudinal wave propagation in heterogeneous media

NASA Astrophysics Data System (ADS)

Farzanian, M.; Arbabi, Freydoon; Pak, Ronald

2016-06-01

This paper describes the development of a model for unbounded heterogeneous domains with radiation damping produced by an unphysical wave absorbing layer. The Perfectly Matched Layer (PML) approach is used along with a displacement-based finite element. The heterogeneous model is validated using the closed-form solution of a benchmark problem: a free rod with two-part modulus subjected to a specified time history. Both elastically supported and unsupported semi-infinite rods with different degrees of inhomogeneity and loading are considered. Numerical results illustrate the effects of inhomogeneity on the response and are compared with those for equivalent homogeneous domains. The effects of characteristic features of the inhomogeneous problem, presence of local maxima and cut-off frequency are determined. A degenerate case of a homogeneous semi-infinite rod on elastic foundations is produced by tending the magnitude of the foundation stiffness to zero. The response of the latter is compared with that of a free rod. The importance of proper selection of the PML parameters to highly accurate and efficient results is demonstrated by example problems.

Option pricing for stochastic volatility model with infinite activity Lévy jumps

NASA Astrophysics Data System (ADS)

Gong, Xiaoli; Zhuang, Xintian

2016-08-01

The purpose of this paper is to apply the stochastic volatility model driven by infinite activity Lévy processes to option pricing which displays infinite activity jumps behaviors and time varying volatility that is consistent with the phenomenon observed in underlying asset dynamics. We specially pay attention to three typical Lévy processes that replace the compound Poisson jumps in Bates model, aiming to capture the leptokurtic feature in asset returns and volatility clustering effect in returns variance. By utilizing the analytical characteristic function and fast Fourier transform technique, the closed form formula of option pricing can be derived. The intelligent global optimization search algorithm called Differential Evolution is introduced into the above highly dimensional models for parameters calibration so as to improve the calibration quality of fitted option models. Finally, we perform empirical researches using both time series data and options data on financial markets to illustrate the effectiveness and superiority of the proposed method.

An energy-optimal solution for transportation control of cranes with double pendulum dynamics: Design and experiments

NASA Astrophysics Data System (ADS)

Sun, Ning; Wu, Yiming; Chen, He; Fang, Yongchun

2018-03-01

Underactuated cranes play an important role in modern industry. Specifically, in most situations of practical applications, crane systems exhibit significant double pendulum characteristics, which makes the control problem quite challenging. Moreover, most existing planners/controllers obtained with standard methods/techniques for double pendulum cranes cannot minimize the energy consumption when fulfilling the transportation tasks. Therefore, from a practical perspective, this paper proposes an energy-optimal solution for transportation control of double pendulum cranes. By applying the presented approach, the transportation objective, including fast trolley positioning and swing elimination, is achieved with minimized energy consumption, and the residual oscillations are suppressed effectively with all the state constrains being satisfied during the entire transportation process. As far as we know, this is the first energy-optimal solution for transportation control of underactuated double pendulum cranes with various state and control constraints. Hardware experimental results are included to verify the effectiveness of the proposed approach, whose superior performance is reflected by being experimentally compared with some comparative controllers.

Recent progress in solution plasma-synthesized-carbon-supported catalysts for energy conversion systems

NASA Astrophysics Data System (ADS)

Lun Li, Oi; Lee, Hoonseung; Ishizaki, Takahiro

2018-01-01

Carbon-based materials have been widely utilized as the electrode materials in energy conversion and storage technologies, such as fuel cells and metal-air batteries. In these systems, the oxygen reduction reaction is an important step that determines the overall performance. A novel synthesis route, named the solution plasma process, has been recently utilized to synthesize various types of metal-based and heteroatom-doped carbon catalysts. In this review, we summarize cutting-edge technologies involving the synthesis and modeling of carbon-supported catalysts synthesized via solution plasma process, followed by current progress on the electrocatalytic performance of these catalysts. This review provides the fundamental and state-of-the-art performance of solution-plasma-synthesized electrode materials, as well as the remaining scientific and technological challenges for this process.

Wavefronts for a global reaction-diffusion population model with infinite distributed delay

NASA Astrophysics Data System (ADS)

Weng, Peixuan; Xu, Zhiting

2008-09-01

We consider a global reaction-diffusion population model with infinite distributed delay which includes models of Nicholson's blowflies and hematopoiesis derived by Gurney, Mackey and Glass, respectively. The existence of monotone wavefronts is derived by using the abstract settings of functional differential equations and Schauder fixed point theory.

Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations.

PubMed

Cooper, F; Hyman, J M; Khare, A

2001-08-01

Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg-de Vries (KdV), nonlinear Schrödinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial differential equation from a four-parameter Lagrangian where the nonlinear dispersion gives rise to solitons with compact support (compactons). The new equation does not seem to be integrable and only mass, momentum, and energy seem to be conserved; yet, the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations. The compactons formed from arbitrary initial data, are nonlinearly self-stabilizing, and maintain their coherence after multiple collisions. The robustness of these compactons and the inapplicability of the inverse scattering tools, that worked so well for the KdV equation, make it clear that there is a fundamental mechanism underlying the processes beyond integrability. We have found explicit formulas for multiple classes of compact traveling wave solutions. When there are more than one compacton solution for a particular set of parameters, the wider compacton is the minimum of a reduced Hamiltonian and is the only one that is stable.

Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary

NASA Astrophysics Data System (ADS)

Imran, M. A.; Riaz, M. B.; Shah, N. A.; Zafar, A. A.

2018-03-01

The aim of this article is to investigate the unsteady natural convection flow of Maxwell fluid with fractional derivative over an exponentially accelerated infinite vertical plate. Moreover, slip condition, radiation, MHD and Newtonian heating effects are also considered. A modern definition of fractional derivative operator recently introduced by Caputo and Fabrizio has been used to formulate the fractional model. Semi analytical solutions of the dimensionless problem are obtained by employing Stehfest's and Tzou's algorithms in order to find the inverse Laplace transforms for temperature and velocity fields. Temperature and rate of heat transfer for non-integer and integer order derivatives are computed and reduced to some known solutions from the literature. Finally, in order to get insight of the physical significance of the considered problem regarding velocity and Nusselt number, some graphical illustrations are made using Mathcad software. As a result, in comparison between Maxwell and viscous fluid (fractional and ordinary) we found that viscous (fractional and ordinary) fluids are swiftest than Maxwell (fractional and ordinary) fluids.

Heat and Mass Transfer on MHD Free convective flow of Second grade fluid through Porous medium over an infinite vertical plate

NASA Astrophysics Data System (ADS)

Dastagiri Babu, D.; Venkateswarlu, S.; Keshava Reddy, E.

2017-08-01

In this paper, we have considered the unsteady free convective two dimensional flow of a viscous incompressible electrically conducting second grade fluid over an infinite vertical porous plate under the influence of uniform transverse magnetic field with time dependent permeability, oscillatory suction. The governing equations of the flow field are solved by a regular perturbation method for small amplitude of the permeability. The closed form solutions for the velocity, temperature and concentration have been derived analytically and also its behavior is computationally discussed with reference to different flow parameters with the help of profiles. The skin fiction on the boundary, the heat flux in terms of the Nusselt number and rate of mass transfer in terms of Sherwood number are also obtained and their behavior computationally discussed.

IN2 Profile: Go Electric Provides Grid Stabilizing Energy Service Solutions to Utilities

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

Pless, Shanti

Through the Wells Fargo Innovation Incubator (IN²) program, Go Electric will validate their Link DR technology, which is an advanced, uninterruptable power supply that provides secure power, lowers facility energy costs, integrates renewables, and generates income from utility demand response programs. The IN² program launched in October 2014 and is part of Wells Fargo’s 2020 Environmental Commitment to provide $100 million to environmentally-focused nonprofits and universities. The goal is to create an ecosystem that fosters and accelerates the commercialization of promising commercial buildings technologies that can provide scalable solutions to reduce the energy impact of buildings. According to the Departmentmore » of Energy, nearly 40 percent of energy consumption in the U.S. today comes from buildings at an estimated cost of $413 billion.« less

Infinite Index Subfactors and the GICAR Categories

NASA Astrophysics Data System (ADS)

Jones, Vaughan F. R.; Penneys, David

2015-10-01

Given a II1-subfactor of arbitrary index, we show that the rectangular GICAR category, also called the rectangular planar rook category, faithfully embeds as A - A bimodule maps among the bimodules . As a corollary, we get a lower bound on the dimension of the centralizer algebras for infinite index subfactors, and we also get that is nonabelian for , where is the Jones tower for . We also show that the annular GICAR/planar rook category acts as maps amongst the A-central vectors in , although this action may be degenerate. We prove these results in more generality using bimodules. The embedding of the GICAR category builds on work of Connes and Evans, who originally found GICAR algebras inside Temperley-Lieb algebras with finite modulus.

FAST TRACK COMMUNICATION: Soliton solutions of the KP equation with V-shape initial waves

NASA Astrophysics Data System (ADS)

Kodama, Y.; Oikawa, M.; Tsuji, H.

2009-08-01

We consider the initial value problems of the Kadomtsev-Petviashvili (KP) equation for symmetric V-shape initial waves consisting of two semi-infinite line solitons with the same amplitude. Those are particularly important for studies of large amplitude waves such as tsunami in shallow water. Numerical simulations show that the solutions of the initial value problem approach asymptotically to certain exact solutions of the KP equation found recently in [1]. We then use a chord diagram to explain the asymptotic result. This provides an analytical method to study asymptotic behavior for the initial value problem of the KP equation. We also demonstrate a real experiment of shallow water waves which may represent the solution discussed in this communication.

Predicting solute partitioning in lipid bilayers: Free energies and partition coefficients from molecular dynamics simulations and COSMOmic

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

Jakobtorweihen, S., E-mail: jakobtorweihen@tuhh.de; Ingram, T.; Gerlach, T.

2014-07-28

Quantitative predictions of biomembrane/water partition coefficients are important, as they are a key property in pharmaceutical applications and toxicological studies. Molecular dynamics (MD) simulations are used to calculate free energy profiles for different solutes in lipid bilayers. How to calculate partition coefficients from these profiles is discussed in detail and different definitions of partition coefficients are compared. Importantly, it is shown that the calculated coefficients are in quantitative agreement with experimental results. Furthermore, we compare free energy profiles from MD simulations to profiles obtained by the recent method COSMOmic, which is an extension of the conductor-like screening model for realisticmore » solvation to micelles and biomembranes. The free energy profiles from these molecular methods are in good agreement. Additionally, solute orientations calculated with MD and COSMOmic are compared and again a good agreement is found. Four different solutes are investigated in detail: 4-ethylphenol, propanol, 5-phenylvaleric acid, and dibenz[a,h]anthracene, whereby the latter belongs to the class of polycyclic aromatic hydrocarbons. The convergence of the free energy profiles from biased MD simulations is discussed and the results are shown to be comparable to equilibrium MD simulations. For 5-phenylvaleric acid the influence of the carboxyl group dihedral angle on free energy profiles is analyzed with MD simulations.« less

The inviscid pressure field on the tip of a semi-infinite wing and its application to the formation of a tip vortex

NASA Technical Reports Server (NTRS)

Hall, G. F.; Shamroth, S. J.; Mcdonald, H.; Briley, W. R.

1976-01-01

A method was developed for determining the aerodynamic loads on the tip of an infinitely thin, swept, cambered semi-infinite wing at an angle of attack which is operating subsonically in an inviscid medium and is subjected to a sinusoidal gust. Under the assumption of linearized aerodynamics, the loads on the tip are obtained by superposition of the steady aerodynamic results for angle of attack and camber, and the unsteady results for the response to the sinusoidal gust. The near field disturbance pressures in the fluid surrounding the tip are obtained by assuming a dipole representation for the loading on the tip and calculating the pressures accordingly. The near field pressures are used to drive a reduced form of the Navier-Stokes equations which yield the tip vortex formation. The combined viscid-inviscid analysis is applied to determining the pressures and examining the vortex rollup in the vicinity of an unswept, uncambered wing moving steadily at a Mach number of 0.2 at an angle of attack of 0.1 rad. The viscous tip flow calculation shows features expected in the tip flow such as the qualitatively proper development of boundary layers on both the upper and lower airfoil surfaces. In addition, application of the viscous solution leads to the generation of a circular type flow pattern above the airfoil suction surface.

Performance of the AMOEBA Water Model in the Vicinity of QM Solutes: A Diagnosis Using Energy Decomposition Analysis.

PubMed

Mao, Yuezhi; Shao, Yihan; Dziedzic, Jacek; Skylaris, Chris-Kriton; Head-Gordon, Teresa; Head-Gordon, Martin

2017-05-09

The importance of incorporating solvent polarization effects into the modeling of solvation processes has been well-recognized, and therefore a new generation of hybrid quantum mechanics/molecular mechanics (QM/MM) approaches that accounts for this effect is desirable. We present a fully self-consistent, mutually polarizable QM/MM scheme using the AMOEBA force field, in which the total energy of the system is variationally minimized with respect to both the QM electronic density and the MM induced dipoles. This QM/AMOEBA model is implemented through the Q-Chem/LibEFP code interface and then applied to the evaluation of solute-solvent interaction energies for various systems ranging from the water dimer to neutral and ionic solutes (NH 3 , NH 4 + , CN - ) surrounded by increasing numbers of water molecules (up to 100). In order to analyze the resulting interaction energies, we also utilize an energy decomposition analysis (EDA) scheme which identifies contributions from permanent electrostatics, polarization, and van der Waals (vdW) interaction for the interaction between the QM solute and the solvent molecules described by AMOEBA. This facilitates a component-wise comparison against full QM calculations where the corresponding energy components are obtained via a modified version of the absolutely localized molecular orbitals (ALMO)-EDA. The results show that the present QM/AMOEBA model can yield reasonable solute-solvent interaction energies for neutral and cationic species, while further scrutiny reveals that this accuracy highly relies on the delicate balance between insufficiently favorable permanent electrostatics and softened vdW interaction. For anionic solutes where the charge penetration effect becomes more pronounced, the QM/MM interface turns out to be unbalanced. These results are consistent with and further elucidate our findings in a previous study using a slightly different QM/AMOEBA model ( Dziedzic et al. J. Chem. Phys. 2016 , 145 , 124106 ). The

Stokes waves revisited: Exact solutions in the asymptotic limit

NASA Astrophysics Data System (ADS)

Davies, Megan; Chattopadhyay, Amit K.

2016-03-01

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic "secular variation" in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n -ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

Scan blindness in infinite phased arrays of printed dipoles

NASA Technical Reports Server (NTRS)

Pozar, D. M.; Schaubert, D. H.

1984-01-01

A comprehensive study of infinite phased arrays of printed dipole antennas is presented, with emphasis on the scan blindness phenomenon. A rigorous and efficient moment method procedure is used to calculate the array impedance versus scan angle. Data are presented for the input reflection coefficient for various element spacings and substrate parameters. A simple theory, based on coupling from Floquet modes to surface wave modes on the substrate, is shown to predict the occurrence of scan blindness. Measurements from a waveguide simulator of a blindness condition confirm the theory.

Finite element solution for energy conservation using a highly stable explicit integration algorithm

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1972-01-01

Theoretical derivation of a finite element solution algorithm for the transient energy conservation equation in multidimensional, stationary multi-media continua with irregular solution domain closure is considered. The complete finite element matrix forms for arbitrarily irregular discretizations are established, using natural coordinate function representations. The algorithm is embodied into a user-oriented computer program (COMOC) which obtains transient temperature distributions at the node points of the finite element discretization using a highly stable explicit integration procedure with automatic error control features. The finite element algorithm is shown to posses convergence with discretization for a transient sample problem. The condensed form for the specific heat element matrix is shown to be preferable to the consistent form. Computed results for diverse problems illustrate the versatility of COMOC, and easily prepared output subroutines are shown to allow quick engineering assessment of solution behavior.

Magnetically driven relativistic jets and winds: Exact solutions

NASA Technical Reports Server (NTRS)

Contopoulos, J.

1994-01-01

We present self-consistent solutions of the full set of ideal MHD equations which describe steady-state relativistic cold outflows from thin accretion disks. The magnetic field forms a spiral which is anchored in the disk, rotates with it, and accelerates the flow out of the disk plane. The collimation at large distances depends on the total amount of electric current that flows along the jet. We considered various distributions of electric current and derived the result that in straight jets which extend to infinite distances, a strong electric current flows along their axis of symmetry. The asymptotic flow velocities are of the order of the initial rotational velocity at the base of the flow (a few tenths of the speed of light). The solutions are applied to both galactic (small-scale) and extragalactic (large-scale) jets.

Thermal Conductivity in Soil: Theoretical Approach by 3D Infinite Resistance Grid Model

NASA Astrophysics Data System (ADS)

Changjan, A.; Intaravicha, N.

2018-05-01

Thermal conductivity in soil was elementary characteristic of soil that conduct heat, measured in terms of Fourier’s Law for heat conduction and useful application in many fields: such as Utilizing underground cable for transmission and distribution systems, the rate of cooling of the cable depends on the thermal properties of the soil surrounding the cable. In this paper, we investigated thermal conductivity in soil by infinite three dimensions (3D) electrical resistance circuit concept. Infinite resistance grid 3D was the grid of resistors that extends to infinity in all directions. Model of thermal conductivity in soil of this research was generated from this concept: comparison between electrical resistance and thermal resistance in soil. Finally, we investigated the analytical form of thermal conductivity in soil which helpful for engineering and science students that could exhibit education with a principle of physics that applied to real situations.

Small data global solutions for the Camassa–Choi equations

NASA Astrophysics Data System (ADS)

Harrop-Griffiths, Benjamin; Marzuola, Jeremy L.

2018-05-01

We consider solutions to the Cauchy problem for an internal-wave model derived by Camassa–Choi (1996 J. Fluid Mech. 313 83–103). This model is a natural generalization of the Benjamin–Ono and intermediate long wave equations for weak transverse effects as in the case of the Kadomtsev–Petviashvili equations for the Korteweg-de Vries equation. For that reason they are often referred to as the KP-ILW or the KP–Benjamin–Ono equations regarding finite or infinite depth respectively. We prove the existence and long-time dynamics of global solutions from small, smooth, spatially localized initial data on . The techniques applied here involve testing by wave packet techniques developed by Ifrim and Tataru in (2015 Nonlinearity 28 2661–75 2016 Bull. Soc. Math. France 144 369–94).

Regulation of Renewable Energy Sources to Optimal Power Flow Solutions Using ADMM

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

Dall-Anese, Emiliano; Zhang, Yijian; Hong, Mingyi

This paper considers power distribution systems featuring renewable energy sources (RESs), and develops a distributed optimization method to steer the RES output powers to solutions of AC optimal power flow (OPF) problems. The design of the proposed method leverages suitable linear approximations of the AC-power flow equations, and is based on the Alternating Direction Method of Multipliers (ADMM). Convergence of the RES-inverter output powers to solutions of the OPF problem is established under suitable conditions on the stepsize as well as mismatches between the commanded setpoints and actual RES output powers. In a broad sense, the methods and results proposedmore » here are also applicable to other distributed optimization problem setups with ADMM and inexact dual updates.« less

Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: one-dimensional soil thaw with conduction and advection

USGS Publications Warehouse

Kurylyk, Barret L.; McKenzie, Jeffrey M; MacQuarrie, Kerry T. B.; Voss, Clifford I.

2014-01-01

Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.

Energy-Water System Solutions | Energy Analysis | NREL

Science.gov Websites

simultaneously. Example Projects Energy, water, and renewable opportunities assessment at Bagram Air Force Base opportunity to plan integrated infrastructure. Example Projects Identification of critical water and campus-level opportunities. Example Projects Net Zero Energy-Water-Waste analysis for Fort Carson Net

Exact solutions for layered thermocapillary convection of a viscous incompressible fluid with specified stresses on the bottom

NASA Astrophysics Data System (ADS)

Prosviryakov, E. Yu.; Spevak, L. F.

2017-12-01

A new exact solution of the Oberbeck-Boussinesq system is found. The Marangoni thermocapillary convection in an infinite fluid layer is described. It is demonstrated that the specification of tangential stresses at both boundaries of the layered velocity field is nonstationary. Velocities describe a superposition of unidirectional flows with an intermediate time interval when there are counterflows.

Flow induced/ refined solution crystallization of a semiconducting polymer

NASA Astrophysics Data System (ADS)

Nguyen, Ngoc A.

morphology formation in comparison to that of the pristine (as-received) P3HT. As a result, single P3HT crystals with high surface energy chain folds were analyzed and determined. Previous reported results of infinite melting enthalpy of extended chain P3HT crystals are much higher than the result discovered in this study. The findings in this study revealed that the infinite melting enthalpy of chain-folded P3HT crystals is considerably decreased due to the presence of this P3HT chain-folded surface energy. In this study, the kinetics and mechanism of P3HT crystallization under shear-flow was thoroughly investigated as well. A homogeneous nucleation of P3HT was observed that allows one dimensional fibril crystal growth. The micrometer long P3HT crystals are formed and limited by the contact time between the P3HT molecules. Furthermore, it was found that phenyl-C61-butyric acid methyl ester (PCBM) nanoparticles inhibit the crystallization of P3HT under shear. However, the shear-flow leads to nanophase agglomeration of PCBM and creates percolation of P3HT fibril crystal networks and the PCBM phase separated domains that apparently present better pathways for transporting electrons and holes. Interestingly, the structured liquid was simply applied onto substrates with a paintbrush resulting in similar device performance to those made with current techniques in which the morphology is commonly formed during application or post-processing steps. These detailed findings are given and discussed in the thesis.

Quasi-integrable non-linear Schrödinger models, infinite towers of exactly conserved charges and bright solitons

NASA Astrophysics Data System (ADS)

Blas, H.; do Bonfim, A. C. R.; Vilela, A. M.

2017-05-01

Deformations of the focusing non-linear Schrödinger model (NLS) are considered in the context of the quasi-integrability concept. We strengthen the results of JHEP 09 (2012) 103 for bright soliton collisions. We addressed the focusing NLS as a complement to the one in JHEP 03 (2016) 005 , in which the modified defocusing NLS models with dark solitons were shown to exhibit an infinite tower of exactly conserved charges. We show, by means of analytical and numerical methods, that for certain two-bright-soliton solutions, in which the modulus and phase of the complex modified NLS field exhibit even parities under a space-reflection symmetry, the first four and the sequence of even order charges are exactly conserved during the scattering process of the solitons. We perform extensive numerical simulations and consider the bright solitons with deformed potential V=2η /2+\\upepsilon{({|ψ |}^2)}^{2+\\upepsilon},\\upepsilon \\in \\mathbb{R},η <0 . However, for two-soliton field components without definite parity we also show numerically the vanishing of the first non-trivial anomaly and the exact conservation of the relevant charge. So, the parity symmetry seems to be a sufficient but not a necessary condition for the existence of the infinite tower of conserved charges. The model supports elastic scattering of solitons for a wide range of values of the amplitudes and velocities and the set { η, ɛ}. Since the NLS equation is ubiquitous, our results may find potential applications in several areas of non-linear science.

A computational exploration of the McCoy-Tracy-Wu solutions of the third Painlevé equation

NASA Astrophysics Data System (ADS)

Fasondini, Marco; Fornberg, Bengt; Weideman, J. A. C.

2018-01-01

The method recently developed by the authors for the computation of the multivalued Painlevé transcendents on their Riemann surfaces (Fasondini et al., 2017) is used to explore families of solutions to the third Painlevé equation that were identified by McCoy et al. (1977) and which contain a pole-free sector. Limiting cases, in which the solutions are singular functions of the parameters, are also investigated and it is shown that a particular set of limiting solutions is expressible in terms of special functions. Solutions that are single-valued, logarithmically (infinitely) branched and algebraically branched, with any number of distinct sheets, are encountered. The algebraically branched solutions have multiple pole-free sectors on their Riemann surfaces that are accounted for by using asymptotic formulae and Bäcklund transformations.

An Approximate Solution and Master Curves for Buckling of Symmetrically Laminated Composite Cylinders

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2013-01-01

Nondimensional linear-bifurcation buckling equations for balanced, symmetrically laminated cylinders with negligible shell-wall anisotropies and subjected to uniform axial compression loads are presented. These equations are solved exactly for the practical case of simply supported ends. Nondimensional quantities are used to characterize the buckling behavior that consist of a stiffness-weighted length-to-radius parameter, a stiffness-weighted shell-thinness parameter, a shell-wall nonhomogeneity parameter, two orthotropy parameters, and a nondimensional buckling load. Ranges for the nondimensional parameters are established that encompass a wide range of laminated-wall constructions and numerous generic plots of nondimensional buckling load versus a stiffness-weighted length-to-radius ratio are presented for various combinations of the other parameters. These plots are expected to include many practical cases of interest to designers. Additionally, these plots show how the parameter values affect the distribution and size of the festoons forming each response curve and how they affect the attenuation of each response curve to the corresponding solution for an infinitely long cylinder. To aid in preliminary design studies, approximate formulas for the nondimensional buckling load are derived, and validated against the corresponding exact solution, that give the attenuated buckling response of an infinitely long cylinder in terms of the nondimensional parameters presented herein. A relatively small number of "master curves" are identified that give a nondimensional measure of the buckling load of an infinitely long cylinder as a function of the orthotropy and wall inhomogeneity parameters. These curves reduce greatly the complexity of the design-variable space as compared to representations that use dimensional quantities as design variables. As a result of their inherent simplicity, these master curves are anticipated to be useful in the ongoing development of

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

Exact Solution of Mutator Model with Linear Fitness and Finite Genome Length

NASA Astrophysics Data System (ADS)

Saakian, David B.

2017-08-01

We considered the infinite population version of the mutator phenomenon in evolutionary dynamics, looking at the uni-directional mutations in the mutator-specific genes and linear selection. We solved exactly the model for the finite genome length case, looking at the quasispecies version of the phenomenon. We calculated the mutator probability both in the statics and dynamics. The exact solution is important for us because the mutator probability depends on the genome length in a highly non-trivial way.

Benchmark solutions for the galactic heavy-ion transport equations with energy and spatial coupling

NASA Technical Reports Server (NTRS)

Ganapol, Barry D.; Townsend, Lawrence W.; Lamkin, Stanley L.; Wilson, John W.

1991-01-01

Nontrivial benchmark solutions are developed for the galactic heavy ion transport equations in the straightahead approximation with energy and spatial coupling. Analytical representations of the ion fluxes are obtained for a variety of sources with the assumption that the nuclear interaction parameters are energy independent. The method utilizes an analytical LaPlace transform inversion to yield a closed form representation that is computationally efficient. The flux profiles are then used to predict ion dose profiles, which are important for shield design studies.

Validity of the semi-infinite tumor model in diffuse reflectance spectroscopy for epithelial cancer diagnosis: a Monte Carlo study

NASA Astrophysics Data System (ADS)

Zhu, Caigang; Liu, Quan

2011-08-01

The accurate understanding of optical properties of human tissues plays an important role in the optical diagnosis of early epithelial cancer. Many inverse models used to determine the optical properties of a tumor have assumed that the tumor was semi-infinite, which infers infinite width and length but finite thickness. However, this simplified assumption could lead to large errors for small tumor, especially at the early stages. We used a modified Monte Carlo code, which is able to simulate light transport in a layered tissue model with buried tumor-like targets, to investigate the validity of the semi-infinite tumor assumption in two common epithelial tissue models: a squamous cell carcinoma (SCC) tissue model and a basal cell carcinoma (BCC) tissue model. The SCC tissue model consisted of three layers, i.e. the top epithelium, the middle tumor and the bottom stroma. The BCC tissue model also consisted of three layers, i.e. the top epidermis, the middle tumor and the bottom dermis. Diffuse reflectance was simulated for two common fiber-optic probes. In one probe, both source and detector fibers were perpendicular to the tissue surface; while in the other, both fibers were tilted at 45 degrees relative to the normal axis of the tissue surface. It was demonstrated that the validity of the semi-infinite tumor model depends on both the fiber-optic probe configuration and the tumor dimensions. Two look-up tables, which relate the validity of the semi-infinite tumor model to the tumor width in terms of the source-detector separation, were derived to guide the selection of appropriate tumor models and fiber optic probe configuration for the optical diagnosis of early epithelial cancers.

Infinitely many {N}=1 dualities from m + 1 - m = 1

NASA Astrophysics Data System (ADS)

Agarwal, Prarit; Intriligator, Kenneth; Song, Jaewon

2015-10-01

We discuss two infinite classes of 4d supersymmetric theories, T N ( m) and {U}_N^{(m)} , labelled by an arbitrary non-negative integer, m. The T N ( m) theory arises from the 6d, A N - 1 type N=(2,0) theory reduced on a 3-punctured sphere, with normal bundle given by line bundles of degree ( m + 1 , - m); the m = 0 case is the N=2 supersymmetric T N theory. The novelty is the negative-degree line bundle. The {U}_N^{(m)} theories likewise arise from the 6d N=(2,0) theory on a 4-punctured sphere, and can be regarded as gluing together two (partially Higgsed) T N ( m) theories. The T N ( m) and {U}_N^{(m)} theories can be represented, in various duality frames, as quiver gauge theories, built from T N components via gauging and nilpotent Higgsing. We analyze the RG flow of the {U}_N^{(m)} theories, and find that, for all integer m > 0, they end up at the same IR SCFT as SU( N) SQCD with 2 N flavors and quartic superpotential. The {U}_N^{(m)} theories can thus be regarded as an infinite set of UV completions, dual to SQCD with N f = 2 N c . The {U}_N^{(m)} duals have different duality frame quiver representations, with 2 m + 1 gauge nodes.

Resilient Energy Systems | Integrated Energy Solutions | NREL

Science.gov Websites

of microgrids Business model and valuation analysis for resilience Photovoltaic plus storage analysis Framework for Mini-Grids NREL has teamed with the Global Lighting and Energy Access Partnership and the U.S mini-grids. NREL Enhances Energy Resiliency at Marine Corps Air Station Miramar NREL has partnered with

Composite polarizability and the construction of an invariant function of refraction and mass density for solutions.

PubMed

Szymański, Krzysztof; Petrache, Horia I

2011-04-14

Re-examination of dynamical ionic polarizabilities in water solutions leads to the formulation of a solution function r(c), which combines the indices of refraction and mass densities of solutions. We show that this function should be independent of ionic concentration if the composite polarizabilities of hydrated solute clusters are constant. Using existing experimental data for a number of aqueous salt and organic solutions, we find that the r(c) function is either constant or varies linearly with concentration, in most cases with negligible slope. We use this function to compare ionic polarizabilities of crystals and aqueous solutions and to highlight how solute polarizabilities at infinite dilution scale with the electronic valence shell of cations and anions. The proposed r(c) function can be used generally to verify the consistency of experimental measurements and of simulation results, and it provides a test of assumptions in current theories of ionic polarizabilities.

Analytical Solutions for the Surface States of Bi1-xSbx (0 ≤ x ≲ 0.1)

NASA Astrophysics Data System (ADS)

Fuseya, Yuki; Fukuyama, Hidetoshi

2018-04-01

Analytical solutions for the surface state (SS) of an extended Wolff Hamiltonian, which is a common Hamiltonian for strongly spin-orbit coupled systems, are obtained both for semi-infinite and finite-thickness boundary conditions. For the semi-infinite system, there are two types of SS solutions: (I-a) linearly crossing SSs in the direct bulk band gap, and (I-b) SSs with linear dispersions entering the bulk conduction or valence bands away from the band edge. For the finite-thickness system, a gap opens in the SS of solution I-a. Numerical solutions for the SS are also obtained based on the tight-binding model of Liu and Allen [Phys. Rev. B 52, 1566 (1995)] for Bi1-xSbx (0 ≤ x ≤ 0.1). A perfect correspondence between the analytic and numerical solutions is obtained around the \\bar{M} point including their thickness dependence. This is the first time that the character of the SS numerically obtained is identified with the help of analytical solutions. The size of the gap for I-a SS can be larger than that of bulk band gap even for a "thick" films ( ≲ 200 bilayers ≃ 80 nm) of pure bismuth. Consequently, in such a film of Bi1-xSbx, there is no apparent change in the SSs through the band inversion at x ≃ 0.04, even though the nature of the SS is changed from solution I-a to I-b. Based on our theoretical results, the experimental results on the SS of Bi1-xSbx (0 ≤ x ≲ 0.1) are discussed.

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

Improvement of finite element meshes - Heat transfer in an infinite cylinder

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.

1989-01-01

An extension of a structural finite element mesh improvement technique to heat conduction analysis is presented. The mesh improvement concept was originally presented by Prager in studying tapered, axially loaded bars. It was further shown that an improved mesh can be obtained by minimizing the trace of the stiffnes matrix. These procedures are extended and applied to the analysis of heat conduction in an infinitely long hollow circular cylinder.

Improvement in finite element meshes: Heat transfer in an infinite cylinder

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.

1988-01-01

An extension of a structural finite element mesh improvement technique to heat conduction analysis is presented. The mesh improvement concept was originally presented by Prager in studying tapered, axially loaded bars. It was further shown that an improved mesh can be obtained by minimizing the trace of the stiffness matrix. These procedures are extended and applied to the analysis of heat conduction in an infinitely long hollow circular cylinder.