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Sample records for analytically solvable model

  1. Quantum quench dynamics in analytically solvable one-dimensional models

    NASA Astrophysics Data System (ADS)

    Iucci, Anibal; Cazalilla, Miguel A.; Giamarchi, Thierry

    2008-03-01

    In connection with experiments in cold atomic systems, we consider the non-equilibrium dynamics of some analytically solvable one-dimensional systems which undergo a quantum quench. In this quench one or several of the parameters of the Hamiltonian of an interacting quantum system are changed over a very short time scale. In particular, we concentrate on the Luttinger model and the sine-Gordon model in the Luther-Emery point. For the latter, we show that the order parameter and the two-point correlation function relax in the long time limit to the values determined by a generalized Gibbs ensemble first discussed by J. T. Jaynes [Phys. Rev. 106, 620 (1957); 108, 171 (1957)], and recently conjectured by M. Rigol et.al. [Phys. Rev. Lett. 98, 050405 (2007)] to apply to the non-equilibrium dynamics of integrable systems.

  2. Magnetic field barriers in graphene: an analytically solvable model.

    PubMed

    Milpas, Enrique; Torres, Manuel; Murguía, Gabriela

    2011-06-22

    We study the dynamics of carriers in graphene subjected to an inhomogeneous magnetic field. For a magnetic field with a hyperbolic profile the corresponding Dirac equation can be analyzed within the formalism of supersymmetric quantum mechanics, and leads to an exactly solvable model. We study in detail the bound-state spectrum. For a narrow barrier the spectrum is characterized by a few bands, except for the zero energy level that remains degenerated. As the width of the barrier increases we can track the band's evolution into the degenerated Landau levels. In the scattering regime a simple analytical formula is obtained for the transmission coefficient, this result allows us to identify the resonant conditions at which the barrier becomes transparent.

  3. Time Fractional Diffusion Equations and Analytical Solvable Models

    NASA Astrophysics Data System (ADS)

    Bakalis, Evangelos; Zerbetto, Francesco

    2016-08-01

    The anomalous diffusion of a particle that moves in complex environments is analytically studied by means of the time fractional diffusion equation. The influence on the dynamics of a random moving particle caused by a uniform external field is taken into account. We extract analytical solutions in terms either of the Mittag-Leffler functions or of the M- Wright function for the probability distribution, for the velocity autocorrelation function as well as for the mean and the mean square displacement. Discussion of the applicability of the model to real systems is made in order to provide new insight of the medium from the analysis of the motion of a particle embedded in it.

  4. Construction of analytically solvable models for interacting species. [biological species competition

    NASA Technical Reports Server (NTRS)

    Rosen, G.

    1976-01-01

    The basic form of a model representation for systems of n interacting biological species is a set of essentially nonlinear autonomous ordinary differential equations. A generic canonical expression for the rate functions in the equations is reported which permits the analytical general solution to be obtained by elementary computation. It is shown that a general analytical solution is directly obtainable for models where the rate functions are prescribed by the generic canonical expression from the outset. Some illustrative examples are given which demonstrate that the generic canonical expression can be used to construct analytically solvable models for two interacting species with limit-cycle dynamics as well as for a three-species interdependence.

  5. Construction of analytically solvable models for interacting species. [biological species competition

    NASA Technical Reports Server (NTRS)

    Rosen, G.

    1976-01-01

    The basic form of a model representation for systems of n interacting biological species is a set of essentially nonlinear autonomous ordinary differential equations. A generic canonical expression for the rate functions in the equations is reported which permits the analytical general solution to be obtained by elementary computation. It is shown that a general analytical solution is directly obtainable for models where the rate functions are prescribed by the generic canonical expression from the outset. Some illustrative examples are given which demonstrate that the generic canonical expression can be used to construct analytically solvable models for two interacting species with limit-cycle dynamics as well as for a three-species interdependence.

  6. Solvable models of material breakdown

    NASA Astrophysics Data System (ADS)

    Leath, P. L.; Duxbury, P. M.

    The history of the study of fracture of materials is briefly reviewed. Then the importance of analytically solvable models in understanding material breakdown is illustrated by a review of the work of Duxbury, Leath and Beale on simple analytically solvable models of fuse network breakdown in brittle systems. We then review recent work extending this analytically to include close pairs of clusters of defects or double clusters, which also exhibit the double-exponential failure distribution. Finally, a new analytic recursion method is presented for breakdown of systems with linear cracks, but a continuous distribution of breaking strengths. Remarkably, these systems exhibit an optimum sample size where the failure probability can, at low stress, be reduced by many orders of magnitude below that of a single bond.

  7. Analytically Solvable Quantum Hamiltonians and Relations to Orthogonal Polynomials

    SciTech Connect

    Regniers, G.; Van der Jeugt, J.

    2010-06-17

    Quantum systems consisting of a linear chain of n harmonic oscillators coupled by a quadratic nearest-neighbour interaction are considered. We investigate when such a system is analytically solvable, in the sense that the eigenvalues and eigenvectors of the interaction matrix have analytically closed expressions. This leads to a relation with Jacobi matrices of systems of discrete orthogonal polynomials. Our study is first performed in the case of canonical quantization. Then we consider these systems under Wigner quantization, leading to solutions in terms of representations of Lie superalgebras. Finally, we show how such analytically solvable Hamiltonians also play a role in another application, that of spin chains used as communication channels in quantum computing. In this context, the analytic solvability leads to closed form expressions for certain transition amplitudes.

  8. Solvable model of a strongly driven micromaser

    SciTech Connect

    Lougovski, P.; Walther, H.; Casagrande, F.; Lulli, A.; Englert, B.-G.; Solano, E.

    2004-02-01

    We study the dynamics of a micromaser where the pumping atoms are strongly driven by a resonant classical field during their transit through the cavity mode. We derive a master equation for this strongly driven micromaser, involving the contributions of the unitary atom-field interactions and the dissipative effects of a thermal bath. We find analytical solutions for the temporal evolution and the steady state of this system by means of phase-space techniques, providing an unusual solvable model of an open quantum system, including pumping and decoherence. We derive closed expressions for all relevant expectation values, describing the statistics of the cavity field and the detected atomic levels. The transient regime shows the buildup of mixtures of mesoscopic fields evolving towards a super-Poissonian steady-state field that, nevertheless, yields atomic correlations that exhibit stronger nonclassical features than the conventional micromaser.

  9. Interplay of non-Markov and internal friction effects in the barrier crossing kinetics of biopolymers: insights from an analytically solvable model.

    PubMed

    Makarov, Dmitrii E

    2013-01-07

    Conformational rearrangements in biomolecules (such as protein folding or enzyme-ligand binding) are often interpreted in terms of low-dimensional models of barrier crossing such as Kramers' theory. Dimensionality reduction, however, entails memory effects; as a result, the effective frictional drag force along the reaction coordinate nontrivially depends on the time scale of the transition. Moreover, when both solvent and "internal" friction effects are important, their interplay results in a highly nonlinear dependence of the effective friction on solvent viscosity that is not captured by common phenomenological models of barrier crossing. Here, these effects are illustrated using an analytically solvable toy model of an unstructured polymer chain involved in an inter- or intramolecular transition. The transition rate is calculated using the Grote-Hynes and Langer theories, which--unlike Kramers' theory--account for memory. The resulting effective frictional force exerted by the polymer along the reaction coordinate can be rationalized in terms of the effective number of monomers engaged in the transition. Faster transitions (relative to the polymer reconfiguration time scale) involve fewer monomers and, correspondingly, lower friction forces, because the polymer chain does not have enough time to reconfigure in response to the transition.

  10. Inhomogeneous random phase approximation: A solvable model

    SciTech Connect

    Lemm, J.C.

    1995-11-15

    A recently developed method to include particle-hole correlations into the time-independent mean field theory for scattering (TIMF) by an inhomogeneous random phase approximation (IRPA) is applied to a numerically solvable model. Having adapted the procedure according to numerical requirements, IRPA calculations turn out to be tractable. The obtained results improve TIMF results. 8 refs., 28 figs., 3 tabs.

  11. Solvable stochastic dealer models for financial markets

    NASA Astrophysics Data System (ADS)

    Yamada, Kenta; Takayasu, Hideki; Ito, Takatoshi; Takayasu, Misako

    2009-05-01

    We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise generator, the model becomes fairly realistic by adding only two effects: the self-modulation of transaction intervals and a forecasting tendency, which uses a moving average of the latest market price changes. Based on the present microscopic model of markets, we find a quantitative relation with market potential forces, which have recently been discovered in the study of market price modeling based on random walks.

  12. Solvable stochastic dealer models for financial markets.

    PubMed

    Yamada, Kenta; Takayasu, Hideki; Ito, Takatoshi; Takayasu, Misako

    2009-05-01

    We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise generator, the model becomes fairly realistic by adding only two effects: the self-modulation of transaction intervals and a forecasting tendency, which uses a moving average of the latest market price changes. Based on the present microscopic model of markets, we find a quantitative relation with market potential forces, which have recently been discovered in the study of market price modeling based on random walks.

  13. Fracture surfaces of heterogeneous materials: A 2D solvable model

    NASA Astrophysics Data System (ADS)

    Katzav, E.; Adda-Bedia, M.; Derrida, B.

    2007-05-01

    Using an elastostatic description of crack growth based on the Griffith criterion and the principle of local symmetry, we present a stochastic model describing the propagation of a crack tip in a 2D heterogeneous brittle material. The model ensures the stability of straight cracks and allows for the study of the roughening of fracture surfaces. When neglecting the effect of the nonsingular stress, the problem becomes exactly solvable and yields analytic predictions for the power spectrum of the paths. This result suggests an alternative to the conventional power law analysis often used in the analysis of experimental data.

  14. The quest for solvable multistate Landau-Zener models

    NASA Astrophysics Data System (ADS)

    Sinitsyn, Nikolai A.; Chernyak, Vladimir Y.

    2017-06-01

    Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed [1]. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient computer assisted search for new solvable MLZ models that span complexity range from several interacting states to mesoscopic systems with many-body dynamics and combinatorially large phase space. This diversity suggests that nontrivial solvable MLZ models are numerous. In addition, we refine the formulation of ICs and extend the class of solvable systems to models with points of multiple diabatic level crossing.

  15. The quest for solvable multistate Landau-Zener models

    DOE PAGES

    Sinitsyn, Nikolai A.; Chernyak, Vladimir Y.

    2017-05-24

    Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient computer assisted search for new solvable MLZ models that span complexity range from several interacting states to mesoscopic systems with many-body dynamics and combinatorially large phase space. This diversity suggests that nontrivial solvable MLZ models are numerous. Additionally, we refine the formulation of ICs and extend the class of solvable systems to models with points of multiple diabatic level crossing.

  16. Exactly solvable models for multiatomic molecular Bose-Einstein condensates

    NASA Astrophysics Data System (ADS)

    Santos, G.

    2011-08-01

    I introduce two families of exactly solvable models for multiatomic hetero-nuclear and homo-nuclear molecular Bose-Einstein condensates through the algebraic Bethe ansatz method. The conserved quantities of the respective models are also shown.

  17. An exactly solvable model for quantum communications.

    PubMed

    Smith, Graeme; Smolin, John A

    2013-12-12

    Information theory establishes the ultimate limits on performance for noisy communication systems. Accurate models of physical communication devices must include quantum effects, but these typically make the theory intractable. As a result, communication capacities--the maximum possible rates of data transmission--are not known, even for transmission between two users connected by an electromagnetic waveguide with Gaussian noise. Here we present an exactly solvable model of communication with a fully quantum electromagnetic field. This gives explicit expressions for all point-to-point capacities of noisy quantum channels, with implications for quantum key distribution and fibre-optic communications. We also develop a theory of quantum communication networks by solving some rudimentary models including broadcast and multiple-access channels. We compare the predictions of our model with the orthodox Gaussian model and in all cases find agreement to within a few bits. At high signal-to-noise ratios, our simple model captures the relevant physics while remaining amenable to exact solution.

  18. Algebraic spin liquid in an exactly solvable spin model

    SciTech Connect

    Yao, Hong; Zhang, Shou-Cheng; Kivelson, Steven A.; /Stanford U., Phys. Dept.

    2010-03-25

    We have proposed an exactly solvable quantum spin-3/2 model on a square lattice. Its ground state is a quantum spin liquid with a half integer spin per unit cell. The fermionic excitations are gapless with a linear dispersion, while the topological 'vison' excitations are gapped. Moreover, the massless Dirac fermions are stable. Thus, this model is, to the best of our knowledge, the first exactly solvable model of half-integer spins whose ground state is an 'algebraic spin liquid.'

  19. Solvable models and hidden symmetries in QCD

    SciTech Connect

    Yepez-Martinez, Tochtli; Hess, P. O.; Civitarese, O.; Lerma H., S.

    2010-12-23

    We show that QCD Hamiltonians at low energy exhibit an SU(2) structure, when only few orbital levels are considered. In case many orbital levels are taken into account we also find a semi-analytic solution for the energy levels of the dominant part of the QCD Hamiltonian. The findings are important to propose the structure of phenomenological models.

  20. Solvable model for polymorphic dynamics of biofilaments.

    PubMed

    Mohrbach, Hervé; Kulić, Igor M

    2012-03-01

    We investigate an analytically tractable toy model for thermally induced polymorphic dynamics of cooperatively rearranging biofilaments-like microtubules. The proposed four-block model, which can be seen as a coarse-grained approximation of the full polymorphic tube model, permits a complete analytical treatment of all thermodynamic properties including correlation functions and angular Fourier mode distributions. Due to its mathematical tractability the model straightforwardly leads to some physical insights in recently discussed phenomena like the "length dependent persistence length." We show that a polymorphic filament can disguise itself as a classical worm-like chain on small and on large scales and yet display distinct anomalous tell-tale features indicating an inner switching dynamics on intermediate length scales.

  1. Density functionals and dimensional renormalization for an exactly solvable model

    NASA Astrophysics Data System (ADS)

    Kais, S.; Herschbach, D. R.; Handy, N. C.; Murray, C. W.; Laming, G. J.

    1993-07-01

    We treat an analytically solvable version of the ``Hooke's Law'' model for a two-electron atom, in which the electron-electron repulsion is Coulombic but the electron-nucleus attraction is replaced by a harmonic oscillator potential. Exact expressions are obtained for the ground-state wave function and electron density, the Hartree-Fock solution, the correlation energy, the Kohn-Sham orbital, and, by inversion, the exchange and correlation functionals. These functionals pertain to the ``intermediate'' density regime (rs≥1.4) for an electron gas. As a test of customary approximations employed in density functional theory, we compare our exact density, exchange, and correlation potentials and energies with results from two approximations. These use Becke's exchange functional and either the Lee-Yang-Parr or the Perdew correlation functional. Both approximations yield rather good results for the density and the exchange and correlation energies, but both deviate markedly from the exact exchange and correlation potentials. We also compare properties of the Hooke's Law model with those of two-electron atoms, including the large dimension limit. A renormalization procedure applied to this very simple limit yields correlation energies as good as those obtained from the approximate functionals, for both the model and actual atoms.

  2. An analytically solvable eigenvalue problem for the linear elasticity equations.

    SciTech Connect

    Day, David Minot; Romero, Louis Anthony

    2004-07-01

    Analytic solutions are useful for code verification. Structural vibration codes approximate solutions to the eigenvalue problem for the linear elasticity equations (Navier's equations). Unfortunately the verification method of 'manufactured solutions' does not apply to vibration problems. Verification books (for example [2]) tabulate a few of the lowest modes, but are not useful for computations of large numbers of modes. A closed form solution is presented here for all the eigenvalues and eigenfunctions for a cuboid solid with isotropic material properties. The boundary conditions correspond physically to a greased wall.

  3. Exactly solvable relativistic model with the anomalous interaction

    NASA Astrophysics Data System (ADS)

    Ferraro, Elena; Messina, Antonino; Nikitin, A. G.

    2010-04-01

    A special class of Dirac-Pauli equations with time-like vector potentials of an external field is investigated. An exactly solvable relativistic model describing the anomalous interaction of a neutral Dirac fermion with a cylindrically symmetric external electromagnetic field is presented. The related external field is a superposition of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line current. In the nonrelativistic approximation the considered model is reduced to the integrable Pron’ko-Stroganov model.

  4. Elliptic pfaffians and solvable lattice models

    NASA Astrophysics Data System (ADS)

    Rosengren, Hjalmar

    2016-08-01

    We introduce and study twelve multivariable theta functions defined by pfaffians with elliptic function entries. We show that, when the crossing parameter is a cubic root of unity, the domain wall partition function for the eight-vertex-solid-on-solid model can be written as a sum of two of these pfaffians. As a limit case, we express the domain wall partition function for the three-colour model as a sum of two Hankel determinants. We also show that certain solutions of the TQ-equation for the supersymmetric eight-vertex model can be expressed in terms of elliptic pfaffians.

  5. A solvable model for localized adsorption in a Coulomb system

    SciTech Connect

    Rosinberg, M.L.; Blum, L.; Lebowitz, J.L.

    1986-07-01

    A model for an interface with localized adsorption is presented, in which the surface has a distribution of sticky adhesive sites in contact with a Coulomb fluid. Contrary to the current literature on the electrical double layer the surface charge is in dynamic equilibrium with the bulk fluid. The sum rules obeyed by the one- and two-body correlation functions are investigated. Explicit results are obtained for a solvable model, the two-dimensional one-component plasma at reduced temperature 2. The effect of the granularity of the adsorbed charge on the adsorption isotherm is discussed.

  6. A Solvable Twisted One-Plaquette Model

    NASA Astrophysics Data System (ADS)

    Billó, M.; D'Adda, A.

    We solve a hot twisted Eguchi-Kawai model with only timelike plaquettes in the deconfined phase, by computing the quadratic quantum fluctuations around the classical vacuum. The solution of the model has some novel features: the eigenvalues of the timelike link variable are separated in L bunches, if L is the number of links of the original lattice in the time direction, and each bunch obeys a Wigner semicircular distribution of eigenvalues. This solution becomes unstable at a critical value of the coupling constant, where it is argued that a condensation of classical solutions takes place. This can be inferred by comparison with the heat-kernel model in the Hamiltonian limit, and the related Douglas-Kazakov phase transition in QCD2. As a byproduct of our solution, we can reproduce the dependence of the coupling constant from the parameter describing the asymmetry of the lattice, and compare it to previous results by Karsch.

  7. Gegenbauer-solvable quantum chain model

    SciTech Connect

    Znojil, Miloslav

    2010-11-15

    An N-level quantum model is proposed in which the energies are represented by an N-plet of zeros of a suitable classical orthogonal polynomial. The family of Gegenbauer polynomials G(n,a,x) is selected for illustrative purposes. The main obstacle lies in the non-Hermiticity (aka crypto-Hermiticity) of Hamiltonians H{ne}H{sup {dagger}.} We managed to (i) start from elementary secular equation G(N,a,E{sub n})=0, (ii) keep our H, in the nearest-neighbor-interaction spirit, tridiagonal, (iii) render it Hermitian in an ad hoc, nonunique Hilbert space endowed with metric {Theta}{ne}I, (iv) construct eligible metrics in closed forms ordered by increasing nondiagonality, and (v) interpret the model as a smeared N-site lattice.

  8. Analytically solvable chaotic oscillator based on a first-order filter

    SciTech Connect

    Corron, Ned J.; Cooper, Roy M.; Blakely, Jonathan N.

    2016-02-15

    A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform for any stable infinite-impulse response filter is chaotic.

  9. Model for microemulsions: An exactly solvable case

    SciTech Connect

    Renlie, L. ); Hoye, J.S. ); Skaf, M.S. ); Stell, G. )

    1991-10-01

    The microscopic model for microemulsions, introduced earlier by Ciach, Hoye, and Stell (J. Chem. Phys. {bold 90}, 1214 (1989)) is here specialized to a one-dimensional lattice and solved exactly by the transfer matrix method. The microemulsion phase is identified by the formation of thermally distributed surfactant-bounded domains of oil. For this phase we find scattering functions and characteristic lengths that have some of the same features found in experimental data for microemulsions. Mean-field interactions beyond nearest-neighbor sites are introduced in order to study the phase diagram for the nonperiodic phases we encounter.

  10. Decoherence and Exponential Law: A Solvable Model

    NASA Technical Reports Server (NTRS)

    Pascazio, Saverio; Namiki, Mikio

    1996-01-01

    We analyze a modified version of the 'AgBr' Hamiltonian, solve exactly the equations of motion in terms of SU(2) coherent states, and study the weak-coupling, macroscopic limit of the model, obtaining an exponential behavior at all times. The asymptotic dominance of the exponential behavior is representative of a purely stochastic evolution and can be derived quantum mechanically in the so-called van Hove's limit (which is a weak-coupling, macroscopic limit). At the same time, a temporal behavior of the exponential type, yielding a 'probability dissipation' is closely related to dephasing ('decoherence') effects and one can expect a close connection with a dissipative and irreversible behavior. We stress the central relevance of the problem of dissipation to the quantum measurement theory and to the general topic of decoherence.

  11. An Exactly Solvable Supersymmetric Model of Semimagic Nuclei

    SciTech Connect

    Balantekin, A. B.; Gueven, Nurtac; Pehlivan, Yamac

    2008-11-11

    A simple model of nucleons coupled to angular momentum zero (s-pairs) occupying the valance shell of a semi-magic nuclei is considered. The model has a separable, orbit dependent pairing interaction which dominates over the kinetic term. It is shown that such an interaction leads to an exactly solvable model whose (0{sup +}) eigenstates and energies can be computed very easily with the help of the algebraic Bethe ansatz method. It is also shown that the model has a supersymmetry which connects the spectra of some semimagic nuclei. The results obtained from this model for the semimagic Ni isotopes from {sup 58}Ni to {sup 68}Ni are given. In addition, a new and easier technique for calculating the energy eigenvalues from the Bethe ansatz equations is also presented.

  12. An Exactly Solvable Supersymmetric Model of Semimagic Nuclei

    NASA Astrophysics Data System (ADS)

    Balantekin, A. B.; Güven, Nurtaç; Pehlivan, Yamaç

    2008-11-01

    A simple model of nucleons coupled to angular momentum zero (s-pairs) occupying the valance shell of a semi-magic nuclei is considered. The model has a separable, orbit dependent pairing interaction which dominates over the kinetic term. It is shown that such an interaction leads to an exactly solvable model whose (0+) eigenstates and energies can be computed very easily with the help of the algebraic Bethe ansatz method. It is also shown that the model has a supersymmetry which connects the spectra of some semimagic nuclei. The results obtained from this model for the semimagic Ni isotopes from 58Ni to 68Ni are given. In addition, a new and easier technique for calculating the energy eigenvalues from the Bethe ansatz equations is also presented.

  13. 3-state Hamiltonians associated to solvable 33-vertex models

    NASA Astrophysics Data System (ADS)

    Crampé, N.; Frappat, L.; Ragoucy, E.; Vanicat, M.

    2016-09-01

    Using the nested coordinate Bethe ansatz, we study 3-state Hamiltonians with 33 non-vanishing entries, or 33-vertex models, where only one global charge with degenerate eigenvalues exists and each site possesses three internal degrees of freedom. In the context of Markovian processes, they correspond to diffusing particles with two possible internal states which may be exchanged during the diffusion (transmutation). The first step of the nested coordinate Bethe ansatz is performed providing the eigenvalues in terms of rapidities. We give the constraints ensuring the consistency of the computations. These rapidities also satisfy Bethe equations involving 4 × 4 R-matrices, solutions of the Yang-Baxter equation which implies new constraints on the models. We solve them allowing us to list all the solvable 33-vertex models.

  14. Topological order in an exactly solvable 3D spin model

    SciTech Connect

    Bravyi, Sergey; Leemhuis, Bernhard; Terhal, Barbara M.

    2011-04-15

    Research highlights: RHtriangle We study exactly solvable spin model with six-qubit nearest neighbor interactions on a 3D face centered cubic lattice. RHtriangle The ground space of the model exhibits topological quantum order. RHtriangle Elementary excitations can be geometrically described as the corners of rectangular-shaped membranes. RHtriangle The ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. RHtriangle Logical operators acting on the encoded qubits are described in terms of closed strings and closed membranes. - Abstract: We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest-neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order. The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes. We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on {Omega}(R{sup 2}) qubits. Composite particles that consist of two monopoles (dipoles) and four monopoles (quadrupoles) can be described as end-points of strings. The peculiar feature of the model is that dipole-type strings are rigid, that is, such strings must be aligned with face-diagonals of the lattice. For periodic boundary conditions the ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. We describe a complete set of logical operators acting on the encoded qubits in terms of closed strings and closed membranes.

  15. Propagation of microwaves in gradient transmission lines: exactly solvable model

    NASA Astrophysics Data System (ADS)

    Shvartsburg, A. B.; Silin, N. V.

    2015-08-01

    Propagation of microwaves along the transmission line with smoothly continuously distributed capacitance and inductance (gradient transmission line) is considered in the framework of an exactly solvable model. The appearance of strong heterogeneity-induced plasma-like dispersion in gradient transmission line determined by the sizes and shapes of these distributions, is visualized by means of this model. Owing to this dispersion the energy transport in the line discussed can be ensured by both travelling and evanescent microwave modes, characterized by the real and imaginary wave numbers, respectively. The reflectance spectra for microwaves, incident on this heterogeneous transition section located between two homogeneous sections of transmission line are presented, the antireflection properties of this section are demonstrated. The interference of evanescent and anti-evanescent microwave modes is shown to provide the effective weakly attenuated energy transfer in the tunneling regime. The analogy between this microwave system and gradient nano-optical photonic barrier in revealed.

  16. Effective viscosity and dynamics of spreading epithelia: a solvable model.

    PubMed

    Blanch-Mercader, C; Vincent, R; Bazellières, E; Serra-Picamal, X; Trepat, X; Casademunt, J

    2017-02-08

    Collective cell migration in spreading epithelia in controlled environments has become a landmark in our current understanding of fundamental biophysical processes in development, regeneration, wound healing or cancer. Epithelial monolayers are treated as thin layers of a viscous fluid that exert active traction forces on the substrate. The model is exactly solvable and shows a broad range of applicabilities for the quantitative analysis and interpretation of force microscopy data of monolayers from a variety of experiments and cell lines. In addition, the proposed model provides physical insights into how the biological regulation of the tissue is encoded in a reduced set of time-dependent physical parameters. In particular the temporal evolution of the effective viscosity entails a mechanosensitive regulation of adhesion. Besides, the observation of an effective elastic tensile modulus can be interpreted as an emergent phenomenon in an active fluid.

  17. Two-Dimensional Massless Light Front Fields and Solvable Models

    NASA Astrophysics Data System (ADS)

    Martinovic̆, L'ubomír; Grangé, Pierre

    2016-07-01

    Quantum field theory formulated in terms of light front (LF) variables has a few attractive as well as some puzzling features. The latter hindered a wider acceptance of LF methods. In two space-time dimensions, it has been a long-standing puzzle how to correctly quantize massless fields, in particular fermions. Here we show that two-dimensional massless LF fields (scalar and fermion) can be recovered in a simple way as limits of the corresponding massive fields and thereby quantized without any loss of physical information. Bosonization of the fermion field then follows in a straightforward manner and the solvable models can be studied directly in the LF theory. We sketch the LF operator solution of the Thirring-Wess model and also point out the closeness of the massless LF fields to those of conformal field theory.

  18. Solvable model in renormalization group analysis for effective eddy viscosity.

    PubMed

    Chang, Chien C; Lin, Bin-Shei; Wang, Chi-Tzung

    2003-04-01

    This study presents a solvable model in renormalization group analysis for the effective eddy viscosity. It is found fruitful to take a simple hypothesis that large-scale eddies are statistically independent of those of smaller scales. A limiting operation of renormalization group analysis yields an inhomogeneous ordinary differential equation for the invariant effective eddy viscosity. The closed-form solution of the equation facilitates derivations of an expression of the Kolmogorov constant C(K) and of the Smagorinsky model for large-eddy simulation of turbulent flow. The Smagorinsky constant C(S) is proportional to C(3/4)(K). In particular, we shall illustrate that the value of C(K) ranges from 1.35 to 2.06, which is in close agreement with the generally accepted experimental values (1.2 approximately 2.2).

  19. Solvable four-state Landau-Zener model of two interacting qubits with path interference

    SciTech Connect

    Sinitsyn, Nikolai A.

    2015-11-30

    In this paper, I identify a nontrivial four-state Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. The model describes an experimentally accessible system of two interacting qubits, such as a localized state in a Dirac material with both valley and spin degrees of freedom or a singly charged quantum dot (QD) molecule with spin orbit coupling. Application of the linearly time-dependent magnetic field induces a sequence of quantum level crossings with possibility of interference of different trajectories in a semiclassical picture. I argue that this system satisfies the criteria of integrability in the multistate Landau-Zener theory, which allows one to derive explicit exact analytical expressions for the transition probability matrix. Finally, I also argue that this model is likely a special case of a larger class of solvable systems, and present a six-state generalization as an example.

  20. An exactly solvable, spatial model of mutation accumulation in cancer

    NASA Astrophysics Data System (ADS)

    Paterson, Chay; Nowak, Martin A.; Waclaw, Bartlomiej

    2016-12-01

    One of the hallmarks of cancer is the accumulation of driver mutations which increase the net reproductive rate of cancer cells and allow them to spread. This process has been studied in mathematical models of well mixed populations, and in computer simulations of three-dimensional spatial models. But the computational complexity of these more realistic, spatial models makes it difficult to simulate realistically large and clinically detectable solid tumours. Here we describe an exactly solvable mathematical model of a tumour featuring replication, mutation and local migration of cancer cells. The model predicts a quasi-exponential growth of large tumours, even if different fragments of the tumour grow sub-exponentially due to nutrient and space limitations. The model reproduces clinically observed tumour growth times using biologically plausible rates for cell birth, death, and migration rates. We also show that the expected number of accumulated driver mutations increases exponentially in time if the average fitness gain per driver is constant, and that it reaches a plateau if the gains decrease over time. We discuss the realism of the underlying assumptions and possible extensions of the model.

  1. An exactly solvable, spatial model of mutation accumulation in cancer

    PubMed Central

    Paterson, Chay; Nowak, Martin A.; Waclaw, Bartlomiej

    2016-01-01

    One of the hallmarks of cancer is the accumulation of driver mutations which increase the net reproductive rate of cancer cells and allow them to spread. This process has been studied in mathematical models of well mixed populations, and in computer simulations of three-dimensional spatial models. But the computational complexity of these more realistic, spatial models makes it difficult to simulate realistically large and clinically detectable solid tumours. Here we describe an exactly solvable mathematical model of a tumour featuring replication, mutation and local migration of cancer cells. The model predicts a quasi-exponential growth of large tumours, even if different fragments of the tumour grow sub-exponentially due to nutrient and space limitations. The model reproduces clinically observed tumour growth times using biologically plausible rates for cell birth, death, and migration rates. We also show that the expected number of accumulated driver mutations increases exponentially in time if the average fitness gain per driver is constant, and that it reaches a plateau if the gains decrease over time. We discuss the realism of the underlying assumptions and possible extensions of the model. PMID:28004754

  2. Exactly solvable models of spin liquids with spinons, and of three-dimensional topological paramagnets

    NASA Astrophysics Data System (ADS)

    Ben-Zion, Daniel; Das, Diptarka; McGreevy, John

    2016-04-01

    We develop a scheme to make exactly solvable gauge theories whose electric flux lines host (1+1)-dimensional topological phases. We use this exact "decorated-string-net" framework to construct several classes of interesting models. In particular, we construct an exactly solvable model of a quantum spin liquid whose (gapped) elementary excitations form doublets under an internal symmetry, and hence may be regarded as spin-carrying spinons. The model may be formulated, and is solvable, in any number of dimensions on any bipartite graph. Another example, in any dimension, has Z2 topological order and anyons which are Kramers' doublets of time-reversal symmetry. Further, we make exactly solvable models of three-dimensional topological paramagnets.

  3. Exact solutions for a class of quasi-exactly solvable models: A unified treatment

    NASA Astrophysics Data System (ADS)

    Hatami, N.; Setare, M. R.

    2017-07-01

    The exact solution of the Schrödinger equation for the four quasi-exactly solvable potentials is presented using the functional Bethe ansatz method. It is shown that all models give rise to the same basic differential equation which is quasi-exactly solvable. The eigenvalues, eigenfunctions and the allowed potential parameters are given for each of the four models in terms of the roots of a set of algebraic Bethe ansatz equations.

  4. Neutron-proton correlations in an exactly solvable model

    SciTech Connect

    Engel, J.; Pittel, S.; Stoitsov, M.; Vogel, P.; Dukelsky, J.

    1997-04-01

    We examine isovector and isoscalar neutron-proton correlations in an exactly solvable model based on the algebra SO(8). We look particularly closely at Gamow-Teller strength and double {beta} decay, both to isolate the effects of the two kinds of pairing and to test two approximation schemes: the renormalized neutron-proton quasiparticle random phase approximation (QRPA) and generalized BCS theory. When isoscalar pairing correlations become strong enough a phase transition occurs and the dependence of the Gamow-Teller {beta}{sup +} strength on isospin changes in a dramatic and unfamiliar way, actually increasing as neutrons are added to an N=Z core. Renormalization eliminates the well-known instabilities that plague the QRPA as the phase transition is approached, but only by unnaturally suppressing the isoscalar correlations. Generalized BCS theory, on the other hand, reproduces the Gamow-Teller strength more accurately in the isoscalar phase than in the usual isovector phase, even though its predictions for energies are equally good everywhere. It also mixes T=0 and T=1 pairing, but only on the isoscalar side of the phase transition. {copyright} {ital 1997} {ital The American Physical Society}

  5. An exactly solvable model of random site-specific recombinations

    PubMed Central

    Wei, Yi; Koulakov, Alexei A.

    2017-01-01

    Cre-lox and other systems are used as genetic tools to control site-specific recombination (SSR) events in genomic DNA. If multiple recombination sites are organized in a compact cluster within the same genome, a series of random recombination events may generate substantial cell specific genomic diversity. This diversity is used, for example, to distinguish neurons in the brain of the same multicellular mosaic organism, within the brainbow approach to neuronal connectome. In this paper we study an exactly solvable statistical model for SSR operating on a cluster of recombination sites. We consider two types of recombination events: inversions and excisions. Both of these events are available in the Cre-lox system. We derive three properties of the sequences generated by multiple recombination events. First, we describe the set of sequences that can in principle be generated by multiple inversions operating on the given initial sequence. We call this description the ergodicity theorem. On the basis of this description we calculate the number of sequences that can be generated from an initial sequence. This number of sequences is experimentally testable. Second, we demonstrate that after a large number of random inversions every sequence that can be generated is generated with equal probability. Lastly, we derive the equations for the probability to find a sequence as a function of time in the limit when excisions are much less frequent than inversions, such as in shufflon sequences. PMID:23151958

  6. Minimal cooling speed for glass transition in a simple solvable energy landscape model

    NASA Astrophysics Data System (ADS)

    Toledo-Marín, J. Quetzalcóatl; Castillo, Isaac Pérez; Naumis, Gerardo G.

    2016-06-01

    The minimal cooling speed required to form a glass is obtained for a simple solvable energy landscape model. The model, made from a two-level system modified to include the topology of the energy landscape, is able to capture either a glass transition or a crystallization depending on the cooling rate. In this setup, the minimal cooling speed to achieve glass formation is then found to be related with the crystallization relaxation time, energy barrier and with the thermal history. In particular, we obtain that the thermal history encodes small fluctuations around the equilibrium population which are exponentially amplified near the glass transition, which mathematically corresponds to the boundary layer of the master equation. The change in the glass transition temperature is also found as a function of the cooling rate. Finally, to verify our analytical results, a kinetic Monte Carlo simulation was implemented.

  7. An Exactly Solvable Model for the Spread of Disease

    ERIC Educational Resources Information Center

    Mickens, Ronald E.

    2012-01-01

    We present a new SIR epidemiological model whose exact analytical solution can be calculated. In this model, unlike previous models, the infective population becomes zero at a finite time. Remarkably, these results can be derived from only an elementary knowledge of differential equations.

  8. An Exactly Solvable Model for the Spread of Disease

    ERIC Educational Resources Information Center

    Mickens, Ronald E.

    2012-01-01

    We present a new SIR epidemiological model whose exact analytical solution can be calculated. In this model, unlike previous models, the infective population becomes zero at a finite time. Remarkably, these results can be derived from only an elementary knowledge of differential equations.

  9. Solvable time-dependent models in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Cordero-Soto, Ricardo J.

    In the traditional setting of quantum mechanics, the Hamiltonian operator does not depend on time. While some Schrodinger equations with time-dependent Hamiltonians have been solved, explicitly solvable cases are typically scarce. This thesis is a collection of papers in which this first author along with Suslov, Suazo, and Lopez, has worked on solving a series of Schrodinger equations with a time-dependent quadratic Hamiltonian that has applications in problems of quantum electrodynamics, lasers, quantum devices such as quantum dots, and external varying fields. In particular the author discusses a new completely integrable case of the time-dependent Schrodinger equation in Rn with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator considered by Meiler, Cordero-Soto, and Suslov. A second pair of dual Hamiltonians is found in the momentum representation. Our examples show that in mathematical physics and quantum mechanics a change in the direction of time may require a total change of the system dynamics in order to return the system back to its original quantum state. The author also considers several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schrodinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time-evolution of the expectation values of the energy related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator. Finally, the author constructs integrals of motion for several models

  10. The anisotropic oscillator on curved spaces: A new exactly solvable model

    NASA Astrophysics Data System (ADS)

    Ballesteros, Ángel; Herranz, Francisco J.; Kuru, Şengül; Negro, Javier

    2016-10-01

    We present a new exactly solvable (classical and quantum) model that can be interpreted as the generalization to the two-dimensional sphere and to the hyperbolic space of the two-dimensional anisotropic oscillator with any pair of frequencies ωx and ωy. The new curved Hamiltonian Hκ depends on the curvature κ of the underlying space as a deformation/contraction parameter, and the Liouville integrability of Hκ relies on its separability in terms of geodesic parallel coordinates, which generalize the Cartesian coordinates of the plane. Moreover, the system is shown to be superintegrable for commensurate frequencies ωx :ωy, thus mimicking the behaviour of the flat Euclidean case, which is always recovered in the κ → 0 limit. The additional constant of motion in the commensurate case is, as expected, of higher-order in the momenta and can be explicitly deduced by performing the classical factorization of the Hamiltonian. The known 1 : 1 and 2 : 1 anisotropic curved oscillators are recovered as particular cases of Hκ, meanwhile all the remaining ωx :ωy curved oscillators define new superintegrable systems. Furthermore, the quantum Hamiltonian Hˆκ is fully constructed and studied by following a quantum factorization approach. In the case of commensurate frequencies, the Hamiltonian Hˆκ turns out to be quantum superintegrable and leads to a new exactly solvable quantum model. Its corresponding spectrum, that exhibits a maximal degeneracy, is explicitly given as an analytical deformation of the Euclidean eigenvalues in terms of both the curvature κ and the Planck constant ħ. In fact, such spectrum is obtained as a composition of two one-dimensional (either trigonometric or hyperbolic) Pösch-Teller set of eigenvalues.

  11. Solvable four-state Landau-Zener model of two interacting qubits with path interference

    DOE PAGES

    Sinitsyn, Nikolai A.

    2015-11-30

    In this paper, I identify a nontrivial four-state Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. The model describes an experimentally accessible system of two interacting qubits, such as a localized state in a Dirac material with both valley and spin degrees of freedom or a singly charged quantum dot (QD) molecule with spin orbit coupling. Application of the linearly time-dependent magnetic field induces a sequence of quantum level crossings with possibility of interference of different trajectories in a semiclassical picture. I argue that this system satisfies the criteria ofmore » integrability in the multistate Landau-Zener theory, which allows one to derive explicit exact analytical expressions for the transition probability matrix. Finally, I also argue that this model is likely a special case of a larger class of solvable systems, and present a six-state generalization as an example.« less

  12. Non-cooperative Brownian donkeys: A solvable 1D model

    NASA Astrophysics Data System (ADS)

    Jiménez de Cisneros, B.; Reimann, P.; Parrondo, J. M. R.

    2003-12-01

    A paradigmatic 1D model for Brownian motion in a spatially symmetric, periodic system is tackled analytically. Upon application of an external static force F the system's response is an average current which is positive for F < 0 and negative for F > 0 (absolute negative mobility). Under suitable conditions, the system approaches 100% efficiency when working against the external force F.

  13. Solvable structures of a simple model of earthquakes

    NASA Astrophysics Data System (ADS)

    Białecki, Mariusz

    2016-01-01

    This paper propose an extension of Random Domino Automaton by introducing extra parameter related to a very short-distance interactions between clusters which allows to isolate influence two mechanisms of clusters grow, namely enlarging and coalescence. In this setting statistically stationary state under assumption of independence of clusters is investigated and respective set of equations is derived. Moreover, a special solvable case is studied in detail and it is shown how to derive Motzkin numbers out of the automaton for a family of parameters without considering a limit.

  14. Localized Majorana-Like Modes in a Number-Conserving Setting: An Exactly Solvable Model.

    PubMed

    Iemini, Fernando; Mazza, Leonardo; Rossini, Davide; Fazio, Rosario; Diehl, Sebastian

    2015-10-09

    In this Letter we present, in a number conserving framework, a model of interacting fermions in a two-wire geometry supporting nonlocal zero-energy Majorana-like edge excitations. The model has an exactly solvable line, on varying the density of fermions, described by a topologically nontrivial ground state wave function. Away from the exactly solvable line we study the system by means of the numerical density matrix renormalization group. We characterize its topological properties through the explicit calculation of a degenerate entanglement spectrum and of the braiding operators which are exponentially localized at the edges. Furthermore, we establish the presence of a gap in its single particle spectrum while the Hamiltonian is gapless, and compute the correlations between the edge modes as well as the superfluid correlations. The topological phase covers a sizable portion of the phase diagram, the solvable line being one of its boundaries.

  15. Quasi exactly solvable extension of Calogero model associated with exceptional orthogonal polynomials

    NASA Astrophysics Data System (ADS)

    Basu-Mallick, B.; Mandal, Bhabani Prasad; Roy, Pinaki

    2017-05-01

    By using the technique of supersymmetric quantum mechanics, we study a quasi exactly solvable extension of the N-particle rational Calogero model with harmonic confining interaction. Such quasi exactly solvable many particle system, whose effective potential in the radial direction yields a supersymmetric partner of the radial harmonic oscillator, is constructed by including new long-range interactions to the rational Calogero model. An infinite number of bound state energy levels are obtained for this system under certain conditions. We also calculate the corresponding bound state wave functions in terms of the recently discovered exceptional orthogonal Laguerre polynomials.

  16. Exactly solvable models for symmetry-enriched topological phases

    NASA Astrophysics Data System (ADS)

    Cheng, Meng; Gu, Zheng-Cheng; Jiang, Shenghan; Qi, Yang

    2017-09-01

    We construct fixed-point wave functions and exactly solvable commuting-projector Hamiltonians for a large class of bosonic symmetry-enriched topological (SET) phases, based on the concept of equivalent classes of symmetric local unitary transformations. We argue that for onsite unitary symmetries, our construction realizes all SETs free of anomaly, as long as the underlying topological order itself can be realized with a commuting-projector Hamiltonian. We further extend the construction to antiunitary symmetries (e.g., time-reversal symmetry), mirror-reflection symmetries, and to anomalous SETs on the surface of three-dimensional symmetry-protected topological phases. Mathematically, our construction naturally leads to a generalization of group extensions of unitary fusion categories to antiunitary symmetries.

  17. PREFACE: Singular interactions in quantum mechanics: solvable models

    NASA Astrophysics Data System (ADS)

    Dell'Antonio, Gianfausto; Exner, Pavel; Geyler, Vladimir

    2005-06-01

    This issue comprises two dozen research papers which are all in one sense or another devoted to models in which the interaction is singular and sharply localized; a typical example is a quantum particle interacting with a family of δ-type potentials. Such an idealization usually makes analysis of their properties considerably easier, sometimes allowing us to reduce it to a simple algebraic problem—this is why one speaks about solvable models. The subject can be traced back to the early days of quantum mechanics; however, the progress in this field was slow and uneven until the 1960s, mostly because singular interactions are often difficult to deal with mathematically and intuitive arguments do not work. After overcoming the initial difficulties the `classical' theory of point interactions was developed, and finally summarized in 1988 in a monograph by Albeverio, Gesztesy, Høegh-Krohn, and Holden, which you will find quoted in numerous places within this issue. A reliable way to judge theories is to observe the progress they make within one or two decades. In this case there is no doubt that the field has witnessed a continuous development and covered areas which nobody had thought of when the subject first emerged. The reader may see it in the second edition of the aforementioned book which was published by AMS Chelsea only recently and contained a brief survey of these new achievements. It is no coincidence that this topical issue appears at the same time; it has been conceived as its counterpart and a forum at which fresh results in the field can demonstrated. Let us briefly survey the contents of the issue. While the papers included have in common the basic subject, they represent a broad spectrum philosophically as well as technically, and any attempt to classify them is somewhat futile. Nevertheless, we will divide them into a few groups. The first comprises contributions directly related to the usual point-interaction ideology. M Correggi and one of the

  18. Current fluctuations and statistics during a large deviation event in an exactly solvable transport model

    NASA Astrophysics Data System (ADS)

    Hurtado, Pablo I.; Garrido, Pedro L.

    2009-02-01

    We study the distribution of the time-integrated current in an exactly solvable toy model of heat conduction, both analytically and numerically. The simplicity of the model allows us to derive the full current large deviation function and the system statistics during a large deviation event. In this way we unveil a relation between system statistics at the end of a large deviation event and for intermediate times. The mid-time statistics is independent of the sign of the current, a reflection of the time-reversal symmetry of microscopic dynamics, while the end-time statistics does depend on the current sign, and also on its microscopic definition. We compare our exact results with simulations based on the direct evaluation of large deviation functions, analyzing the finite-size corrections of this simulation method and deriving detailed bounds for its applicability. We also show how the Gallavotti-Cohen fluctuation theorem can be used to determine the range of validity of simulation results.

  19. On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations

    SciTech Connect

    Zhang, Yao-Zhong

    2013-10-15

    We study the solvability of the time-independent matrix Schrödinger differential equations of the quantum Rabi model and its 2-photon and two-mode generalizations in Bargmann Hilbert spaces of entire functions. We show that the Rabi model and its 2-photon and two-mode analogs are quasi-exactly solvable. We derive the exact, closed-form expressions for the energies and the allowed model parameters for all the three cases in the solvable subspaces. Up to a normalization factor, the eigenfunctions for these models are given by polynomials whose roots are determined by systems of algebraic equations.

  20. Entanglement dynamics in a non-Markovian environment: An exactly solvable model

    NASA Astrophysics Data System (ADS)

    Wilson, Justin H.; Fregoso, Benjamin M.; Galitski, Victor M.

    2012-05-01

    We study the non-Markovian effects on the dynamics of entanglement in an exactly solvable model that involves two independent oscillators, each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time correlations, we see nonmonotonic evolution of the uncertainties in observables. Further, we extend this exact solution to the two-particle problem and find the dynamics of entanglement in a subspace. We find the phenomena of “sudden death” and “rebirth” of entanglement. Interestingly, all memory effects enter via the functional form of the energy and hence the time of death and rebirth is controlled by the amount of noisy energy added into each oscillator. If this energy increases above (decreases below) a threshold, we obtain sudden death (rebirth) of entanglement.

  1. Quasi-exactly solvable relativistic soft-core Coulomb models

    SciTech Connect

    Agboola, Davids Zhang, Yao-Zhong

    2012-09-15

    By considering a unified treatment, we present quasi exact polynomial solutions to both the Klein-Gordon and Dirac equations with the family of soft-core Coulomb potentials V{sub q}(r)=-Z/(r{sup q}+{beta}{sup q}){sup 1/q}, Z>0, {beta}>0, q{>=}1. We consider cases q=1 and q=2 and show that both cases are reducible to the same basic ordinary differential equation. A systematic and closed form solution to the basic equation is obtained using the Bethe ansatz method. For each case, the expressions for the energies and the allowed parameters are obtained analytically and the wavefunctions are derived in terms of the roots of a set of Bethe ansatz equations. - Highlights: Black-Right-Pointing-Pointer The relativistic bound-state solutions of the soft-core Coulomb models. Black-Right-Pointing-Pointer Quasi-exact treatments of the Dirac and Klein-Gordon equations for the soft-core Coulomb models. Black-Right-Pointing-Pointer Solutions obtained in terms of the roots to the Bethe ansatz equations. Black-Right-Pointing-Pointer The hidden Lie algebraic structure discussed for the models. Black-Right-Pointing-Pointer Results useful in describing mesonic atoms and interaction of intense laser fields with atom.

  2. Isovector Pairing within the so(5) Richardson-Gaudin Exactly Solvable Model

    SciTech Connect

    Dimitrova, S S; Dukelsky, J; Gueorguiev, V G; Van Isacker, P

    2005-10-10

    Properties of a nucleon system interacting via isovector proton-neutron pairing can be described within the so(5) generalized Richardson-Gaudin exactly-solvable model [1]. We present results for a system of 12 nucleon pairs within the full f{sub p} + g{sub 9/2} shell-model space. We discuss coupling constant dependence of the pair energies, total energy of the system, and the occupation numbers.

  3. Phase transitions in community detection: A solvable toy model

    NASA Astrophysics Data System (ADS)

    Ver Steeg, Greg; Moore, Cristopher; Galstyan, Aram; Allahverdyan, Armen

    2014-05-01

    Recently, it was shown that there is a phase transition in the community detection problem. This transition was first computed using the cavity method, and has been proved rigorously in the case of q = 2 groups. However, analytic calculations using the cavity method are challenging since they require us to understand probability distributions of messages. We study analogous transitions in the so-called “zero-temperature inference” model, where this distribution is supported only on the most likely messages. Furthermore, whenever several messages are equally likely, we break the tie by choosing among them with equal probability, corresponding to an infinitesimal random external field. While the resulting analysis overestimates the thresholds, it reproduces some of the qualitative features of the system. It predicts a first-order detectability transition whenever q > 2 (as opposed to q > 4 according to the finite-temperature cavity method). It also has a regime analogous to the “hard but detectable” phase, where the community structure can be recovered, but only when the initial messages are sufficiently accurate. Finally, we study a semisupervised setting where we are given the correct labels for a fraction ρ of the nodes. For q > 2, we find a regime where the accuracy jumps discontinuously at a critical value of ρ.

  4. Universal Finite Size Corrections and the Central Charge in Non-solvable Ising Models

    NASA Astrophysics Data System (ADS)

    Giuliani, Alessandro; Mastropietro, Vieri

    2013-11-01

    We investigate a non-solvable two-dimensional ferromagnetic Ising model with nearest neighbor plus weak finite range interactions of strength λ. We rigorously establish one of the predictions of Conformal Field Theory (CFT), namely the fact that at the critical temperature the finite size corrections to the free energy are universal, in the sense that they are exactly independent of the interaction. The corresponding central charge, defined in terms of the coefficient of the first subleading term to the free energy, as proposed by Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2 for all and λ 0 a small but finite convergence radius. This is one of the very few cases where the predictions of CFT can be rigorously verified starting from a microscopic non solvable statistical model. The proof uses a combination of rigorous renormalization group methods with a novel partition function inequality, valid for ferromagnetic interactions.

  5. A generalisation of a solvable model in population dynamics

    NASA Astrophysics Data System (ADS)

    DeRise, G.; Adam, J. A.

    1990-07-01

    Biswas and Karmakar (1976) were the first to consider a periodic rate transform for an autocatalytic growth process, G(x)=-tan( alpha ln x). They obtained an exact analytic solution for the probability density function by solving the equivalent Schrodinger equation for the Fokker-Planck equation, and utilised this function to calculate various moments. In this letter the authors extend their work to a more general rate transfer G(x)= alpha tan ( beta ln x)+ delta cot ( beta ln x).

  6. Dynamics of Gas Exchange through the Fractal Architecture of the Human Lung, Modeled as an Exactly Solvable Hierarchical Tree

    NASA Astrophysics Data System (ADS)

    Mayo, Michael; Pfeifer, Peter; Gheorghiu, Stefan

    2008-03-01

    The acinar airways lie at the periphery of the human lung and are responsible for the transfer of oxygen from air to the blood during respiration. This transfer occurs by the diffusion-reaction of oxygen over the irregular surface of the alveolar membranes lining the acinar airways. We present an exactly solvable diffusion-reaction model on a hierarchically branched tree, allowing a quantitative prediction of the oxygen current over the entire system of acinar airways responsible for the gas exchange. We discuss the effect of diffusional screening, which is strongly coupled to oxygen transport in the human lung. We show that the oxygen current is insensitive to a loss of permeability of the alveolar membranes over a wide range of permeabilities, similar to a ``constant-current source'' in an electric network. Such fault tolerance has been observed in other treatments of the gas exchange in the lung and is obtained here as a fully analytical result.

  7. Solvable model of a trapped mixture of Bose-Einstein condensates

    NASA Astrophysics Data System (ADS)

    Klaiman, Shachar; Streltsov, Alexej I.; Alon, Ofir E.

    2017-01-01

    A mixture of two kinds of identical bosons held in a harmonic potential and interacting by harmonic particle-particle interactions is discussed. This is an exactly-solvable model of a mixture of two trapped Bose-Einstein condensates which allows us to examine analytically various properties. Generalizing the treatments in Cohen and Lee (1985) and Osadchii and Muraktanov (1991), closed form expressions for the mixture's frequencies and ground-state energy and wave-function, and the lowest-order densities are obtained and analyzed for attractive and repulsive intra-species and inter-species particle-particle interactions. A particular mean-field solution of the corresponding Gross-Pitaevskii theory is also found analytically. This allows us to compare properties of the mixture at the exact, many-body and mean-field levels, both for finite systems and at the limit of an infinite number of particles. We discuss the renormalization of the mixture's frequencies at the mean-field level. Mainly, we hereby prove that the exact ground-state energy per particle and lowest-order intra-species and inter-species densities per particle converge at the infinite-particle limit (when the products of the number of particles times the intra-species and inter-species interaction strengths are held fixed) to the results of the Gross-Pitaevskii theory for the mixture. Finally and on the other end, we use the mixture's and each species' center-of-mass operators to show that the Gross-Pitaevskii theory for mixtures is unable to describe the variance of many-particle operators in the mixture, even in the infinite-particle limit. The variances are computed both in position and momentum space and the respective uncertainty products compared and discussed. The role of the center-of-mass separability and, for generically trapped mixtures, inseparability is elucidated when contrasting the variance at the many-body and mean-field levels in a mixture. Our analytical results show that many

  8. Unitary-matrix models as exactly solvable string theories

    NASA Technical Reports Server (NTRS)

    Periwal, Vipul; Shevitz, Danny

    1990-01-01

    Exact differential equations are presently found for the scaling functions of models of unitary matrices which are solved in a double-scaling limit, using orthogonal polynomials on a circle. For the case of the simplest, k = 1 model, the Painleve II equation with constant 0 is obtained; possible nonperturbative phase transitions exist for these models. Equations are presented for k = 2 and 3, and discussed with a view to asymptotic behavior.

  9. Pressure in an exactly solvable model of active fluid

    NASA Astrophysics Data System (ADS)

    Marini Bettolo Marconi, Umberto; Maggi, Claudio; Paoluzzi, Matteo

    2017-07-01

    We consider the pressure in the steady-state regime of three stochastic models characterized by self-propulsion and persistent motion and widely employed to describe the behavior of active particles, namely, the Active Brownian particle (ABP) model, the Gaussian colored noise (GCN) model, and the unified colored noise approximation (UCNA) model. Whereas in the limit of short but finite persistence time, the pressure in the UCNA model can be obtained by different methods which have an analog in equilibrium systems, in the remaining two models only the virial route is, in general, possible. According to this method, notwithstanding each model obeys its own specific microscopic law of evolution, the pressure displays a certain universal behavior. For generic interparticle and confining potentials, we derive a formula which establishes a correspondence between the GCN and the UCNA pressures. In order to provide explicit formulas and examples, we specialize the discussion to the case of an assembly of elastic dumbbells confined to a parabolic well. By employing the UCNA we find that, for this model, the pressure determined by the thermodynamic method coincides with the pressures obtained by the virial and mechanical methods. The three methods when applied to the GCN give a pressure identical to that obtained via the UCNA. Finally, we find that the ABP virial pressure exactly agrees with the UCNA and GCN results.

  10. Numerically Solvable Model for Resonant Collisions of Electronswith Diatomic Molecules

    SciTech Connect

    Houfek, Karel; Rescigno, T.N.; McCurdy, C.W.

    2006-01-27

    We describe a simple model for electron-molecule collisions that has one nuclear and one electronic degree of freedom and that can be solved to arbitrarily high precision, without making the Born-Oppenheimer approximation, by employing a combination of the exterior complex scaling method and a finite-element implementation of the discrete variable representation. We compare exact cross sections for vibrational excitation and dissociative attachment with results obtained using the local complex potential approximation as commonly applied in the ''boomerang'' model, and suggest how this two-dimensional model can be used to test the underpinnings of contemporary nonlocal approximations to resonant collisions.

  11. An (almost) solvable model for bacterial pattern formation

    NASA Astrophysics Data System (ADS)

    Grammaticos, B.; Badoual, M.; Aubert, M.

    2007-10-01

    We present a simple model for the description of ring-like concentric structures in bacterial colonies. We model the differences between Bacillus subtilis and Proteus mirabilis colonies by using a different dependence of the duration of the consolidation phase on the concentration of agar. We compare our results to experimental data from these two bacterial species colonies and obtain a good agreement. Based on this analysis, we formulate a hypothesis on the connection of the diffusion constant that appears in the model to the experimental agar concentration.

  12. Solvable model for chimera states of coupled oscillators.

    PubMed

    Abrams, Daniel M; Mirollo, Rennie; Strogatz, Steven H; Wiley, Daniel A

    2008-08-22

    Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.

  13. Oscillations and chaos in neural networks: an exactly solvable model.

    PubMed Central

    Wang, L P; Pichler, E E; Ross, J

    1990-01-01

    We consider a randomly diluted higher-order network with noise, consisting of McCulloch-Pitts neurons that interact by Hebbian-type connections. For this model, exact dynamical equations are derived and solved for both parallel and random sequential updating algorithms. For parallel dynamics, we find a rich spectrum of different behaviors including static retrieving and oscillatory and chaotic phenomena in different parts of the parameter space. The bifurcation parameters include first- and second-order neuronal interaction coefficients and a rescaled noise level, which represents the combined effects of the random synaptic dilution, interference between stored patterns, and additional background noise. We show that a marked difference in terms of the occurrence of oscillations or chaos exists between neural networks with parallel and random sequential dynamics. Images PMID:2251287

  14. An exactly solvable model for the graphene transistor in the quantum capacitance limit

    NASA Astrophysics Data System (ADS)

    Parrish, Kristen N.; Akinwande, Deji

    2012-07-01

    We explore the ultimate behavior of the graphene transistor in the quantum capacitance limit. The quantum capacitance formulation allows for an exactly solvable model, and the ideal assumptions provide an upper bound on performance, including peak currents of 1 mA/μm with mobilities as low as 2000 cm2/V s for channel length of 1 μm, as well as linearly increasing transconductance not observed in conventional transistors. A negative differential resistance is predicted under certain conditions, with a maximum peak-to-valley-current ratio of 4. Finally, the effects of oxide scaling are elucidated and the oxide capacitances required for quantum capacitance limited behavior are quantified.

  15. Spreading of correlations in exactly solvable quantum models with long-range interactions in arbitrary dimensions

    NASA Astrophysics Data System (ADS)

    Cevolani, Lorenzo; Carleo, Giuseppe; Sanchez-Palencia, Laurent

    2016-09-01

    We study the out-of-equilibrium dynamics induced by quantum quenches in quadratic Hamiltonians featuring both short- and long-range interactions. The spreading of correlations in the presence of algebraic decaying interactions, 1/R α , is studied for lattice Bose models in arbitrary dimension D. These models are exactly solvable and provide useful insight in the universal description of more complex systems as well as comparisons to the known universal upper bounds for the spreading of correlations. Using analytical calculations of the dominant terms and full numerical integration of all quasi-particle contributions, we identify three distinct dynamical regimes. For strong decay of interactions, α \\gt D+1, we find a causal regime, qualitatively similar to what previously found for short-range interactions. This regime is characterized by ballistic (linear cone) spreading of the correlations with a cone velocity equal to twice the maximum group velocity of the quasi-particles. For weak decay of interactions, α < D, we find instantaneous activation of correlations at arbitrary distance. This signals the breaking of causality, which can be associated with the divergence of the quasi-particle energy spectrum. Finite-size scaling of the activation time precisely confirms this interpretation. For intermediate decay of interactions, D\\lt α \\lt D+1, we find a sub-ballistic, algebraic (bent cone) spreading and determine the corresponding exponent as a function of α. These outcomes generalize existing results for one-dimensional systems to arbitrary dimension. We precisely relate the three regimes to the first- and second-order divergences of the quasi-particle energy spectrum for any dimension. The long-range transverse Ising model in dimensions D = 1, 2, and 3 in the (quadratic) spin-wave approximation is more specifically studied and we also discuss the shape of the correlation front in dimension higher than one. Our results apply to several condensed

  16. Solvable light-front model of the electromagnetic form factor of the relativistic two-body bound state in 1+1 dimensions

    SciTech Connect

    Mankiewicz, L. ); Sawicki, M. )

    1989-11-15

    Within a relativistically correct yet analytically solvable model of light-front quantum mechanics we construct the electromagnetic form factor of the two-body bound state and we study the validity of the static approximation to the full form factor. Upon comparison of full form factors calculated for different values of binding energy we observe an unexpected effect that for very strongly bound states further increase in binding leads to an increase in the size of the bound system. A similar effect is found for another quantum-mechanical model of relativistic dynamics.

  17. Exactly solvable spin chain models corresponding to BDI class of topological superconductors

    PubMed Central

    Jafari, S. A.; Shahbazi, Farhad

    2016-01-01

    We present an exactly solvable extension of the quantum XY chain with longer range multi-spin interactions. Topological phase transitions of the model are classified in terms of the number of Majorana zero modes, nM which are in turn related to an integer winding number, nW. The present class of exactly solvable models belong to the BDI class in the Altland-Zirnbauer classification of topological superconductors. We show that time reversal symmetry of the spin variables translates into a sliding particle-hole (PH) transformation in the language of Jordan-Wigner fermions – a PH transformation followed by a π shift in the wave vector which we call it the πPH. Presence of πPH symmetry restricts the nW (nM) of time-reversal symmetric extensions of XY to odd (even) integers. The πPH operator may serve in further detailed classification of topological superconductors in higher dimensions as well. PMID:27596804

  18. Exactly solvable spin chain models corresponding to BDI class of topological superconductors

    NASA Astrophysics Data System (ADS)

    Jafari, S. A.; Shahbazi, Farhad

    2016-09-01

    We present an exactly solvable extension of the quantum XY chain with longer range multi-spin interactions. Topological phase transitions of the model are classified in terms of the number of Majorana zero modes, nM which are in turn related to an integer winding number, nW. The present class of exactly solvable models belong to the BDI class in the Altland-Zirnbauer classification of topological superconductors. We show that time reversal symmetry of the spin variables translates into a sliding particle-hole (PH) transformation in the language of Jordan-Wigner fermions – a PH transformation followed by a π shift in the wave vector which we call it the πPH. Presence of πPH symmetry restricts the nW (nM) of time-reversal symmetric extensions of XY to odd (even) integers. The πPH operator may serve in further detailed classification of topological superconductors in higher dimensions as well.

  19. Exactly solvable spin chain models corresponding to BDI class of topological superconductors.

    PubMed

    Jafari, S A; Shahbazi, Farhad

    2016-09-06

    We present an exactly solvable extension of the quantum XY chain with longer range multi-spin interactions. Topological phase transitions of the model are classified in terms of the number of Majorana zero modes, nM which are in turn related to an integer winding number, nW. The present class of exactly solvable models belong to the BDI class in the Altland-Zirnbauer classification of topological superconductors. We show that time reversal symmetry of the spin variables translates into a sliding particle-hole (PH) transformation in the language of Jordan-Wigner fermions - a PH transformation followed by a π shift in the wave vector which we call it the πPH. Presence of πPH symmetry restricts the nW (nM) of time-reversal symmetric extensions of XY to odd (even) integers. The πPH operator may serve in further detailed classification of topological superconductors in higher dimensions as well.

  20. Symmetry-enriched string nets: Exactly solvable models for SET phases

    NASA Astrophysics Data System (ADS)

    Heinrich, Chris; Burnell, Fiona; Fidkowski, Lukasz; Levin, Michael

    2016-12-01

    We construct exactly solvable models for a wide class of symmetry-enriched topological (SET) phases. Our construction applies to two-dimensional (2D) bosonic SET phases with finite unitary on-site symmetry group G and we conjecture that our models realize every phase in this class that can be described by a commuting projector Hamiltonian. Our models are designed so that they have a special property: If we couple them to a dynamical lattice gauge field with gauge group G , the resulting gauge theories are equivalent to string-net models. This property is what allows us to analyze our models in generality. As an example, we present a model for a phase with the same anyon excitations as the toric code and with a Z2 symmetry which exchanges the e and m type anyons. We further illustrate our construction with a number of additional examples.

  1. Solvability of the Initial Value Problem to the Isobe-Kakinuma Model for Water Waves

    NASA Astrophysics Data System (ADS)

    Nemoto, Ryo; Iguchi, Tatsuo

    2017-09-01

    We consider the initial value problem to the Isobe-Kakinuma model for water waves and the structure of the model. The Isobe-Kakinuma model is the Euler-Lagrange equations for an approximate Lagrangian which is derived from Luke's Lagrangian for water waves by approximating the velocity potential in the Lagrangian. The Isobe-Kakinuma model is a system of second order partial differential equations and is classified into a system of nonlinear dispersive equations. Since the hypersurface t=0 is characteristic for the Isobe-Kakinuma model, the initial data have to be restricted in an infinite dimensional manifold for the existence of the solution. Under this necessary condition and a sign condition, which corresponds to a generalized Rayleigh-Taylor sign condition for water waves, on the initial data, we show that the initial value problem is solvable locally in time in Sobolev spaces. We also discuss the linear dispersion relation to the model.

  2. A solvable model of axisymmetric and non-axisymmetric droplet bouncing.

    PubMed

    Andrew, Matthew; Yeomans, Julia M; Pushkin, Dmitri O

    2017-02-07

    We introduce a solvable Lagrangian model for droplet bouncing. The model predicts that, for an axisymmetric drop, the contact time decreases to a constant value with increasing Weber number, in qualitative agreement with experiments, because the system is well approximated as a simple harmonic oscillator. We introduce asymmetries in the velocity, initial droplet shape, and contact line drag acting on the droplet and show that asymmetry can often lead to a reduced contact time and lift-off in an elongated shape. The model allows us to explain the mechanisms behind non-axisymmetric bouncing in terms of surface tension forces. Once the drop has an elliptical footprint the surface tension force acting on the longer sides is greater. Therefore the shorter axis retracts faster and, due to the incompressibility constraints, pumps fluid along the more extended droplet axis. This leads to a positive feedback, allowing the drop to jump in an elongated configuration, and more quickly.

  3. Efficient Solvability of Hamiltonians and Limits on the Power of Some Quantum Computational Models

    NASA Astrophysics Data System (ADS)

    Somma, Rolando; Barnum, Howard; Ortiz, Gerardo; Knill, Emanuel

    2006-11-01

    One way to specify a model of quantum computing is to give a set of control Hamiltonians acting on a quantum state space whose initial state and final measurement are specified in terms of the Hamiltonians. We formalize such models and show that they can be simulated classically in a time polynomial in the dimension of the Lie algebra generated by the Hamiltonians and logarithmic in the dimension of the state space. This leads to a definition of Lie-algebraic “generalized mean-field Hamiltonians.” We show that they are efficiently (exactly) solvable. Our results generalize the known weakness of fermionic linear optics computation and give conditions on control needed to exploit the full power of quantum computing.

  4. Solvability condition for needle crystals at large undercooling in a nonlocal model of solidification

    NASA Technical Reports Server (NTRS)

    Caroli, B.; Caroli, C.; Roulet, B.; Langer, J. S.

    1986-01-01

    It is explicitly shown that, in a realistic model of diffusion-controlled dendritic solidification, Ivantsov's continuous family of steady-state needle crystals is destroyed by the addition of surface tension. The starting point is in the exact integro-differential equation for the one-sided model, in two dimensions, in a moving frame of reference. In the limit of large undercooling, where the range of the diffusion field is much smaller than the radius of curvature of the tip of the needle, this problem is reduced to a linear, inhomogeneous differential equation of infinite order. A solvability condition for this equation is derived and it is shown that solutions cease to exist for arbitrarily small but finite isotropic surface tension.

  5. Quantum scattering theory in light of an exactly solvable model with rearrangement collisions

    SciTech Connect

    Varma, S.; Sudarshan, E.C.

    1996-04-01

    We present an exactly solvable quantum field theory which allows rearrangement collisions. We solve the model in the relevant sectors and demonstrate the orthonormality and completeness of the solutions, and construct the {ital S}-matrix. In light of the exact solutions constructed, we discuss various issues and assumptions in quantum scattering theory, including the isometry of the M{umlt o}ller wave matrix, the normalization and completeness of asymptotic states, and the nonorthogonality of basis states. We show that these common assertions are not obtained in this model. We suggest a general formalism for scattering theory which overcomes these and other shortcomings and limitations of the existing formalisms in the literature. {copyright} {ital 1996 American Institute of Physics.}

  6. CALL FOR PAPERS: Special Issue on `Singular Interactions in Quantum Mechanics: Solvable Models'

    NASA Astrophysics Data System (ADS)

    Dell'Antonio, G.; Exner, P.; Geyler, V.

    2004-07-01

    This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General entitled `Singular Interactions in Quantum Mechanics: Solvable Models'. This issue should be a repository for high quality original work. We are interested in having the topic interpreted broadly, that is, to include contributions dealing with point-interaction models, one- and many-body, quantum graphs, including graph-like structures coupling different dimensions, interactions supported by curves, manifolds, and more complicated sets, random and nonlinear couplings, etc., as well as approximations helping us to understand the meaning of singular couplings and applications of such models on different parts of quantum mechanics. We believe that when the second printing of the `bible' of the field, the book Solvable Models in Quantum Mechanics by S Albeverio, F Gesztesy, the late R Høegh-Krohn and H Holden, appears it is the right moment to review new developments in this area, with the hope of stimulating further development of these extremely useful techniques. The Editorial Board has invited G Dell'Antonio, P Exner and V Geyler to serve as Guest Editors for the special issue. Their criteria for acceptance of contributions are as follows: bullet The subject of the paper should relate to singular interactions in quantum mechanics in the sense described above. bullet Contributions will be refereed and processed according to the usual procedure of the journal. bullet Papers should be original; reviews of a work published elsewhere will not be accepted. The guidelines for the preparation of contributions are as follows: bullet The DEADLINE for submission of contributions is 31 October 2004. This deadline will allow the special issue to appear in about April 2005. bullet There is a nominal page limit of 15 printed pages (approximately 9000 words) per contribution. Papers exceeding these limits may be accepted at the discretion of the Guest Editors. Further advice on

  7. A dynamical systems approach to the tilted Bianchi models of solvable type

    NASA Astrophysics Data System (ADS)

    Coley, Alan; Hervik, Sigbjørn

    2005-02-01

    We use a dynamical systems approach to analyse the tilting spatially homogeneous Bianchi models of solvable type (e.g., types VIh and VIIh) with a perfect fluid and a linear barotropic γ-law equation of state. In particular, we study the late-time behaviour of tilted Bianchi models, with an emphasis on the existence of equilibrium points and their stability properties. We briefly discuss the tilting Bianchi type V models and the late-time asymptotic behaviour of irrotational Bianchi type VII0 models. We prove the important result that for non-inflationary Bianchi type VIIh models vacuum plane-wave solutions are the only future attracting equilibrium points in the Bianchi type VIIh invariant set. We then investigate the dynamics close to the plane-wave solutions in more detail, and discover some new features that arise in the dynamical behaviour of Bianchi cosmologies with the inclusion of tilt. We point out that in a tiny open set of parameter space in the type IV model (the loophole) there exist closed curves which act as attracting limit cycles. More interestingly, in the Bianchi type VIIh models there is a bifurcation in which a set of equilibrium points turns into closed orbits. There is a region in which both sets of closed curves coexist, and it appears that for the type VIIh models in this region the solution curves approach a compact surface which is topologically a torus.

  8. Filtering a statistically exactly solvable test model for turbulent tracers from partial observations

    SciTech Connect

    Gershgorin, B.; Majda, A.J.

    2011-02-20

    A statistically exactly solvable model for passive tracers is introduced as a test model for the authors' Nonlinear Extended Kalman Filter (NEKF) as well as other filtering algorithms. The model involves a Gaussian velocity field and a passive tracer governed by the advection-diffusion equation with an imposed mean gradient. The model has direct relevance to engineering problems such as the spread of pollutants in the air or contaminants in the water as well as climate change problems concerning the transport of greenhouse gases such as carbon dioxide with strongly intermittent probability distributions consistent with the actual observations of the atmosphere. One of the attractive properties of the model is the existence of the exact statistical solution. In particular, this unique feature of the model provides an opportunity to design and test fast and efficient algorithms for real-time data assimilation based on rigorous mathematical theory for a turbulence model problem with many active spatiotemporal scales. Here, we extensively study the performance of the NEKF which uses the exact first and second order nonlinear statistics without any approximations due to linearization. The role of partial and sparse observations, the frequency of observations and the observation noise strength in recovering the true signal, its spectrum, and fat tail probability distribution are the central issues discussed here. The results of our study provide useful guidelines for filtering realistic turbulent systems with passive tracers through partial observations.

  9. Does really Born Oppenheimer approximation break down in charge transfer processes? An exactly solvable model

    NASA Astrophysics Data System (ADS)

    Kuznetsov, Alexander M.; Medvedev, Igor G.

    2006-05-01

    Effects of deviation from the Born-Oppenheimer approximation (BOA) on the non-adiabatic transition probability for the transfer of a quantum particle in condensed media are studied within an exactly solvable model. The particle and the medium are modeled by a set of harmonic oscillators. The dynamic interaction of the particle with a single local mode is treated explicitly without the use of BOA. Two particular situations (symmetric and non-symmetric systems) are considered. It is shown that the difference between the exact solution and the true BOA is negligibly small at realistic parameters of the model. However, the exact results differ considerably from those of the crude Condon approximation (CCA) which is usually considered in the literature as a reference point for BOA (Marcus-Hush-Dogonadze formula). It is shown that the exact rate constant can be smaller (symmetric system) or larger (non-symmetric one) than that obtained in CCA. The non-Condon effects are also studied.

  10. Centralized versus decentralized control—A solvable stylized model in transportation

    NASA Astrophysics Data System (ADS)

    Hongler, Max-Olivier; Gallay, Olivier; Hülsmann, Michael; Cordes, Philip; Colmorn, Richard

    2010-10-01

    Today’s supply networks consist of a certain amount of logistics objects that are enabled to interact with each other and to decide autonomously upon their next steps; in other words, they exhibit a certain degree of autonomous cooperation. Therefore, modern logistics research regards them as complex adaptive logistics systems. In order to analyze evolving dynamics and underlying implications for the respective systems’ behavior as well as the potential outcomes resulting from the interaction between autonomous decision-making “smart parts”, we propose in this contribution a fully solvable stylized model. We consider a population of homogeneous, autonomous interacting agents traveling on R with a given velocity that is itself corrupted by White Gaussian Noise. Based on real time observations of the positions of his neighbors, each agent is allowed to adapt his traveling velocity. These agent interactions are restricted to neighboring entities confined in finite spatial clusters ( i.e. we have range-limited interactions). In the limit of a large population of neighboring agents, a mean-field dynamics can be derived and, for small interaction range, the resulting dynamics coincides with the exactly solvable Burgers’ nonlinear field equation. Explicit Burgers’ solution enables to explicitly appreciate the emergent structure due to the local and individual agent interactions. In particular, for strongly interactive regimes in the present model, the resulting spatial distribution of agents converges to a shock wave pattern. To compare performances of centralized versus decentralized organization, we assign cost functions incurred when velocity adaptations are triggered either by multi-agent interactions or by central control. The multi-agent cumulative costs are then compared with the costs that would be incurred by implementing an effective optimal central controller able, for a given time horizon, to reproduce an identical spatial probability distribution

  11. Geometric structure and geodesic in a solvable model of nonequilibrium process

    NASA Astrophysics Data System (ADS)

    Kim, Eun-jin; Lee, UnJin; Heseltine, James; Hollerbach, Rainer

    2016-06-01

    We investigate the geometric structure of a nonequilibrium process and its geodesic solutions. By employing an exactly solvable model of a driven dissipative system (generalized nonautonomous Ornstein-Uhlenbeck process), we compute the time-dependent probability density functions (PDFs) and investigate the evolution of this system in a statistical metric space where the distance between two points (the so-called information length) quantifies the change in information along a trajectory of the PDFs. In this metric space, we find a geodesic for which the information propagates at constant speed, and demonstrate its utility as an optimal path to reduce the total time and total dissipated energy. In particular, through examples of physical realizations of such geodesic solutions satisfying boundary conditions, we present a resonance phenomenon in the geodesic solution and the discretization into cyclic geodesic solutions. Implications for controlling population growth are further discussed in a stochastic logistic model, where a periodic modulation of the diffusion coefficient and the deterministic force by a small amount is shown to have a significant controlling effect.

  12. Quasi-exactly solvable quasinormal modes

    SciTech Connect

    Ho, C.-L.; Cho, H.-T.

    2007-11-20

    We consider quasinormal modes with complex energies from the point of view of the theory of quasi-exactly solvable (QES) models. We demonstrate that it is possible to find new potentials which admit exactly solvable or QES quasinormal modes by suitable complexification of parameters defining the QES potentials. Particularly, we obtain one QES and four exactly solvable potentials out of the five one-dimensional QES systems based on the sl(2) algebra.

  13. Violation of the quantum regression theorem and the Leggett-Garg inequality in an exactly solvable model

    NASA Astrophysics Data System (ADS)

    Ban, Masashi

    2017-08-01

    Violation of the quantum regression theorem and the Leggett-Garg inequality is studied by means of the exactly solvable multi-mode Jaynes-Cummings model. An exact expression of a two-time correlation function is compared with that derived by the quantum regression theorem. It is found that the quantum regression theorem is not valid even if the reduced time evolution of the qubit is Markovian. Furthermore, it is shown that if the quantum regression theorem is applied in this model, the Leggett-Garg inequality is satisfied while it is violated by the exact correlation function.

  14. Solvable model of a generic trapped mixture of interacting bosons: reduced density matrices and proof of Bose-Einstein condensation

    NASA Astrophysics Data System (ADS)

    Alon, Ofir E.

    2017-07-01

    A mixture of two kinds of identical bosons, species 1 with N 1 bosons of mass m 1 and species 2 with N 2 bosons of mass m 2, held in a harmonic potential of frequency ω and interacting by harmonic intra-species and inter-species particle-particle interactions of strengths λ1 , λ2 , and λ12 is discussed. This is an exactly-solvable model of a generic mixture of trapped interacting bosons which allows one to investigate and determine analytically properties of interest. To start, closed form expressions for the frequencies, ground-state energy, and wave-function of the mixture are obtained and briefly analyzed as a function of the masses, numbers of particles, and strengths and signs of interactions. To prove Bose-Einstein condensation of the mixture three steps are needed. First, we integrate the all-particle density matrix, employing a four-parameter matrix-recurrence relations, down to the lowest-order intra-species and inter-species reduced density matrices of the mixture. Second, the coupled Gross-Pitaevskii (mean-field) equations of the mixture are solved analytically. Third, we analyze the mixture’s reduced density matrices in the limit of an infinite number of particles of both species 1 and 2 (when the interaction parameters, i.e. the products of the number of particles times the intra-species and inter-species interaction strengths, are held fixed) and prove that: (i) both species 1 and 2 are 100% condensed; (ii) the inter-species reduced density matrix per particle is separable and given by the product of the intra-species reduced density matrices per particle; and (iii) the mixture’s energy per particle, and reduced density matrices and densities per particle all coincide with the Gross-Pitaevskii quantities. Finally, when the infinite-particle limit is taken with respect to, say, species 1 only (with interaction parameters held fixed) we prove that: (iv) only species 1 is 100% condensed and its reduced density matrix and density per particle, as

  15. Analytic Modeling of Insurgencies

    DTIC Science & Technology

    2014-08-01

    influenced by interests and utilities. 4.1 Carrots and Sticks An analytic model that captures the aforementioned utilitarian aspect is presented in...instead of the insurgents, to improve or worsen their welfare . The insurgents execute two types of actions: (a) violent actions, aimed to coerce potential

  16. The Marsden-Weinstein Reduction Structure of Integrable Dynamical Systems and a Generalized Exactly Solvable Quantum Superradiance Model

    NASA Astrophysics Data System (ADS)

    Bogolubov, N. N.; Prykarpatsky, Y. A.

    2013-03-01

    An approach to describing nonlinear Lax type integrable dynamical systems of modern mathematical and theoretical physics, based on the Marsden-Weinstein reduction method on canonically symplectic manifolds with group symmetry, is proposed. Its natural relationship with the well-known Adler-Kostant-Souriau-Berezin-Kirillov method and the associated R-matrix approach is analyzed. A new generalized exactly solvable spatially one-dimensional quantum superradiance model, describing a charged fermionic medium interacting with external electromagnetic field, is suggested. The Lax type operator spectral problem is presented, the related R-structure is calculated. The Hamilton operator renormalization procedure subject to a physically stable vacuum is described, the quantum excitations and quantum solitons, related with the thermodynamical equilibrity of the model, are discussed.

  17. Statistics of avalanches with relaxation and Barkhausen noise: a solvable model.

    PubMed

    Dobrinevski, Alexander; Le Doussal, Pierre; Wiese, Kay Jörg

    2013-09-01

    We study a generalization of the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model of a particle in a Brownian force landscape, including retardation effects. We show that under monotonous driving the particle moves forward at all times, as it does in absence of retardation (Middleton's theorem). This remarkable property allows us to develop an analytical treatment. The model with an exponentially decaying memory kernel is realized in Barkhausen experiments with eddy-current relaxation and has previously been shown numerically to account for the experimentally observed asymmetry of Barkhausen pulse shapes. We elucidate another qualitatively new feature: the breakup of each avalanche of the standard ABBM model into a cluster of subavalanches, sharply delimited for slow relaxation under quasistatic driving. These conditions are typical for earthquake dynamics. With relaxation and aftershock clustering, the present model includes important ingredients for an effective description of earthquakes. We analyze quantitatively the limits of slow and fast relaxation for stationary driving with velocity v>0. The v-dependent power-law exponent for small velocities, and the critical driving velocity at which the particle velocity never vanishes, are modified. We also analyze nonstationary avalanches following a step in the driving magnetic field. Analytically, we obtain the mean avalanche shape at fixed size, the duration distribution of the first subavalanche, and the time dependence of the mean velocity. We propose to study these observables in experiments, allowing a direct measurement of the shape of the memory kernel and tracing eddy current relaxation in Barkhausen noise.

  18. Solvable model for solitons pinned to a parity-time-symmetric dipole

    NASA Astrophysics Data System (ADS)

    Mayteevarunyoo, Thawatchai; Malomed, Boris A.; Reoksabutr, Athikom

    2013-08-01

    We introduce the simplest one-dimensional nonlinear model with parity-time (PT) symmetry, which makes it possible to find exact analytical solutions for localized modes (“solitons”). The PT-symmetric element is represented by a pointlike (δ-functional) gain-loss dipole ˜δ'(x), combined with the usual attractive potential ˜δ(x). The nonlinearity is represented by self-focusing (SF) or self-defocusing (SDF) Kerr terms, both spatially uniform and localized. The system can be implemented in planar optical waveguides. For the sake of comparison, also introduced is a model with separated δ-functional gain and loss, embedded into the linear medium and combined with the δ-localized Kerr nonlinearity and attractive potential. Full analytical solutions for pinned modes are found in both models. The exact solutions are compared with numerical counterparts, which are obtained in the gain-loss-dipole model with the δ' and δ functions replaced by their Lorentzian regularization. With the increase of the dipole's strength γ, the single-peak shape of the numerically found mode, supported by the uniform SF nonlinearity, transforms into a double peak. This transition coincides with the onset of the escape instability of the pinned soliton. In the case of the SDF uniform nonlinearity, the pinned modes are stable, keeping the single-peak shape.

  19. Active-absorbing-state phase transition beyond directed percolation: a class of exactly solvable models.

    PubMed

    Basu, Urna; Mohanty, P K

    2009-04-01

    We introduce and solve a model of hardcore particles on a one-dimensional periodic lattice which undergoes an active-absorbing-state phase transition at finite density. In this model, an occupied site is defined to be active if its left neighbor is occupied and the right neighbor is vacant. Particles from such active sites hop stochastically to their right. We show that both the density of active sites and the survival probability vanish as the particle density is decreased below half. The critical exponents and spatial correlations of the model are calculated exactly using the matrix product ansatz. Exact analytical study of several variations of the model reveals that these nonequilibrium phase transitions belong to a new universality class different from the generic active-absorbing-state phase transition, namely, directed percolation.

  20. Metric measures of interparticle interaction in an exactly solvable two-electron model atom

    SciTech Connect

    Nagy, I.; Aldazabal, I.

    2011-09-15

    The exact ground-state solutions for the model of two particles in a confining harmonic oscillator potential interacting through a repulsive harmonic oscillator force are used from the standpoint of geometric distances [Phys. Rev. Lett. 106, 050401 (2011).] between wave functions and densities. The distances from the noninteracting reference state are calculated at a specified confinement by increasing the coupling of the interparticle interaction. Based on the analytic expressions for coupling-dependent geometric measures, a discussion of the Hohenberg-Kohn mapping is given.

  1. An exactly solvable Ogston model of gel electrophoresis: X. Application to high-field separation techniques.

    PubMed

    Gauthier, Michel G; Slater, Gary W

    2003-01-01

    Recently, we generalized our lattice model of gel electrophoresis to study the net velocity of particles being pulled by a high-intensity electric field through an arbitrary distribution of immobile obstacles (Gauthier, M. G., Slater, G. W., J. Chem. Phys. 2002, 117, 6745-6756). In this article, we show how the high-field version of our model can be used to compare the velocity of particles with different electric charges and/or physical sizes. We then investigate specific two-dimensional distributions of obstacles that can be used to separate particles, e.g., in a microfluidic device. More precisely, we compare the velocity of differently charged or sized analytes in sieving, trapping and deflecting systems to model various electrophoretic separation techniques. In particular, we study the nonlinear effects present in ratchet systems and how they can be combined with time-asymmetric pulsed fields to provide new modes of separation.

  2. Quantum quench dynamics of the sine-Gordon model in some solvable limits

    NASA Astrophysics Data System (ADS)

    Iucci, A.; Cazalilla, M. A.

    2010-05-01

    With regard to the thermalization problem in isolated quantum systems, we investigate the dynamics following a quantum quench of the sine-Gordon model (sGM) in the Luther-Emery and the semiclassical limits. We consider the quench from the gapped to the gapless phase, as well as the reverse one. By obtaining analytic expressions for the one- and two-point correlation functions of the order parameter operator at zero-temperature, the manifestations of integrability in the absence of thermalization in the sGM are studied. It is shown that correlations in the long-time regime after the quench are well described by a generalized Gibbs ensemble. We also consider the case where the system is initially in contact with a reservoir at finite temperature. The possible relevance of our results to current and future experiments with ultracold atomic systems is also considered.

  3. Solvable random-walk model with memory and its relations with Markovian models of anomalous diffusion

    NASA Astrophysics Data System (ADS)

    Boyer, D.; Romo-Cruz, J. C. R.

    2014-10-01

    Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random-walk model with long-range memory for which not only the mean-square displacement (MSD) but also the propagator can be obtained exactly in the asymptotic limit. The model consists of a random walker on a lattice, which, at a constant rate, stochastically relocates at a site occupied at some earlier time. This time in the past is chosen randomly according to a memory kernel, whose temporal decay can be varied via an exponent parameter. In the weakly non-Markovian regime, memory reduces the diffusion coefficient from the bare value. When the mean backward jump in time diverges, the diffusion coefficient vanishes and a transition to an anomalous subdiffusive regime occurs. Paradoxically, at the transition, the process is an anticorrelated Lévy flight. Although in the subdiffusive regime the model exhibits some features of the continuous time random walk with infinite mean waiting time, it belongs to another universality class. If memory is very long-ranged, a second transition takes place to a regime characterized by a logarithmic growth of the MSD with time. In this case the process is asymptotically Gaussian and effectively described as a scaled Brownian motion with a diffusion coefficient decaying as 1 /t .

  4. Multicritical absorbing phase transition in a class of exactly solvable models

    NASA Astrophysics Data System (ADS)

    Chatterjee, Arijit; Mohanty, P. K.

    2016-12-01

    We study diffusion of hard-core particles on a one-dimensional periodic lattice subjected to a constraint that the separation between any two consecutive particles does not increase beyond a fixed value n +1 ; an initial separation larger than n +1 can however decrease. These models undergo an absorbing state phase transition when the conserved particle density of the system falls below a critical threshold ρc=1 /(n +1 ) . We find that the ϕk, the density of 0-clusters (0 representing vacancies) of size 0 ≤k models can be written in matrix product form to obtain analytically the static exponents βk=n -k and ν =1 =η corresponding to each ϕk. We also show from numerical simulations that, starting from a natural condition, ϕk(t ) s decay as t-αk with αk=(n -k ) /2 even though other dynamic exponents νt=2 =z are independent of k ; this ensures the validity of scaling laws β =α νt and νt=z ν .

  5. Energy and angular distributions of detached electrons in a solvable model of ion-atom collisions

    SciTech Connect

    Macek, J.H.; Ovchinnikov, S.Y. |; Solovev, E.A.

    1999-08-01

    Electron energy and angular distributions are computed for a model of atom{endash}negative-ion collisions. In this model, electron-atom interactions are represented by zero-range potentials in an approximation where two identical atoms move along straight-line classical trajectories in head-on collisions. Analytic expressions for the ionization amplitudes are interpreted in terms of Sturmian eigenvalues and eigenfunctions. At high velocity, the computed distributions exhibit direct excitation and continuum capture cusps in addition to the binary encounter ridge. At low velocities, a single feature corresponding to an electron distribution centered midway between the target and projectile emerges. For initial conditions corresponding to gerade symmetry a single broad peak appears, while for ungerade symmetry there is a node at the midpoint so that the peak splits into two parts. It is confirmed that the advanced adiabatic approximation gives an accurate description of the ungerade distribution at low and intermediate velocities. {copyright} {ital 1999} {ital The American Physical Society}

  6. Energy and angular distributions of detached electrons in a solvable model of ion-atom collisions

    SciTech Connect

    Macek, J.H.; Ovchinnikov, S.Y. Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831 ); Solovev, E.A. )

    1999-08-01

    Electron energy and angular distributions are computed for a model of atom[endash]negative-ion collisions. In this model, electron-atom interactions are represented by zero-range potentials in an approximation where two identical atoms move along straight-line classical trajectories in head-on collisions. Analytic expressions for the ionization amplitudes are interpreted in terms of Sturmian eigenvalues and eigenfunctions. At high velocity, the computed distributions exhibit direct excitation and continuum capture cusps in addition to the binary encounter ridge. At low velocities, a single feature corresponding to an electron distribution centered midway between the target and projectile emerges. For initial conditions corresponding to gerade symmetry a single broad peak appears, while for ungerade symmetry there is a node at the midpoint so that the peak splits into two parts. It is confirmed that the advanced adiabatic approximation gives an accurate description of the ungerade distribution at low and intermediate velocities. [copyright] [ital 1999] [ital The American Physical Society

  7. Exactly solvable U (1) × U (1) boson models for integer and fractional quantum Hall insulators in two dimensions

    NASA Astrophysics Data System (ADS)

    Motrunich, Olexei; Geraedts, Scott

    2013-03-01

    We present a solvable boson model with U (1) × U (1) symmetry in (2+1) dimensions that realizes insulating phases with a quantized Hall conductivity σxy. The model is short-ranged, with no topological terms, and can be realized by a local Hamiltonian. For one set of parameters, the model has a non-fractionalized phase with σxy = 2 n in appropriate units, with n an integer. In this case, the physical origin is dynamical binding between n bosons of one species and a vortex of the other species and condensation of such composites. Other choices for the parameters of the model yield a phase with σxy = 2c/d , where c and d are mutually prime integers. In this phase, c bosons dynamically bind to d vortices and such objects condense. The are two species of excitations that are bosonic by themselves but carry fractional charge 1 / d and have mutual statistics 2 πb/d , where b is an integer such that ad - bc = 1 , and a is also an integer. The model can be studied using sign-free Monte Carlo. We have performed simulations which include a boundary between a quantum Hall insulator and a trivial insulator, and found gapless edge states on the boundary.

  8. A position-dependent mass model for the Thomas–Fermi potential: Exact solvability and relation to δ-doped semiconductors

    SciTech Connect

    Schulze-Halberg, Axel; García-Ravelo, Jesús; Pacheco-García, Christian; Juan Peña Gil, José

    2013-06-15

    We consider the Schrödinger equation in the Thomas–Fermi field, a model that has been used for describing electron systems in δ-doped semiconductors. It is shown that the problem becomes exactly-solvable if a particular effective (position-dependent) mass distribution is incorporated. Orthogonal sets of normalizable bound state solutions are constructed in explicit form, and the associated energies are determined. We compare our results with the corresponding findings on the constant-mass problem discussed by Ioriatti (1990) [13]. -- Highlights: ► We introduce an exactly solvable, position-dependent mass model for the Thomas–Fermi potential. ► Orthogonal sets of solutions to our model are constructed in closed form. ► Relation to delta-doped semiconductors is discussed. ► Explicit subband bottom energies are calculated and compared to results obtained in a previous study.

  9. Mathematical analysis and validation of an exactly solvable model for upstream migration of fish schools in one-dimensional rivers.

    PubMed

    Yoshioka, Hidekazu

    2016-11-01

    Upstream migration of fish schools in 1-D rivers as an optimal control problem is formulated where their swimming velocity and the horizontal oblateness are taken as control variables. The objective function to be maximized through a migration process consists of the biological and ecological profit to be gained at the upstream-end of a river, energetic cost of swimming against the flow, and conceptual cost of forming a school. Under simplified conditions where the flow is uniform in both space and time and the profit to be gained at the goal of migration is sufficiently large, the optimal control variables are determined from a system of algebraic equations that can be solved in a cascading manner. Mathematical analysis of the system reveals that the optimal controls are uniquely found and the model is exactly solvable under certain conditions on the functions and parameters, which turn out to be realistic and actually satisfied in experimental fish migration. Identification results of the functional shapes of the functions and the parameters with experimentally observed data of swimming schools of Plecoglossus altivelis (Ayu) validate the present mathematical model from both qualitative and quantitative viewpoints. The present model thus turns out to be consistent with the reality, showing its potential applicability to assessing fish migration in applications.

  10. Ion-trap simulation of the quantum phase transition in an exactly solvable model of spins coupled to bosons

    SciTech Connect

    Giorgi, Gian Luca; Galve, Fernando; Paganelli, Simone

    2010-05-15

    It is known that arrays of trapped ions can be used to efficiently simulate a variety of many-body quantum systems. Here we show how it is possible to build a model representing a spin chain interacting with bosons that is exactly solvable. The exact spectrum of the model at zero temperature and the ground-state properties are studied. We show that a quantum phase transition occurs when the coupling between spins and bosons reaches a critical value, which corresponds to a level crossing in the energy spectrum. Once the critical point is reached, the number of bosonic excitations in the ground state, which can be assumed as an order parameter, starts to be different from zero. The population of the bosonic mode is accompanied by a macroscopic magnetization of the spins. This double effect could represent a useful resource for phase transition detection since a measure of the phonon can give information about the phase of the spin system. A finite-temperature phase diagram is also given in the adiabatic regime.

  11. An exactly solvable model for calculating critical misfit and thickness in epitaxial superlattices - Layers of equal elastic constants and thicknesses

    NASA Technical Reports Server (NTRS)

    Van Der Merwe, Jan H.; Jesser, W. A.

    1988-01-01

    A parabolic interaction potential has been used to develop a model for calculating the misfit dislocation (MD) energy in the case of a superlattice of alternating layers of materials with equal elastic constants and thicknesses. The model, which is believed to be a good one for small misfits and to have some merit for covalent bonded materials, is exactly solvable for the critical thickness above which it is energetically favorable to lose coherency by the introduction of MDs into the interfaces. It was found, for a given misfit f, that the critical thickness for epitaxial superlattices free from their substrate is somewhat more than four times that for a single epilayer on a thick substrate. Furthermore, the critical thickness varies almost inversely with misfit to the power 1.22 when Poisson's ratio is 1/3. It was also shown that the critical misfit f(c) obtained by equating maximal misfit strain and MD energies is a significant overestimate of f(c). The results for a superlattice are compared with those of a thin layer on a thick substrate.

  12. Exactly solvable model of resonance tunneling of an electromagnetic wave in plasma containing short-scale inhomogeneities

    SciTech Connect

    Erokhin, N. S. Zakharov, V. E.; Zol’nikova, N. N.; Mikhailovskaya, L. A.

    2015-02-15

    Different variants of resonance tunneling of a transverse electromagnetic wave through a plasma layer containing short-scale (subwavelength) inhomogeneities, including evanescence regions to which approximate methods are inapplicable, are analyzed in the framework of an exactly solvable one-dimensional model. Complex plasma density profiles described by a number of free parameters determining the permittivity modulation depth, the characteristic scale lengths of plasma structures, their number, and the thickness of the inhomogeneous plasma layer are considered. It is demonstrated that reflection-free propagation of the wave incident on the layer from vacuum (the effect of wave-barrier transillumination) can be achieved for various sets of such structures, including plasma density profiles containing a stochastic component. Taking into account cubic nonlinearity, it is also possible to obtain an exact solution to the one-dimensional problem on the nonlinear transillumination of nonuniform plasma. In this case, the thicknesses of the evanescence regions decrease appreciably. The problem of resonance tunneling of electromagnetic waves through such barriers is of interest for a number of practical applications.

  13. Exactly solvable model for nonlinear light-matter interaction in an arbitrary time-dependent field

    SciTech Connect

    Brown, J. M.; Lotti, A.; Teleki, A.; Kolesik, M.

    2011-12-15

    Exact analytic expressions are derived for the dipole moment and nonlinear current of a one-dimensional quantum particle subject to a short-range attractive potential and an arbitrary time-dependent electric field. An efficient algorithm for the current evaluation is described and a robust implementation suitable for numerical simulations is demonstrated.

  14. Evaluation of linearly solvable Markov decision process with dynamic model learning in a mobile robot navigation task.

    PubMed

    Kinjo, Ken; Uchibe, Eiji; Doya, Kenji

    2013-01-01

    Linearly solvable Markov Decision Process (LMDP) is a class of optimal control problem in which the Bellman's equation can be converted into a linear equation by an exponential transformation of the state value function (Todorov, 2009b). In an LMDP, the optimal value function and the corresponding control policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunction problem in a continuous state using the knowledge of the system dynamics and the action, state, and terminal cost functions. In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in which the dynamics of the body and the environment have to be learned from experience. We first perform a simulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynamics model on the derived the action policy. The result shows that a crude linear approximation of the non-linear dynamics can still allow solution of the task, despite with a higher total cost. We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robot platform. The state is given by the position and the size of a battery in its camera view and two neck joint angles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servo controller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state cost functions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics model performed equivalently with the optimal linear quadratic regulator (LQR). In the non-quadratic task, the LMDP controller with a linear dynamics model showed the best performance. The results demonstrate the usefulness of the LMDP framework in real robot control even when simple linear models are used for dynamics learning.

  15. Evaluation of linearly solvable Markov decision process with dynamic model learning in a mobile robot navigation task

    PubMed Central

    Kinjo, Ken; Uchibe, Eiji; Doya, Kenji

    2013-01-01

    Linearly solvable Markov Decision Process (LMDP) is a class of optimal control problem in which the Bellman's equation can be converted into a linear equation by an exponential transformation of the state value function (Todorov, 2009b). In an LMDP, the optimal value function and the corresponding control policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunction problem in a continuous state using the knowledge of the system dynamics and the action, state, and terminal cost functions. In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in which the dynamics of the body and the environment have to be learned from experience. We first perform a simulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynamics model on the derived the action policy. The result shows that a crude linear approximation of the non-linear dynamics can still allow solution of the task, despite with a higher total cost. We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robot platform. The state is given by the position and the size of a battery in its camera view and two neck joint angles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servo controller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state cost functions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics model performed equivalently with the optimal linear quadratic regulator (LQR). In the non-quadratic task, the LMDP controller with a linear dynamics model showed the best performance. The results demonstrate the usefulness of the LMDP framework in real robot control even when simple linear models are used for dynamics learning. PMID:23576983

  16. Exactly solvable nonlinear model for a Smith-Purcell free-electron laser

    NASA Astrophysics Data System (ADS)

    Crowne, F. J.; Leavitt, R. P.; Worchesky, T. L.

    1981-08-01

    A model is presented for a Smith-Purcell free-electron laser, including nonlinear effects, that can be solved in closed form. The model is shown to obey the pendulum equation. The average electron efficiency calculated by means of this model is compared with that obtained from an exact numerical calculation and from a simpler 'phase-space' model for a wide range of physical parameters.

  17. Entropy-enthalpy compensation in chemical reactions and adsorption: an exactly solvable model.

    PubMed

    Freed, Karl F

    2011-02-24

    The free energies of reaction or activation for many systems respond in a common fashion to a perturbing parameter, such as the concentration of an "inert" additive. Arrhenius plots as a function of the perturbing parameter display a "'compensation temperature" at which the free energy appears to be independent of the perturber, an entropy-enthalpy compensation process. Thus, as the perturber's concentration varies, Arrhenius plots of the rate constant or equilibrium constant exhibit a rotation about the fixed compensation temperature. While this (isokinetic/isoequilibrium) component of the phenomenon of entropy-enthalpy compensation appears in a huge number of situations of relevance to chemistry, biology, and materials science, statistical mechanical descriptions have been almost completely lacking. We provide the general statistical mechanical basis for solvent induced isokinetic/isoequilibrium entropy-enthalpy compensation in chemical reactions and adsorption, understanding that can be used to control of rate processes and binding constants in diverse applications. The general behavior is illustrated with an analytical solution for the dilute gas limit.

  18. Solvable non-Markovian dynamic network

    NASA Astrophysics Data System (ADS)

    Georgiou, Nicos; Kiss, Istvan Z.; Scalas, Enrico

    2015-10-01

    Non-Markovian processes are widespread in natural and human-made systems, yet explicit modeling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy-tailed Mittag-Leffler distribution for the interevent times. We derive an analytically and computationally tractable system of Kolmogorov-like forward equations utilizing the Caputo derivative for the probability of having a given number of active links in the network and solve them. Simulations for the RLAD are also studied for power-law interevent times and we show excellent agreement with the Mittag-Leffler model. This agreement holds even when the RLAD network dynamics is coupled with the susceptible-infected-susceptible spreading dynamics. Thus, the analytically solvable Mittag-Leffler model provides an excellent approximation to the case when the network dynamics is characterized by power-law-distributed interevent times. We further discuss possible generalizations of our result.

  19. Improved analytic nutation model

    NASA Technical Reports Server (NTRS)

    Yoder, C. F.; Ivins, E. R.

    1988-01-01

    Models describing the earth's nutations are discussed. It is found that the simple model of Sasao et al., (1981) differs from Wahr's (1981) theory term by term by less than 0.3 marcsec if a modern earth structure model is used to evaluate the nutation structure constants. In addition, the effect of oceans is estimated.

  20. An exactly solvable model of an oscillator with nonlinear coupling and zeros of Bessel functions

    NASA Technical Reports Server (NTRS)

    Dodonov, V. V.; Klimov, A. B.

    1993-01-01

    We consider an oscillator model with nonpolynomial interaction. The model admits exact solutions for two situations: for energy eigenvalues in terms of zeros of Bessel functions, that were considered as functions of the continuous index; and for the corresponding eigenstates in terms of Lommel polynomials.

  1. Thermodynamics of information processing based on enzyme kinetics: An exactly solvable model of an information pump

    NASA Astrophysics Data System (ADS)

    Cao, Yuansheng; Gong, Zongping; Quan, H. T.

    2015-06-01

    Motivated by the recent proposed models of the information engine [Proc. Natl. Acad. Sci. USA 109, 11641 (2012), 10.1073/pnas.1204263109] and the information refrigerator [Phys. Rev. Lett. 111, 030602 (2013), 10.1103/PhysRevLett.111.030602], we propose a minimal model of the information pump and the information eraser based on enzyme kinetics. This device can either pump molecules against the chemical potential gradient by consuming the information to be encoded in the bit stream or (partially) erase the information initially encoded in the bit stream by consuming the Gibbs free energy. The dynamics of this model is solved exactly, and the "phase diagram" of the operation regimes is determined. The efficiency and the power of the information machine is analyzed. The validity of the second law of thermodynamics within our model is clarified. Our model offers a simple paradigm for the investigating of the thermodynamics of information processing involving the chemical potential in small systems.

  2. Work and information processing in a solvable model of Maxwell’s demon

    PubMed Central

    Mandal, Dibyendu; Jarzynski, Christopher

    2012-01-01

    We describe a minimal model of an autonomous Maxwell demon, a device that delivers work by rectifying thermal fluctuations while simultaneously writing information to a memory register. We solve exactly for the steady-state behavior of our model, and we construct its phase diagram. We find that our device can also act as a “Landauer eraser”, using externally supplied work to remove information from the memory register. By exposing an explicit, transparent mechanism of operation, our model offers a simple paradigm for investigating the thermodynamics of information processing by small systems. PMID:22753515

  3. Work and information processing in a solvable model of Maxwell's demon.

    PubMed

    Mandal, Dibyendu; Jarzynski, Christopher

    2012-07-17

    We describe a minimal model of an autonomous Maxwell demon, a device that delivers work by rectifying thermal fluctuations while simultaneously writing information to a memory register. We solve exactly for the steady-state behavior of our model, and we construct its phase diagram. We find that our device can also act as a "Landauer eraser", using externally supplied work to remove information from the memory register. By exposing an explicit, transparent mechanism of operation, our model offers a simple paradigm for investigating the thermodynamics of information processing by small systems.

  4. Solvable continuous-time random walk model of the motion of tracer particles through porous media.

    PubMed

    Fouxon, Itzhak; Holzner, Markus

    2016-08-01

    We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015)PLEEE81539-375510.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ, length l, and velocity v. We solve our model with independent l and v. The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α. Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α, ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ. Universality of tracer diffusion in the porous medium is considered.

  5. Solvable continuous-time random walk model of the motion of tracer particles through porous media

    NASA Astrophysics Data System (ADS)

    Fouxon, Itzhak; Holzner, Markus

    2016-08-01

    We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015), 10.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ , length l , and velocity v . We solve our model with independent l and v . The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α . Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α , ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ . Universality of tracer diffusion in the porous medium is considered.

  6. About a solvable mean field model of a Gaussian spin glass

    NASA Astrophysics Data System (ADS)

    Barra, Adriano; Genovese, Giuseppe; Guerra, Francesco; Tantari, Daniele

    2014-04-01

    In a series of papers, we have studied a modified Hopfield model of a neural network, with learned words characterized by a Gaussian distribution. The model can be represented as a bipartite spin glass, with one party described by dichotomic Ising spins, and the other party by continuous spin variables, with an a priori Gaussian distribution. By application of standard interpolation methods, we have found it useful to compare the neural network model (bipartite) from one side, with two spin glass models, each monopartite, from the other side. Of these, the first is the usual Sherrington-Kirkpatrick model, the second is a spin glass model, with continuous spins and inbuilt highly nonlinear smooth cut-off interactions. This model is an invaluable laboratory for testing all techniques which have been useful in the study of spin glasses. The purpose of this paper is to give a synthetic description of the most peculiar aspects, by stressing the necessary novelties in the treatment. In particular, it will be shown that the control of the infinite volume limit, according to the well-known Guerra-Toninelli strategy, requires in addition one to consider the involvement of the cut-off interaction in the interpolation procedure. Moreover, the control of the ergodic region, the annealed case, cannot be directly achieved through the standard application of the Borel-Cantelli lemma, but requires previous modification of the interaction. This remark could find useful application in other cases. The replica symmetric expression for the free energy can be easily reached through a suitable version of the doubly stochastic interpolation technique. However, this model shares the unique property that the fully broken replica symmetry ansatz can be explicitly calculated. A very simple sum rule connects the general expression of the fully broken free energy trial function with the replica symmetric one. The definite sign of the error term shows that the replica solution is optimal. Then

  7. Simple solvable energy-landscape model that shows a thermodynamic phase transition and a glass transition.

    PubMed

    Naumis, Gerardo G

    2012-06-01

    When a liquid melt is cooled, a glass or phase transition can be obtained depending on the cooling rate. Yet, this behavior has not been clearly captured in energy-landscape models. Here, a model is provided in which two key ingredients are considered in the landscape, metastable states and their multiplicity. Metastable states are considered as in two level system models. However, their multiplicity and topology allows a phase transition in the thermodynamic limit for slow cooling, while a transition to the glass is obtained for fast cooling. By solving the corresponding master equation, the minimal speed of cooling required to produce the glass is obtained as a function of the distribution of metastable states.

  8. Correlation effects in sequential energy branching: An exactly solvable model of Fano statistics

    SciTech Connect

    Subashiev, Arsen V.; Luryi, Serge

    2010-02-15

    Correlation effects in the fluctuation of the number of particles in the process of energy branching by sequential impact ionizations are studied using an exactly soluble model of random parking on a line. The Fano factor F calculated in an uncorrelated final-state 'shot-glass' model does not give an accurate answer even with the exact gap-distribution statistics. Allowing for the nearest-neighbor correlation effects gives a correction to F that brings F very close to its exact value. We discuss the implications of our results for energy resolution of semiconductor gamma detectors, where the value of F is of the essence. We argue that F is controlled by correlations in the cascade energy branching process and hence the widely used final-state model estimates are not reliable - especially in the practically relevant cases when the energy branching is terminated by competition between impact ionization and phonon emission.

  9. Rectification of asymmetric surface vibrations with dry friction: An exactly solvable model

    NASA Astrophysics Data System (ADS)

    Baule, A.; Sollich, P.

    2013-03-01

    We consider a stochastic model for the directed motion of a solid object due to the rectification of asymmetric surface vibrations with Poissonian shot-noise statistics. The friction between the object and the surface is given by a piecewise-linear friction force. This models the combined effect of dynamic friction and singular dry friction. We derive an exact solution of the stationary Kolmogorov-Feller (KF) equation in the case of two-sided exponentially distributed amplitudes. The stationary density of the velocity exhibits singular features such as a discontinuity and a delta-peak singularity at zero velocity, and also contains contributions from nonintegrable solutions of the KF equation. The mean velocity in our model generally varies nonmonotonically as the strength of the dry friction is increased, indicating that transport improves for increased dissipation.

  10. Explore or Exploit? A Generic Model and an Exactly Solvable Case

    NASA Astrophysics Data System (ADS)

    Gueudré, Thomas; Dobrinevski, Alexander; Bouchaud, Jean-Philippe

    2014-02-01

    Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a stylized model for these exploration-exploitation situations, including population or economic growth, portfolio optimization, evolutionary dynamics, or the problem of optimal pinning of vortices or dislocations in disordered materials. We find the exact growth rate of this model for treelike geometries and prove the existence of an optimal migration rate in this case. Numerical simulations in the one-dimensional case confirm the generic existence of an optimum.

  11. Explore or exploit? A generic model and an exactly solvable case.

    PubMed

    Gueudré, Thomas; Dobrinevski, Alexander; Bouchaud, Jean-Philippe

    2014-02-07

    Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a stylized model for these exploration-exploitation situations, including population or economic growth, portfolio optimization, evolutionary dynamics, or the problem of optimal pinning of vortices or dislocations in disordered materials. We find the exact growth rate of this model for treelike geometries and prove the existence of an optimal migration rate in this case. Numerical simulations in the one-dimensional case confirm the generic existence of an optimum.

  12. Solvable model for a dynamical quantum phase transition from fast to slow scrambling

    NASA Astrophysics Data System (ADS)

    Banerjee, Sumilan; Altman, Ehud

    2017-04-01

    We propose an extension of the Sachdev-Ye-Kitaev (SYK) model that exhibits a quantum phase transition from the previously identified non-Fermi-liquid fixed point to a Fermi-liquid-like state, while still allowing an exact solution in a suitable large-N limit. The extended model involves coupling the interacting N -site SYK model to a new set of p N peripheral sites with only quadratic hopping terms between them. The conformal fixed point of the SYK model remains a stable low-energy phase below a critical ratio of peripheral sites p pc the quadratic sites effectively screen the SYK dynamics, leading to a quadratic fixed point in the low-temperature and low-frequency limit. The interactions have a perturbative effect in this regime leading to scrambling with Lyapunov exponent λL∝T2 .

  13. Quantum measurement as a driven phase transition: An exactly solvable model

    NASA Astrophysics Data System (ADS)

    Allahverdyan, Armen E.; Balian, Roger; Nieuwenhuizen, Theo M.

    2001-09-01

    A model of quantum measurement is proposed, which aims to describe statistical mechanical aspects of this phenomenon, starting from a purely Hamiltonian formulation. The macroscopic measurement apparatus is modeled as an ideal Bose gas, the order parameter of which, that is, the amplitude of the condensate, is the pointer variable. It is shown that properties of irreversibility and ergodicity breaking, which are inherent in the model apparatus, ensure the appearance of definite results of the measurement, and provide a dynamical realization of wave-function reduction or collapse. The measurement process takes place in two steps: First, the reduction of the state of the tested system occurs over a time of order ħ/(TN1/4), where T is the temperature of the apparatus, and N is the number of its degrees of freedom. This decoherence process is governed by the apparatus-system interaction. During the second step classical correlations are established between the apparatus and the tested system over the much longer time scale of equilibration of the apparatus. The influence of the parameters of the model on nonideality of the measurement is discussed. Schrödinger kittens, EPR setups, and information transfer are analyzed.

  14. Accountability in Training Transfer: Adapting Schlenker's Model of Responsibility to a Persistent but Solvable Problem

    ERIC Educational Resources Information Center

    Burke, Lisa A.; Saks, Alan M.

    2009-01-01

    Decades have been spent studying training transfer in organizational environments in recognition of a transfer problem in organizations. Theoretical models of various antecedents, empirical studies of transfer interventions, and studies of best practices have all been advanced to address this continued problem. Yet a solution may not be so…

  15. Entanglement entropy production in gravitational collapse: covariant regularization and solvable models

    NASA Astrophysics Data System (ADS)

    Bianchi, Eugenio; De Lorenzo, Tommaso; Smerlak, Matteo

    2015-06-01

    We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole "exterior entropy" and "radiation entropy." For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the "black hole fireworks" model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that ( i) in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, ( ii) in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the "purifying" phase, ( iii) at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.

  16. Solvable model of the collective motion of heterogeneous particles interacting on a sphere

    NASA Astrophysics Data System (ADS)

    Tanaka, Takuma

    2014-02-01

    I propose a model of mutually interacting particles on an M-dimensional unit sphere. I derive the dynamics of the particles by extending the dynamics of the Kuramoto-Sakaguchi model. The dynamics include a natural-frequency matrix, which determines the motion of a particle with no external force, and an external force vector. The position (state variable) of a particle at a given time is obtained by the projection transformation of the initial position of the particle. The same projection transformation gives the position of the particles with the same natural-frequency matrix. I show that the motion of the center of mass of an infinite number of heterogeneous particles whose natural-frequency matrices are obtained from a class of multivariate Lorentz distribution is given by an M-dimensional ordinary differential equation in closed form. This result is an extension of the Ott-Antonsen theory.

  17. Solvable multistate model of Landau-Zener transitions in cavity QED

    NASA Astrophysics Data System (ADS)

    Sinitsyn, Nikolai A.; Li, Fuxiang

    2016-06-01

    We consider the model of a single optical cavity mode interacting with two-level systems (spins) driven by a linearly time-dependent field. When this field passes through values at which spin energy-level splittings become comparable to spin coupling to the optical mode, a cascade of Landau-Zener transitions leads to coflips of spins in exchange for photons of the cavity. We derive exact transition probabilities between different diabatic states induced by such a sweep of the field.

  18. Solvable multistate model of Landau-Zener transitions in cavity QED

    DOE PAGES

    Sinitsyn, Nikolai; Li, Fuxiang

    2016-06-29

    We consider the model of a single optical cavity mode interacting with two-level systems (spins) driven by a linearly time-dependent field. When this field passes through values at which spin energy level splittings become comparable to spin coupling to the optical mode, a cascade of Landau-Zener (LZ) transitions leads to co-flips of spins in exchange for photons of the cavity. We derive exact transition probabilities between different diabatic states induced by such a sweep of the field.

  19. Family of exactly solvable models with an ultimate quantum paramagnetic ground state.

    PubMed

    Schmidt, Kai Phillip; Laad, Mukul

    2010-06-11

    We present a family of two-dimensional frustrated quantum magnets solely based on pure nearest-neighbor Heisenberg interactions which can be solved quasiexactly. All lattices are constructed in terms of frustrated quantum cages containing a chiral degree of freedom protected by frustration. The ground states of these models are dubbed ultimate quantum paramagnets and exhibit an extensive entropy at zero temperature. We discuss the unusual and extensively degenerate excitations in such phases. Implications for thermodynamic properties as well as for decoherence free quantum computation are discussed.

  20. Solvable models with self-triality in statistical mechanics and field theory

    SciTech Connect

    Shankar, R.

    1981-02-09

    The notion of self-duality is extended to self-triality. One example from spin systems is given and completely solved by use of fermion variables. It is then shown that the O(8) Gross-Neveu model has self-triality: The Lagrangian L(psi)=L(R)=L(L) where psi is the original fermion while R and L are two types of kinks that occur dynamically. The anatomy of self-duality (triality) in the Ising and present examples is exposed as is the origin of the fermionic solutions.

  1. Nonlinear Fano interferences in open quantum systems: An exactly solvable model

    NASA Astrophysics Data System (ADS)

    Finkelstein-Shapiro, Daniel; Calatayud, Monica; Atabek, Osman; Mujica, Vladimiro; Keller, Arne

    2016-06-01

    We obtain an explicit solution for the stationary-state populations of a dissipative Fano model, where a discrete excited state is coupled to a continuum set of states; both excited sets of states are reachable by photoexcitation from the ground state. The dissipative dynamic is described by a Liouville equation in Lindblad form and the field intensity can take arbitrary values within the model. We show that the population of the continuum states as a function of laser frequency can always be expressed as a Fano profile plus a Lorentzian function with effective parameters whose explicit expressions are given in the case of a closed system coupled to a bath as well as for the original Fano scattering framework. Although the solution is intricate, it can be elegantly expressed as a linear transformation of the kernel of a 4 ×4 matrix which has the meaning of an effective Liouvillian. We unveil key notable processes related to the optical nonlinearity and which had not been reported to date: electromagnetic-induced transparency, population inversions, power narrowing and broadening, as well as an effective reduction of the Fano asymmetry parameter.

  2. Explicitly Solvable Model of the Charge Carriers' Phenomena in Isotropic Conducting Crystals

    NASA Astrophysics Data System (ADS)

    Budzak, Yaroslav S.; Wacławski, Tadeusz

    2017-01-01

    In this paper, a theoretical analysis of the kinetic properties of the isotropic conducting crystals is presented. The general formulas for these kinetic properties are expressed in terms of the Fermi integrals. These integrals were obtained using methods of statistical ensembles with varying number of particles and the Gibbs's grand canonical distribution. The determination of the scattering function and the exploration of its relation with the mobility of the current carriers inside these crystals have been made. Together with the results of theoretical analysis of the scattering function and its relation with the current carriers' mobility, these formulas constitute the mathematical model of the charge carriers' transport phenomena in conducting crystals (where a non-parabolic energy spectrum is described by Kane's formula) and provide algorithms for the calculation of these properties.

  3. Classical and Quantum Algebraic Screening in a Coulomb Plasma near a Wall: A Solvable Model

    NASA Astrophysics Data System (ADS)

    Aqua, J. N.; Cornu, F.

    1999-10-01

    The static position correlation in a quantum Coulomb plasma near a wall is studied by means of a model where two quantum charges are embedded in a classical plasma at equilibrium. Three kinds of walls are considered: a wall without electrostatic properties, a dielectric, and an ideal conductor. At large separations y along the wall, the correlation exactly decays as 1/ y 3, though no algebraic tail exists for classical charges near an ideal conductor. This tail originates from thermal statistical and purely quantum fluctuations of polarization clouds which are deformed by the geometric constraint due to the wall and by the charges induced by influence inside a wall with electrical properties. The coefficient of the 1/ y 3 tail can be calculated explicitly in a weak-coupling and low-delocalization regime. Then classical, diffraction, and purely quantum contributions are disentangled.

  4. Explicitly Solvable Model of the Charge Carriers' Phenomena in Isotropic Conducting Crystals

    NASA Astrophysics Data System (ADS)

    Budzak, Yaroslav S.; Wacławski, Tadeusz

    2017-04-01

    In this paper, a theoretical analysis of the kinetic properties of the isotropic conducting crystals is presented. The general formulas for these kinetic properties are expressed in terms of the Fermi integrals. These integrals were obtained using methods of statistical ensembles with varying number of particles and the Gibbs's grand canonical distribution. The determination of the scattering function and the exploration of its relation with the mobility of the current carriers inside these crystals have been made. Together with the results of theoretical analysis of the scattering function and its relation with the current carriers' mobility, these formulas constitute the mathematical model of the charge carriers' transport phenomena in conducting crystals (where a non-parabolic energy spectrum is described by Kane's formula) and provide algorithms for the calculation of these properties.

  5. Rate of Adaptation in Sexuals and Asexuals: A Solvable Model of the Fisher–Muller Effect

    PubMed Central

    Park, Su-Chan; Krug, Joachim

    2013-01-01

    The adaptation of large asexual populations is hampered by the competition between independently arising beneficial mutations in different individuals, which is known as clonal interference. In classic work, Fisher and Muller proposed that recombination provides an evolutionary advantage in large populations by alleviating this competition. Based on recent progress in quantifying the speed of adaptation in asexual populations undergoing clonal interference, we present a detailed analysis of the Fisher–Muller mechanism for a model genome consisting of two loci with an infinite number of beneficial alleles each and multiplicative (nonepistatic) fitness effects. We solve the deterministic, infinite population dynamics exactly and show that, for a particular, natural mutation scheme, the speed of adaptation in sexuals is twice as large as in asexuals. This result is argued to hold for any nonzero value of the rate of recombination. Guided by the infinite population result and by previous work on asexual adaptation, we postulate an expression for the speed of adaptation in finite sexual populations that agrees with numerical simulations over a wide range of population sizes and recombination rates. The ratio of the sexual to asexual adaptation speed is a function of population size that increases in the clonal interference regime and approaches 2 for extremely large populations. The simulations also show that the imbalance between the numbers of accumulated mutations at the two loci is strongly suppressed even by a small amount of recombination. The generalization of the model to an arbitrary number L of loci is briefly discussed. If each offspring samples the alleles at each locus from the gene pool of the whole population rather than from two parents, the ratio of the sexual to asexual adaptation speed is approximately equal to L in large populations. A possible realization of this scenario is the reassortment of genetic material in RNA viruses with L genomic

  6. Ultrametricity and memory in a solvable model of self-organized criticality

    SciTech Connect

    Boettcher, S.; Paczuski, M. |

    1996-08-01

    Slowly driven dissipative systems may evolve to a critical state where long periods of apparent equilibrium are punctuated by intermittent avalanches of activity. We present a self-organized critical model of punctuated equilibrium behavior in the context of biological evolution, and solve it in the limit that the number of independent traits for each species diverges. We derive an exact equation of motion for the avalanche dynamics from the microscopic rules. In the continuum limit, avalanches propagate via a diffusion equation with a nonlocal, history dependent potential representing memory. This nonlocal potential gives rise to a non-Gaussian (fat) tail for the subdiffusive spreading of activity. The probability for the activity to spread beyond a distance {ital r} in time {ital s} decays as {radical}(24/{pi}){ital s}{sup {minus}3/2}{ital x}{sup 1/3}exp[{minus}3/4{ital x}{sup 1/3}] for {ital x}={ital r}{sup 4}/{ital s}{gt}1. The potential represents a hierarchy of time scales that is dynamically generated by the ultrametric structure of avalanches, which can be quantified in terms of {open_quote}{open_quote}backward{close_quote}{close_quote} avalanches. In addition, a number of other correlation functions characterizing the punctuated equilibrium dynamics are determined exactly.

  7. Asymptotically solvable model for a solitonic vortex in a compressible superfluid

    NASA Astrophysics Data System (ADS)

    Toikka, L. A.; Brand, J.

    2017-02-01

    Vortex motion is a complex problem due to the interplay between the short-range physics at the vortex core level and the long-range hydrodynamical effects. Here we show that the hydrodynamic equations of vortex motion in a compressible superfluid can be solved asymptotically in a model ‘slab’ geometry. Starting from an exact solution for an incompressible fluid, the hydrodynamic equations are solved with a series expansion in a small tunable parameter provided by the ratio of the healing length, characterising the vortex cores, to the slab width. The key dynamical properties of the vortex, the inertial and physical masses, are well defined and renormalizable. They are calculated at leading order beyond the logarithmic accuracy that has limited previous approaches. Subtracting the asymptotic solutions of the universal hydrodynamic problem from experimental observations of vortex motion exposes the physics of the vortex core and provides a window into interesting many-body phenomena that are currently poorly understood including the role of quantum pressure. Our results provide a solid framework for further detailed study of the vortex mass and vortex forces in strongly correlated and exotic superfluids.

  8. Automated dynamic analytical model improvement

    NASA Technical Reports Server (NTRS)

    Berman, A.

    1981-01-01

    A method is developed and illustrated which finds minimum changes in analytical mass and stiffness matrices to make them consistent with a set of measured normal modes and natural frequencies. The corrected model is an improved base for studies of physical changes, changes in boundary conditions, and for prediction of forced responses. Features of the method are: efficient procedures not requiring solutions of the eigenproblem; the model may have more degrees of freedom than the test data; modal displacements at all the analytical degrees of freedom are obtained; the frequency dependence of the coordinate transformations are properly treated.

  9. Analytic model of ocean color

    NASA Astrophysics Data System (ADS)

    Sathyendranath, Shubha; Platt, Trevor

    1997-04-01

    Ocean color is determined by spectral variations in reflectance at the sea surface. In the analytic model presented here, reflectance at the sea surface is estimated with the quasi-single-scattering approximation that ignores transspectral processes. The analytic solutions we obtained are valid for a vertically homogeneous water column. The solution provides a theoretical expression for the dimensionless, quasi-stable parameter ( r ), with a value of 0.33, that appears in many models in which reflectance at the sea surface is expressed as a function of absorption coefficient ( a ) and backscattering coefficient ( b b ). In the solution this parameter is represented as a function of the mean cosines for downwelling and upwelling irradiances and as the ratio of the upward-scattering coefficient to the backscattering coefficient. Implementation of the model is discussed for two cases: (1) that in which molecular scattering is the main source of upwelling light, and (2) that in which particle scattering is responsible for all the upwelled light. Computations for the two cases are compared with Monte Carlo simulations, which accounts for processes not considered in the analytic model (multiple scattering, and consequent depth-dependent changes in apparent optical properties). The Monte Carlo models show variations in reflectance with the zenith angle of the incident light. The analytic model can be used to reproduce these variations fairly well for the case of molecular scattering. For the particle-scattering case also, the analytic and Monte Carlo models show similar variations in r with zenith angle. However, the analytic model (as implemented here) appears to underestimate r when the value of the backscattering coefficient b b increases relative to the absorption coefficient a . The errors also vary with the zenith angle of the incident light field, with the maximum underestimate being approximately 0.06 (equivalent to relative errors from 12 to 17 ) for the range of

  10. Realizing exactly solvable SU (N ) magnets with thermal atoms

    NASA Astrophysics Data System (ADS)

    Beverland, Michael E.; Alagic, Gorjan; Martin, Michael J.; Koller, Andrew P.; Rey, Ana M.; Gorshkov, Alexey V.

    2016-05-01

    We show that n thermal fermionic alkaline-earth-metal atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the Sn symmetry that permutes atoms occupying different vibrational levels of the trap and the SU (N ) symmetry associated with N nuclear spin states. The symmetries make the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this SU (N ) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary nonthermal distribution.

  11. Continuous family of finite-dimensional representations of a solvable Lie algebra arising from singularities

    PubMed Central

    Yau, Stephen S.-T.

    1983-01-01

    A natural mapping from the set of complex analytic isolated hypersurface singularities to the set of finite dimensional Lie algebras is first defined. It is proven that the image under this natural mapping is contained in the set of solvable Lie algebras. This approach gives rise to a continuous inequivalent family of finite dimensional representations of a solvable Lie algebra. PMID:16593401

  12. Exactly solvable quantum Sturm-Liouville problems

    SciTech Connect

    Bueyuekasik, Sirin A.; Pashaev, Oktay K.; Tigrak-Ulas, Esra

    2009-07-15

    The harmonic oscillator with time-dependent parameters covers a broad spectrum of physical problems from quantum transport, quantum optics, and quantum information to cosmology. Several methods have been developed to quantize this fundamental system, such as the path integral method, the Lewis-Riesenfeld time invariant method, the evolution operator or dynamical symmetry method, etc. In all these methods, solution of the quantum problem is given in terms of the classical one. However, only few exactly solvable problems of the last one, such as the damped oscillator or the Caldirola-Kanai model, have been treated. The goal of the present paper is to introduce a wide class of exactly solvable quantum models in terms of the Sturm-Liouville problem for classical orthogonal polynomials. This allows us to solve exactly the corresponding quantum parametric oscillators with specific damping and frequency dependence, which can be considered as quantum Sturm-Liouville problems.

  13. Solvable biological evolution models with general fitness functions and multiple mutations in parallel mutation-selection scheme

    NASA Astrophysics Data System (ADS)

    Saakian, David B.; Hu, Chin-Kun; Khachatryan, H.

    2004-10-01

    In a recent paper [Phys. Rev. E 69, 046121 (2004)], we used the Suzuki-Trottere formalism to study a quasispecies biological evolution model in a parallel mutation-selection scheme with a single-peak fitness function and a point mutation. In the present paper, we extend such a study to evolution models with more general fitness functions or multiple mutations in the parallel mutation-selection scheme. We give some analytical equations to define the error thresholds for some general cases of mean-field-like or symmetric mutation schemes and fitness functions. We derive some equations for the dynamics in the case of a point mutation and polynomial fitness functions. We derive exact dynamics for two-point mutations, asymmetric mutations, and the four-value spin model with a single-peak fitness function. The same method is applied for the model with a royal road fitness function. We derive the steady-state distribution for the single-peak fitness function.

  14. Predictive analytics can support the ACO model.

    PubMed

    Bradley, Paul

    2012-04-01

    Predictive analytics can be used to rapidly spot hard-to-identify opportunities to better manage care--a key tool in accountable care. When considering analytics models, healthcare providers should: Make value-based care a priority and act on information from analytics models. Create a road map that includes achievable steps, rather than major endeavors. Set long-term expectations and recognize that the effectiveness of an analytics program takes time, unlike revenue cycle initiatives that may show a quick return.

  15. Analytic Model of Reactive Flow

    SciTech Connect

    Souers, P C; Vitello, P

    2004-08-02

    A simple analytic model allows prediction of rate constants and size effect behavior before a hydrocode run if size effect data exists. At infinite radius, it defines not only detonation velocity but also average detonation rate, pressure and energy. This allows the derivation of a generalized radius, which becomes larger as the explosive becomes more non-ideal. The model is applied to near-ideal PBX 9404, in-between ANFO and most non-ideal AN. The power of the pressure declines from 2.3, 1.5 to 0.8 across this set. The power of the burn fraction, F, is 0.8, 0 and 0, so that an F-term is important only for the ideal explosives. The size effect shapes change from concave-down to nearly straight to concave-up. Failure is associated with ideal explosives when the calculated detonation velocity turns in a double-valued way. The effect of the power of the pressure may be simulated by including a pressure cutoff in the detonation rate. The models allows comparison of a wide spectrum of explosives providing that a single detonation rate is feasible.

  16. Analytic Model of Reactive Flow

    SciTech Connect

    Souers, P C; Vitello, P

    2004-11-15

    A simple analytic model allows prediction of rate constants and size effect behavior before a hydrocode run if size effect data exists. At infinite radius, it defines not only detonation velocity but also average detonation rate, pressure and energy. This allows the derivation of a generalized radius, which becomes larger as the explosive becomes more non-ideal. The model is applied to near-ideal PBX 9404, in-between ANFO and most non-ideal AN. The power of the pressure declines from 2.3, 1.5 to 0.8 across this set. The power of the burn fraction, F, is 0.8, 0 and 0, so that an F-term is important only for the ideal explosives. The size effect shapes change from concave-down to nearly straight to concave-up. Failure is associated with ideal explosives when the calculated detonation velocity turns in a double-valued way. The effect of the power of the pressure may be simulated by including a pressure cutoff in the detonation rate. The models allows comparison of a wide spectrum of explosives providing that a single detonation rate is feasible.

  17. Physics of transformation from Schrödinger theory to Kohn-Sham density-functional theory: Application to an exactly solvable model

    NASA Astrophysics Data System (ADS)

    Qian, Zhixin; Sahni, Viraht

    1998-04-01

    According to Hohenberg-Kohn-Sham density-functional theory (DFT), and its constrained search formulation, the Schrödinger ground-state wave function Ψ is a functional of the ground-state electronic density ρ(r). But the explicit functional dependence of Ψ on ρ is unknown. It is, however, possible to describe Kohn-Sham (KS) DFT and its electron-interaction energy functional and functional derivative rigorously in terms of the wave function Ψ. This description involves a conservative field which is a sum of two fields, the first representative of electron correlations due to the Pauli exclusion principle and Coulomb repulsion, and the second of correlation-kinetic effects. The sources of these fields are expectations of Hermitian operators with respect to Ψ. The energy functional is expressed in integral virial form in terms of these fields, whereas the functional derivative is the work done to move an electron in the conservative field of their sum. In this paper we illustrate the physics of transformation from Schrödinger to KS theory by application of this description to a ground state of the exactly solvable Hooke's atom. As such we determine properties such as the pair-correlation density, the Fermi and Coulomb holes, the Schrödinger and KS kinetic-energy-density tensors and kinetic fields, and the electron-interaction and correlation-kinetic fields, potentials, and energies, the majority of these constituent properties of the transformation being obtained analytically. In this manner we demonstrate the separate contributions and significance of each type of electron correlation to the KS electron-interaction energy and its functional derivative. Based on this study and previous work, it is proposed that in the construction of approximate energy functionals and their derivatives for application to more complex systems, it is the fields that be directly approximated.

  18. Analytical model for random dopant fluctuation in double-gate MOSFET in the subthreshold region using macroscopic modeling method

    NASA Astrophysics Data System (ADS)

    Shin, Yong Hyeon; Yun, Ilgu

    2016-12-01

    An analytical model is proposed for the random dopant fluctuation (RDF) in a symmetric double-gate metal-oxidesemiconductor field-effect-transistor (DG MOSFET) in the subthreshold region. Unintended impurity dopants cannot be absolutely prevented during the device fabrication; hence, it is important to analytically model the fluctuations in the electrical characteristics caused by these impurity dopants. Therefore, a macroscopic modeling method is applied to represent the impurity dopants in DG MOSFETs. With this method, the two-dimensional (2D) Poisson equation is separated into a basic analytical DG MOSFET model with channel doping concentration NA and an impurity-dopant-related term with local doping concentration NRD confined in a specific rectangular area. To solve the second term, the manually solvable 2D Green's function for DG MOSFETs is used. Through calculation of the channel potential (ϕ(x, y)), the variations in the drive current (IDS) and threshold voltage (Vth) are extracted from the analytical model. All results from the analytical model for an impurity dopant in a DG MOSFET are examined by comparisons with the commercially available 2D numerical simulation results, with respect to various oxide thicknesses (tox), channel lengths (L), and location of impurity dopants.

  19. Stochastic genetic networks with solvable structures

    SciTech Connect

    Lipan, Ovidiu

    2014-12-10

    We describe a set of basic stochastic biocircuits for which the Master Equation is completely solvable. Beside linear circuits, which are known to be solvable, we show that tree-like circuits with polynomial transition functions are also completely solvable. We associate a simple but unambiguous graphical representation to such circuits. The graphical representation shows the signal propagation through these simple circuits.

  20. The Computer-Aided Analytic Process Model. Operations Handbook for the Analytic Process Model Demonstration Package

    DTIC Science & Technology

    1986-01-01

    Research Note 86-06 THE COMPUTER-AIDED ANALYTIC PROCESS MODEL : OPERATIONS HANDBOOK FOR THE ANALYTIC PROCESS MODEL DE ONSTRATION PACKAGE Ronald G...ic Process Model ; Operations Handbook; Tutorial; Apple; Systems Taxonomy Mod--l; Training System; Bradl1ey infantry Fighting * Vehicle; BIFV...8217. . . . . . . .. . . . . . . . . . . . . . . . * - ~ . - - * m- .. . . . . . . item 20. Abstract -continued companion volume-- "The Analytic Process Model for

  1. Classical and quantum harmonic oscillators with time dependent mass and frequency: A new class of exactly solvable model

    NASA Astrophysics Data System (ADS)

    Mandal, Swapan

    2017-03-01

    The classical harmonic oscillator with time dependent mass and frequency is investigated to obtain a closed form exact analytical solution. It is found that the closed form analytical solutions are indeed possible if the time dependent mass of the oscillator is inversely proportional to the time dependent frequency. The scaled wronskian obtained from the linearly independent solutions of the equation of motion of the classical oscillator is used to obtain the solution corresponding to its quantum mechanical counterpart. The analytical solution of the present oscillator is used to obtain the squeezing effects of the input coherent light. In addition to the possibilities of getting the squeezed states, the present solution will be of use for investigating various quantum statistical properties of the radiation fields. As an example, we investigate the antibunching of the input thermal (chaotic) light coupled to the oscillator. Therefore, the appearance of the photon antibunching does not warrant the squeezing and vice-versa. The exact solution is obtained at the cost of the stringent condition where the product of time dependent mass and frequency of the oscillator is time invariant.

  2. ANALYTICAL ELEMENT MODELING OF COASTAL AQUIFERS

    EPA Science Inventory

    Four topics were studied concerning the modeling of groundwater flow in coastal aquifers with analytic elements: (1) practical experience was obtained by constructing a groundwater model of the shallow aquifers below the Delmarva Peninsula USA using the commercial program MVAEM; ...

  3. ANALYTICAL ELEMENT MODELING OF COASTAL AQUIFERS

    EPA Science Inventory

    Four topics were studied concerning the modeling of groundwater flow in coastal aquifers with analytic elements: (1) practical experience was obtained by constructing a groundwater model of the shallow aquifers below the Delmarva Peninsula USA using the commercial program MVAEM; ...

  4. Generations of solvable discrete-time dynamical systems

    NASA Astrophysics Data System (ADS)

    Bihun, Oksana; Calogero, Francesco

    2017-05-01

    A technique is introduced which allows to generate—starting from any solvable discrete-time dynamical system involving N time-dependent variables—new, generally nonlinear, generations of discrete-time dynamical systems, also involving N time-dependent variables and being as well solvable by algebraic operations (essentially by finding the N zeros of explicitly known polynomials of degree N). The dynamical systems constructed using this technique may also feature large numbers of arbitrary constants, and they need not be autonomous. The solvable character of these models allows to identify special cases with remarkable time evolutions: for instance, isochronous or asymptotically isochronous discrete-time dynamical systems. The technique is illustrated by a few examples.

  5. Toward a gradiometer analytic model

    NASA Technical Reports Server (NTRS)

    Sonnabend, Dave

    1992-01-01

    A new model is developed to model the data type, formulate the filter structure, and perform covariance for an orbiting gravity gradiometer, which is much more elaborate and realistic than the earlier gravity gradient model of Sonnabend and McEneaney (1988). The main new features of the new model are a general inertia tensor for the floated instrument, air drag and radiation pressure models using cubic power spectra, and more reasonable kinematics.

  6. Disturbance accommodating control design for wind turbines using solvability conditions

    DOE PAGES

    Wang, Na; Wright, Alan D.; Balas, Mark J.

    2017-02-07

    In this study, solvability conditions for disturbance accommodating control (DAC) have been discussed and applied on wind turbine controller design in above-rated wind speed to regulate rotor speed and to mitigate turbine structural loads. DAC incorporates a predetermined waveform model and uses it as part of the state-space formulation, which is known as the internal model principle to reduce or minimize the wind disturbance effects on the outputs of the wind turbine. An asymptotically stabilizing DAC controller with disturbance impact on the wind turbine being totally canceled out can be found if certain conditions are fulfilled. Designing a rotor speedmore » regulation controller without steady-state error is important for applying linear control methodology such as DAC on wind turbines. Therefore, solvability conditions of DAC without steady-state error are attractive and can be taken as examples when designing a multitask turbine controller. DAC controllers solved via Moore-Penrose Pseudoinverse and the Kronecker product are discussed, and solvability conditions of using them are given. Additionally, a new solvability condition based on inverting the feed-through D term is proposed for the sake of reducing computational burden in the Kronecker product. Applications of designing collective pitch and independent pitch controllers based on DAC are presented. Recommendations of designing a DAC-based wind turbine controller are given. A DAC controller motivated by the proposed solvability condition that utilizes the inverse of feed-through D term is developed to mitigate the blade flapwise once-per-revolution bending moment together with a standard proportional integral controller in the control loop to assist rotor speed regulation. Simulation studies verify the discussed solvability conditions of DAC and show the effectiveness of the proposed DAC control design methodology.« less

  7. Reply to ``Comment on `Single-particle Green functions in exactly solvable models of Bose and Fermi liquids' ''

    NASA Astrophysics Data System (ADS)

    Setlur, Girish S.; Chang, Yia-Chung

    1999-09-01

    It is shown that the sea-boson model given in G.S. Setlur and Y.C. Chang, Phys. Rev. B 57, 15 144 (1998), is capable of reproducing the four-point correlation functions of fermion operators within the random-phase approximation, although an explicit expression for the sea-boson operator is still lacking.

  8. Analytic gain in probabilistic decompression sickness models.

    PubMed

    Howle, Laurens E

    2013-11-01

    Decompression sickness (DCS) is a disease known to be related to inert gas bubble formation originating from gases dissolved in body tissues. Probabilistic DCS models, which employ survival and hazard functions, are optimized by fitting model parameters to experimental dive data. In the work reported here, I develop methods to find the survival function gain parameter analytically, thus removing it from the fitting process. I show that the number of iterations required for model optimization is significantly reduced. The analytic gain method substantially improves the condition number of the Hessian matrix which reduces the model confidence intervals by more than an order of magnitude. Copyright © 2013 Elsevier Ltd. All rights reserved.

  9. Knowledge Generation Model for Visual Analytics.

    PubMed

    Sacha, Dominik; Stoffel, Andreas; Stoffel, Florian; Kwon, Bum Chul; Ellis, Geoffrey; Keim, Daniel A

    2014-12-01

    Visual analytics enables us to analyze huge information spaces in order to support complex decision making and data exploration. Humans play a central role in generating knowledge from the snippets of evidence emerging from visual data analysis. Although prior research provides frameworks that generalize this process, their scope is often narrowly focused so they do not encompass different perspectives at different levels. This paper proposes a knowledge generation model for visual analytics that ties together these diverse frameworks, yet retains previously developed models (e.g., KDD process) to describe individual segments of the overall visual analytic processes. To test its utility, a real world visual analytics system is compared against the model, demonstrating that the knowledge generation process model provides a useful guideline when developing and evaluating such systems. The model is used to effectively compare different data analysis systems. Furthermore, the model provides a common language and description of visual analytic processes, which can be used for communication between researchers. At the end, our model reflects areas of research that future researchers can embark on.

  10. MPD Thruster Performance Analytic Models

    NASA Technical Reports Server (NTRS)

    Gilland, James; Johnston, Geoffrey

    2007-01-01

    Magnetoplasmadynamic (MPD) thrusters are capable of accelerating quasi-neutral plasmas to high exhaust velocities using Megawatts (MW) of electric power. These characteristics make such devices worthy of consideration for demanding, far-term missions such as the human exploration of Mars or beyond. Assessment of MPD thrusters at the system and mission level is often difficult due to their status as ongoing experimental research topics rather than developed thrusters. However, in order to assess MPD thrusters utility in later missions, some adequate characterization of performance, or more exactly, projected performance, and system level definition are required for use in analyses. The most recent physical models of self-field MPD thrusters have been examined, assessed, and reconfigured for use by systems and mission analysts. The physical models allow for rational projections of thruster performance based on physical parameters that can be measured in the laboratory. The models and their implications for the design of future MPD thrusters are presented.

  11. MPD Thruster Performance Analytic Models

    NASA Technical Reports Server (NTRS)

    Gilland, James; Johnston, Geoffrey

    2003-01-01

    Magnetoplasmadynamic (MPD) thrusters are capable of accelerating quasi-neutral plasmas to high exhaust velocities using Megawatts (MW) of electric power. These characteristics make such devices worthy of consideration for demanding, far-term missions such as the human exploration of Mars or beyond. Assessment of MPD thrusters at the system and mission level is often difficult due to their status as ongoing experimental research topics rather than developed thrusters. However, in order to assess MPD thrusters utility in later missions, some adequate characterization of performance, or more exactly, projected performance, and system level definition are required for use in analyses. The most recent physical models of self-field MPD thrusters have been examined, assessed, and reconfigured for use by systems and mission analysts. The physical models allow for rational projections of thruster performance based on physical parameters that can be measured in the laboratory. The models and their implications for the design of future MPD thrusters are presented.

  12. Analytic modeling of aerosol size distributions

    NASA Technical Reports Server (NTRS)

    Deepack, A.; Box, G. P.

    1979-01-01

    Mathematical functions commonly used for representing aerosol size distributions are studied parametrically. Methods for obtaining best fit estimates of the parameters are described. A catalog of graphical plots depicting the parametric behavior of the functions is presented along with procedures for obtaining analytical representations of size distribution data by visual matching of the data with one of the plots. Examples of fitting the same data with equal accuracy by more than one analytic model are also given.

  13. INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Solvable Catalyzed Birth-Death-Exchange Competition Model of Three Species

    NASA Astrophysics Data System (ADS)

    Wang, Hai-Feng; Lin, Zhen-Quan; Gao, Yan; Zhang, Heng

    2009-10-01

    A competition model of three species in exchange-driven aggregation growth is proposed. In the model, three distinct aggregates grow by exchange of monomers and in parallel, birth of species A is catalyzed by species B and death of species A is catalyzed by species C. The rates for both catalysis processes are proportional to kjν and kjω respectively, where ν(Ω) is a parameter reflecting the dependence of the catalysis reaction rate of birth (death) on the catalyst aggregate's size. The kinetic evolution behaviors of the three species are investigated by the rate equation approach based on the mean-field theory. The form of the aggregate size distribution of A-species ak(t) is found to be dependent crucially on the two catalysis rate kernel parameters. The results show that (i) in case of μ <= 0, the form of ak(t) mainly depends on the competition between self-exchange of species A and species-C-catalyzed death of species A; (ii) in case of ν > 0, the form of ak(t) mainly depends on the competition between species-B-catalyzed birth of species A and species-C-catalyzed death of species A.

  14. Nonanalytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable one-dimensional model for evaporation

    NASA Astrophysics Data System (ADS)

    Hilbert, Stefan; Dunkel, Jörn

    2006-07-01

    We calculate exactly both the microcanonical and canonical thermodynamic functions (TDFs) for a one-dimensional model system with piecewise constant Lennard-Jones type pair interactions. In the case of an isolated N -particle system, the microcanonical TDFs exhibit (N-1) singular (nonanalytic) microscopic phase transitions of the formal order N/2 , separating N energetically different evaporation (dissociation) states. In a suitably designed evaporation experiment, these types of phase transitions should manifest themselves in the form of pressure and temperature oscillations, indicating cooling by evaporation. In the presence of a heat bath (thermostat), such oscillations are absent, but the canonical heat capacity shows a characteristic peak, indicating the temperature-induced dissociation of the one-dimensional chain. The distribution of complex zeros of the canonical partition may be used to identify different degrees of dissociation in the canonical ensemble.

  15. Approach of the associated Laguerre functions to the su(1,1) coherent states for some quantum solvable models

    NASA Astrophysics Data System (ADS)

    Fakhri, H.; Dehghani, A.; Mojaveri, B.

    Using second-order differential operators as a realization of the su(1,1) Lie algebra by the associated Laguerre functions, it is shown that the quantum states of the Calogero-Sutherland, half-oscillator and radial part of a 3D harmonic oscillator constitute the unitary representations for the same algebra. This su(1,1) Lie algebra symmetry leads to derivation of the Barut-Girardello and Klauder-Perelomov coherent states for those models. The explicit compact forms of these coherent states are calculated. Also, to realize the resolution of the identity, their corresponding positive definite measures on the complex plane are obtained in terms of the known functions.

  16. A relativistically interacting exactly solvable multi-time model for two massless Dirac particles in 1 + 1 dimensions

    SciTech Connect

    Lienert, Matthias

    2015-04-15

    The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e., a map from (space-time){sup N} to a spin space. This concept was originally proposed by Dirac as the basis of relativistic quantum mechanics. In such a view, interaction potentials are mathematically inconsistent. This fact motivates the search for new mechanisms for relativistic interactions. In this paper, we explore the idea that relativistic interaction can be described by boundary conditions on the set of coincidence points of two particles in space-time. This extends ideas from zero-range physics to a relativistic setting. We illustrate the idea at the simplest model which still possesses essential physical properties like Lorentz invariance and a positive definite density: two-time equations for massless Dirac particles in 1 + 1 dimensions. In order to deal with a spatio-temporally non-trivial domain, a necessity in the multi-time picture, we develop a new method to prove existence and uniqueness of classical solutions: a generalized version of the method of characteristics. Both mathematical and physical considerations are combined to precisely formulate and answer the questions of probability conservation, Lorentz invariance, interaction, and antisymmetry.

  17. Full self-consistency versus quasiparticle self-consistency in diagrammatic approaches: Exactly solvable two-site Hubbard model

    DOE PAGES

    Kutepov, A. L.

    2015-07-22

    Self-consistent solutions of Hedin's equations (HE) for the two-site Hubbard model (HM) have been studied. They have been found for three-point vertices of increasing complexity (Γ = 1 (GW approximation), Γ₁ from the first-order perturbation theory, and the exact vertex ΓE). Comparison is made between the cases when an additional quasiparticle (QP) approximation for Green's functions is applied during the self-consistent iterative solving of HE and when QP approximation is not applied. Results obtained with the exact vertex are directly related to the present open question—which approximation is more advantageous for future implementations, GW + DMFT or QPGW + DMFT.more » It is shown that in a regime of strong correlations only the originally proposed GW + DMFT scheme is able to provide reliable results. Vertex corrections based on Perturbation Theory systematically improve the GW results when full self-consistency is applied. The application of QP self-consistency combined with PT vertex corrections shows similar problems to the case when the exact vertex is applied combined with QP sc. An analysis of Ward Identity violation is performed for all studied in this work's approximations and its relation to the general accuracy of the schemes used is provided.« less

  18. Full self-consistency versus quasiparticle self-consistency in diagrammatic approaches: Exactly solvable two-site Hubbard model

    SciTech Connect

    Kutepov, A. L.

    2015-07-22

    Self-consistent solutions of Hedin's equations (HE) for the two-site Hubbard model (HM) have been studied. They have been found for three-point vertices of increasing complexity (Γ = 1 (GW approximation), Γ₁ from the first-order perturbation theory, and the exact vertex ΓE). Comparison is made between the cases when an additional quasiparticle (QP) approximation for Green's functions is applied during the self-consistent iterative solving of HE and when QP approximation is not applied. Results obtained with the exact vertex are directly related to the present open question—which approximation is more advantageous for future implementations, GW + DMFT or QPGW + DMFT. It is shown that in a regime of strong correlations only the originally proposed GW + DMFT scheme is able to provide reliable results. Vertex corrections based on Perturbation Theory systematically improve the GW results when full self-consistency is applied. The application of QP self-consistency combined with PT vertex corrections shows similar problems to the case when the exact vertex is applied combined with QP sc. An analysis of Ward Identity violation is performed for all studied in this work's approximations and its relation to the general accuracy of the schemes used is provided.

  19. ESTIMATING UNCERTAINITIES IN FACTOR ANALYTIC MODELS

    EPA Science Inventory

    When interpreting results from factor analytic models as used in receptor modeling, it is important to quantify the uncertainties in those results. For example, if the presence of a species on one of the factors is necessary to interpret the factor as originating from a certain ...

  20. ESTIMATING UNCERTAINITIES IN FACTOR ANALYTIC MODELS

    EPA Science Inventory

    When interpreting results from factor analytic models as used in receptor modeling, it is important to quantify the uncertainties in those results. For example, if the presence of a species on one of the factors is necessary to interpret the factor as originating from a certain ...

  1. Analytical galactic models with mild stellar cusps

    NASA Astrophysics Data System (ADS)

    Rindler-Daller, T.

    2009-06-01

    In the past two decades, it has been established by high-resolution observations of early-type galaxies that their nuclear surface brightness and corresponding stellar mass densities are characterized by cusps. In this paper, we present a new spherical analytical model family describing mild cuspy centres. We study isotropic and anisotropic models of Osipkov-Merritt type. It is shown that the associated distribution functions and intrinsic velocity dispersions can be represented analytically in a unified way in terms of hypergeometric series, allowing thus a straightforward comparison of these important global quantities for galaxies having underlying mass densities which may differ significantly in their degree of central cuspiness or radial falloff.

  2. On solvable Dirac equation with polynomial potentials

    SciTech Connect

    Stachowiak, Tomasz

    2011-01-15

    One-dimensional Dirac equation is analyzed with regard to the existence of exact (or closed-form) solutions for polynomial potentials. The notion of Liouvillian functions is used to define solvability, and it is shown that except for the linear potentials the equation in question is not solvable.

  3. Modeling of the Global Water Cycle - Analytical Models

    Treesearch

    Yongqiang Liu; Roni Avissar

    2005-01-01

    Both numerical and analytical models of coupled atmosphere and its underlying ground components (land, ocean, ice) are useful tools for modeling the global and regional water cycle. Unlike complex three-dimensional climate models, which need very large computing resources and involve a large number of complicated interactions often difficult to interpret, analytical...

  4. Some analytical models of radiating collapsing spheres

    SciTech Connect

    Herrera, L.; Di Prisco, A; Ospino, J.

    2006-08-15

    We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each solution, using a hyperbolic transport equation, which permits to exhibit the influence of relaxational effects on the dynamics of the system.

  5. Bond indices in solids: extended analytical model.

    PubMed

    Ponec, Robert

    2011-11-15

    The analytical model suggested some time ago for the calculation of bond indices in infinite periodical structures was reconsidered and extended so as to provide not only realistic estimate of the extent of electron sharing localized among individual pairs of the atoms in the lattice but also to detect the eventual presence of multicenter bonding in metallic solids. Copyright © 2011 Wiley Periodicals, Inc.

  6. Analytical Modeling of Reinforced Concrete in Tension

    DTIC Science & Technology

    1989-04-01

    microcracks having a blunt front. This concept was pioneered by Rashid (Ref 3), developed by Bazant et al. (Ref 4 through 7), and is also known as the...size. In order to circumvent this condition, Bazant and Cedolin (Ref 5) suggested linking the rela- tionship to the fracture energy, Gf, forcing the...analytical models which represent the nonlinear relationships between shear stress and slip are the Rough Crack Model of Bazant and Gambarova (Ref 19

  7. Analytical steam injection model for layered systems

    SciTech Connect

    Abdual-Razzaq; Brigham, W.E.; Castanier, L.M.

    1993-08-01

    Screening, evaluation and optimization of the steam flooding process in homogeneous reservoirs can be performed by using simple analytical predictive models. In the absence of any analytical model for layered reservoirs, at present, only numerical simulators can be used. And these are expensive. In this study, an analytical model has been developed considering two isolated layers of differing permeabilities. The principle of equal flow potential is applied across the two layers. Gajdica`s (1990) single layer linear steam drive model is extended for the layered system. The formulation accounts for variation of heat loss area in the higher permeability layer, and the development of a hot liquid zone in the lower permeability layer. These calculations also account for effects of viscosity, density, fractional flow curves and pressure drops in the hot liquid zone. Steam injection rate variations in the layers are represented by time weighted average rates. For steam zone calculations, Yortsos and Gavalas`s (1981) upper bound method is used with a correction factor. The results of the model are compared with a numerical simulator. Comparable oil and water flow rates, and breakthrough times were achieved for 100 cp oil. Results with 10 cp and 1000 cp oils indicate the need to improve the formulation to properly handle differing oil viscosities.

  8. Hidden algebra method (quasi-exact-solvability in quantum mechanics)

    SciTech Connect

    Turbiner, Alexander

    1996-02-20

    A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.

  9. MATLAB/Simulink analytic radar modeling environment

    NASA Astrophysics Data System (ADS)

    Esken, Bruce L.; Clayton, Brian L.

    2001-09-01

    Analytic radar models are simulations based on abstract representations of the radar, the RF environment that radar signals are propagated, and the reflections produced by targets, clutter and multipath. These models have traditionally been developed in FORTRAN and have evolved over the last 20 years into efficient and well-accepted codes. However, current models are limited in two primary areas. First, by the nature of algorithm based analytical models, they can be difficult to understand by non-programmers and equally difficult to modify or extend. Second, there is strong interest in re-using these models to support higher-level weapon system and mission level simulations. To address these issues, a model development approach has been demonstrated which utilizes the MATLAB/Simulink graphical development environment. Because the MATLAB/Simulink environment graphically represents model algorithms - thus providing visibility into the model - algorithms can be easily analyzed and modified by engineers and analysts with limited software skills. In addition, software tools have been created that provide for the automatic code generation of C++ objects. These objects are created with well-defined interfaces enabling them to be used by modeling architectures external to the MATLAB/Simulink environment. The approach utilized is generic and can be extended to other engineering fields.

  10. Exactly solvable birth and death processes

    SciTech Connect

    Sasaki, Ryu

    2009-10-15

    Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable 'matrix' quantum mechanics, which is recently proposed by Odake and the author [S. Odake and R. Sasaki, J. Math. Phys. 49, 053503 (2008)]. The (q-) Askey scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of q{sup x} (with x being the population) corresponding to the q-Racah polynomial.

  11. Vortex microscope: analytical model and experiment

    NASA Astrophysics Data System (ADS)

    Masajada, Jan; Popiołek-Masajada, Agnieszka; Szatkowski, Mateusz; Plociniczak, Łukasz

    2015-11-01

    We present the analytical model describing the Gaussian beam propagation through the off axis vortex lens and the set of axially positioned ideal lenses. The model is derived on the base of Fresnel diffraction integral. The model is extended to the case of vortex lens with any topological charge m. We have shown that the Gaussian beam propagation can be represented by function G which depends on four coefficients. When propagating from one lens to another the function holds its form but the coefficient changes.

  12. An analytical model of memristors in plants.

    PubMed

    Markin, Vladislav S; Volkov, Alexander G; Chua, Leon

    2014-01-01

    The memristor, a resistor with memory, was postulated by Chua in 1971 and the first solid-state memristor was built in 2008. Recently, we found memristors in vivo in plants. Here we propose a simple analytical model of 2 types of memristors that can be found within plants. The electrostimulation of plants by bipolar periodic waves induces electrical responses in the Aloe vera and Mimosa pudica with fingerprints of memristors. Memristive properties of the Aloe vera and Mimosa pudica are linked to the properties of voltage gated K(+) ion channels. The potassium channel blocker TEACl transform plant memristors to conventional resistors. The analytical model of a memristor with a capacitor connected in parallel exhibits different characteristic behavior at low and high frequency of applied voltage, which is the same as experimental data obtained by cyclic voltammetry in vivo.

  13. An analytical model of memristors in plants

    PubMed Central

    Markin, Vladislav S; Volkov, Alexander G; Chua, Leon

    2014-01-01

    The memristor, a resistor with memory, was postulated by Chua in 1971 and the first solid-state memristor was built in 2008. Recently, we found memristors in vivo in plants. Here we propose a simple analytical model of 2 types of memristors that can be found within plants. The electrostimulation of plants by bipolar periodic waves induces electrical responses in the Aloe vera and Mimosa pudica with fingerprints of memristors. Memristive properties of the Aloe vera and Mimosa pudica are linked to the properties of voltage gated K+ ion channels. The potassium channel blocker TEACl transform plant memristors to conventional resistors. The analytical model of a memristor with a capacitor connected in parallel exhibits different characteristic behavior at low and high frequency of applied voltage, which is the same as experimental data obtained by cyclic voltammetry in vivo. PMID:25482769

  14. Mission Stream Analysis - Delta Analytic Model. Revision

    DTIC Science & Technology

    2014-09-01

    demonstrating mission effectiveness. The second tool is the  ( Delta ) Analytic Model, which provides an approach for identifying disparate...requirements into a system’s technical performance and operator workload requirements; and help minimize the “ delta ” between domains across the system’s...mission and system capability requirements into a system’s technical performance and operator workload requirements; and help minimize the “ delta

  15. Analytical Modeling of High Rate Processes.

    DTIC Science & Technology

    2007-11-02

    TYPE AND DATES COVERED 1 13 Apr 98 Final (01 Sep 94 - 31 Aug 97) 4. TITLE AND SUBTITLE 5 . FUNDING NUMBERS Analytical Modeling of High Rate Processes...20332- 8050 FROM: S. E. Jones, University Research Professor Department of Aerospace Engineering and Mechanics University of Alabama SUBJECT: Final...Mr. Sandor Augustus and Mr. Jeffrey A. Drinkard. There are no outstanding commitments. The balance in the account, as of July 31 , 1997, was $102,916.42

  16. Transonic Cascade Measurements to Support Analytical Modeling

    DTIC Science & Technology

    2007-11-02

    RECEIVED JUL 0 12005 FINAL REPORT FOR: AFOSR GRANT F49260-02-1-0284 TRANSONIC CASCADE MEASUREMENTS TO SUPPORT ANALYTICAL MODELING Paul A. Durbin ...PAD); 650-723-1971 (JKE) durbin @vk.stanford.edu; eaton@vk.stanford.edu submitted to: Attn: Dr. John Schmisseur Air Force Office of Scientific Research...both spline and control points for subsequent wall shape definitions. An algebraic grid generator was used to generate the grid for the blade-wall

  17. Analytic Modeling of Severe Vortical Storms.

    DTIC Science & Technology

    1980-07-08

    AD---AO86 919 TR DEFENSE AND SPACE SYSTEMS GROUP REDONDO BEACH CA -ETC F/6 4/2 ANALYTIC MODELING OF SEVERE VORTICAL, STDRMS.CW),7JUL G0 F FENDELL ...and Space Systems Group One Space 1ark ___Redondo Beach, California 90278 Francis E. Fendell , Principal Investigator for Artic and Earth Sciences... Fendell , principal investigator, and Phillip Feldman, numerical analyst, of TRW Defense and Space Systems Group, and George Carrier of Harvard University

  18. Structure theorem for Vaisman completely solvable solvmanifolds

    NASA Astrophysics Data System (ADS)

    Sawai, Hiroshi

    2017-04-01

    Locally conformal Kähler manifold is said to be a Vaisman manifold if the Lee form is parallel with respect to the Riemannian metric. In this paper, we have the structure theorem for Vaisman completely solvable solvmanifolds.

  19. Representations of filtered solvable Lie algebras

    SciTech Connect

    Panov, Alexander N

    2012-01-31

    The representation theory of filtered solvable Lie algebras is constructed. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found. Bibliography: 9 titles.

  20. Analytical halo model of galactic conformity

    NASA Astrophysics Data System (ADS)

    Pahwa, Isha; Paranjape, Aseem

    2017-09-01

    We present a fully analytical halo model of colour-dependent clustering that incorporates the effects of galactic conformity in a halo occupation distribution framework. The model, based on our previous numerical work, describes conformity through a correlation between the colour of a galaxy and the concentration of its parent halo, leading to a correlation between central and satellite galaxy colours at fixed halo mass. The strength of the correlation is set by a tunable 'group quenching efficiency', and the model can separately describe group-level correlations between galaxy colour (1-halo conformity) and large-scale correlations induced by assembly bias (2-halo conformity). We validate our analytical results using clustering measurements in mock galaxy catalogues, finding that the model is accurate at the 10-20 per cent level for a wide range of luminosities and length-scales. We apply the formalism to interpret the colour-dependent clustering of galaxies in the Sloan Digital Sky Survey (SDSS). We find good overall agreement between the data and a model that has 1-halo conformity at a level consistent with previous results based on an SDSS group catalogue, although the clustering data require satellites to be redder than suggested by the group catalogue. Within our modelling uncertainties, however, we do not find strong evidence of 2-halo conformity driven by assembly bias in SDSS clustering.

  1. An Improved Analytic Model for Microdosimeter Response

    NASA Technical Reports Server (NTRS)

    Shinn, Judy L.; Wilson, John W.; Xapsos, Michael A.

    2001-01-01

    An analytic model used to predict energy deposition fluctuations in a microvolume by ions through direct events is improved to include indirect delta ray events. The new model can now account for the increase in flux at low lineal energy when the ions are of very high energy. Good agreement is obtained between the calculated results and available data for laboratory ion beams. Comparison of GCR (galactic cosmic ray) flux between Shuttle TEPC (tissue equivalent proportional counter) flight data and current calculations draws a different assessment of developmental work required for the GCR transport code (HZETRN) than previously concluded.

  2. Analytic models of relativistic accretion disks

    NASA Astrophysics Data System (ADS)

    Zhuravlev, V. V.

    2015-06-01

    We present not a literature review but a description, as detailed and consistent as possible, of two analytic models of disk accretion onto a rotating black hole: a standard relativistic disk and a twisted relativistic disk. Although one of these models is older than the other, both are of topical interest for black hole studies. The treatment is such that the reader with only a limited knowledge of general relativity and relativistic hydrodynamics, with little or no use of additional sources, can gain insight into many technical details lacking in the original papers.

  3. Analytical model of the optical vortex microscope.

    PubMed

    Płocinniczak, Łukasz; Popiołek-Masajada, Agnieszka; Masajada, Jan; Szatkowski, Mateusz

    2016-04-20

    This paper presents an analytical model of the optical vortex scanning microscope. In this microscope the Gaussian beam with an embedded optical vortex is focused into the sample plane. Additionally, the optical vortex can be moved inside the beam, which allows fine scanning of the sample. We provide an analytical solution of the whole path of the beam in the system (within paraxial approximation)-from the vortex lens to the observation plane situated on the CCD camera. The calculations are performed step by step from one optical element to the next. We show that at each step, the expression for light complex amplitude has the same form with only four coefficients modified. We also derive a simple expression for the vortex trajectory of small vortex displacements.

  4. Exactly solvable interacting two-particle quantum graphs

    NASA Astrophysics Data System (ADS)

    Bolte, Jens; Garforth, George

    2017-03-01

    We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint realisations of the two-particle Laplacian. Showing compatibility with the Bethe ansatz method, we calculate quantisation conditions in the form of secular equations from which the spectra can be deduced. We compare spectral statistics of some examples to well known results in random matrix theory, analysing the chaotic properties of their classical counterparts.

  5. Analytic Models of Plausible Gravitational Lens Potentials

    SciTech Connect

    Baltz, Edward A.; Marshall, Phil; Oguri, Masamune

    2007-05-04

    Gravitational lenses on galaxy scales are plausibly modeled as having ellipsoidal symmetry and a universal dark matter density profile, with a Sersic profile to describe the distribution of baryonic matter. Predicting all lensing effects requires knowledge of the total lens potential: in this work we give analytic forms for that of the above hybrid model. Emphasizing that complex lens potentials can be constructed from simpler components in linear combination, we provide a recipe for attaining elliptical symmetry in either projected mass or lens potential.We also provide analytic formulae for the lens potentials of Sersic profiles for integer and half-integer index. We then present formulae describing the gravitational lensing effects due to smoothly-truncated universal density profiles in cold dark matter model. For our isolated haloes the density profile falls off as radius to the minus fifth or seventh power beyond the tidal radius, functional forms that allow all orders of lens potential derivatives to be calculated analytically, while ensuring a non-divergent total mass. We show how the observables predicted by this profile differ from that of the original infinite-mass NFW profile. Expressions for the gravitational flexion are highlighted. We show how decreasing the tidal radius allows stripped haloes to be modeled, providing a framework for a fuller investigation of dark matter substructure in galaxies and clusters. Finally we remark on the need for finite mass halo profiles when doing cosmological ray-tracing simulations, and the need for readily-calculable higher order derivatives of the lens potential when studying catastrophes in strong lenses.

  6. Analytical Performance Models for Geologic Repositories

    SciTech Connect

    Chambre, P.L.; Pigford, T.H.; Fujita, A.; Kanki, T.; Kobayashi,A.; Lung, H.; Ting, D.; Sato, Y.; Savoshy, S.J.

    1982-10-01

    This report presents analytical solutions of the dissolution and hydrogeologic transport of radionuclides in geologic repositories. Numerical examples are presented to demonstrate the equations resulting from these analyses. The subjects treated in the present report are: (a) Solubility-limited transport with transverse dispersion (Chapter 2); (b) Transport of a radionuclide chain with nonequilibrium chemical reactions (Chapter 3); (c) Advective transport in a two-dimensional flow field (Chapter 4); (d) Radionuclide.transport in fractured media (Chapter 5); (e) A mathematical model for EPA's analysis of generic repositories (Chapter 6); and (f) Dissolution of radionuclides from solid waste (Chapter 7).

  7. Analytical modeling of materialized view maintenance algorithms

    SciTech Connect

    Srivastava, J.; Rotem, D.

    1987-10-01

    In the recent past there has been increasing interest in the idea of maintaining materialized copies of views, and use them to process view queries (ADIB 80, LIND 86, BLAK 86, ROSS 86, HANS 87). Various algorithms have been proposed, and their performance analyzed. However, there does not exist a comprehensive analytical framework under which the problem can be systematically studied. We present a queueing model which facilitates both a systematic study of the problem, and provides a means to compare various proposed algorithms. Specifically, we propose a parametrized approach in which both the user and system viewpoints are integrated, and the setting of the parameter decides the relative importance of each table.

  8. Analytical modeling of satellites in geosynchronous environment

    NASA Technical Reports Server (NTRS)

    Stevens, N. J.

    1980-01-01

    Experiences with surface charging of geosynchronous satellites are reviewed and mechanisms leading to discharges on satellite surfaces are considered. It was found that the large differential voltages between the surface and the substrate required to produce massive laboratory discharges do not occur on satellites in space. Analytical modeling predictions supported by dielectric charging data from P78-2, SCATHA (Spacecraft Charging at High Altitudes) flight results are discussed. Ungrounded insulator areas, buried charge layers (due to mid-energy range particles), and positive differential voltages (where structure voltages are less negative than surrounding dielectric surface voltages) are considered as possible mechanisms producing satellite charge up.

  9. Analytical modeling of orthogonal spiral structures

    NASA Astrophysics Data System (ADS)

    Santos, Auteliano A.; Hobeck, Jared D.; Inman, Daniel J.

    2016-11-01

    This paper presents the analytical modeling of orthogonal spiral structures (OSS), a promising option for small-scale energy harvesting applications. This unique multi-beam structure is analyzed using a distributed parameter approach with Euler-Bernoulli assumptions. First, an aluminum substrate is evaluated to determine if the proposed design can be used to capture vibration energy in the desired frequency range using a twelve beam OSS. Finite element calculations are used to validate the analytical model. This model is then modified to include the electromechanical effects of a piezoelectric layer added to the aluminum substrate. Lastly, the effects of the beam width and the number of beams is analyzed for a particular surface area of the OSS. Results show that increasing the number of beams causes a reduction in the first natural frequency. From those results, it is possible to conclude that OSS can be used as an alternative to current energy harvesting systems for MEMS applications, allowing the capture of environmental energy in the frequency range of common mechanical systems.

  10. Analytical model for a vertical buoyant jet

    SciTech Connect

    Lee, D.W.

    1980-10-01

    An analytical model for a round and two-dimensional turbulent buoyant jet which is discharged vertically into a stagnant ambient is developed. The buoyant jet is considered to have three separate zone models which are matched to form a complete solution. The velocity field is determined for the entire jet and plume regions by the use of an eddy viscosity which varies along the axis of the jet. The centerline decay of buoyancy is determined throughout and the results are compared to existing numerical codes. The model is applied to the disposal of carbon dioxide enriched seawater. The results can be used to provide design information for minimizing or maximizing the dilution of a discharge by the receiving environment.

  11. Analytic Modeling of Pressurization and Cryogenic Propellant

    NASA Technical Reports Server (NTRS)

    Corpening, Jeremy H.

    2010-01-01

    An analytic model for pressurization and cryogenic propellant conditions during all mission phases of any liquid rocket based vehicle has been developed and validated. The model assumes the propellant tanks to be divided into five nodes and also implements an empirical correlation for liquid stratification if desired. The five nodes include a tank wall node exposed to ullage gas, an ullage gas node, a saturated propellant vapor node at the liquid-vapor interface, a liquid node, and a tank wall node exposed to liquid. The conservation equations of mass and energy are then applied across all the node boundaries and, with the use of perfect gas assumptions, explicit solutions for ullage and liquid conditions are derived. All fluid properties are updated real time using NIST Refprop.1 Further, mass transfer at the liquid-vapor interface is included in the form of evaporation, bulk boiling of liquid propellant, and condensation given the appropriate conditions for each. Model validation has proven highly successful against previous analytic models and various Saturn era test data and reasonably successful against more recent LH2 tank self pressurization ground test data. Finally, this model has been applied to numerous design iterations for the Altair Lunar Lander, Ares V Core Stage, and Ares V Earth Departure Stage in order to characterize Helium and autogenous pressurant requirements, propellant lost to evaporation and thermodynamic venting to maintain propellant conditions, and non-uniform tank draining in configurations utilizing multiple LH2 or LO2 propellant tanks. In conclusion, this model provides an accurate and efficient means of analyzing multiple design configurations for any cryogenic propellant tank in launch, low-acceleration coast, or in-space maneuvering and supplies the user with pressurization requirements, unusable propellants from evaporation and liquid stratification, and general ullage gas, liquid, and tank wall conditions as functions of time.

  12. Analytical model of Europa's O2 exosphere

    NASA Astrophysics Data System (ADS)

    Milillo, Anna; Plainaki, Christina; Orsini, Stefano; Mangano, Valeria; Massetti, Stefano; Mura, Alessandro

    2014-05-01

    The origin of the exosphere of Europa is its water ice surface. The existing exosphere models, assuming either a collisionless environment (simple Monte Carlo techniques) or a kinetic approach (Direct Monte Carlo Method) both predicts that the major constituent of the exosphere is molecular oxygen. Specifically, O2 is generated at the surface through radiolysis and chemical interactions of the water dissociation products. The non-escaping O2 molecules circulate around the moon impacting the surface several times, due to their long lifetime and due to their non-sticking, suffering thermalization to the surface temperature after each impact. In fact, the HST observations of the O emission lines have manifested the presence of an asymmetric atomic Oxygen envelope, evidencing the existence of a thin asymmetric molecular Oxygen atmosphere. The existing Monte Carlo models are not easily applicable as input of simulations devoted to the study of the plasma interactions with the moon. On the contrary, it would be important to have a suitable and user-friendly model to use as a tool. This study presents an analytical 3D model that is able to describe the molecular Oxygen exosphere by reproducing the asymmetries due to different configurations among Europa, Jupiter and the Sun. This model is obtained by a non-linear fit procedure of the EGEON Monte Carlo model results to a Chamberlain density profile. Different parameters of the model are able to describe various exosphere properties thus allowing a detailed investigation of the exospheric characteristics.

  13. An analytical model of crater count equilibrium

    NASA Astrophysics Data System (ADS)

    Hirabayashi, Masatoshi; Minton, David A.; Fassett, Caleb I.

    2017-06-01

    Crater count equilibrium occurs when new craters form at the same rate that old craters are erased, such that the total number of observable impacts remains constant. Despite substantial efforts to understand this process, there remain many unsolved problems. Here, we propose an analytical model that describes how a heavily cratered surface reaches a state of crater count equilibrium. The proposed model formulates three physical processes contributing to crater count equilibrium: cookie-cutting (simple, geometric overlap), ejecta-blanketing, and sandblasting (diffusive erosion). These three processes are modeled using a degradation parameter that describes the efficiency for a new crater to erase old craters. The flexibility of our newly developed model allows us to represent the processes that underlie crater count equilibrium problems. The results show that when the slope of the production function is steeper than that of the equilibrium state, the power law of the equilibrium slope is independent of that of the production function slope. We apply our model to the cratering conditions in the Sinus Medii region and at the Apollo 15 landing site on the Moon and demonstrate that a consistent degradation parameterization can successfully be determined based on the empirical results of these regions. Further developments of this model will enable us to better understand the surface evolution of airless bodies due to impact bombardment.

  14. The Immediate Exchange model: an analytical investigation

    NASA Astrophysics Data System (ADS)

    Katriel, Guy

    2015-01-01

    We study the Immediate Exchange model, recently introduced by Heinsalu and Patriarca [Eur. Phys. J. B 87, 170 (2014)], who showed by simulations that the wealth distribution in this model converges to a Gamma distribution with shape parameter 2. Here we justify this conclusion analytically, in the infinite-population limit. An infinite-population version of the model is derived, describing the evolution of the wealth distribution in terms of iterations of a nonlinear operator on the space of probability densities. It is proved that the Gamma distributions with shape parameter 2 are fixed points of this operator, and that, starting with an arbitrary wealth distribution, the process converges to one of these fixed points. We also discuss the mixed model introduced in the same paper, in which exchanges are either bidirectional or unidirectional with fixed probability. We prove that, although, as found by Heinsalu and Patriarca, the equilibrium distribution can be closely fit by Gamma distributions, the equilibrium distribution for this model is not a Gamma distribution.

  15. Simple analytic model for astrophysical S factors

    SciTech Connect

    Yakovlev, D. G.; Beard, M.; Gasques, L. R.; Wiescher, M.

    2010-10-15

    We propose a physically transparent analytic model of astrophysical S factors as a function of a center-of-mass energy E of colliding nuclei (below and above the Coulomb barrier) for nonresonant fusion reactions. For any given reaction, the S(E) model contains four parameters [two of which approximate the barrier potential, U(r)]. They are easily interpolated along many reactions involving isotopes of the same elements; they give accurate practical expressions for S(E) with only several input parameters for many reactions. The model reproduces the suppression of S(E) at low energies (of astrophysical importance) due to the shape of the low-r wing of U(r). The model can be used to reconstruct U(r) from computed or measured S(E). For illustration, we parametrize our recent calculations of S(E) (using the Sao Paulo potential and the barrier penetration formalism) for 946 reactions involving stable and unstable isotopes of C, O, Ne, and Mg (with nine parameters for all reactions involving many isotopes of the same elements, e.g., C+O). In addition, we analyze astrophysically important {sup 12}C+{sup 12}C reaction, compare theoretical models with experimental data, and discuss the problem of interpolating reliably known S(E) values to low energies (E < or approx. 2-3 MeV).

  16. Simple Analytic Models of Gravitational Collapse

    SciTech Connect

    Adler, R.

    2005-02-09

    Most general relativity textbooks devote considerable space to the simplest example of a black hole containing a singularity, the Schwarzschild geometry. However only a few discuss the dynamical process of gravitational collapse, by which black holes and singularities form. We present here two types of analytic models for this process, which we believe are the simplest available; the first involves collapsing spherical shells of light, analyzed mainly in Eddington-Finkelstein coordinates; the second involves collapsing spheres filled with a perfect fluid, analyzed mainly in Painleve-Gullstrand coordinates. Our main goal is pedagogical simplicity and algebraic completeness, but we also present some results that we believe are new, such as the collapse of a light shell in Kruskal-Szekeres coordinates.

  17. Analytic Treatment of a Trading Market Model

    NASA Astrophysics Data System (ADS)

    Das, Arnab; Yarlagadda, Sudhaker

    We mathematically analyze a simple market model where trading at each point in time involves only two agents with the sum of their money being conserved and with neither parties resulting with negative money after the interaction process. The exchange involves random re-distribution among the two players of a fixed fraction of their total money. We obtain a simple integral nonlinear equation for the money distribution. We find that the zero savings and finite savings cases belong to different universality classes. While the zero savings case can be solved analytically, the finite savings solution is obtained by numerically solving the integral equation. We find remarkable agreement with results obtained by other researchers using sophisticated numerical techniques [Chatterjee et al., these proceedings].

  18. WHAEM: PROGRAM DOCUMENTATION FOR THE WELLHEAD ANALYTIC ELEMENT MODEL

    EPA Science Inventory

    The Wellhead Analytic Element Model (WhAEM) demonstrates a new technique for the definition of time-of-travel capture zones in relatively simple geohydrologic settings. he WhAEM package includes an analytic element model that uses superposition of (many) analytic solutions to gen...

  19. WHAEM: PROGRAM DOCUMENTATION FOR THE WELLHEAD ANALYTIC ELEMENT MODEL

    EPA Science Inventory

    The Wellhead Analytic Element Model (WhAEM) demonstrates a new technique for the definition of time-of-travel capture zones in relatively simple geohydrologic settings. he WhAEM package includes an analytic element model that uses superposition of (many) analytic solutions to gen...

  20. An analytical model of flagellate hydrodynamics

    NASA Astrophysics Data System (ADS)

    Dölger, Julia; Bohr, Tomas; Andersen, Anders

    2017-04-01

    Flagellates are unicellular microswimmers that propel themselves using one or several beating flagella. We consider a hydrodynamic model of flagellates and explore the effect of flagellar arrangement and beat pattern on swimming kinematics and near-cell flow. The model is based on the analytical solution by Oseen for the low Reynolds number flow due to a point force outside a no-slip sphere. The no-slip sphere represents the cell and the point force a single flagellum. By superposition we are able to model a freely swimming flagellate with several flagella. For biflagellates with left–right symmetric flagellar arrangements we determine the swimming velocity, and we show that transversal forces due to the periodic movements of the flagella can promote swimming. For a model flagellate with both a longitudinal and a transversal flagellum we determine radius and pitch of the helical swimming trajectory. We find that the longitudinal flagellum is responsible for the average translational motion whereas the transversal flagellum governs the rotational motion. Finally, we show that the transversal flagellum can lead to strong feeding currents to localized capture sites on the cell surface.

  1. ANALYTIC MODELING OF THE MORETON WAVE KINEMATICS

    SciTech Connect

    Temmer, M.; Veronig, A. M.

    2009-09-10

    The issue whether Moreton waves are flare-ignited or coronal mass ejection (CME)-driven, or a combination of both, is still a matter of debate. We develop an analytical model describing the evolution of a large-amplitude coronal wave emitted by the expansion of a circular source surface in order to mimic the evolution of a Moreton wave. The model results are confronted with observations of a strong Moreton wave observed in association with the X3.8/3B flare/CME event from 2005 January 17. Using different input parameters for the expansion of the source region, either derived from the real CME observations (assuming that the upward moving CME drives the wave), or synthetically generated scenarios (expanding flare region, lateral expansion of the CME flanks), we calculate the kinematics of the associated Moreton wave signature. Those model input parameters are determined which fit the observed Moreton wave kinematics best. Using the measured kinematics of the upward moving CME as the model input, we are not able to reproduce the observed Moreton wave kinematics. The observations of the Moreton wave can be reproduced only by applying a strong and impulsive acceleration for the source region expansion acting in a piston mechanism scenario. Based on these results we propose that the expansion of the flaring region or the lateral expansion of the CME flanks is more likely the driver of the Moreton wave than the upward moving CME front.

  2. Analytical model of Europa's O2 exosphere

    NASA Astrophysics Data System (ADS)

    Milillo, Anna; Plainaki, Christina; De Angelis, Elisabetta; Mangano, Valeria; Massetti, Stefano; Mura, Alessandro; Orsini, Stefano; Rispoli, Rosanna

    2016-10-01

    The origin of the exosphere of Europa is its water ice surface. The existing exosphere models, assuming either a collisionless environment (simple Monte Carlo techniques) or a kinetic approach (Direct Monte Carlo Method) both predict that the major constituent of the exosphere is molecular oxygen. Specifically, O2 is generated at the surface through radiolysis and chemical interactions of the water dissociation products. The non-escaping O2 molecules circulate around the moon impacting the surface several times, due to their long lifetime and due to their non- sticking, suffering thermalization to the surface temperature after each impact. In fact, the HST observations of the O emission lines proved the presence of an asymmetric atomic Oxygen distribution, related to a thin asymmetric molecular Oxygen atmosphere. The existing Monte Carlo models are not easily applicable as input of simulations devoted to the study of the plasma interactions with the moon. On the other hand, the simple exponential density profiles cannot well depict the higher temperature/higher altitudes component originating by radiolysis. It would thus be important to have a suitable and user-friendly model able to describe the major exospheric characteristics to use as a tool. This study presents an analytical 3D model that is able to describe the molecular Oxygen exosphere by reproducing the two-component profiles and the asymmetries due to diverse configurations among Europa, Jupiter and the Sun. This model is obtained by a non-linear fit procedure of the EGEON Monte Carlo model (Plainaki et al. 2013) to a Chamberlain density profile. Different parameters of the model are able to describe various exosphere properties thus allowing a detailed investigation of the exospheric characteristics. As an example a discussion on the exospheric temperatures in different configurations and space regions is given.

  3. Analytical model of Europa's O2 exosphere

    NASA Astrophysics Data System (ADS)

    Milillo, Anna; Plainaki, Christina; Orsini, Stefano; De Angelis, Elisabetta; Mangano, Valeria; Massetti, Stefano; Mura, Alessandro; Rispoli, Rosanna; Colasanti, Luca

    2015-04-01

    The origin of the exosphere of Europa is its water ice surface. The existing exosphere models, assuming either a collisionless environment (simple Monte Carlo techniques) or a kinetic approach (Direct Monte Carlo Method) both predict that the major constituent of the exosphere is molecular oxygen. Specifically, O2 is generated at the surface through radiolysis and chemical interactions of the water dissociation products. The non-escaping O2 molecules circulate around the moon impacting the surface several times, due to their long lifetime and due to their non- sticking, suffering thermalization to the surface temperature after each impact. In fact, the HST observations of the O emission lines have manifested the presence of an asymmetric atomic Oxygen envelope, evidencing the possible existence of a thin asymmetric molecular Oxygen atmosphere. The existing Monte Carlo models are not easily applicable as input of simulations devoted to the study of the plasma interactions with the moon. On the other hand, the simple exponential density profiles cannot well depict the higher temperature/higher altitudes component originating by radiolysis. On the contrary, it would be important to have a suitable and user-friendly model to use as a tool. This study presents an analytical 3D model that is able to describe the molecular Oxygen exosphere by reproducing the asymmetries due to two configurations among Europa, Jupiter and the Sun, that is illumination at leading and at trailing side. This model is obtained by a non-linear fit procedure of the EGEON Monte Carlo model to a Chamberlain density profile. Different parameters of the model are able to describe various exosphere properties thus allowing a detailed investigation of the exospheric characteristics.

  4. Modeling Biodegradation and Reactive Transport: Analytical and Numerical Models

    SciTech Connect

    Sun, Y; Glascoe, L

    2005-06-09

    The computational modeling of the biodegradation of contaminated groundwater systems accounting for biochemical reactions coupled to contaminant transport is a valuable tool for both the field engineer/planner with limited computational resources and the expert computational researcher less constrained by time and computer power. There exists several analytical and numerical computer models that have been and are being developed to cover the practical needs put forth by users to fulfill this spectrum of computational demands. Generally, analytical models provide rapid and convenient screening tools running on very limited computational power, while numerical models can provide more detailed information with consequent requirements of greater computational time and effort. While these analytical and numerical computer models can provide accurate and adequate information to produce defensible remediation strategies, decisions based on inadequate modeling output or on over-analysis can have costly and risky consequences. In this chapter we consider both analytical and numerical modeling approaches to biodegradation and reactive transport. Both approaches are discussed and analyzed in terms of achieving bioremediation goals, recognizing that there is always a tradeoff between computational cost and the resolution of simulated systems.

  5. An Analytical Model of Iceberg Drift

    NASA Astrophysics Data System (ADS)

    Wagner, Till J. W.; Dell, Rebecca W.; Eisenman, Ian

    2017-07-01

    Iceberg drift and decay and the associated freshwater release are increasingly seen as important processes in Earth's climate system, yet a detailed understanding of their dynamics has remained elusive. Here, an idealized model of iceberg drift is presented. The model is designed to include the most salient physical processes that determine iceberg motion while remaining sufficiently simple to facilitate physical insight into iceberg drift dynamics. We derive an analytical solution of the model, which helps build understanding and also enables the rapid computation of large numbers of iceberg trajectories. The long-standing empirical rule of thumb that icebergs drift at 2% of the wind velocity, relative to the ocean current, is derived here from physical first principles, and it is shown that this relation only holds in the limit of strong winds or small icebergs, which approximately applies for typical icebergs in the Arctic. It is demonstrated that the opposite limit of weak winds or large icebergs approximately applies for typical Antarctic tabular icebergs, and that in this case the icebergs simply move with the ocean surface current. It is furthermore found that when winds are strong, wind drag drives icebergs in the direction the wind blows, whereas weak winds drive icebergs at a 90 degree angle to the wind direction.

  6. Semi-analytical proton exchange membrane fuel cell modeling

    NASA Astrophysics Data System (ADS)

    Cheddie, Denver F.; Munroe, Norman D. H.

    Mathematical techniques are presented which allow for analytical solutions of the catalyst layer transport and electrochemical problem in PEM fuel cells. These techniques transform the volumetric reaction terms to boundary flux terms, thereby eliminating the need for computational solving of the catalyst layer problem. The result is a semi-analytical fuel cell model-a computational model that entails analytical rather than computational catalyst layer solutions. This helps to alleviate the meshing difficulties inherent in the catalyst layers caused by large geometric aspect ratios, and hence reduce the computational requirements for fuel cell models. These analytical solutions are implemented in a 3D PEM fuel cell model, and the results of the semi-analytical model match well with the full computational model in terms of the polarization performance and species concentration distribution. In addition, these analytical solutions were able to reduce the required computational memory by a factor of approximately 3, and the computational time by a factor of approximately 4.

  7. Analytic wave model of Stark deceleration dynamics

    SciTech Connect

    Gubbels, Koos; Meijer, Gerard; Friedrich, Bretislav

    2006-06-15

    Stark deceleration relies on time-dependent inhomogeneous electric fields which repetitively exert a decelerating force on polar molecules. Fourier analysis reveals that such fields, generated by an array of field stages, consist of a superposition of partial waves with well-defined phase velocities. Molecules whose velocities come close to the phase velocity of a given wave get a ride from that wave. For a square-wave temporal dependence of the Stark field, the phase velocities of the waves are found to be odd-fraction multiples of a fundamental phase velocity {lambda}/{tau}, with {lambda} and {tau} the spatial and temporal periods of the field. Here we study explicitly the dynamics due to any of the waves as well as due to their mutual perturbations. We first solve the equations of motion for the case of single-wave interactions and exploit their isomorphism with those for the biased pendulum. Next we analyze the perturbations of the single-wave dynamics by other waves and find that these have no net effect on the phase stability of the acceleration or deceleration process. Finally, we find that a packet of molecules can also ride a wave which results from an interference of adjacent waves. In this case, small phase stability areas form around phase velocities that are even-fraction multiples of the fundamental velocity. A detailed comparison with classical trajectory simulations and with experiment demonstrates that the analytic 'wave model' encompasses all the longitudinal physics encountered in a Stark decelerator.

  8. An analytical model of joint contact.

    PubMed

    Eberhardt, A W; Keer, L M; Lewis, J L; Vithoontien, V

    1990-11-01

    The stress distribution in the region of contact between a layered elastic sphere and a layered elastic cavity is determined using an analytical model to stimulate contact of articulating joints. The purpose is to use the solution to analyze the effects of cartilage thickness and stiffness, bone stiffness and joint curvature on the resulting stress field, and investigate the possibility of cracking of the material due to tensile and shear stresses. Vertical cracking of cartilage as well as horizontal splitting at the cartilage-calcified cartilage interface has been observed in osteoarthritic joints. The current results indicate that for a given system (material properties mu and nu constant), the stress distribution is a function of the ratio of contact radius to layer thickness (a/h), and while tensile stresses are seen to occur only when a/h is small, tensile strain is observed for all a/h values. Significant shear stresses are observed at the cartilage-bone interface. Softening of cartilage results in an increase in a/h, and a decrease in maximum normal stress. Cartilage thinning increases a/h and the maximum contact stress, while thickening has the opposite effect. A reduction in the indenting radius reduces a/h and increases the maximum normal stress. Bone softening is seen to have negligible effect on the resulting contact parameters and stress distribution.

  9. Universal analytical modeling of plasmonic nanoparticles.

    PubMed

    Yu, Renwen; Liz-Marzán, Luis M; García de Abajo, F Javier

    2017-09-20

    Control over the optical response of metal nanoparticles and their associated plasmons is currently enabling many promising applications in areas as diverse as biosensing and photocatalysis. In this context, experiments based upon colloid synthesis and nanofabricated structures are assisted by numerical electromagnetic modeling, which supplies predictive simulations, but not the kind of physical intuition needed for exploration of new ideas, such as one finds when simple mathematical expressions can describe a problem. This tutorial review presents and extends a simple analytical simulation method that allows us to accurately describe the optical response of metal nanoparticles, including retardation effects, without the requirement of large computational resources. More precisely, plasmonic extinction spectra and near-field enhancement are described through a small set of real numbers for each nanoparticle shape, which we tabulate for a wide selection of common morphologies. Remarkably, these numbers are independent of size, composition and environment. We further present a compilation of nanoplasmonic experimental data that are excellently described by the simple mathematical expressions here introduced.

  10. Analytic Ballistic Performance Model of Whipple Shields

    NASA Technical Reports Server (NTRS)

    Miller, J. E.; Bjorkman, M. D.; Christiansen, E. L.; Ryan, S. J.

    2015-01-01

    The dual-wall, Whipple shield is the shield of choice for lightweight, long-duration flight. The shield uses an initial sacrificial wall to initiate fragmentation and melt an impacting threat that expands over a void before hitting a subsequent shield wall of a critical component. The key parameters to this type of shield are the rear wall and its mass which stops the debris, as well as the minimum shock wave strength generated by the threat particle impact of the sacrificial wall and the amount of room that is available for expansion. Ensuring the shock wave strength is sufficiently high to achieve large scale fragmentation/melt of the threat particle enables the expansion of the threat and reduces the momentum flux of the debris on the rear wall. Three key factors in the shock wave strength achieved are the thickness of the sacrificial wall relative to the characteristic dimension of the impacting particle, the density and material cohesion contrast of the sacrificial wall relative to the threat particle and the impact speed. The mass of the rear wall and the sacrificial wall are desirable to minimize for launch costs making it important to have an understanding of the effects of density contrast and impact speed. An analytic model is developed here, to describe the influence of these three key factors. In addition this paper develops a description of a fourth key parameter related to fragmentation and its role in establishing the onset of projectile expansion.

  11. CO2-Leaking Well - Analytical Modeling

    NASA Astrophysics Data System (ADS)

    Wertz, F.; Audigane, P.; Bouc, O.

    2009-04-01

    The long-term integrity of CO2 storage in geological system relies highly on local trapping mechanisms but also on the absence/control of any kind of outlets. Indeed numerous pathways (faults, wells, rock heterogeneities…) exist that can lead stored gas back to the surface. Thus, such leakage risks must be assessed and quantified if possible. In France, BRGM is inquired for evaluating safety criteria and developing a methodology for qualifying potential geological storage sites. This implies in particular to study the leakage scenario, here through a water-filled well as a worth scenario case. In order to determine the kinds of impacts leaking CO2 can have; knowing the velocity and flow rate of uprising CO2 is a necessity. That is why a better knowledge of CO2 in storage conditions and its behaviour with the environment is required. The following study aims at characterising the CO2 flowing into the well and then rising up in a water column over the vertical dimension. An analytical model was built that describes: - In a first step, the CO2 flow between the reservoir and the inside of the well, depending on quality and thickness of different seals, which determines the flow rate through the well. - In a second step, the CO2 uprising through an open and water filled well, however in steady state, which excludes a priori the characterisation of periodic or chaotic behaviours such as geyser formation. The objective is to give numerous orders of magnitude concerning CO2 thermodynamic properties while rising up: specific enthalpy, density, viscosity, velocity, flow, gas volume fraction and expansion, pressure and temperature gradient. Dissolution is partially taken into account, however without kinetic. The strength of this model is to compute analytically - easily and instantaneously - the 1-dimensional rising velocity of CO2 in a water column as a function of the CO2 density, interfacial tension and initial volume fraction. Characteristic speeds - the ones given by

  12. Analytical modeling of Cosmic Winds and Jets

    NASA Astrophysics Data System (ADS)

    Vlahakis, Nektarios

    1998-11-01

    stellar wind and the Blandford and Payne (1982) model of a disk-wind; it also contains nonpolytropic models, such as those of winds/jets in Sauty and Tsinganos (1994), Lima et al (1996) and Trussoni et al (1997). Besides the unification of all known cases under a common scheme, several new classes emerge and some are briefly analyzed; they could be explored for a further understanding of the physical properties of MHD outflows from various magnetized astrophysical rotators. We also propose a new class of exact and self-consistent MHD solutions which describe steady and axisymmetric hydromagnetic outflows from the magnetized atmosphere of a rotating gravitating central object with possibly an orbiting accretion disk. The plasma is driven by a thermal pressure gradient, as well as by magnetic rotator and radiative forces. At the Alfvenic and fast critical points the appropriate criticality conditions are applied. The outflows start almost radially but after the Alfven transition and before the fast critical surface is encountered the magnetic pinching force bends the poloidal streamlines into a cylindrical jet-type shape. The terminal speed, Alfven number, cross-sectional area of the jet, as well as its final pressure and density obtain uniform values at large distances from the source. The goal of the study is to give an analytical discussion of the two-dimensional interplay of the thermal pressure gradient, gravitational, Lorentz and inertial forces in accelerating and collimating an MHD flow. A parametric study of the model is given, as well as a brief sketch of its applicability to a self-consistent modeling of collimated outflows from various astrophysical objects. For example, the obtained characteristics of the collimated outflow in agreement with those in jets associated with YSO's. General theoretical arguments and various analytic self-similar solutions have recently shown that magnetized and rotating astrophysical outflows may become asymptotically cylindrical

  13. Analytical solution of a model for complex food webs

    NASA Astrophysics Data System (ADS)

    Camacho, Juan; Guimerà, Roger; Amaral, Luís A.

    2002-03-01

    We investigate numerically and analytically a recently proposed model for food webs [Nature 404, 180 (2000)] in the limit of large web sizes and sparse interaction matrices. We obtain analytical expressions for several quantities with ecological interest, in particular, the probability distributions for the number of prey and the number of predators. We find that these distributions have fast-decaying exponential and Gaussian tails, respectively. We also find that our analytical expressions are robust to changes in the details of the model.

  14. Demonstration of Detection and Ranging Using Solvable Chaos

    NASA Technical Reports Server (NTRS)

    Corron, Ned J.; Stahl, Mark T.; Blakely, Jonathan N.

    2013-01-01

    Acoustic experiments demonstrate a novel approach to ranging and detection that exploits the properties of a solvable chaotic oscillator. This nonlinear oscillator includes an ordinary differential equation and a discrete switching condition. The chaotic waveform generated by this hybrid system is used as the transmitted waveform. The oscillator admits an exact analytic solution that can be written as the linear convolution of binary symbols and a single basis function. This linear representation enables coherent reception using a simple analog matched filter and without need for digital sampling or signal processing. An audio frequency implementation of the transmitter and receiver is described. Successful acoustic ranging measurements are presented to demonstrate the viability of the approach.

  15. Modified Riccati approach to partially solvable quantum Hamiltonians. II. Morse-oscillator-related family

    NASA Astrophysics Data System (ADS)

    Montemayor, R.; Salem, L. D.

    1991-12-01

    We extend the scope of the modified Riccati approach to partial solubility in quantum mechanics introduced in a previous work [L. D. Salem and R. Montemayor, Phys. Rev. A 43, 1169 (1991)]. With the use of adequate mappings u(x), we show the convenience of the modified Riccati approach to analyze potentials that can be written as rational functions on u. The necessary conditions for a Hamiltonian to be solvable are discussed in detail. By considering the exponential mapping u=e-x, we construct a family of potentials related to the exactly solvable Morse oscillator. Within this family, we have identified a three-parameter quasiexactly solvable potential, which, depending on the value of its coupling constants, leads to a symmetric or asymmetric confining potential, with a single-well or a double-well structure. Explicit expressions for the energies and eigenfunctions are given for particular cases. The analytic continuation of the symmetric subset gives rise to a quasiexactly solvable periodic potential.

  16. A Structural Comparison of Analytical Models for University Planning.

    ERIC Educational Resources Information Center

    Weathersby, George B.; Weinstein, Milton C.

    This paper provides a conceptual framework for the evaluation of analytical planning models designed for application in institutions of higher education. In an attempt to address the most important and difficult decisions facing managers of higher education, the majority of the analytical models that have been recently developed have focused upon…

  17. Project Summary. ANALYTICAL ELEMENT MODELING OF COASTAL AQUIFERS

    EPA Science Inventory

    Four topics were studied concerning the modeling of groundwater flow in coastal aquifers with analytic elements: (1) practical experience was obtained by constructing a groundwater model of the shallow aquifers below the Delmarva Peninsula USA using the commercial program MVAEM; ...

  18. Project Summary. ANALYTICAL ELEMENT MODELING OF COASTAL AQUIFERS

    EPA Science Inventory

    Four topics were studied concerning the modeling of groundwater flow in coastal aquifers with analytic elements: (1) practical experience was obtained by constructing a groundwater model of the shallow aquifers below the Delmarva Peninsula USA using the commercial program MVAEM; ...

  19. Automated dynamic analytical model improvement for damped structures

    NASA Technical Reports Server (NTRS)

    Fuh, J. S.; Berman, A.

    1985-01-01

    A method is described to improve a linear nonproportionally damped analytical model of a structure. The procedure finds the smallest changes in the analytical model such that the improved model matches the measured modal parameters. Features of the method are: (1) ability to properly treat complex valued modal parameters of a damped system; (2) applicability to realistically large structural models; and (3) computationally efficiency without involving eigensolutions and inversion of a large matrix.

  20. The Computer-Aided Analytic Process Model. Operations Handbook for the APM (Analytic Process Model) Demonstration Package. Appendix

    DTIC Science & Technology

    1986-01-01

    The Analytic Process Model for System Design and Measurement: A Computer-Aided Tool for Analyzing Training Systems and Other Human-Machine Systems. A...separate companion volume--The Computer-Aided Analytic Process Model : Operations Handbook for the APM Demonstration Package is also available under

  1. An analytically linearized helicopter model with improved modeling accuracy

    NASA Technical Reports Server (NTRS)

    Jensen, Patrick T.; Curtiss, H. C., Jr.; Mckillip, Robert M., Jr.

    1991-01-01

    An analytically linearized model for helicopter flight response including rotor blade dynamics and dynamic inflow, that was recently developed, was studied with the objective of increasing the understanding, the ease of use, and the accuracy of the model. The mathematical model is described along with a description of the UH-60A Black Hawk helicopter and flight test used to validate the model. To aid in utilization of the model for sensitivity analysis, a new, faster, and more efficient implementation of the model was developed. It is shown that several errors in the mathematical modeling of the system caused a reduction in accuracy. These errors in rotor force resolution, trim force and moment calculation, and rotor inertia terms were corrected along with improvements to the programming style and documentation. Use of a trim input file to drive the model is examined. Trim file errors in blade twist, control input phase angle, coning and lag angles, main and tail rotor pitch, and uniform induced velocity, were corrected. Finally, through direct comparison of the original and corrected model responses to flight test data, the effect of the corrections on overall model output is shown.

  2. Boundedly solvable multipoint differential operators of first order on right semi-axis

    NASA Astrophysics Data System (ADS)

    Ismailov, Zameddin I.; Ipek, Pembe

    2015-09-01

    Using the methods of operator theory all boundedly solvable extensions of the minimal operator generated by some multipoint differential-operator expression of first order in the direct sum of Hilbert spaces of vector-functions are described. The obtain results are applied to Hutchinson's model in mathematical biology.

  3. A simple, analytical, axisymmetric microburst model for downdraft estimation

    NASA Technical Reports Server (NTRS)

    Vicroy, Dan D.

    1991-01-01

    A simple analytical microburst model was developed for use in estimating vertical winds from horizontal wind measurements. It is an axisymmetric, steady state model that uses shaping functions to satisfy the mass continuity equation and simulate boundary layer effects. The model is defined through four model variables: the radius and altitude of the maximum horizontal wind, a shaping function variable, and a scale factor. The model closely agrees with a high fidelity analytical model and measured data, particularily in the radial direction and at lower altitudes. At higher altitudes, the model tends to overestimate the wind magnitude relative to the measured data.

  4. Analytic Model For Estimation Of Cold Bulk Metal Forming Simulations

    SciTech Connect

    Skunca, Marko; Keran, Zdenka; Math, Miljenko

    2007-05-17

    Numerical simulation of bulk metal forming plays an important role in predicting a key parameters in cold forging. Comparison of numerical and experimental data is of great importance, but there is always a need of more universal analytical tools. Therefore, many papers besides experiment and simulation of a particular bulk metal forming technology, include an analytic model. In this paper an analytical model for evaluation of commercially available simulation program packages is proposed. Based on elementary theory of plasticity, being only geometry dependent, model represents a good analytical reference to estimate given modeling preferences like; element types, solver, remeshing influence and many others. Obtained, geometry dependent, stress fields compared with numerical data give a clear picture of numerical possibilities and limitations of particular modeling program package.

  5. An analytic performance model of disk arrays and its application

    NASA Technical Reports Server (NTRS)

    Lee, Edward K.; Katz, Randy H.

    1991-01-01

    As disk arrays become widely used, tools for understanding and analyzing their performance become increasingly important. In particular, performance models can be invaluable in both configuring and designing disk arrays. Accurate analytic performance models are desirable over other types of models because they can be quickly evaluated, are applicable under a wide range of system and workload parameters, and can be manipulated by a range of mathematical techniques. Unfortunately, analytical performance models of disk arrays are difficult to formulate due to the presence of queuing and fork-join synchronization; a disk array request is broken up into independent disk requests which must all complete to satisfy the original request. We develop, validate, and apply an analytic performance model for disk arrays. We derive simple equations for approximating their utilization, response time, and throughput. We then validate the analytic model via simulation and investigate the accuracy of each approximation used in deriving the analytical model. Finally, we apply the analytical model to derive an equation for the optimal unit of data striping in disk arrays.

  6. Feedbacks Between Numerical and Analytical Models in Hydrogeology

    NASA Astrophysics Data System (ADS)

    Zlotnik, V. A.; Cardenas, M. B.; Toundykov, D.; Cohn, S.

    2012-12-01

    Hydrogeology is a relatively young discipline which combines elements of Earth science and engineering. Mature fundamental disciplines (e.g., physics, chemistry, fluid mechanics) have centuries-long history of mathematical modeling even prior to discovery of Darcy's law. Thus, in hydrogeology, relatively few classic analytical models (such those by Theis, Polubarinova-Kochina, Philip, Toth, Henry, Dagan, Neuman) were developed by the early 1970's. The advent of computers and practical demands refocused mathematical models towards numerical techniques. With more diverse but less mathematically-oriented training, most hydrogeologists shifted from analytical methods to use of standardized computational software. Spatial variability in internal properties and external boundary conditions and geometry, and the added complexity of chemical and biological processes will remain major challenges for analytical modeling. Possibly, analytical techniques will play a subordinate role to numerical approaches in many applications. On the other hand, the rise of analytical element modeling of groundwater flow is a strong alternative to numerical models when data demand and computational efficiency is considered. The hallmark of analytical models - transparency and accuracy - will remain indispensable for scientific exploration of complex phenomena and for benchmarking numerical models. Therefore, there will always be feedbacks and complementarities between numerical and analytical techniques, as well as a certain ideological schism among various views to modeling. We illustrate the idea of feedbacks by reviewing evolution of Joszef Toth's analytical model of gravity driven flow systems. Toth's (1963) approach was to reduce the flow domain to a rectangle which allowed for closed-form solution of the governing equations. Succeeding numerical finite-element models by Freeze and Witherspoon (1966-1968) explored the effects of geometry and heterogeneity on regional groundwater flow

  7. Combining Modeling and Gaming for Predictive Analytics

    SciTech Connect

    Riensche, Roderick M.; Whitney, Paul D.

    2012-08-22

    Many of our most significant challenges involve people. While human behavior has long been studied, there are recent advances in computational modeling of human behavior. With advances in computational capabilities come increases in the volume and complexity of data that humans must understand in order to make sense of and capitalize on these modeling advances. Ultimately, models represent an encapsulation of human knowledge. One inherent challenge in modeling is efficient and accurate transfer of knowledge from humans to models, and subsequent retrieval. The simulated real-world environment of games presents one avenue for these knowledge transfers. In this paper we describe our approach of combining modeling and gaming disciplines to develop predictive capabilities, using formal models to inform game development, and using games to provide data for modeling.

  8. High Fidelity Quantum Gates via Analytically Solvable Pulses

    DTIC Science & Technology

    2012-06-06

    generally allow for higher fidelities as compared to their unchirped coun- terparts, an effect reminiscent of the robust population transfer to an...2 + λ), the effective pulse area is the same as that of the RZ sech pulse, so that for Ω/σ = integer, the induced evolution is cyclic. I focus on...larger detuning required for the same phase. Since the detuning is large, from a qualitative effective Rabi frequency argument, the relative

  9. Analytical Ion Thruster Discharge Performance Model

    NASA Technical Reports Server (NTRS)

    Goebel, Dan M.; Wirz, Richard E.; Katz, Ira

    2006-01-01

    A particle and energy balance model of the plasma discharge in magnetic ring-cusp ion thrusters has been developed. The model follows the original work of Brophy in the development of global 0-D discharge models that utilize conservation of particles into and out of the thruster and conservation of energy into the discharge and out of the plasma in the form of charged particles to the walls and beam and plasma radiation. The present model is significantly expanded over Brophy's original work by including self-consistent calculations of the internal neutral pressure, electron temperature, primary electron density, electrostatic ion confinement (due to the ring-cusp fields), plasma potential, discharge stability, and time dependent behavior during recycling. The model only requires information on the thruster geometry, ion optics performance and electrical inputs such as discharge voltage and currents, etc. to produce accurate performance curves of discharge loss versus mass utilization efficiency. The model has been benchmarked against the NEXIS Laboratory Model (LM) and Development Model (DM) thrusters, and successfully predicts the thruster discharge loss as a function of mass utilization efficiency for a variety of thrusters. The discharge performance model will be presented and results showing ion thruster performance and stability given.

  10. Analytical Ion Thruster Discharge Performance Model

    NASA Technical Reports Server (NTRS)

    Goebel, Dan M.; Wirz, Richard E.; Katz, Ira

    2006-01-01

    A particle and energy balance model of the plasma discharge in magnetic ring-cusp ion thrusters has been developed. The model follows the original work of Brophy in the development of global 0-D discharge models that utilize conservation of particles into and out of the thruster and conservation of energy into the discharge and out of the plasma in the form of charged particles to the walls and beam and plasma radiation. The present model is significantly expanded over Brophy's original work by including self-consistent calculations of the internal neutral pressure, electron temperature, primary electron density, electrostatic ion confinement (due to the ring-cusp fields), plasma potential, discharge stability, and time dependent behavior during recycling. The model only requires information on the thruster geometry, ion optics performance and electrical inputs such as discharge voltage and currents, etc. to produce accurate performance curves of discharge loss versus mass utilization efficiency. The model has been benchmarked against the NEXIS Laboratory Model (LM) and Development Model (DM) thrusters, and successfully predicts the thruster discharge loss as a function of mass utilization efficiency for a variety of thrusters. The discharge performance model will be presented and results showing ion thruster performance and stability given.

  11. An analytical model and verification for MEMS Pirani gauges

    NASA Astrophysics Data System (ADS)

    Santagata, F.; Iervolino, E.; Mele, L.; van Herwaarden, A. W.; Creemer, J. F.; Sarro, P. M.

    2011-11-01

    A new analytical model for the design of micromachined Pirani gauges operating in constant current mode is presented. This model expresses the pressure range as a closed-form analytical function of the design variables such as geometry and biasing. Furthermore, it yields simplified expressions for other performance parameters such as the sensitivity, output swing and power consumption. A Pirani gauge has been designed according to the presented model and has been fabricated and characterized in order to verify the validity of the model. The measurements match the theory closely. The model will be useful to designers who need to trade off performance against the costs of chip area and biasing power.

  12. Analytical model for orbital debris environmental management

    NASA Technical Reports Server (NTRS)

    Talent, David L.

    1990-01-01

    A differential equation, also referred to as the PIB (particle-in-a-box) model, expressing the time rate of change of the number of objects in orbit, is developed, and its applicability is illustrated. The model can be used as a tool for the assessment of LEO environment stability, and as a starting point for the development of numerical evolutionary models. Within the context of the model, evolutionary scenarios are examined, and found to be sensitive to the growth rate. It is determined that the present environment is slightly unstable to catastrophic growth, and that the number of particles on orbit will continue to increase until approximately 2250-2350 AD, with a maximum of 2,000,000. The model is expandable to the more realistic (complex) case of multiple species in a multiple-tier system.

  13. Analytical model for orbital debris environmental management

    NASA Technical Reports Server (NTRS)

    Talent, David L.

    1990-01-01

    A differential equation, also referred to as the PIB (particle-in-a-box) model, expressing the time rate of change of the number of objects in orbit, is developed, and its applicability is illustrated. The model can be used as a tool for the assessment of LEO environment stability, and as a starting point for the development of numerical evolutionary models. Within the context of the model, evolutionary scenarios are examined, and found to be sensitive to the growth rate. It is determined that the present environment is slightly unstable to catastrophic growth, and that the number of particles on orbit will continue to increase until approximately 2250-2350 AD, with a maximum of 2,000,000. The model is expandable to the more realistic (complex) case of multiple species in a multiple-tier system.

  14. Decision-analytic models: current methodological challenges.

    PubMed

    Caro, J Jaime; Möller, Jörgen

    2014-10-01

    Modelers seeking to help inform decisions about insurance (public or private) coverage of the cost of pharmaceuticals or other health care interventions face various methodological challenges. In this review, which is not meant to be comprehensive, we cover those that in our experience are most vexing. The biggest challenge is getting decision makers to trust the model. This is a major problem because most models undergo only cursory validation; our field has lacked the motivation, time, and data to properly validate models intended to inform health care decisions. Without documented, adequate validation, there is little basis for decision makers to have confidence that the model's results are credible and should be used in a health technology appraisal. A fundamental problem for validation is that the models are very artificial and lack sufficient depth to adequately represent the reality they are simulating. Typically, modelers assume that all resources have infinite capacity so any patient needing care receives it immediately; there are no waiting times or queues, contrary to the common experience in actual practice. Moreover, all the patients enter the model simultaneously at time zero rather than over time as happens in actuality; differences between patients are ignored or minimized and structural modeling choices that make little sense (e.g., using states to represent events) are forced by commitment to a technique (and even to specific spreadsheet software!). The resulting structural uncertainty is rarely addressed, because methods are lacking and even probabilistic analysis of parameter uncertainty suffers from weak consideration of correlation and arbitrary distribution choices. Stakeholders must see to it that models are fit for the stated purpose and provide the best possible estimates given available data-the decisions at stake deserve nothing less.

  15. Retardation analytical model to extend service life

    NASA Technical Reports Server (NTRS)

    Matejczyk, D.

    1984-01-01

    A fatigue crack growth model that incorporates crack growth retardation effects and is applicable to the materials characteristics and service environments of high performance LH2/LO2 engine systems was developed and tested.

  16. Quasi-exact-solvability of the {{A}_{2}}/{{G}_{2}} elliptic model: algebraic forms, sl(3)/{{g}^{(2)}} hidden algebra, and polynomial eigenfunctions

    NASA Astrophysics Data System (ADS)

    Sokolov, Vladimir V.; Turbiner, Alexander V.

    2015-04-01

    The potential of the A2 quantum elliptic model (three-body Calogero-Moser elliptic model) is defined by the pairwise three-body interaction through the Weierstrass ℘-function and has a single coupling constant. A change of variables has been found, which are A2 elliptic invariants, such that the potential becomes a rational function, while the flat space metric, as well as its associated vector, are polynomials in two variables. It is shown that the model possesses the hidden sl(3) algebra—the Hamiltonian is an element of the universal enveloping algebra {{U}sl(3)} for the arbitrary coupling constant—thus, it is equivalent to the sl(3)-quantum Euler-Arnold top. The integral, in a form of the third order differential operator with polynomial coefficients, is constructed explicitly, being also an element of {{U}sl(3)}. It is shown that there exists a discrete sequence of the coupling constants for which a finite number of polynomial eigenfunctions, up to a (non-singular) gauge factor, occurs. For these values of the coupling constants there exists a particular integral: it commutes with the Hamiltonian in action on the space of polynomial eigenfunctions, and the Hamiltonian is invariant with respect to two-dimensional projective transformations. It is shown that the A2 model has another hidden algebra {{g}(2)} introduced in Rosenbaum et al (1998 Int. J. Mod. Phys. A 13 3885). The potential of the G2 quantum elliptic model (three-body Wolfes elliptic model) is defined by the pairwise and three-body interactions through the Weierstrass ℘-function and has two coupling constants. A change of variables has been found, which are G2 elliptic invariants, such that the potential becomes a rational function, while the flat space metric, as well as its associated vector, are polynomials in two variables. It is shown the model possesses the hidden {{g}(2)} algebra. It is shown that there exists a discrete family of the coupling constants for which a finite number of

  17. Analytical Modeling of Groundwater Seepages to St. Lucie Estuary

    NASA Astrophysics Data System (ADS)

    Lee, J.; Yeh, G.; Hu, G.

    2008-12-01

    In this paper, six analytical models describing hydraulic interaction of stream-aquifer systems were applied to St Lucie Estuary (SLE) River Estuaries. These are analytical solutions for: (1) flow from a finite aquifer to a canal, (2) flow from an infinite aquifer to a canal, (3) the linearized Laplace system in a seepage surface, (4) wave propagation in the aquifer, (5) potential flow through stratified unconfined aquifers, and (6) flow through stratified confined aquifers. Input data for analytical solutions were obtained from monitoring wells and river stages at seepage-meter sites. Four transects in the study area are available: Club Med, Harbour Ridge, Lutz/MacMillan, and Pendarvis Cove located in the St. Lucie River. The analytical models were first calibrated with seepage meter measurements and then used to estimate of groundwater discharges into St. Lucie River. From this process, analytical relationships between the seepage rate and river stages and/or groundwater tables were established to predict the seasonal and monthly variation in groundwater seepage into SLE. It was found the seepage rate estimations by analytical models agreed well with measured data for some cases but only fair for some other cases. This is not unexpected because analytical solutions have some inherently simplified assumptions, which may be more valid for some cases than the others. From analytical calculations, it is possible to predict approximate seepage rates in the study domain when the assumptions underlying these analytical models are valid. The finite and infinite aquifer models and the linearized Laplace method are good for sites Pendarvis Cove and Lutz/MacMillian, but fair for the other two sites. The wave propagation model gave very good agreement in phase but only fairly agreement in magnitude for all four sites. The stratified unconfined and confined aquifer models gave similarly good agreements with measurements at three sites but poorly at the Club Med site. None of

  18. Evaluating Child Welfare policies with decision-analytic simulation models

    PubMed Central

    Goldhaber-Fiebert, Jeremy D.; Bailey, Stephanie L.; Hurlburt, Michael S.; Zhang, Jinjin; Snowden, Lonnie R.; Wulczyn, Fred; Landsverk, John; Horwitz, Sarah M.

    2013-01-01

    The objective was to demonstrate decision-analytic modeling in support of Child Welfare policymakers considering implementing evidence-based interventions. Outcomes included permanency (e.g., adoptions) and stability (e.g., foster placement changes). Analyses of a randomized trial of KEEP -- a foster parenting intervention -- and NSCAW-1 estimated placement change rates and KEEP's effects. A microsimulation model generalized these findings to other Child Welfare systems. The model projected that KEEP could increase permanency and stability, identifying strategies targeting higher-risk children and geographical regions that achieve benefits efficiently. Decision-analytic models enable planners to gauge the value of potential implementations. PMID:21861204

  19. Improved Analytical Model for Infiltration Towards the Water Table

    NASA Astrophysics Data System (ADS)

    Avina, J. L.; Mishra, P. K.

    2015-12-01

    We present mathematical model which describes one dimensional flow of water from the land surface to the water table. Following Mishra and Neuman (2010), we consider four-parameter exponential model to describe soil-water characteristics curves. A system with initial flux into soil from above and boundary conditions at the water table and soil surface is considered. Analytical solutions to two cases (homogeneous and layered soils) of water infiltration towards the water table and the prescribed initial and boundary conditions are presented. We conclude by comparing the developed model with existing analytical and numerical models.

  20. Analytic modeling of a spray diffusion flame

    NASA Technical Reports Server (NTRS)

    Harsha, P. T.; Edelman, R. B.

    1984-01-01

    A detailed model for a spray diffusion flame is described. The model is based on the boundary layer form of the equations of motion, with droplet transport accounted for using a discretized droplet size distribution function. Interphase transport of mass and energy are accounted for, with a flame-sheet model used to describe the combustion process on a droplet scale. Near dynamic equilibrium is assumed for the description of droplet transport; droplets can diffuse relative to the gas phase. Gas-phase mixing is accounted for using a two-equation turbulence model; buoyancy effects are included, with a temperature fluctuation equation used to account for buoyancy effects on turbulence structure. Thermal radiation from gas-phase CO2 and H2O is included. Gas-phase chemical kinetics are modeled using a 20-reaction, 10-species version of the advanced quasi-global chemical kinetics formulation. Results are compared with data for a vaporizing Freon spray and a pentane spray flame. It is shown that the computational approach provides a reasonably valid picture of the overall development of a spray diffusion flame, and, furthermore, provides a useful tool for the parametric examination of the spray combustion process.

  1. Analytic modeling of a spray diffusion flame

    NASA Astrophysics Data System (ADS)

    Harsha, P. T.; Edelman, R. B.

    1984-06-01

    A detailed model for a spray diffusion flame is described. The model is based on the boundary layer form of the equations of motion, with droplet transport accounted for using a discretized droplet size distribution function. Interphase transport of mass and energy are accounted for, with a flame-sheet model used to describe the combustion process on a droplet scale. Near dynamic equilibrium is assumed for the description of droplet transport; droplets can diffuse relative to the gas phase. Gas-phase mixing is accounted for using a two-equation turbulence model; buoyancy effects are included, with a temperature fluctuation equation used to account for buoyancy effects on turbulence structure. Thermal radiation from gas-phase CO2 and H2O is included. Gas-phase chemical kinetics are modeled using a 20-reaction, 10-species version of the advanced quasi-global chemical kinetics formulation. Results are compared with data for a vaporizing Freon spray and a pentane spray flame. It is shown that the computational approach provides a reasonably valid picture of the overall development of a spray diffusion flame, and, furthermore, provides a useful tool for the parametric examination of the spray combustion process.

  2. An Analytical Model of Tribocharging in Regolith

    NASA Astrophysics Data System (ADS)

    Carter, D. P.; Hartzell, C. M.

    2015-12-01

    Nongravitational forces, including electrostatic forces and cohesion, can drive the behavior of regolith in low gravity environments such as the Moon and asteroids. Regolith is the 'skin' of solid planetary bodies: it is the outer coating that is observed by orbiters and the first material contacted by landers. Triboelectric charging, the phenomenon by which electrical charge accumulates during the collision or rubbing of two surfaces, has been found to occur in initially electrically neutral granular mixtures. Although charge transfer is often attributed to chemical differences between the different materials, charge separation has also been found to occur in mixtures containing grains of a single material, but with a variety of grain sizes. In such cases, the charge always separates according to grain size; typically the smaller grains acquire a more negative charge than the larger grains. Triboelectric charging may occur in a variety of planetary phenomena (including mass wasting and dust storms) as well as during spacecraft-surface interactions (including sample collection and wheel motion). Interactions between charged grains or with the solar wind plasma could produce regolith motion. However, a validated, predictive model of triboelectric charging between dielectric grains has not yet been developed. A model for such size-dependent charge separation will be presented, demonstrating how random collisions between initially electrically neutral grains lead to net migration of electrons toward the smaller grains. The model is applicable to a wide range of single-material granular mixtures, including those with unusual or wildly varying size distributions, and suggests a possible mechanism for the reversal of the usual size-dependent charge polarity described above. This is a significant improvement over existing charge exchange models, which are restricted to two discrete grains sizes and provide severely limited estimates for charge magnitude. We will also

  3. Analytical results for a three-phase traffic model.

    PubMed

    Huang, Ding-wei

    2003-10-01

    We study analytically a cellular automaton model, which is able to present three different traffic phases on a homogeneous highway. The characteristics displayed in the fundamental diagram can be well discerned by analyzing the evolution of density configurations. Analytical expressions for the traffic flow and shock speed are obtained. The synchronized flow in the intermediate-density region is the result of aggressive driving scheme and determined mainly by the stochastic noise.

  4. Frustration in an exactly solvable mixed-spin Ising model with bilinear and three-site four-spin interactions on a decorated square lattice

    NASA Astrophysics Data System (ADS)

    Jaščur, M.; Štubňa, V.; Szałowski, K.; Balcerzak, T.

    2016-11-01

    Competitive effects of so-called three-site four-spin interactions, single ion anisotropy and bilinear interactions is studied in the mixed spin-1/2 and spin-1 Ising model on a decorated square lattice. Exploring the decoration-iteration transformation, we have obtained exact closed-form expressions for the partition function and other thermodynamic quantities of the model. From these relations, we have numerically determined ground-state and finite-temperature phase diagrams of the system. We have also investigated temperature variations of the correlation functions, internal energy, entropy, specific heat and Helmholtz free energy of the system. From the physical point of view, the most interesting result represents our observation of a partially ordered ferromagnetic or phase in the system with zero bilinear interactions. It is remarkable, that due to strong frustrations disordered spins survive in the system even at zero temperature, so that the ground state of the system becomes macroscopically degenerate with non-zero entropy. Introduction of arbitrarily small bilinear interaction completely removes degeneracy and the entropy always goes to zero at the ground state.

  5. Analytical and numerical modeling for flexible pipes

    NASA Astrophysics Data System (ADS)

    Wang, Wei; Chen, Geng

    2011-12-01

    The unbonded flexible pipe of eight layers, in which all the layers except the carcass layer are assumed to have isotropic properties, has been analyzed. Specifically, the carcass layer shows the orthotropic characteristics. The effective elastic moduli of the carcass layer have been developed in terms of the influence of deformation to stiffness. With consideration of the effective elastic moduli, the structure can be properly analyzed. Also the relative movements of tendons and relative displacements of wires in helical armour layer have been investigated. A three-dimensional nonlinear finite element model has been presented to predict the response of flexible pipes under axial force and torque. Further, the friction and contact of interlayer have been considered. Comparison between the finite element model and experimental results obtained in literature has been given and discussed, which might provide practical and technical support for the application of unbonded flexible pipes.

  6. Analytical model for screening potential CO2 repositories

    USGS Publications Warehouse

    Okwen, R.T.; Stewart, M.T.; Cunningham, J.A.

    2011-01-01

    Assessing potential repositories for geologic sequestration of carbon dioxide using numerical models can be complicated, costly, and time-consuming, especially when faced with the challenge of selecting a repository from a multitude of potential repositories. This paper presents a set of simple analytical equations (model), based on the work of previous researchers, that could be used to evaluate the suitability of candidate repositories for subsurface sequestration of carbon dioxide. We considered the injection of carbon dioxide at a constant rate into a confined saline aquifer via a fully perforated vertical injection well. The validity of the analytical model was assessed via comparison with the TOUGH2 numerical model. The metrics used in comparing the two models include (1) spatial variations in formation pressure and (2) vertically integrated brine saturation profile. The analytical model and TOUGH2 show excellent agreement in their results when similar input conditions and assumptions are applied in both. The analytical model neglects capillary pressure and the pressure dependence of fluid properties. However, simulations in TOUGH2 indicate that little error is introduced by these simplifications. Sensitivity studies indicate that the agreement between the analytical model and TOUGH2 depends strongly on (1) the residual brine saturation, (2) the difference in density between carbon dioxide and resident brine (buoyancy), and (3) the relationship between relative permeability and brine saturation. The results achieved suggest that the analytical model is valid when the relationship between relative permeability and brine saturation is linear or quasi-linear and when the irreducible saturation of brine is zero or very small. ?? 2011 Springer Science+Business Media B.V.

  7. A Simple Analytic ICP Model and Comparison to Experiment

    NASA Astrophysics Data System (ADS)

    Juliano, Daniel R.; Hayden, Douglas B.; Ruzic, David N.

    1996-10-01

    An analytic model is developed for a cylindrically symmetric inductively coupled plasma system in order to find the electron temperature and density distribution. Boltzmann's equation is solved by a computer code using a 2-term spherical harmonic expansion. Analytic results are compared to experimental measurements made with a Langmuir probe. The apparatus is a magnetron system (magnetron system donated by MRC) with an RF coil or other ionization source inserted between the target and substrate. Far from the target, the resulting plasma is dominated by this ionization source, so the plasma at the magnetron target is not accounted for in the analytic model. In the model, electric and magnetic fields from the RF coil are found as a function of position and the power deposition profile is calculated. Insights gained from this model have been used to guide research efforts in ionizing the sputter flux in the magnetron.

  8. Unjamming in models with analytic pairwise potentials

    NASA Astrophysics Data System (ADS)

    Kooij, Stefan; Lerner, Edan

    2017-06-01

    Canonical models for studying the unjamming scenario in systems of soft repulsive particles assume pairwise potentials with a sharp cutoff in the interaction range. The sharp cutoff renders the potential nonanalytic but makes it possible to describe many properties of the solid in terms of the coordination number z , which has an unambiguous definition in these cases. Pairwise potentials without a sharp cutoff in the interaction range have not been studied in this context, but should in fact be considered to understand the relevance of the unjamming phenomenology in systems where such a cutoff is not present. In this work we explore two systems with such interactions: an inverse power law and an exponentially decaying pairwise potential, with the control parameters being the exponent (of the inverse power law) for the former and the number density for the latter. Both systems are shown to exhibit the characteristic features of the unjamming transition, among which are the vanishing of the shear-to-bulk modulus ratio and the emergence of an excess of low-frequency vibrational modes. We establish a relation between the pressure-to-bulk modulus ratio and the distance to unjamming in each of our model systems. This allows us to predict the dependence of other key observables on the distance to unjamming. Our results provide the means for a quantitative estimation of the proximity of generic glass-forming models to the unjamming transition in the absence of a clear-cut definition of the coordination number and highlight the general irrelevance of nonaffine contributions to the bulk modulus.

  9. Exactly solvable Hermite, Laguerre, and Jacobi type quantum parametric oscillators

    NASA Astrophysics Data System (ADS)

    A. Büyükaşık, Şirin; ćayiç, Zehra

    2016-12-01

    We introduce exactly solvable quantum parametric oscillators, which are generalizations of the quantum problems related with the classical orthogonal polynomials of Hermite, Laguerre, and Jacobi type, introduced in the work of Büyükaşık et al. [J. Math. Phys. 50, 072102 (2009)]. Quantization of these models with specific damping, frequency, and external forces is obtained using the Wei-Norman Lie algebraic approach. This determines the evolution operator exactly in terms of two linearly independent homogeneous solutions and a particular solution of the corresponding classical equation of motion. Then, time-evolution of wave functions and coherent states are found explicitly. Probability densities, expectation values, and uncertainty relations are evaluated and their properties are investigated under the influence of the external terms.

  10. Analytical Models for Parallel Processing Systems

    DTIC Science & Technology

    1986-05-01

    v12 s 12, and A u2 2 z r2 v1 2 s22 Then using the MVA algorithm for mixed QNs [REI 801, we have, - Qi(N) - sil[l+ L11 (N-1l)/(l-ul2 ) .. 021IN) 0 s2111...Sasolution [CHA77]. The QN can then be analyzed by the fast and simple Mean Value Analysis ( MVA ) algorithm of Reiser and Lavenberg [REI8]. However, an...extended MVA algorithm developed by Bard [BAR791. At the higher level of the hierarchy, the behaviour or structure of jobs is modeled by means of a

  11. Maximum Likelihood Estimation in Meta-Analytic Structural Equation Modeling

    ERIC Educational Resources Information Center

    Oort, Frans J.; Jak, Suzanne

    2016-01-01

    Meta-analytic structural equation modeling (MASEM) involves fitting models to a common population correlation matrix that is estimated on the basis of correlation coefficients that are reported by a number of independent studies. MASEM typically consist of two stages. The method that has been found to perform best in terms of statistical…

  12. A physically based analytical spatial air temperature and humidity model

    Treesearch

    Yang Yang; Theodore A. Endreny; David J. Nowak

    2013-01-01

    Spatial variation of urban surface air temperature and humidity influences human thermal comfort, the settling rate of atmospheric pollutants, and plant physiology and growth. Given the lack of observations, we developed a Physically based Analytical Spatial Air Temperature and Humidity (PASATH) model. The PASATH model calculates spatial solar radiation and heat...

  13. Maximum Likelihood Estimation in Meta-Analytic Structural Equation Modeling

    ERIC Educational Resources Information Center

    Oort, Frans J.; Jak, Suzanne

    2016-01-01

    Meta-analytic structural equation modeling (MASEM) involves fitting models to a common population correlation matrix that is estimated on the basis of correlation coefficients that are reported by a number of independent studies. MASEM typically consist of two stages. The method that has been found to perform best in terms of statistical…

  14. An Analytic Model of Dusty, Stratified, Spherical H II Regions

    NASA Astrophysics Data System (ADS)

    Rodríguez-Ramírez, J. C.; Raga, A. C.; Lora, V.; Cantó, J.

    2016-12-01

    We study analytically the effect of radiation pressure (associated with photoionization processes and with dust absorption) on spherical, hydrostatic H ii regions. We consider two basic equations, one for the hydrostatic balance between the radiation-pressure components and the gas pressure, and another for the balance among the recombination rate, the dust absorption, and the ionizing photon rate. Based on appropriate mathematical approximations, we find a simple analytic solution for the density stratification of the nebula, which is defined by specifying the radius of the external boundary, the cross section of dust absorption, and the luminosity of the central star. We compare the analytic solution with numerical integrations of the model equations of Draine, and find a wide range of the physical parameters for which the analytic solution is accurate.

  15. Tests characterizing bioprocessor hardware for analytical modeling

    NASA Technical Reports Server (NTRS)

    Gustavino, S.; Mccormack, A.

    1992-01-01

    The tests outlined in this paper were used to characterize the hardware components of the Salad Machine, a small NASA-developed bioprocessor. The data from these tests are presented, and the methods by which this data can be integrated into system mathematical models are briefly discussed. The subsystems and physical processes discussed include the lighting system, the air loop (condensing heat exchanger and the blower), heat transfer to the surroundings, and leakage. Through this effort it was learned that in the development of a test protocol, care should be taken to order the tests such that environmental parameters, particularly humidity, require as few large adjustments as possible. Sensor calibration and installation take a substantial amount of time, which should be built into the test schedule. Two properties were particularly hard to quantify: the air flow rate and the energy from the lighting system entering into the growth volume. Flow rate can be measured using the appropriate device for the system configuration and airflow. Lighting system radiation level was measured using three methods. The results of these methods varied substantially, putting off conclusive quantification of this value.

  16. Tests characterizing bioprocessor hardware for analytical modeling

    NASA Technical Reports Server (NTRS)

    Gustavino, S.; Mccormack, A.

    1992-01-01

    The tests outlined in this paper were used to characterize the hardware components of the Salad Machine, a small NASA-developed bioprocessor. The data from these tests are presented, and the methods by which this data can be integrated into system mathematical models are briefly discussed. The subsystems and physical processes discussed include the lighting system, the air loop (condensing heat exchanger and the blower), heat transfer to the surroundings, and leakage. Through this effort it was learned that in the development of a test protocol, care should be taken to order the tests such that environmental parameters, particularly humidity, require as few large adjustments as possible. Sensor calibration and installation take a substantial amount of time, which should be built into the test schedule. Two properties were particularly hard to quantify: the air flow rate and the energy from the lighting system entering into the growth volume. Flow rate can be measured using the appropriate device for the system configuration and airflow. Lighting system radiation level was measured using three methods. The results of these methods varied substantially, putting off conclusive quantification of this value.

  17. Combined experimental/analytical modeling of shell/payload structures

    SciTech Connect

    Martinez, D.R.; Miller, A.K.; Carne, T.G.

    1985-12-01

    This study evaluates the accuracy of computed modal frequencies obtained from a combined experimental/analytical model of a shell/payload structure. A component mode synthesis technique was used which incorporated free modes and residual effects. The total structure is physically divided into the two subsystems which are connected through stiff joints. The payload was tested to obtain its free-free modes, while a finite element model of the shell was analyzed to obtain its modal description. Both the translational and rotational components of the experimental mode shapes at the payload interface were used in the coupling. Sensitivity studies were also performed to determine the effect of neglecting the residual terms of the payload. Results from a previous study of a combined experimental/analytical model for a beam structure are also given. The beam structure was used to examine the basic procedures and difficulties in experimentally measuring, and analytically accounting for the rotational and residual quantities.

  18. A non-grey analytical model for irradiated atmospheres. II. Analytical vs. numerical solutions

    NASA Astrophysics Data System (ADS)

    Parmentier, Vivien; Guillot, Tristan; Fortney, Jonathan J.; Marley, Mark S.

    2015-02-01

    Context. The recent discovery and characterization of the diversity of the atmospheres of exoplanets and brown dwarfs calls for the development of fast and accurate analytical models. Aims: We wish to assess the goodness of the different approximations used to solve the radiative transfer problem in irradiated atmospheres analytically, and we aim to provide a useful tool for a fast computation of analytical temperature profiles that remains correct over a wide range of atmospheric characteristics. Methods: We quantify the accuracy of the analytical solution derived in paper I for an irradiated, non-grey atmosphere by comparing it to a state-of-the-art radiative transfer model. Then, using a grid of numerical models, we calibrate the different coefficients of our analytical model for irradiated solar-composition atmospheres of giant exoplanets and brown dwarfs. Results: We show that the so-called Eddington approximation used to solve the angular dependency of the radiation field leads to relative errors of up to ~5% on the temperature profile. For grey or semi-grey atmospheres (i.e., when the visible and thermal opacities, respectively, can be considered independent of wavelength), we show that the presence of a convective zone has a limited effect on the radiative atmosphere above it and leads to modifications of the radiative temperature profile of approximately ~2%. However, for realistic non-grey planetary atmospheres, the presence of a convective zone that extends to optical depths smaller than unity can lead to changes in the radiative temperature profile on the order of 20% or more. When the convective zone is located at deeper levels (such as for strongly irradiated hot Jupiters), its effect on the radiative atmosphere is again on the same order (~2%) as in the semi-grey case. We show that the temperature inversion induced by a strong absorber in the optical, such as TiO or VO is mainly due to non-grey thermal effects reducing the ability of the upper

  19. An analytical model of the HINT performance metric

    SciTech Connect

    Snell, Q.O.; Gustafson, J.L.

    1996-10-01

    The HINT benchmark was developed to provide a broad-spectrum metric for computers and to measure performance over the full range of memory sizes and time scales. We have extended our understanding of why HINT performance curves look the way they do and can now predict the curves using an analytical model based on simple hardware specifications as input parameters. Conversely, by fitting the experimental curves with the analytical model, hardware specifications such as memory performance can be inferred to provide insight into the nature of a given computer system.

  20. Analytic model to predict the strength of tendon repairs.

    PubMed

    Lotz, J C; Hariharan, J S; Diao, E

    1998-07-01

    We developed an analytic model to predict suture load-sharing immediately after flexor tendon repair in the hand. Tendon repair was mathematically modeled as two nonlinear springs in parallel, representing separate core and peripheral sutures that were in series with a third nonlinear spring representing the tendon. To serve as a basis for, and validation of, our analytic model, fresh human flexor digitorum profundus tendons were harvested and mechanically tested either intact or after surgical repair in a variety of ways: core suture alone, superficial peripheral suture alone, deep peripheral suture alone, core suture plus superficial peripheral suture, and core suture plus deep peripheral suture. The stiffness and strength of the composite repairs predicted with use of the analytic model were comparable with those determined experimentally. Furthermore, the model predicted inequities in suture load-sharing, with 64% of the applied load carried by the peripheral suture when it was placed superficially, as compared with 77% when the peripheral suture was placed deep. Our results demonstrate a disparity in load-sharing within composite suture systems, the rectification of which may lead to significant improvement in the repair strength. To this end, we expect that our analytic model will serve as a basis for the design of more efficient, and consequently stronger, suture techniques.

  1. An exactly solvable model of polymerization

    NASA Astrophysics Data System (ADS)

    Lushnikov, A. A.

    2017-08-01

    This paper considers the evolution of a polydisperse polymerizing system comprising g1,g2 … - mers carrying ϕ1,ϕ2 … functional groups reacting with one another and binding the g-mers together. In addition, the g-mers are assumed to be added at random by one at a time with a known rate depending on their mass g and functionality ϕ . Assuming that the rate of binding of two g-mers is proportional to the product of the numbers of nonreacted functional groups the kinetic equation for the distribution of clusters (g-mers) over their mass and functionalities is formulated and then solved by applying the generating function method. In contrast to existing approaches this kinetic equation operates with the efficiencies proportional to the product of the numbers of active functional groups in the clusters rather than to the product of their masses. The evolution process is shown to reveal a phase transition: the emergence of a giant linked cluster (the gel) whose mass is comparable to the total mass of the whole polymerizing system. The time dependence of the moments of the distribution of linked components over their masses and functionalities is investigated. The polymerization process terminates by forming a residual spectrum of sol particles in addition to the gel.

  2. Helicopter derivative identification from analytic models and flight test data

    NASA Technical Reports Server (NTRS)

    Molusis, J. H.; Briczinski, S.

    1974-01-01

    Recent results of stability derivative identification from helicopter analytic models and flight test data are presented. Six and nine degree-of-freedom (DOF) linear models are identified from an analytic nonlinear helicopter simulation using a least square technique. The identified models are compared with the convectional partial differentiation method for obtaining derivatives to form the basis for interpretation of derivatives identified from flight data. Six degree-of-freedom models are identified from CH-53A and CH-54B flight data, using an extended Kalman filter modified to process several maneuvers simultaneously. The a priori derivative estimate is obtained by optimal filtering of the data and then using a least square method. The results demonstrate that a six DOF identified model is sufficient to determine the low frequency modes of motion, but a nine DOF rotor/body model is necessary for proper representation of short-term response.

  3. Analytic models of the chemical evolution of galaxies

    NASA Astrophysics Data System (ADS)

    Clayton, Donald D.

    1986-10-01

    Techniques are described for constructing analytic models of the chemical evolution of galaxies subject to infall of metal-poor material onto a maturing disk. A class of linear models is discussed which takes the star-formation rate within a defined region to be proportional to the mass of interstellar gas within that region, and the instantaneous recycling approximation is adopted. The solutions are obtained by approximately matching the infall rate to parametrized familiies of functions for which the equations are exactly soluble. The masses, the primary and secondary metallicities, and the gas concentrations of radioactive chronometers can all then be analytically expressed. Surveys of galactic abundances in location and in time can be compared to the parameter spaces of the analytic representations.

  4. Analytic models of the chemical evolution of galaxies

    NASA Technical Reports Server (NTRS)

    Clayton, Donald D.

    1986-01-01

    Techniques are described for constructing analytic models of the chemical evolution of galaxies subject to infall of metal-poor material onto a maturing disk. A class of linear models is discussed which takes the star-formation rate within a defined region to be proportional to the mass of interstellar gas within that region, and the instantaneous recycling approximation is adopted. The solutions are obtained by approximately matching the infall rate to parametrized familiies of functions for which the equations are exactly soluble. The masses, the primary and secondary metallicities, and the gas concentrations of radioactive chronometers can all then be analytically expressed. Surveys of galactic abundances in location and in time can be compared to the parameter spaces of the analytic representations.

  5. Approximate Solvability of Forward-Backward Stochastic Differential Equations

    SciTech Connect

    Ma, J. Yong, J.

    2002-07-01

    The solvability of forward-backward stochastic differential equations (FBSDEs for short) has been studied extensively in recent years. To guarantee the existence and uniqueness of adapted solutions, many different conditions, some quite restrictive, have been imposed. In this paper we propose a new notion: the approximate solvability of FBSDEs, based on the method of optimal control introduced in our primary work [15]. The approximate solvability of a class of FBSDEs is shown under mild conditions; and a general scheme for constructing approximate adapted solutions is proposed.

  6. Elliptic-cylindrical analytical flux-rope model for ICMEs

    NASA Astrophysics Data System (ADS)

    Nieves-Chinchilla, T.; Linton, M.; Hidalgo, M. A. U.; Vourlidas, A.

    2016-12-01

    We present an analytical flux-rope model for realistic magnetic structures embedded in Interplanetary Coronal Mass Ejections. The framework of this model was established by Nieves-Chinchilla et al. (2016) with the circular-cylindrical analytical flux rope model and under the concept developed by Hidalgo et al. (2002). Elliptic-cylindrical geometry establishes the first-grade of complexity of a series of models. The model attempts to describe the magnetic flux rope topology with distorted cross-section as a possible consequence of the interaction with the solar wind. In this model, the flux rope is completely described in the non-euclidean geometry. The Maxwell equations are solved using tensor calculus consistently with the geometry chosen, invariance along the axial component, and with the only assumption of no radial current density. The model is generalized in terms of the radial dependence of the poloidal current density component and axial current density component. The misalignment between current density and magnetic field is studied in detail for the individual cases of different pairs of indexes for the axial and poloidal current density components. This theoretical analysis provides a map of the force distribution inside of the flux-rope. The reconstruction technique has been adapted to the model and compared with in situ ICME set of events with different in situ signatures. The successful result is limited to some cases with clear in-situ signatures of distortion. However, the model adds a piece in the puzzle of the physical-analytical representation of these magnetic structures. Other effects such as axial curvature, expansion and/or interaction could be incorporated in the future to fully understand the magnetic structure. Finally, the mathematical formulation of this model opens the door to the next model: toroidal flux rope analytical model.

  7. A non linear analytical model of switched reluctance machines

    NASA Astrophysics Data System (ADS)

    Sofiane, Y.; Tounzi, A.; Piriou, F.

    2002-06-01

    Nowadays, the switched reluctance machine are widely used. To determine their performances and to elaborate control strategy, we generally use the linear analytical model. Unhappily, this last is not very accurate. To yield accurate modelling results, we use then numerical models based on either 2D or 3D Finite Element Method. However, this approach is very expensive in terms of computation time and remains suitable to study the behaviour of eventually a whole device. However, it is not, a priori, adapted to elaborate control strategy for electrical machines. This paper deals with a non linear analytical model in terms of variable inductances. The theoretical development of the proposed model is introduced. Then, the model is applied to study the behaviour of a whole controlled switched reluctance machine. The parameters of the structure are identified from a 2D numerical model. They can also be determined from an experimental bench. Then, the results given by the proposed model are compared to those issue from the 2D-FEM approach and from the classical linear analytical model.

  8. Modeling Analyte Transport and Capture in Porous Bead Sensors

    PubMed Central

    Chou, Jie; Lennart, Alexis; Wong, Jorge; Ali, Mehnaaz F.; Floriano, Pierre N.; Christodoulides, Nicolaos; Camp, James; McDevitt, John T.

    2013-01-01

    Porous agarose microbeads, with high surface to volume ratios and high binding densities, are attracting attention as highly sensitive, affordable sensor elements for a variety of high performance bioassays. While such polymer microspheres have been extensively studied and reported on previously and are now moving into real-world clinical practice, very little work has been completed to date to model the convection, diffusion, and binding kinetics of soluble reagents captured within such fibrous networks. Here, we report the development of a three-dimensional computational model and provide the initial evidence for its agreement with experimental outcomes derived from the capture and detection of representative protein and genetic biomolecules in 290μm porous beads. We compare this model to antibody-mediated capture of C-reactive protein and bovine serum albumin, along with hybridization of oligonucleotide sequences to DNA probes. These results suggest that due to the porous interior of the agarose bead, internal analyte transport is both diffusion- and convection-based, and regardless of the nature of analyte, the bead interiors reveal an interesting trickle of convection-driven internal flow. Based on this model, the internal to external flow rate ratio is found to be in the range of 1:3100 to 1:170 for beads with agarose concentration ranging from 0.5% to 8% for the sensor ensembles here studied. Further, both model and experimental evidence suggest that binding kinetics strongly affect analyte distribution of captured reagents within the beads. These findings reveal that high association constants create a steep moving boundary in which unbound analytes are held back at the periphery of the bead sensor. Low association constants create a more shallow moving boundary in which unbound analytes diffuse further into the bead before binding. These models agree with experimental evidence and thus serve as a new tool set for the study of bio-agent transport processes

  9. FACTOR ANALYTIC MODELS OF CLUSTERED MULTIVARIATE DATA WITH INFORMATIVE CENSORING

    EPA Science Inventory

    This paper describes a general class of factor analytic models for the analysis of clustered multivariate data in the presence of informative missingness. We assume that there are distinct sets of cluster-level latent variables related to the primary outcomes and to the censorin...

  10. Piezoresistive Cantilever Performance—Part I: Analytical Model for Sensitivity

    PubMed Central

    Park, Sung-Jin; Doll, Joseph C.; Pruitt, Beth L.

    2010-01-01

    An accurate analytical model for the change in resistance of a piezoresistor is necessary for the design of silicon piezoresistive transducers. Ion implantation requires a high-temperature oxidation or annealing process to activate the dopant atoms, and this treatment results in a distorted dopant profile due to diffusion. Existing analytical models do not account for the concentration dependence of piezoresistance and are not accurate for nonuniform dopant profiles. We extend previous analytical work by introducing two nondimensional factors, namely, the efficiency and geometry factors. A practical benefit of this efficiency factor is that it separates the process parameters from the design parameters; thus, designers may address requirements for cantilever geometry and fabrication process independently. To facilitate the design process, we provide a lookup table for the efficiency factor over an extensive range of process conditions. The model was validated by comparing simulation results with the experimentally determined sensitivities of piezoresistive cantilevers. We performed 9200 TSUPREM4 simulations and fabricated 50 devices from six unique process flows; we systematically explored the design space relating process parameters and cantilever sensitivity. Our treatment focuses on piezoresistive cantilevers, but the analytical sensitivity model is extensible to other piezoresistive transducers such as membrane pressure sensors. PMID:20336183

  11. An Evaluation of Cluster Analytic Approaches to Initial Model Specification.

    ERIC Educational Resources Information Center

    Bacon, Donald R.

    2001-01-01

    Evaluated the performance of several alternative cluster analytic approaches to initial model specification using population parameter analyses and a Monte Carlo simulation. Of the six cluster approaches evaluated, the one using the correlations of item correlations as a proximity metric and average linking as a clustering algorithm performed the…

  12. An Analytical Model for Learning: An Applied Approach.

    ERIC Educational Resources Information Center

    Kassebaum, Peter Arthur

    A mediated-learning package, geared toward non-traditional students, was developed for use in the College of Marin's cultural anthropology courses. An analytical model for learning was used in the development of the package, utilizing concepts related to learning objectives, programmed instruction, Gestalt psychology, cognitive psychology, and…

  13. Analytical modeling of printed metasurface cavities for computational imaging

    NASA Astrophysics Data System (ADS)

    F. Imani, Mohammadreza; Sleasman, Timothy; Gollub, Jonah N.; Smith, David R.

    2016-10-01

    We derive simple analytical expressions to model the electromagnetic response of an electrically large printed cavity. The analytical model is then used to develop printed cavities for microwave imaging purposes. The proposed cavity is excited by a cylindrical source and has boundaries formed by subwavelength metallic cylinders (vias) placed at subwavelength distances apart. Given their small size, the electric currents induced on the vias are assumed to have no angular dependence. Applying this approximation simplifies the electromagnetic problem to a matrix equation which can be solved to directly compute the electric current induced on each via. Once the induced currents are known, the electromagnetic field inside the cavity can be computed for every location. We verify the analytical model by comparing its prediction to full-wave simulations. To utilize this cavity in imaging settings, we perforate one side of the printed cavity with radiative slots such that they act as the physical layer of a computational imaging system. An analytical approximation for the slots is also developed, enabling us to obtain estimates of the cavity performance in imaging scenarios. This ability allows us to make informed decisions on the design of the printed metasurface cavity. The utility of the proposed model is further highlighted by demonstrating high-quality experimental imaging; performance metrics, which are consistent between theory and experiment, are also estimated.

  14. Analytical modeling of organic solar cells and photodiodes

    NASA Astrophysics Data System (ADS)

    Altazin, S.; Clerc, R.; Gwoziecki, R.; Pananakakis, G.; Ghibaudo, G.; Serbutoviez, C.

    2011-10-01

    An analytical and physically based expression of organic solar cell I-V characteristic under dark and illuminated conditions has been derived. This model has been found in very good agreement with both experimental data and drift-diffusion numerical simulations accounting for the coupling with Poisson equation and optical propagation.

  15. Fitting Meta-Analytic Structural Equation Models with Complex Datasets

    ERIC Educational Resources Information Center

    Wilson, Sandra Jo; Polanin, Joshua R.; Lipsey, Mark W.

    2016-01-01

    A modification of the first stage of the standard procedure for two-stage meta-analytic structural equation modeling for use with large complex datasets is presented. This modification addresses two common problems that arise in such meta-analyses: (a) primary studies that provide multiple measures of the same construct and (b) the correlation…

  16. FACTOR ANALYTIC MODELS OF CLUSTERED MULTIVARIATE DATA WITH INFORMATIVE CENSORING

    EPA Science Inventory

    This paper describes a general class of factor analytic models for the analysis of clustered multivariate data in the presence of informative missingness. We assume that there are distinct sets of cluster-level latent variables related to the primary outcomes and to the censorin...

  17. Fitting Meta-Analytic Structural Equation Models with Complex Datasets

    ERIC Educational Resources Information Center

    Wilson, Sandra Jo; Polanin, Joshua R.; Lipsey, Mark W.

    2016-01-01

    A modification of the first stage of the standard procedure for two-stage meta-analytic structural equation modeling for use with large complex datasets is presented. This modification addresses two common problems that arise in such meta-analyses: (a) primary studies that provide multiple measures of the same construct and (b) the correlation…

  18. Analytical Models of Legislative Texts for Muslim Scholars

    ERIC Educational Resources Information Center

    Alwan, Ammar Abdullah Naseh; Yusoff, Mohd Yakubzulkifli Bin Mohd; Al-Hami, Mohammad Said M.

    2011-01-01

    The significance of the analytical models in traditional Islamic studies is that they contribute in sharpening the intellectual capacity of the students of Islamic studies. Research literature in Islamic studies has descriptive side predominantly; the information is gathered and compiled and rarely analyzed properly. This weakness is because of…

  19. Analytical approach to quasiperiodic beam Coulomb field modeling

    NASA Astrophysics Data System (ADS)

    Rubtsova, I. D.

    2016-09-01

    The paper is devoted to modeling of space charge field of quasiperiodic axial- symmetric beam. Particle beam is simulated by charged disks. Two analytical Coulomb field expressions are presented, namely, Fourier-Bessel series and trigonometric polynomial. Both expressions permit the integral representation. It provides the possibility of integro-differential beam dynamics description. Consequently, when beam dynamics optimization problem is considered, it is possible to derive the analytical formula for quality functional gradient and to apply directed optimization methods. In addition, the paper presents the method of testing of space charge simulation code.

  20. Palm: Easing the Burden of Analytical Performance Modeling

    SciTech Connect

    Tallent, Nathan R.; Hoisie, Adolfy

    2014-06-01

    Analytical (predictive) application performance models are critical for diagnosing performance-limiting resources, optimizing systems, and designing machines. Creating models, however, is difficult because they must be both accurate and concise. To ease the burden of performance modeling, we developed Palm, a modeling tool that combines top-down (human-provided) semantic insight with bottom-up static and dynamic analysis. To express insight, Palm defines a source code modeling annotation language. By coordinating models and source code, Palm's models are `first-class' and reproducible. Unlike prior work, Palm formally links models, functions, and measurements. As a result, Palm (a) uses functions to either abstract or express complexity (b) generates hierarchical models (representing an application's static and dynamic structure); and (c) automatically incorporates measurements to focus attention, represent constant behavior, and validate models. We discuss generating models for three different applications.

  1. The Analytical Limits of Modeling Short Diffusion Timescales

    NASA Astrophysics Data System (ADS)

    Bradshaw, R. W.; Kent, A. J.

    2016-12-01

    Chemical and isotopic zoning in minerals is widely used to constrain the timescales of magmatic processes such as magma mixing and crystal residence, etc. via diffusion modeling. Forward modeling of diffusion relies on fitting diffusion profiles to measured compositional gradients. However, an individual measurement is essentially an average composition for a segment of the gradient defined by the spatial resolution of the analysis. Thus there is the potential for the analytical spatial resolution to limit the timescales that can be determined for an element of given diffusivity, particularly where the scale of the gradient approaches that of the measurement. Here we use a probabilistic modeling approach to investigate the effect of analytical spatial resolution on estimated timescales from diffusion modeling. Our method investigates how accurately the age of a synthetic diffusion profile can be obtained by modeling an "unknown" profile derived from discrete sampling of the synthetic compositional gradient at a given spatial resolution. We also include the effects of analytical uncertainty and the position of measurements relative to the diffusion gradient. We apply this method to the spatial resolutions of common microanalytical techniques (LA-ICP-MS, SIMS, EMP, NanoSIMS). Our results confirm that for a given diffusivity, higher spatial resolution gives access to shorter timescales, and that each analytical spacing has a minimum timescale, below which it overestimates the timescale. For example, for Ba diffusion in plagioclase at 750 °C timescales are accurate (within 20%) above 10, 100, 2,600, and 71,000 years at 0.3, 1, 5, and 25 mm spatial resolution, respectively. For Sr diffusion in plagioclase at 750 °C, timescales are accurate above 0.02, 0.2, 4, and 120 years at the same spatial resolutions. Our results highlight the importance of selecting appropriate analytical techniques to estimate accurate diffusion-based timescales.

  2. A first order analytical TOD sensor performance model

    NASA Astrophysics Data System (ADS)

    Bijl, Piet; Hogervorst, Maarten A.

    2016-10-01

    In this paper we present a new, analytical TOD model. The model provides an estimate of the TOD curve for an Optical, Electro-Optical or Thermal Infrared imaging system based on a limited number of essential system parameters. This is useful to get a quick Target Acquisition range prediction but also serves as a first order input to an image-based TOD simulation model. The model is based on a human observer performance dataset on TOD test patterns, systematically degraded by simulated sensor effects. The model is validated against a number of historical TOD tests on visual and thermal camera systems and provides excellent performance predictions.

  3. Analytical model for a polymer optical fiber under dynamic bending

    NASA Astrophysics Data System (ADS)

    Leal Junior, Arnaldo G.; Frizera, Anselmo; Pontes, Maria José

    2017-08-01

    Advantages such as sensibility in bending, high fracture toughness, and high sensibility in strain enable the application of polymer optical fibers as sensors for strain, temperature, level, and for angle measurements. In order to enhance the sensor design, this paper presents an analytical model for a side polished polymer optical fiber under dynamic bending. Differently from analytical models that use only the geometrical optics approach with no correction for the stress-optical effects, here the refractive index is corrected at every bending angle to consider the stress-optical effects observed polymer optical fibers. Furthermore, the viscoelastic response of the polymer is also considered. The model is validated in quasi-static and dynamic tests for a polymer optical fiber curvature sensor. Results show good agreement between the model and the experiments.

  4. Ground water modeling applications using the analytic element method.

    PubMed

    Hunt, Randall J

    2006-01-01

    Though powerful and easy to use, applications of the analytic element method are not as widespread as finite-difference or finite-element models due in part to their relative youth. Although reviews that focus primarily on the mathematical development of the method have appeared in the literature, a systematic review of applications of the method is not available. An overview of the general types of applications of analytic elements in ground water modeling is provided in this paper. While not fully encompassing, the applications described here cover areas where the method has been historically applied (regional, two-dimensional steady-state models, analyses of ground water-surface water interaction, quick analyses and screening models, wellhead protection studies) as well as more recent applications (grid sensitivity analyses, estimating effective conductivity and dispersion in highly heterogeneous systems). The review of applications also illustrates areas where more method development is needed (three-dimensional and transient simulations).

  5. Analytical models for electrically thin flat lenses and reflectors.

    PubMed

    Ruphuy, Miguel; Ramahi, Omar M

    2015-04-01

    This work presents analytical models for two-dimensional (2D) and three-dimensional (3D) electrically thin lenses and reflectors. The 2D formulation is based on infinite current line sources, whereas the 3D formulation is based on electrically small dipoles. These models emulate the energy convergence of an electrically thin flat lens and reflector when illuminated by a plane wave with specific polarization. The advantages of these models are twofold: first, prediction of the performance of electrically thin flat lenses and reflectors can be made significantly faster than full-wave simulators, and second, providing insight on the performance of these electrically thin devices. The analytic models were validated by comparison with full-wave simulation for several interesting examples. The validation results show that the focal point of the electrically thin flat lenses and reflectors can be accurately predicted through a design that assumes low coupling between different layers of an inhomogeneous media.

  6. An analytic model for MODFET capacitance-voltage characteristics

    NASA Astrophysics Data System (ADS)

    George, G.; Hauser, John R.

    1990-05-01

    An analytic model for the capacitance-voltage (C-V) characteristics of n-channel modulation doped FETs (MODFETs) is derived. Gauss law is used to relate the net areal gate charge density in an AlGaAs/GaAs MODFET to the electric field intensity at the metal-AlGaAs interface. An analytic expression for the electric field intensity which accounts for the neutralization of donors and the generation of free electrons is derived. The gate capacitance is derived as a closed-form analytic function of the gate voltage. The expression derived is easily computable and affords physical insight. The results, when compared with numerical calculations and experimental data, yield good agreement over a wide range of gate voltages.

  7. Analytical model for nonlinear piezoelectric energy harvesting devices

    NASA Astrophysics Data System (ADS)

    Neiss, S.; Goldschmidtboeing, F.; Kroener, M.; Woias, P.

    2014-10-01

    In this work we propose analytical expressions for the jump-up and jump-down point of a nonlinear piezoelectric energy harvester. In addition, analytical expressions for the maximum power output at optimal resistive load and the 3 dB-bandwidth are derived. So far, only numerical models have been used to describe the physics of a piezoelectric energy harvester. However, this approach is not suitable to quickly evaluate different geometrical designs or piezoelectric materials in the harvester design process. In addition, the analytical expressions could be used to predict the jump-frequencies of a harvester during operation. In combination with a tuning mechanism, this would allow the design of an efficient control algorithm to ensure that the harvester is always working on the oscillator's high energy attractor.

  8. Superintegrability and quasi-exactly solvable eigenvalue problems

    SciTech Connect

    Kalnins, E. G.; Miller, W.; Pogosyan, G. S.

    2008-05-15

    We show the intimate relationship between quasi-exact solvability, as expounded, for example, by A. Ushveridze, and separation of variables as it applies to specific quantum Hamiltonians. This approach is generalized to apply to finite solutions of quantum Hamiltonians.

  9. Analytic model of an IR radiation heat pipe

    NASA Technical Reports Server (NTRS)

    Hoffman, Pamela J.

    1990-01-01

    An IR radiation heat pipe made from multilayer insulation blankets and proposed to be used aboard spacecraft to transfer waste heat was modeled analytically. A circular cross section pipe 9-in. in diameter, 10-ft long, with a specular reflectivity of 0.94 was found to have an efficiency of 58.6 percent. Several key parameters were varied for the circular model to understand their significance. In addition, square and triangular cross section pipes were investigated.

  10. Analytic solution of the Starobinsky model for inflation

    NASA Astrophysics Data System (ADS)

    Paliathanasis, Andronikos

    2017-07-01

    We prove that the field equations of the Starobinsky model for inflation in a Friedmann-Lemaître-Robertson-Walker metric constitute an integrable system. The analytical solution in terms of a Painlevé series for the Starobinsky model is presented for the case of zero and nonzero spatial curvature. In both cases the leading-order term describes the radiation era provided by the corresponding higher-order theory.

  11. Analytic model of an IR radiation heat pipe

    NASA Technical Reports Server (NTRS)

    Hoffman, Pamela J.

    1990-01-01

    An IR radiation heat pipe made from multilayer insulation blankets and proposed to be used aboard spacecraft to transfer waste heat was modeled analytically. A circular cross section pipe 9-in. in diameter, 10-ft long, with a specular reflectivity of 0.94 was found to have an efficiency of 58.6 percent. Several key parameters were varied for the circular model to understand their significance. In addition, square and triangular cross section pipes were investigated.

  12. Solvability of initial boundary value problem for the equations of filtration in poroelastic media

    NASA Astrophysics Data System (ADS)

    Tokareva, M. A.

    2016-06-01

    The study is devoted to the mathematical model of fluid filtration in poroelastic media. The laws of conservation of mass for each phase, Darcy's law for fluid phase, the rheological law and the general equation of conservation of momentum for system describe this process. The local solvability of the problem is proved in this paper for the case in which the density of the mass forces is equal to zero and the fluid is compressible.

  13. Analytical Expressions for the REM Model of Recognition Memory

    PubMed Central

    Montenegro, Maximiliano; Myung, Jay I.; Pitt, Mark A.

    2014-01-01

    An inordinate amount of computation is required to evaluate predictions of simulation-based models. Following Myung et al (2007), we derived an analytic form expression of the REM model of recognition memory using a Fourier transform technique, which greatly reduces the time required to perform model simulations. The accuracy of the derivation is verified by showing a close correspondence between its predictions and those reported in Shiffrin and Steyvers (1997). The derivation also shows that REM’s predictions depend upon the vector length parameter, and that model parameters are not identifiable unless one of the parameters is fixed. PMID:25089060

  14. Roll levelling semi-analytical model for process optimization

    NASA Astrophysics Data System (ADS)

    Silvestre, E.; Garcia, D.; Galdos, L.; Saenz de Argandoña, E.; Mendiguren, J.

    2016-08-01

    Roll levelling is a primary manufacturing process used to remove residual stresses and imperfections of metal strips in order to make them suitable for subsequent forming operations. In the last years the importance of this process has been evidenced with the apparition of Ultra High Strength Steels with strength > 900 MPa. The optimal setting of the machine as well as a robust machine design has become critical for the correct processing of these materials. Finite Element Method (FEM) analysis is the widely used technique for both aspects. However, in this case, the FEM simulation times are above the admissible ones in both machine development and process optimization. In the present work, a semi-analytical model based on a discrete bending theory is presented. This model is able to calculate the critical levelling parameters i.e. force, plastification rate, residual stresses in a few seconds. First the semi-analytical model is presented. Next, some experimental industrial cases are analyzed by both the semi-analytical model and the conventional FEM model. Finally, results and computation times of both methods are compared.

  15. Physics-based analytical model for ferromagnetic single electron transistor

    NASA Astrophysics Data System (ADS)

    Jamshidnezhad, K.; Sharifi, M. J.

    2017-03-01

    A physically based compact analytical model is proposed for a ferromagnetic single electron transistor (FSET). This model is based on the orthodox theory and solves the master equation, spin conservation equation, and charge neutrality equation simultaneously. The model can be applied to both symmetric and asymmetric devices and does not introduce any limitation on the applied bias voltages. This feature makes the model suitable for both analog and digital applications. To verify the accuracy of the model, its results regarding a typical FSET in both low and high voltage regimes are compared with the existing numerical results. Moreover, the model's results of a parallel configuration FSET, where no spin accumulation exists in the island, are compared with the results obtained from a Monte Carlo simulation using SIMON. These two comparisons show that our model is valid and accurate. As another comparison, the model is compared analytically with an existing model for a double barrier ferromagnetic junction (having no gate). This also verifies the accuracy of the model.

  16. An Analytic Function of Lunar Surface Temperature for Exospheric Modeling

    NASA Technical Reports Server (NTRS)

    Hurley, Dana M.; Sarantos, Menelaos; Grava, Cesare; Williams, Jean-Pierre; Retherford, Kurt D.; Siegler, Matthew; Greenhagen, Benjamin; Paige, David

    2014-01-01

    We present an analytic expression to represent the lunar surface temperature as a function of Sun-state latitude and local time. The approximation represents neither topographical features nor compositional effects and therefore does not change as a function of selenographic latitude and longitude. The function reproduces the surface temperature measured by Diviner to within +/-10 K at 72% of grid points for dayside solar zenith angles of less than 80, and at 98% of grid points for nightside solar zenith angles greater than 100. The analytic function is least accurate at the terminator, where there is a strong gradient in the temperature, and the polar regions. Topographic features have a larger effect on the actual temperature near the terminator than at other solar zenith angles. For exospheric modeling the effects of topography on the thermal model can be approximated by using an effective longitude for determining the temperature. This effective longitude is randomly redistributed with 1 sigma of 4.5deg. The resulting ''roughened'' analytical model well represents the statistical dispersion in the Diviner data and is expected to be generally useful for future models of lunar surface temperature, especially those implemented within exospheric simulations that address questions of volatile transport.

  17. Secondary metallicity in analytic models of chemical evolution of galaxies

    NASA Technical Reports Server (NTRS)

    Clayton, D. D.; Pantelaki, I.

    1986-01-01

    Analytic models of the chemical evolution of galactic regions that grow in mass owing to the continuous infall of matter are characterized, emphasizing the solutions for secondary nuclei (defined as those nuclei whose stellar yields are proportional to the abundance of a primary seed nucleus) in the families of models described by Clayton (1984 and 1985). Wide variations in time dependence of both primary and secondary nuclei as well as in the ratio of secondary to primary are displayed by these model families, confirming again the usefulness of these families as interpretive guides if galaxies do in fact evolve with substantial infall. Additionally, analytic solutions are presented for two other possible interesting systems: the evolution of abundances if the primary metallicity in the infall is increasing in time, and the evolution of abundances if the primary yield changes linearly with time owing to continuous changes in the stellar mass function, the opacity, or other astrophysical agents. Finally, test evaluations of the instantaneous recycling approximation on which these analytic models rely are presented.

  18. Secondary metallicity in analytic models of chemical evolution of galaxies

    NASA Astrophysics Data System (ADS)

    Clayton, D. D.; Pantelaki, I.

    1986-08-01

    Analytic models of the chemical evolution of galactic regions that grow in mass owing to the continuous infall of matter are characterized, emphasizing the solutions for secondary nuclei (defined as those nuclei whose stellar yields are proportional to the abundance of a primary seed nucleus) in the families of models described by Clayton (1984 and 1985). Wide variations in time dependence of both primary and secondary nuclei as well as in the ratio of secondary to primary are displayed by these model families, confirming again the usefulness of these families as interpretive guides if galaxies do in fact evolve with substantial infall. Additionally, analytic solutions are presented for two other possible interesting systems: the evolution of abundances if the primary metallicity in the infall is increasing in time, and the evolution of abundances if the primary yield changes linearly with time owing to continuous changes in the stellar mass function, the opacity, or other astrophysical agents. Finally, test evaluations of the instantaneous recycling approximation on which these analytic models rely are presented.

  19. SINGLE PHASE ANALYTICAL MODELS FOR TERRY TURBINE NOZZLE

    SciTech Connect

    Zhao, Haihua; Zhang, Hongbin; Zou, Ling; O'Brien, James

    2016-11-01

    All BWR RCIC (Reactor Core Isolation Cooling) systems and PWR AFW (Auxiliary Feed Water) systems use Terry turbine, which is composed of the wheel with turbine buckets and several groups of fixed nozzles and reversing chambers inside the turbine casing. The inlet steam is accelerated through the turbine nozzle and impacts on the wheel buckets, generating work to drive the RCIC pump. As part of the efforts to understand the unexpected “self-regulating” mode of the RCIC systems in Fukushima accidents and extend BWR RCIC and PWR AFW operational range and flexibility, mechanistic models for the Terry turbine, based on Sandia National Laboratories’ original work, has been developed and implemented in the RELAP-7 code to simulate the RCIC system. RELAP-7 is a new reactor system code currently under development with the funding support from U.S. Department of Energy. The RELAP-7 code is a fully implicit code and the preconditioned Jacobian-free Newton-Krylov (JFNK) method is used to solve the discretized nonlinear system. This paper presents a set of analytical models for simulating the flow through the Terry turbine nozzles when inlet fluid is pure steam. The implementation of the models into RELAP-7 will be briefly discussed. In the Sandia model, the turbine bucket inlet velocity is provided according to a reduced-order model, which was obtained from a large number of CFD simulations. In this work, we propose an alternative method, using an under-expanded jet model to obtain the velocity and thermodynamic conditions for the turbine bucket inlet. The models include both adiabatic expansion process inside the nozzle and free expansion process out of the nozzle to reach the ambient pressure. The combined models are able to predict the steam mass flow rate and supersonic velocity to the Terry turbine bucket entrance, which are the necessary input conditions for the Terry Turbine rotor model. The nozzle analytical models were validated with experimental data and

  20. Applying generalized Padé approximants in analytic QCD models

    NASA Astrophysics Data System (ADS)

    Cvetič, Gorazd; Kögerler, Reinhart

    2011-09-01

    A method of resummation of truncated perturbation series, related to diagonal Padé approximants but giving results independent of the renormalization scale, was developed more than ten years ago by us with a view of applying it in perturbative QCD. We now apply this method in analytic QCD models, i.e., models where the running coupling has no unphysical singularities, and we show that the method has attractive features, such as a rapid convergence. The method can be regarded as a generalization of the scale-setting methods of Stevenson, Grunberg, and Brodsky-Lepage-Mackenzie. The method involves the fixing of various scales and weight coefficients via an auxiliary construction of diagonal Padé approximant. In low-energy QCD observables, some of these scales become sometimes low at high order, which prevents the method from being effective in perturbative QCD, where the coupling has unphysical singularities at low spacelike momenta. There are no such problems in analytic QCD.

  1. Wake redirection: comparison of analytical, numerical and experimental models

    NASA Astrophysics Data System (ADS)

    Wang, Jiangang; Bottasso, Carlo L.; Campagnolo, Filippo

    2016-09-01

    This paper focuses on wake redirection techniques for wind farm control. Two control strategies are investigated: yaw misalignment and cyclic pitch control. First, analytical formulas are derived for both techniques, with the goal of providing a simple physical interpretation of the behavior of the two methods. Next, more realistic results are obtained by numerical simulations performed with CFD and by experiments conducted with scaled wind turbine models operating in a boundary layer wind tunnel. Comparing the analytical, numerical and experimental models allows for a cross-validation of the results and a better understanding of the two wake redirection techniques. Results indicate that yaw misalignment is more effective than cyclic pitch control in displacing the wake laterally, although the latter may have positive effects on wake recovery.

  2. Pitfalls in TDM of antibiotic drugs: analytical and modelling issues.

    PubMed

    Neef, C; Touw, D J; Harteveld, A R; Eerland, J J; Uges, D R A

    2006-10-01

    The quality assurance program of the Dutch KKGT [Association for Quality Assessment in therapeutic drug monitoring (TDM) and Clinical Toxicology] has been running for more than 25 years. One of these programs concerns TDM of the antibiotic drugs gentamicin, tobramycin, amikacin, and vancomycin. We present two issues encountered in a recent survey. In a case of gentamicin monitoring and dose-adjustment, a systematic analytical error in some centers led to a dosing recommendation that differed from that of the organizers. Correction of the analytical results on the basis of a standard control sample resulted in concentration differences of more than 20% and different dosing recommendations in these centers. In a case of vancomycin TDM, the choice of the population model proved to be critical for dose adjustment. We illustrate this example by presenting the plasma profiles derived from the different population models used by the participants.

  3. Human performance modeling for system of systems analytics.

    SciTech Connect

    Dixon, Kevin R.; Lawton, Craig R.; Basilico, Justin Derrick; Longsine, Dennis E.; Forsythe, James Chris; Gauthier, John Henry; Le, Hai D.

    2008-10-01

    A Laboratory-Directed Research and Development project was initiated in 2005 to investigate Human Performance Modeling in a System of Systems analytic environment. SAND2006-6569 and SAND2006-7911 document interim results from this effort; this report documents the final results. The problem is difficult because of the number of humans involved in a System of Systems environment and the generally poorly defined nature of the tasks that each human must perform. A two-pronged strategy was followed: one prong was to develop human models using a probability-based method similar to that first developed for relatively well-understood probability based performance modeling; another prong was to investigate more state-of-art human cognition models. The probability-based modeling resulted in a comprehensive addition of human-modeling capability to the existing SoSAT computer program. The cognitive modeling resulted in an increased understanding of what is necessary to incorporate cognition-based models to a System of Systems analytic environment.

  4. An analytical model for microsegregation in open and expanding domains

    SciTech Connect

    Nastac, L.; Stefanescu, D.M.; Chuzhoy, L.

    1995-12-31

    A review of existing models for microsegregation shows that there are no analytical models that consider limited diffusion in both liquid and solid phases for an expanding domain (system). Earlier, an analytical mathematical model for microsegregation was introduced for the closed system case. Mass transport by diffusion only was considered, but diffusion in both liquid and solid was assumed. The model proposed in this paper relaxes the assumptions of a closed system. Thus, the contribution of mass transport by fluid flow, and the effects of coarsening and coalescence can be included in microsegregation calculations. The model does not require a prescribed movement of the interface, and therefore, it can be used in microscopic modeling of solidification. The derivation assumed spherical geometry of the domain. Thus, it is possible to calculate microsegregation at the level of equiaxed dendrites. The importance of an open and expanding domain assumptions was studied by comparing results obtained with the present model with calculation based on the closed system assumptions. The microsegregation model was coupled with a macro transport-transformation kinetics code to compare the calculated results with experimental results for spheroidal graphite iron castings.

  5. Dark Sage: Semi-analytic model of galaxy evolution

    NASA Astrophysics Data System (ADS)

    Stevens, Adam R. H.; Croton, Darren J.; Mutch, Simon J.; Sinha, Manodeep

    2017-06-01

    DARK SAGE is a semi-analytic model of galaxy formation that focuses on detailing the structure and evolution of galaxies' discs. The code-base, written in C, is an extension of SAGE (ascl:1601.006) and maintains the modularity of SAGE. DARK SAGE runs on any N-body simulation with trees organized in a supported format and containing a minimum set of basic halo properties.

  6. An analytical thermohydraulic model for discretely fractured geothermal reservoirs

    NASA Astrophysics Data System (ADS)

    Fox, Don B.; Koch, Donald L.; Tester, Jefferson W.

    2016-09-01

    In discretely fractured reservoirs such as those found in Enhanced/Engineered Geothermal Systems (EGS), knowledge of the fracture network is important in understanding the thermal hydraulics, i.e., how the fluid flows and the resulting temporal evolution of the subsurface temperature. The purpose of this study was to develop an analytical model of the fluid flow and heat transport in a discretely fractured network that can be used for a wide range of modeling applications and serve as an alternative analysis tool to more computationally intensive numerical codes. Given the connectivity and structure of a fracture network, the flow in the system was solved using a linear system of algebraic equations for the pressure at the nodes of the network. With the flow determined, the temperature in the fracture was solved by coupling convective heat transport in the fracture with one-dimensional heat conduction perpendicular to the fracture, employing the Green's function derived solution for a single discrete fracture. The predicted temperatures along the fracture surfaces from the analytical solution were compared to numerical simulations using the TOUGH2 reservoir code. Through two case studies, we showed the capabilities of the analytical model and explored the effect of uncertainty in the fracture apertures and network structure on thermal performance. While both sources of uncertainty independently produce large variations in production temperature, uncertainty in the network structure, whenever present, had a predominant influence on thermal performance.

  7. Accuracy of analytic model planning in bimaxillary surgery.

    PubMed

    Park, N; Posnick, J C

    2013-07-01

    The purpose of this study was to assess our method of analytic model planning in achieving a planned maxillary advancement for the correction of a dentofacial deformity. A consecutive series of 20 patients who underwent bimaxillary orthognathic surgery, at a minimum, were included in the study group. For each study subject, consistent analytic model planning with splint fabrication was used to establish the desired horizontal repositioning of the maxilla. Using preoperative and 5-week postoperative lateral cephalometric radiographs, an analysis was designed to assess the difference between the planned and actual advancement of the maxilla. The average difference between the planned and actual 5-week postsurgical advancement of the maxilla was 0.6 mm (range 0.2-1.0, P>0.05). There was a strong correlation between the two data sets (R=0.96). The results of the study indicate that the described method of analytic model planning is reliable (within 1mm) in achieving the planned level of maxillary advancement in bimaxillary orthognathic procedures.

  8. AN ANALYTIC RADIATIVE-CONVECTIVE MODEL FOR PLANETARY ATMOSPHERES

    SciTech Connect

    Robinson, Tyler D.; Catling, David C.

    2012-09-20

    We present an analytic one-dimensional radiative-convective model of the thermal structure of planetary atmospheres. Our model assumes that thermal radiative transfer is gray and can be represented by the two-stream approximation. Model atmospheres are assumed to be in hydrostatic equilibrium, with a power-law scaling between the atmospheric pressure and the gray thermal optical depth. The convective portions of our models are taken to follow adiabats that account for condensation of volatiles through a scaling parameter to the dry adiabat. By combining these assumptions, we produce simple, analytic expressions that allow calculations of the atmospheric-pressure-temperature profile, as well as expressions for the profiles of thermal radiative flux and convective flux. We explore the general behaviors of our model. These investigations encompass (1) worlds where atmospheric attenuation of sunlight is weak, which we show tend to have relatively high radiative-convective boundaries; (2) worlds with some attenuation of sunlight throughout the atmosphere, which we show can produce either shallow or deep radiative-convective boundaries, depending on the strength of sunlight attenuation; and (3) strongly irradiated giant planets (including hot Jupiters), where we explore the conditions under which these worlds acquire detached convective regions in their mid-tropospheres. Finally, we validate our model and demonstrate its utility through comparisons to the average observed thermal structure of Venus, Jupiter, and Titan, and by comparing computed flux profiles to more complex models.

  9. Optimization of Analytical Potentials for Coarse-Grained Biopolymer Models.

    PubMed

    Mereghetti, Paolo; Maccari, Giuseppe; Spampinato, Giulia Lia Beatrice; Tozzini, Valentina

    2016-08-25

    The increasing trend in the recent literature on coarse grained (CG) models testifies their impact in the study of complex systems. However, the CG model landscape is variegated: even considering a given resolution level, the force fields are very heterogeneous and optimized with very different parametrization procedures. Along the road for standardization of CG models for biopolymers, here we describe a strategy to aid building and optimization of statistics based analytical force fields and its implementation in the software package AsParaGS (Assisted Parameterization platform for coarse Grained modelS). Our method is based on the use and optimization of analytical potentials, optimized by targeting internal variables statistical distributions by means of the combination of different algorithms (i.e., relative entropy driven stochastic exploration of the parameter space and iterative Boltzmann inversion). This allows designing a custom model that endows the force field terms with a physically sound meaning. Furthermore, the level of transferability and accuracy can be tuned through the choice of statistical data set composition. The method-illustrated by means of applications to helical polypeptides-also involves the analysis of two and three variable distributions, and allows handling issues related to the FF term correlations. AsParaGS is interfaced with general-purpose molecular dynamics codes and currently implements the "minimalist" subclass of CG models (i.e., one bead per amino acid, Cα based). Extensions to nucleic acids and different levels of coarse graining are in the course.

  10. Comparison of analytical eddy current models using principal components analysis

    NASA Astrophysics Data System (ADS)

    Contant, S.; Luloff, M.; Morelli, J.; Krause, T. W.

    2017-02-01

    Monitoring the gap between the pressure tube (PT) and the calandria tube (CT) in CANDU® fuel channels is essential, as contact between the two tubes can lead to delayed hydride cracking of the pressure tube. Multifrequency transmit-receive eddy current non-destructive evaluation is used to determine this gap, as this method has different depths of penetration and variable sensitivity to noise, unlike single frequency eddy current non-destructive evaluation. An Analytical model based on the Dodd and Deeds solutions, and a second model that accounts for normal and lossy self-inductances, and a non-coaxial pickup coil, are examined for representing the response of an eddy current transmit-receive probe when considering factors that affect the gap response, such as pressure tube wall thickness and pressure tube resistivity. The multifrequency model data was analyzed using principal components analysis (PCA), a statistical method used to reduce the data set into a data set of fewer variables. The results of the PCA of the analytical models were then compared to PCA performed on a previously obtained experimental data set. The models gave similar results under variable PT wall thickness conditions, but the non-coaxial coil model, which accounts for self-inductive losses, performed significantly better than the Dodd and Deeds model under variable resistivity conditions.

  11. Analytical modeling for transient probe response in eddy current testing

    NASA Astrophysics Data System (ADS)

    Desjardins, Daniel

    Analytical models that describe the electromagnetic field interactions arising between field generating and sensing coils in close proximity to conducting structures can be used to enhance analysis and information extracted from signals obtained using electromagnetic non-destructive evaluation technologies. A novel strategy, which enables the derivation of exact solutions describing all electromagnetic interactions arising in inductively coupled circuits due to a voltage excitation, is developed in this work. Differential circuit equations are formulated in terms of an arbitrary voltage excitation and of the magnetic fields arising in inductive systems, using Faraday's law and convolution, and solved using the Fourier transform. The approach is valid for systems containing any number of driving and receiving coils, and include nearby conducting and ferromagnetic structures. In particular, the solutions account for feedback between a ferromagnetic conducting test piece and the driving and sensing coils, providing correct voltage response of the coils. Also arising from the theory are analytical expressions for complex inductances in a circuit, which account for real (inductive) and imaginary (loss) elements associated with conducting and ferromagnetic structures. A novel model-based method for simultaneous characterization of material parameters, which includes magnetic permeability, electrical conductivity, wall thickness and liftoff, is subsequently developed from the forward solutions. Furthermore, arbitrary excitation waveforms, such as a sinusoid or a square wave, for applications in conventional and transient eddy current, respectively, may be considered. Experimental results, obtained for a square wave excitation, are found to be in excellent agreement with the analytical predictions.

  12. An analytic model for buoyancy resonances in protoplanetary disks

    SciTech Connect

    Lubow, Stephen H.; Zhu, Zhaohuan E-mail: zhzhu@astro.princeton.edu

    2014-04-10

    Zhu et al. found in three-dimensional shearing box simulations a new form of planet-disk interaction that they attributed to a vertical buoyancy resonance in the disk. We describe an analytic linear model for this interaction. We adopt a simplified model involving azimuthal forcing that produces the resonance and permits an analytic description of its structure. We derive an analytic expression for the buoyancy torque and show that the vertical torque distribution agrees well with the results of the Athena simulations and a Fourier method for linear numerical calculations carried out with the same forcing. The buoyancy resonance differs from the classic Lindblad and corotation resonances in that the resonance lies along tilted planes. Its width depends on damping effects and is independent of the gas sound speed. The resonance does not excite propagating waves. At a given large azimuthal wavenumber k{sub y} > h {sup –1} (for disk thickness h), the buoyancy resonance exerts a torque over a region that lies radially closer to the corotation radius than the Lindblad resonance. Because the torque is localized to the region of excitation, it is potentially subject to the effects of nonlinear saturation. In addition, the torque can be reduced by the effects of radiative heat transfer between the resonant region and its surroundings. For each azimuthal wavenumber, the resonance establishes a large scale density wave pattern in a plane within the disk.

  13. Analytical dynamics models for space missions around minor bodies

    NASA Astrophysics Data System (ADS)

    Cardoso dos Santos, Josué; dos Santos Carvalho, Jean Paulo; Vilhena de Moraes, Rodolpho; Bertachini de Almeida Prado, Antônio Fernando

    2015-08-01

    In recent years, the dynamics of orbits around minor bodies and icy moons in our solar system has become important in planning future missions that intend to visit dwarf planets, planetary moons, asteroids and comets. Due to their special characteristics, Europa, Ganymede, Callisto, Enceladus, Titan and Triton are among the group of objects with greater potential to receive missions in a near future. In order to provide a semi-analytical theory for tuture space exploration of these celestial bodies, this work aims to present two analytical models to describe and evaluate gravitational disturbances over a spacecrat's orbit around a minor body. A search for these less perturbed orbits is performed. An analytical model for the third-body perturbation is presented and consideres it in an eccentric-inclined orbit. Some harmonic terms due to the non-uniform distribuition of mass are considered according they are available in the literature. The dynamic of these orbits is explored by numerical simulations. The results are in accordance with the requirements for missions present in the literature.

  14. Analytical properties of a three-compartmental dynamical demographic model.

    PubMed

    Postnikov, E B

    2015-07-01

    The three-compartmental demographic model by Korotaeyv-Malkov-Khaltourina, connecting population size, economic surplus, and education level, is considered from the point of view of dynamical systems theory. It is shown that there exist two integrals of motion, which enables the system to be reduced to one nonlinear ordinary differential equation. The study of its structure provides analytical criteria for the dominance ranges of the dynamics of Malthus and Kremer. Additionally, the particular ranges of parameters enable the derived general ordinary differential equations to be reduced to the models of Gompertz and Thoularis-Wallace.

  15. Model and Analytic Processes for Export License Assessments

    SciTech Connect

    Thompson, Sandra E.; Whitney, Paul D.; Weimar, Mark R.; Wood, Thomas W.; Daly, Don S.; Brothers, Alan J.; Sanfilippo, Antonio P.; Cook, Diane; Holder, Larry

    2011-09-29

    This paper represents the Department of Energy Office of Nonproliferation Research and Development (NA-22) Simulations, Algorithms and Modeling (SAM) Program's first effort to identify and frame analytical methods and tools to aid export control professionals in effectively predicting proliferation intent; a complex, multi-step and multi-agency process. The report focuses on analytical modeling methodologies that alone, or combined, may improve the proliferation export control license approval process. It is a follow-up to an earlier paper describing information sources and environments related to international nuclear technology transfer. This report describes the decision criteria used to evaluate modeling techniques and tools to determine which approaches will be investigated during the final 2 years of the project. The report also details the motivation for why new modeling techniques and tools are needed. The analytical modeling methodologies will enable analysts to evaluate the information environment for relevance to detecting proliferation intent, with specific focus on assessing risks associated with transferring dual-use technologies. Dual-use technologies can be used in both weapons and commercial enterprises. A decision-framework was developed to evaluate which of the different analytical modeling methodologies would be most appropriate conditional on the uniqueness of the approach, data availability, laboratory capabilities, relevance to NA-22 and Office of Arms Control and Nonproliferation (NA-24) research needs and the impact if successful. Modeling methodologies were divided into whether they could help micro-level assessments (e.g., help improve individual license assessments) or macro-level assessment. Macro-level assessment focuses on suppliers, technology, consumers, economies, and proliferation context. Macro-level assessment technologies scored higher in the area of uniqueness because less work has been done at the macro level. An approach to

  16. Analytical properties of a three-compartmental dynamical demographic model

    NASA Astrophysics Data System (ADS)

    Postnikov, E. B.

    2015-07-01

    The three-compartmental demographic model by Korotaeyv-Malkov-Khaltourina, connecting population size, economic surplus, and education level, is considered from the point of view of dynamical systems theory. It is shown that there exist two integrals of motion, which enables the system to be reduced to one nonlinear ordinary differential equation. The study of its structure provides analytical criteria for the dominance ranges of the dynamics of Malthus and Kremer. Additionally, the particular ranges of parameters enable the derived general ordinary differential equations to be reduced to the models of Gompertz and Thoularis-Wallace.

  17. Analytical threshold voltage model for strained silicon GAA-TFET

    NASA Astrophysics Data System (ADS)

    Kang, Hai-Yan; Hu, Hui-Yong; Wang, Bin

    2016-11-01

    Tunnel field effect transistors (TFETs) are promising devices for low power applications. An analytical threshold voltage model, based on the channel surface potential and electric field obtained by solving the 2D Poisson’s equation, for strained silicon gate all around TFETs is proposed. The variation of the threshold voltage with device parameters, such as the strain (Ge mole fraction x), gate oxide thickness, gate oxide permittivity, and channel length has also been investigated. The threshold voltage model is extracted using the peak transconductance method and is verified by good agreement with the results obtained from the TCAD simulation. Project supported by the National Natural Science Foundation of China (Grant No. 61474085).

  18. Peat pyrolysis and the analytical semi-empirical model

    SciTech Connect

    Feng, J.; Green, A.E.S.

    2007-07-01

    Pyrolysis of peat could convert this material into useful fuels and valuable hydrocarbons. A study of peat pyrolysis can also serve as a useful bridge between studies of coal pyrolysis and biomass pyrolysis. Using an analytical model of pyrolysis that has previously been applied to biomass and to coal, we present here the results of applications of this model to a representative peat. The analysis suggests means of organizing and processing rate and yield data that should be useful in applications of pyrolysis for the production of fuels and chemicals.

  19. An Analytical Thermal Model for Autonomous Soaring Research

    NASA Technical Reports Server (NTRS)

    Allen, Michael

    2006-01-01

    A viewgraph presentation describing an analytical thermal model used to enable research on autonomous soaring for a small UAV aircraft is given. The topics include: 1) Purpose; 2) Approach; 3) SURFRAD Data; 4) Convective Layer Thickness; 5) Surface Heat Budget; 6) Surface Virtual Potential Temperature Flux; 7) Convective Scaling Velocity; 8) Other Calculations; 9) Yearly trends; 10) Scale Factors; 11) Scale Factor Test Matrix; 12) Statistical Model; 13) Updraft Strength Calculation; 14) Updraft Diameter; 15) Updraft Shape; 16) Smoothed Updraft Shape; 17) Updraft Spacing; 18) Environment Sink; 19) Updraft Lifespan; 20) Autonomous Soaring Research; 21) Planned Flight Test; and 22) Mixing Ratio.

  20. Analytic Element Modeling of Multi-Aquifer Flow

    NASA Astrophysics Data System (ADS)

    Bakker, M.

    2002-05-01

    A new set of analytic elements has been developed for the modeling of steady-state flow in multi-aquifer systems. All analytic elements are exact solutions to the governing system of differential equations. As such, the leakage between aquifers is simulated exactly. Application of the new formulation has the advantage that the model domain is not discretized; all anlaytic elements represent hydrogeologic features in the aquifer system. The new elements may be used to simulate flow in systems with an arbitrary number of aquifers and leaky layers. They may also be applied to approximate three-dimensional flow to partially penetrating features if one is willing to discretize the aquifer vertically. Six multi-aquifer analytic elements have been developed and several more are under development. The following multi-aquifer hydrogeologic features may be modeled at the present time (March, 2002): an ambient flow gradient (uniform flow element); pumping wells, multi-aquifer wells, abandoned multi-aquifer wells, partially penetrating wells (well elements); river or stream segments, arms of radial collector wells (line-sink elements); areal recharge (circular area-sink elements); cylindrical domains with different aquifer and leaky layer properties, cylindrical holes in leaky layers (cylindrical inhomogeneity elements); single aquifers with polygonal domains consisting of multiple aquifers and leaky layers (aquifer-system inhomogeneity elements). Several new analytic elements are in different stages of development; they are intended for the modeling of the following features: impermeable walls, slurry walls (line-doublet elements), elliptical cylinder inclusions with different aquifer and leaky-layer properties (elliptical cylinder inhomogeneity elements), recharge areas bounded by polygons (polygonal area-sink elements). Analytic elements for multi-aquifer flow have been implemented in computational codes written in FORTRAN90 and Python. Practical applications include the

  1. An investigation of helicopter dynamic coupling using an analytical model

    NASA Technical Reports Server (NTRS)

    Keller, Jeffrey D.

    1995-01-01

    Many attempts have been made in recent years to predict the off-axis response of a helicopter to control inputs, and most have had little success. Since physical insight is limited by the complexity of numerical simulation models, this paper examines the off-axis response problem using an analytical model, with the goal of understanding the mechanics of the coupling. A new induced velocity model is extended to include the effects of wake distortion from pitch rate. It is shown that the inclusion of these results in a significant change in the lateral flap response to a steady pitch rate. The proposed inflow model is coupled with the full rotor/body dynamics, and comparisons are made between the model and flight test data for a UH-60 in hover. Results show that inclusion of induced velocity variations due to shaft rate improves correlation in the pitch response to lateral cycle inputs.

  2. Analytical expressions for transition edge sensor excess noise models

    NASA Astrophysics Data System (ADS)

    Brandt, Daniel; Fraser, George W.

    2010-08-01

    Transition edge sensors (TESs) are high-sensitivity thermometers used in cryogenic microcalorimeters which exploit the steep gradient in resistivity with temperature during the superconducting phase transition. Practical TES devices tend to exhibit a white noise of uncertain origin, arising inside the device. We discuss two candidate models for this excess noise, phase slip shot noise (PSSN) and percolation noise. We extend the existing PSSN model to include a magnetic field dependence and derive a basic analytical model for percolation noise. We compare the predicted functional forms of the noise current vs. resistivity curves of both models with experimental data and provide a set of equations for both models to facilitate future experimental efforts to clearly identify the source of excess noise.

  3. Analytical modeling of glucose biosensors based on carbon nanotubes

    PubMed Central

    2014-01-01

    In recent years, carbon nanotubes have received widespread attention as promising carbon-based nanoelectronic devices. Due to their exceptional physical, chemical, and electrical properties, namely a high surface-to-volume ratio, their enhanced electron transfer properties, and their high thermal conductivity, carbon nanotubes can be used effectively as electrochemical sensors. The integration of carbon nanotubes with a functional group provides a good and solid support for the immobilization of enzymes. The determination of glucose levels using biosensors, particularly in the medical diagnostics and food industries, is gaining mass appeal. Glucose biosensors detect the glucose molecule by catalyzing glucose to gluconic acid and hydrogen peroxide in the presence of oxygen. This action provides high accuracy and a quick detection rate. In this paper, a single-wall carbon nanotube field-effect transistor biosensor for glucose detection is analytically modeled. In the proposed model, the glucose concentration is presented as a function of gate voltage. Subsequently, the proposed model is compared with existing experimental data. A good consensus between the model and the experimental data is reported. The simulated data demonstrate that the analytical model can be employed with an electrochemical glucose sensor to predict the behavior of the sensing mechanism in biosensors. PMID:24428818

  4. Analytical model of reactive transport processes with spatially variable coefficients.

    PubMed

    Simpson, Matthew J; Morrow, Liam C

    2015-05-01

    Analytical solutions of partial differential equation (PDE) models describing reactive transport phenomena in saturated porous media are often used as screening tools to provide insight into contaminant fate and transport processes. While many practical modelling scenarios involve spatially variable coefficients, such as spatially variable flow velocity, v(x), or spatially variable decay rate, k(x), most analytical models deal with constant coefficients. Here we present a framework for constructing exact solutions of PDE models of reactive transport. Our approach is relevant for advection-dominant problems, and is based on a regular perturbation technique. We present a description of the solution technique for a range of one-dimensional scenarios involving constant and variable coefficients, and we show that the solutions compare well with numerical approximations. Our general approach applies to a range of initial conditions and various forms of v(x) and k(x). Instead of simply documenting specific solutions for particular cases, we present a symbolic worksheet, as supplementary material, which enables the solution to be evaluated for different choices of the initial condition, v(x) and k(x). We also discuss how the technique generalizes to apply to models of coupled multispecies reactive transport as well as higher dimensional problems.

  5. Analytical Model of Shear of 4-harness Satin Weave Fabrics

    NASA Astrophysics Data System (ADS)

    Liu, Lu; Chen, Julie; Sherwood, James

    2004-06-01

    Trellis shear is the main deformation mode in the thermo-stamping process of woven fabric composites. To model the shear properties of woven fabrics analytically, the equilibrium equation of the unit cell of a 4-harness satin weave glass/polypropylene woven fabric is studied. Frictional resistance moment and lateral compaction resistance moment are then predicted by studying the geometry of the unit cell. Then the model is used to predict the load versus shear angle curves in the picture frame test to reduce or eliminate the test itself. A parametric study is carried out to determine the sensitivity of the friction coefficient. To validate the model, picture-frame experimental results are presented. A very close correlation is observed between the model predictions and the experimental results. Results of plain weave fabrics are included to show the analytical model's ability to predict the effect of weave pattern. Results from an international benchmark testing are also presented to help establish the test standards for experimental characterization of the shear properties of woven fabrics in the thermo-stamping process.

  6. An analytical model of a longitudinal-torsional ultrasonic transducer

    NASA Astrophysics Data System (ADS)

    Al-Budairi, Hassan; Lucas, Margaret

    2012-08-01

    The combination of longitudinal and torsional (LT) vibrations at high frequencies finds many applications such as ultrasonic drilling, ultrasonic welding, and ultrasonic motors. The LT mode can be obtained by modifications to the design of a standard bolted Langevin ultrasonic transducer driven by an axially poled piezoceramic stack, by a technique that degenerates the longitudinal mode to an LT motion by a geometrical alteration of the wave path. The transducer design is developed and optimised through numerical modelling which can represent the geometry and mechanical properties of the transducer and its vibration response to an electrical input applied across the piezoceramic stack. However, although these models can allow accurate descriptions of the mechanical behaviour, they do not generally provide adequate insights into the electrical characteristics of the transducer. In this work, an analytical model is developed to present the LT transducer based on the equivalent circuit method. This model can represent both the mechanical and electrical aspects and is used to extract many of the design parameters, such as resonance and anti-resonance frequencies, the impedance spectra and the coupling coefficient of the transducer. The validity of the analytical model is demonstrated by close agreement with experimental results.

  7. Analytical characterization of a Bruderhedral calibration target model

    NASA Astrophysics Data System (ADS)

    Cremona-Simmons, Peter M.

    1996-06-01

    The Army Research Laboratory (ARL) has constructed a variation of the bruderhedral calibration and radar cross section (RCS) target model and measured its radar characteristics in the field. A computer version of the same model was generated, and later characterized in both elevation and azimuth for validation. Our goal is to develop a millimeter-wave (MMW) signature generation tool for guidance integrated fuzing (GIF) systems and applications. Before realizing this goal, one must develop a test-bed of tools and approaches upon which to build. ARL has identified approaches to developing generic analytical target-signature models based on some existing electromagnetic scattering codes. A high-frequency RCS and signature prediction software model was selected to perform the radar analysis and provide a mechanism, a synthetic aperture radar (SAR) model, for recognizing prominent scatterers off high-fidelity target models. This method will assist us in creating suitable far- to near-field 3-D transitional models at MMW frequencies. Two target model descriptions were used in the signature prediction model: a flat facet format and a curved surface format. This paper introduces these software models, and some optics and SAR considerations relating to the test wavelength and the size of the target. Also, the simulated azimuthal and elevation response patterns, along with some results from the SAR model, are presented.

  8. Dynamic fragmentation of brittle materials: analytical mechanics-based models

    NASA Astrophysics Data System (ADS)

    Drugan, W. J.

    2001-06-01

    Two analytical mechanics-based models of dynamic fragmentation in brittle materials are proposed and solved to predict fragment size and time to fragmentation onset in terms of fundamental material properties and the applied strain rate. Previous widely adopted analytical models of dynamic fragmentation are based on relatively simple energy balance arguments, and assume that the fragmentation event occurs instantaneously. The present models account for the actual time-varying dynamic deformation that occurs prior to fragmentation onset. One of the models treats the fragmenting material as initially flaw-free, and determines the minimum fragment size predicted by a dynamic instability analysis. The second model accounts for initial flaw spacing (which may correlate physically with, for example, grain size), and a dynamic instability analysis is employed to determine which flaws become critical. The fragment size predictions of the present models and two previous energy-based models are found to agree at extremely high strain rates (≈5×10 7/s for dense alumina), but the present, more realistic analysis indicates that the regime of validity of the energy-based models is rather restricted. The predictions of the present models are also shown to agree with those of a recent numerical finite element simulation of dynamic fragmentation which applies to a lower strain rate regime. Comparisons of the two new models show that if a material contains initial flaws whose spacing is smaller than the predicted fragment size of an equivalent "unflawed" material, the fragment size of the preflawed material will be smaller in general, but usually not as small as the initial flaw spacing. The analysis also permits determination of the evolution of the strain rate distribution in a prospective fragment before and after fragmentation initiation; results are presented for some example cases. Finally, closed-form analytical results are derived for minimum fragment size and time to

  9. A two-dimensional analytical model of petroleum vapor intrusion

    NASA Astrophysics Data System (ADS)

    Yao, Yijun; Verginelli, Iason; Suuberg, Eric M.

    2016-02-01

    In this study we present an analytical solution of a two-dimensional petroleum vapor intrusion model, which incorporates a steady-state diffusion-dominated vapor transport in a homogeneous soil and piecewise first-order aerobic biodegradation limited by oxygen availability. This new model can help practitioners to easily generate two-dimensional soil gas concentration profiles for both hydrocarbons and oxygen and estimate hydrocarbon indoor air concentrations as a function of site-specific conditions such as source strength and depth, reaction rate constant, soil characteristics and building features. The soil gas concentration profiles generated by this new model are shown in good agreement with three-dimensional numerical simulations and two-dimensional measured soil gas data from a field study. This implies that for cases involving diffusion dominated soil gas transport, steady state conditions and homogenous source and soil, this analytical model can be used as a fast and easy-to-use risk screening tool by replicating the results of 3-D numerical simulations but with much less computational effort.

  10. A semi-analytic model of magnetized liner inertial fusion

    SciTech Connect

    McBride, Ryan D.; Slutz, Stephen A.

    2015-05-15

    Presented is a semi-analytic model of magnetized liner inertial fusion (MagLIF). This model accounts for several key aspects of MagLIF, including: (1) preheat of the fuel (optionally via laser absorption); (2) pulsed-power-driven liner implosion; (3) liner compressibility with an analytic equation of state, artificial viscosity, internal magnetic pressure, and ohmic heating; (4) adiabatic compression and heating of the fuel; (5) radiative losses and fuel opacity; (6) magnetic flux compression with Nernst thermoelectric losses; (7) magnetized electron and ion thermal conduction losses; (8) end losses; (9) enhanced losses due to prescribed dopant concentrations and contaminant mix; (10) deuterium-deuterium and deuterium-tritium primary fusion reactions for arbitrary deuterium to tritium fuel ratios; and (11) magnetized α-particle fuel heating. We show that this simplified model, with its transparent and accessible physics, can be used to reproduce the general 1D behavior presented throughout the original MagLIF paper [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)]. We also discuss some important physics insights gained as a result of developing this model, such as the dependence of radiative loss rates on the radial fraction of the fuel that is preheated.

  11. A two-dimensional analytical model of petroleum vapor intrusion

    PubMed Central

    Yao, Yijun; Verginelli, Iason; Suuberg, Eric M.

    2017-01-01

    In this study we present an analytical solution of a two-dimensional petroleum vapor intrusion model, which incorporates a steady-state diffusion-dominated vapor transport in a homogeneous soil and piecewise first-order aerobic biodegradation limited by oxygen availability. This new model can help practitioners to easily generate two-dimensional soil gas concentration profiles for both hydrocarbons and oxygen and estimate hydrocarbon indoor air concentrations as a function of site-specific conditions such as source strength and depth, reaction rate constant, soil characteristics and building features. The soil gas concentration profiles generated by this new model are shown in good agreement with three-dimensional numerical simulations and two-dimensional measured soil gas data from a field study. This implies that for cases involving diffusion dominated soil gas transport, steady state conditions and homogenous source and soil, this analytical model can be used as a fast and easy-to-use risk screening tool by replicating the results of 3-D numerical simulations but with much less computational effort. PMID:28255184

  12. A semi-analytic model of magnetized liner inertial fusion

    DOE PAGES

    McBride, Ryan D.; Slutz, Stephen A.

    2015-05-21

    Presented is a semi-analytic model of magnetized liner inertial fusion (MagLIF). This model accounts for several key aspects of MagLIF, including: (1) preheat of the fuel (optionally via laser absorption); (2) pulsed-power-driven liner implosion; (3) liner compressibility with an analytic equation of state, artificial viscosity, internal magnetic pressure, and ohmic heating; (4) adiabatic compression and heating of the fuel; (5) radiative losses and fuel opacity; (6) magnetic flux compression with Nernst thermoelectric losses; (7) magnetized electron and ion thermal conduction losses; (8) end losses; (9) enhanced losses due to prescribed dopant concentrations and contaminant mix; (10) deuterium-deuterium and deuterium-tritium primarymore » fusion reactions for arbitrary deuterium to tritium fuel ratios; and (11) magnetized α-particle fuel heating. We show that this simplified model, with its transparent and accessible physics, can be used to reproduce the general 1D behavior presented throughout the original MagLIF paper [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)]. We also discuss some important physics insights gained as a result of developing this model, such as the dependence of radiative loss rates on the radial fraction of the fuel that is preheated.« less

  13. Target normal sheath acceleration analytical modeling, comparative study and developments

    SciTech Connect

    Perego, C.; Batani, D.; Zani, A.; Passoni, M.

    2012-02-15

    Ultra-intense laser interaction with solid targets appears to be an extremely promising technique to accelerate ions up to several MeV, producing beams that exhibit interesting properties for many foreseen applications. Nowadays, most of all the published experimental results can be theoretically explained in the framework of the target normal sheath acceleration (TNSA) mechanism proposed by Wilks et al. [Phys. Plasmas 8(2), 542 (2001)]. As an alternative to numerical simulation various analytical or semi-analytical TNSA models have been published in the latest years, each of them trying to provide predictions for some of the ion beam features, given the initial laser and target parameters. However, the problem of developing a reliable model for the TNSA process is still open, which is why the purpose of this work is to enlighten the present situation of TNSA modeling and experimental results, by means of a quantitative comparison between measurements and theoretical predictions of the maximum ion energy. Moreover, in the light of such an analysis, some indications for the future development of the model proposed by Passoni and Lontano [Phys. Plasmas 13(4), 042102 (2006)] are then presented.

  14. Comparison between analytical and numerical solution of mathematical drying model

    NASA Astrophysics Data System (ADS)

    Shahari, N.; Rasmani, K.; Jamil, N.

    2016-02-01

    Drying is often related to the food industry as a process of shifting heat and mass inside food, which helps in preserving food. Previous research using a mass transfer equation showed that the results were mostly concerned with the comparison between the simulation model and the experimental data. In this paper, the finite difference method was used to solve a mass equation during drying using different kinds of boundary condition, which are equilibrium and convective boundary conditions. The results of these two models provide a comparison between the analytical and the numerical solution. The result shows a close match between the two solution curves. It is concluded that the two proposed models produce an accurate solution to describe the moisture distribution content during the drying process. This analysis indicates that we have confidence in the behaviour of moisture in the numerical simulation. This result demonstrated that a combined analytical and numerical approach prove that the system is behaving physically. Based on this assumption, the model of mass transfer was extended to include the temperature transfer, and the result shows a similar trend to those presented in the simpler case.

  15. Analytical results on the Beauchemin model of lymphocyte migration

    PubMed Central

    2013-01-01

    The Beauchemin model is a simple particle-based description of stochastic lymphocyte migration in tissue, which has been successfully applied to studying immunological questions. In addition to being easy to implement, the model is also to a large extent mathematically tractable. This article provides a comprehensive overview of both existing and new analytical results on the Beauchemin model within a common mathematical framework. Specifically, we derive the motility coefficient, the mean square displacement, and the confinement ratio, and discuss four different methods for simulating biased migration of pre-defined speed. The results provide new insight into published studies and a reference point for future research based on this simple and popular lymphocyte migration model. PMID:23734948

  16. Laser satellite constellations for strategic defense - an analytic model

    SciTech Connect

    Parmentola, J.A.; Milton, A.F.

    1987-10-01

    Using mainly geometric reasoning, an analytic model is constructed that predicts the required characteristics of an orbiting constellation of laser battle stations, each of which is designed to destroy ballistic missiles during their boost phase. The geometry of the constellation configuration and some general aspects of the coverage problem are discussed. The determination of the absentee ratio falls into two main categories that depend upon whether the Soviet ICBM threat is concentrated at a single location or whether it is distributed as it is now. A point-threat model and a distributive threat model are considered, the determination of the respective kill rates for these models is discussed, and the scaling properties of the laser constellation with respect to a change in the quantitative nature of the two types of ICBM threats are considered.

  17. A semi-analytical Lagrangian dispersion model in inhomogeneous turbulence

    SciTech Connect

    Zhuang, Y.

    1996-12-31

    Probably the most natural method to describe turbulent dispersion in the atmosphere is the Lagrangian trajectory model. In this approach, one builds the joint probability density function (PDF) of particle velocity and position by following a large number of particle trajectories in a turbulent flow given the Eulerian flow statistics. The statistics of the concentration can then be found from the joint PDF. However, the usefulness of the Lagrangian trajectory model in practice has been hindered by the necessary lengthy and stochastic numerical calculations. As a result, few operational models based on the Lagrangian trajectory approach have been proposed. This paper reports the first attempt to solve the Fokker-Planck equation using the function expansion method. The semi-analytical solution retains the characteristics of the Lagrangian trajectory model, but takes little computation effort. The solutions for Gaussian inhomogeneous turbulence and skewed homogeneous turbulence are discussed by comparing them with those calculated using the trajectory simulation method.

  18. Analytical model of an isolated single-atom electron source.

    PubMed

    Engelen, W J; Vredenbregt, E J D; Luiten, O J

    2014-12-01

    An analytical model of a single-atom electron source is presented, where electrons are created by near-threshold photoionization of an isolated atom. The model considers the classical dynamics of the electron just after the photon absorption, i.e. its motion in the potential of a singly charged ion and a uniform electric field used for acceleration. From closed expressions for the asymptotic transverse electron velocities and trajectories, the effective source temperature and the virtual source size can be calculated. The influence of the acceleration field strength and the ionization laser energy on these properties has been studied. With this model, a single-atom electron source with the optimum electron beam properties can be designed. Furthermore, we show that the model is also applicable to ionization of rubidium atoms, and thus also describes the ultracold electron source, which is based on photoionization of laser-cooled alkali atoms.

  19. Use of groundwater levels with the PULSE analytical model.

    PubMed

    Rutledge, Albert T

    2014-01-01

    The PULSE analytical model, which calculates daily groundwater discharge on the basis of user-specified recharge, was originally developed for calibration using streamflow data. This article describes a model application in which groundwater level data constitute the primary control on model input. As a test case, data were analyzed from a small basin in central Pennsylvania in which extensive groundwater level data are available. The timing and intensity of daily water-level rises are used to ascertain temporal distribution of recharge, and the simulated groundwater discharge hydrograph has shape features that are similar to the streamflow hydrograph. This article does not include details about calibration, but some steps are illustrated and general procedures are described for calibration in specific hydrologic studies. The PULSE model can be used to assess results of fully automated base flow methods and can be used to define groundwater recharge and discharge at a relatively small time scale.

  20. An analytical model for a full wind turbine wake

    NASA Astrophysics Data System (ADS)

    Keane, Aidan; Olmos Aguirre, Pablo E.; Ferchland, Hannah; Clive, Peter; Gallacher, Daniel

    2016-09-01

    An analytical wind turbine wake model is proposed to predict the wind velocity distribution for all distances downwind of a wind turbine, including the near-wake. This wake model augments the Jensen model and subsequent derivations thereof, and is a direct generalization of that recently proposed by Bastankhah and Porté-Agel. The model is derived by applying conservation of mass and momentum in the context of actuator disk theory, and assuming a distribution of the double-Gaussian type for the velocity deficit in the wake. The physical solutions are obtained by appropriate mixing of the waked- and freestream velocity deficit solutions, reflecting the fact that only a portion of the fluid particles passing through the rotor disk will interact with a blade.

  1. A workflow learning model to improve geovisual analytics utility.

    PubMed

    Roth, Robert E; Maceachren, Alan M; McCabe, Craig A

    2009-01-01

    INTRODUCTION: This paper describes the design and implementation of the G-EX Portal Learn Module, a web-based, geocollaborative application for organizing and distributing digital learning artifacts. G-EX falls into the broader context of geovisual analytics, a new research area with the goal of supporting visually-mediated reasoning about large, multivariate, spatiotemporal information. Because this information is unprecedented in amount and complexity, GIScientists are tasked with the development of new tools and techniques to make sense of it. Our research addresses the challenge of implementing these geovisual analytics tools and techniques in a useful manner. OBJECTIVES: The objective of this paper is to develop and implement a method for improving the utility of geovisual analytics software. The success of software is measured by its usability (i.e., how easy the software is to use?) and utility (i.e., how useful the software is). The usability and utility of software can be improved by refining the software, increasing user knowledge about the software, or both. It is difficult to achieve transparent usability (i.e., software that is immediately usable without training) of geovisual analytics software because of the inherent complexity of the included tools and techniques. In these situations, improving user knowledge about the software through the provision of learning artifacts is as important, if not more so, than iterative refinement of the software itself. Therefore, our approach to improving utility is focused on educating the user. METHODOLOGY: The research reported here was completed in two steps. First, we developed a model for learning about geovisual analytics software. Many existing digital learning models assist only with use of the software to complete a specific task and provide limited assistance with its actual application. To move beyond task-oriented learning about software use, we propose a process-oriented approach to learning based on

  2. A workflow learning model to improve geovisual analytics utility

    PubMed Central

    Roth, Robert E; MacEachren, Alan M; McCabe, Craig A

    2011-01-01

    Introduction This paper describes the design and implementation of the G-EX Portal Learn Module, a web-based, geocollaborative application for organizing and distributing digital learning artifacts. G-EX falls into the broader context of geovisual analytics, a new research area with the goal of supporting visually-mediated reasoning about large, multivariate, spatiotemporal information. Because this information is unprecedented in amount and complexity, GIScientists are tasked with the development of new tools and techniques to make sense of it. Our research addresses the challenge of implementing these geovisual analytics tools and techniques in a useful manner. Objectives The objective of this paper is to develop and implement a method for improving the utility of geovisual analytics software. The success of software is measured by its usability (i.e., how easy the software is to use?) and utility (i.e., how useful the software is). The usability and utility of software can be improved by refining the software, increasing user knowledge about the software, or both. It is difficult to achieve transparent usability (i.e., software that is immediately usable without training) of geovisual analytics software because of the inherent complexity of the included tools and techniques. In these situations, improving user knowledge about the software through the provision of learning artifacts is as important, if not more so, than iterative refinement of the software itself. Therefore, our approach to improving utility is focused on educating the user. Methodology The research reported here was completed in two steps. First, we developed a model for learning about geovisual analytics software. Many existing digital learning models assist only with use of the software to complete a specific task and provide limited assistance with its actual application. To move beyond task-oriented learning about software use, we propose a process-oriented approach to learning based on the

  3. Analytic Thermoelectric Couple Modeling: Variable Material Properties and Transient Operation

    NASA Technical Reports Server (NTRS)

    Mackey, Jonathan A.; Sehirlioglu, Alp; Dynys, Fred

    2015-01-01

    To gain a deeper understanding of the operation of a thermoelectric couple a set of analytic solutions have been derived for a variable material property couple and a transient couple. Using an analytic approach, as opposed to commonly used numerical techniques, results in a set of useful design guidelines. These guidelines can serve as useful starting conditions for further numerical studies, or can serve as design rules for lab built couples. The analytic modeling considers two cases and accounts for 1) material properties which vary with temperature and 2) transient operation of a couple. The variable material property case was handled by means of an asymptotic expansion, which allows for insight into the influence of temperature dependence on different material properties. The variable property work demonstrated the important fact that materials with identical average Figure of Merits can lead to different conversion efficiencies due to temperature dependence of the properties. The transient couple was investigated through a Greens function approach; several transient boundary conditions were investigated. The transient work introduces several new design considerations which are not captured by the classic steady state analysis. The work helps to assist in designing couples for optimal performance, and also helps assist in material selection.

  4. Simulations and analytic models of relativistic magnetized jets

    NASA Astrophysics Data System (ADS)

    Tchekhovskoi, Alexandre Dmitrievich

    Astrophysical jets are tightly collimated streams that are often observed to move at velocities close to the speed of light. While many such systems are known, understanding and explaining how jets collimate and accelerate has been a long-standing challenge and is currently an area of active research. Finding analytic solutions for jets is extremely hard because the equations that describe the jets are highly nonlinear and difficult to solve analytically. Only in the last few years has it become possible to simulate ultrarelativistic jets computationally, which has led to unprecedented insights into their structure. We now think that many relativistic jets are produced by magnetic fields twisted by the rotation of a central compact object, which can be a black hole or a neutron star. In this thesis I present numerical and analytical studies of relativistic jets. In Chapter 2, I start with a discussion of a simple, idealized model that has the bare minimum of ingredients needed for the production of jets: regular magnetic field, spinning central compact object, and externally imposed collimation. The model assumes that magnetic field in the jet is so strong that plasma inertia is negligible and can be ignored. The simplicity of this model allows for a fully analytic description and an intuitive understanding of the results. Despite being simple, this model possesses non-trivial properties and has important applications to various astrophysical systems --- compact object binaries, gamma-ray bursts, and active galactic nuclei. Chapters 3 -- 7 add an extra level of realism (and sophistication) into jet models: they account for mass inertia of the jet fluid and study its effects on the jet structure. Chapter 4 discusses the effect of jet confinement on the acceleration of the jet. Chapter 5 shows that deconfinement can also have a dramatic effect on the jet. Chapter 6 studies how the structure of the jet changes if the central object driving the jet is a black hole

  5. Analytical model for flow duration curves in seasonally dry climates

    NASA Astrophysics Data System (ADS)

    Müller, Marc F.; Dralle, David N.; Thompson, Sally E.

    2014-07-01

    Flow duration curves (FDC) display streamflow values against their relative exceedance time. They provide critical information for watershed management by representing the variation in the availability and reliability of surface water to supply ecosystem services and satisfy anthropogenic needs. FDCs are particularly revealing in seasonally dry climates, where surface water supplies are highly variable. While useful, the empirical computation of FDCs is data intensive and challenging in sparsely gauged regions, meaning that there is a need for robust, predictive models to evaluate FDCs with simple parameterization. Here, we derive a process-based analytical expression for FDCs in seasonally dry climates. During the wet season, streamflow is modeled as a stochastic variable driven by rainfall, following the stochastic analytical model of Botter et al. (2007a). During the dry season, streamflow is modeled as a deterministic recession with a stochastic initial condition that accounts for the carryover of catchment storage across seasons. The resulting FDC model is applied to 38 catchments in Nepal, coastal California, and Western Australia, where FDCs are successfully modeled using five physically meaningful parameters with minimal calibration. A Monte Carlo analysis revealed that the model is robust to deviations from its assumptions of Poissonian rainfall, exponentially distributed response times and constant seasonal timing. The approach successfully models period-of-record FDCs and allows interannual and intra-annual sources of variations in dry season streamflow to be separated. The resulting median annual FDCs and confidence intervals allow the simulation of the consequences of interannual flow variations for infrastructure projects. We present an example using run-of-river hydropower in Nepal as a case study.

  6. Untangling Slab Dynamics Using 3-D Numerical and Analytical Models

    NASA Astrophysics Data System (ADS)

    Holt, A. F.; Royden, L.; Becker, T. W.

    2016-12-01

    Increasingly sophisticated numerical models have enabled us to make significant strides in identifying the key controls on how subducting slabs deform. For example, 3-D models have demonstrated that subducting plate width, and the related strength of toroidal flow around the plate edge, exerts a strong control on both the curvature and the rate of migration of the trench. However, the results of numerical subduction models can be difficult to interpret, and many first order dynamics issues remain at least partially unresolved. Such issues include the dominant controls on trench migration, the interdependence of asthenospheric pressure and slab dynamics, and how nearby slabs influence each other's dynamics. We augment 3-D, dynamically evolving finite element models with simple, analytical force-balance models to distill the physics associated with subduction into more manageable parts. We demonstrate that for single, isolated subducting slabs much of the complexity of our fully numerical models can be encapsulated by simple analytical expressions. Rates of subduction and slab dip correlate strongly with the asthenospheric pressure difference across the subducting slab. For double subduction, an additional slab gives rise to more complex mantle pressure and flow fields, and significantly extends the range of plate kinematics (e.g., convergence rate, trench migration rate) beyond those present in single slab models. Despite these additional complexities, we show that much of the dynamics of such multi-slab systems can be understood using the physics illuminated by our single slab study, and that a force-balance method can be used to relate intra-plate stress to viscous pressure in the asthenosphere and coupling forces at plate boundaries. This method has promise for rapid modeling of large systems of subduction zones on a global scale.

  7. Thermal analytic model of 30 cm engineering model mercury ion thruster

    NASA Technical Reports Server (NTRS)

    Oglebay, J. C.

    1975-01-01

    A lumped parameter thermal nodal network was developed for a 30 cm Engineering Model Mercury Ion Thruster. The network consists of approximately 100 nodes coded in SINDA format for use on the Univac 1106/1108 computer. This model takes into account internal dissipation, radiation, and conduction as well as environmental heating. A series of tests were performed to simulate a wide range of thermal environments on an operating 30 cm thruster, instrumented to measure the temperature distribution within the thruster. The results of these tests were used to calibrate the analytical model. The analytical model along with comparisons between analytical and experimental results for the various operating conditions are presented.

  8. Digital forensics: an analytical crime scene procedure model (ACSPM).

    PubMed

    Bulbul, Halil Ibrahim; Yavuzcan, H Guclu; Ozel, Mesut

    2013-12-10

    In order to ensure that digital evidence is collected, preserved, examined, or transferred in a manner safeguarding the accuracy and reliability of the evidence, law enforcement and digital forensic units must establish and maintain an effective quality assurance system. The very first part of this system is standard operating procedures (SOP's) and/or models, conforming chain of custody requirements, those rely on digital forensics "process-phase-procedure-task-subtask" sequence. An acceptable and thorough Digital Forensics (DF) process depends on the sequential DF phases, and each phase depends on sequential DF procedures, respectively each procedure depends on tasks and subtasks. There are numerous amounts of DF Process Models that define DF phases in the literature, but no DF model that defines the phase-based sequential procedures for crime scene identified. An analytical crime scene procedure model (ACSPM) that we suggest in this paper is supposed to fill in this gap. The proposed analytical procedure model for digital investigations at a crime scene is developed and defined for crime scene practitioners; with main focus on crime scene digital forensic procedures, other than that of whole digital investigation process and phases that ends up in a court. When reviewing the relevant literature and interrogating with the law enforcement agencies, only device based charts specific to a particular device and/or more general perspective approaches to digital evidence management models from crime scene to courts are found. After analyzing the needs of law enforcement organizations and realizing the absence of crime scene digital investigation procedure model for crime scene activities we decided to inspect the relevant literature in an analytical way. The outcome of this inspection is our suggested model explained here, which is supposed to provide guidance for thorough and secure implementation of digital forensic procedures at a crime scene. In digital forensic

  9. Coherent hole propagation in an exactly solvable gapless spin liquid

    NASA Astrophysics Data System (ADS)

    Halász, Gábor B.; Chalker, J. T.

    2016-12-01

    We examine the dynamics of a single hole in the gapless phase of the Kitaev honeycomb model, focusing on the slow-hole regime where the bare hopping amplitude t is much less than the Kitaev exchange energy J . In this regime, the hole does not generate gapped flux excitations and is dressed only by the gapless fermion excitations. Investigating the single-hole spectral function, we find that the hole propagates coherently with a quasiparticle weight that is finite but approaches zero as t /J →0 . This conclusion follows from two approximate treatments, which capture the same physics in complementary ways. Both treatments use the stationary limit as an exactly solvable starting point to study the spectral function approximately (i) by employing a variational approach in terms of a trial state that interpolates between the limits of a stationary hole and an infinitely fast hole and (ii) by considering a special point in the gapless phase that corresponds to a simplified one-dimensional problem.

  10. A hybrid finite-difference and analytic element groundwater model.

    PubMed

    Haitjema, H M; Feinstein, D T; Hunt, R J; Gusyev, M A

    2010-01-01

    Regional finite-difference models tend to have large cell sizes, often on the order of 1-2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW-MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models.

  11. Solvable Hamiltonians and Fermionization Transformations Obtained from Operators Satisfying Specific Commutation Relations

    NASA Astrophysics Data System (ADS)

    Minami, Kazuhiko

    2016-02-01

    It is shown that a solvable Hamiltonian can be obtained from a series of operators satisfying specific commutation relations. A transformation that diagonalize the Hamiltonian is obtained simultaneously. The two-dimensional Ising model with periodic interactions, the one-dimensional XY model with period 2, the transverse Ising chain, the one-dimensional Kitaev model and the cluster model, and other composite quantum spin chains are diagonalized following this procedure. The Jordan-Wigner transformation, the transformation from the Pauli spin operators to the Majorana fermion used by Shankar and Murthy, and the transformation introduced by Nambu, are special cases of this treatment.

  12. Analytical and numerical modeling of surface morphologies in thin films

    SciTech Connect

    Genin, F.Y.

    1995-05-01

    Experimental studies have show that strains due to thermal expansion mismatch between a film and its substrate can produce very large stresses in the film that can lead to the formation of holes and hillocks. Based on a phenomenological description of the evolution of a solid surface under both capillary and stress driving forces and for surface and grain boundary self-diffusion, this article provides analytical and numerical solutions for surface profiles of model geometries in polycrystalline thin films. Results can explain a variety of surface morphologies commonly observed experimentally and are discussed to give some practical insights on how to control the growth of holes and hillocks in thin films.

  13. Analytical approximations for a population growth model with fractional order

    NASA Astrophysics Data System (ADS)

    Xu, Hang

    2009-05-01

    In this paper, we apply the homotopy analysis method (HAM) to solve the fractional Volterra's model for population growth of a species in a closed system. This technique is extended to give solutions for nonlinear fractional integro-differential equations. The whole HAM solution procedure for nonlinear fractional differential equations is established. Further, the accurate analytical approximations are obtained for the first time, which are valid and convergent for all time t. This indicates the validity and great potential of the homotopy analysis method for solving nonlinear fractional integro-differential equations.

  14. "Violent Intent Modeling: Incorporating Cultural Knowledge into the Analytical Process

    SciTech Connect

    Sanfilippo, Antonio P.; Nibbs, Faith G.

    2007-08-24

    While culture has a significant effect on the appropriate interpretation of textual data, the incorporation of cultural considerations into data transformations has not been systematic. Recognizing that the successful prevention of terrorist activities could hinge on the knowledge of the subcultures, Anthropologist and DHS intern Faith Nibbs has been addressing the need to incorporate cultural knowledge into the analytical process. In this Brown Bag she will present how cultural ideology is being used to understand how the rhetoric of group leaders influences the likelihood of their constituents to engage in violent or radicalized behavior, and how violent intent modeling can benefit from understanding that process.

  15. Analytical model for the radio-frequency sheath.

    PubMed

    Czarnetzki, Uwe

    2013-12-01

    A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary

  16. Analytical model of spin-polarized semiconductor lasers

    NASA Astrophysics Data System (ADS)

    Gøthgen, Christian; Oszwałdowski, Rafał; Petrou, Athos; Žutić, Igor

    2008-07-01

    We formulate an analytical model for semiconductor lasers with injection (pump) of spin-polarized electrons, allowing us to systematically investigate different operating regimes. We demonstrate that the maximum threshold reduction by electrically pumped spin-polarized carriers is larger than previously thought possible and, surprisingly, can be enhanced by ultrafast spin relaxation of holes. We reveal how different modes of carrier recombination directly affect the threshold reduction. Neither spin-up nor spin-down electron populations are separately clamped (pinned) near the threshold, where such lasers can act as effective nonlinear filters of circularly polarized light, owing to their spin-dependent gain.

  17. Multidisciplinary optimization in aircraft design using analytic technology models

    NASA Technical Reports Server (NTRS)

    Malone, Brett; Mason, W. H.

    1991-01-01

    An approach to multidisciplinary optimization is presented which combines the Global Sensitivity Equation method, parametric optimization, and analytic technology models. The result is a powerful yet simple procedure for identifying key design issues. It can be used both to investigate technology integration issues very early in the design cycle, and to establish the information flow framework between disciplines for use in multidisciplinary optimization projects using much more computational intense representations of each technology. To illustrate the approach, an examination of the optimization of a short takeoff heavy transport aircraft is presented for numerous combinations of performance and technology constraints.

  18. Analytical model for the radio-frequency sheath

    NASA Astrophysics Data System (ADS)

    Czarnetzki, Uwe

    2013-12-01

    A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary

  19. Analytical performance models for geologic repositories. Volume 2

    SciTech Connect

    Chambre, P.L.; Pigford, T.H.; Fujita, A.; Kanki, T.; Kobayashi, A.; Lung, H.; Ting, D.; Sato, Y.; Zavoshy, S.J.

    1982-10-01

    This report presents analytical solutions of the dissolution and hydrogeologic transport of radionuclides in geologic repositories. Numerical examples are presented to demonstrate the equations resulting from these analyses. The subjects treated in this report are: solubility-limited transport with transverse dispersion (chapter 2); transport of a radionuclide chain with nonequilibrium chemical reactions (chapter 3); advective transport in a two-dimensional flow field (chapter 4); radionuclide transport in fractured media (chapter 5); a mathematical model for EPA's analysis of generic repositories (chapter 6); and dissolution of radionuclides from solid waste (chapter 7). Volume 2 contains chapters 5, 6, and 7.

  20. X: A Comprehensive Analytic Model for Parallel Machines

    SciTech Connect

    Li, Ang; Song, Shuaiwen; Brugel, Eric; Kumar, Akash; Chavarría-Miranda, Daniel; Corporaal, Henk

    2016-05-23

    To continuously comply with Moore’s Law, modern parallel machines become increasingly complex. Effectively tuning application performance for these machines therefore becomes a daunting task. Moreover, identifying performance bottlenecks at application and architecture level, as well as evaluating various optimization strategies, are becoming extremely difficult when the entanglement of numerous correlated factors is being presented. To tackle these challenges, we present a visual analytical model named “X”. It is intuitive and sufficiently flexible to track all the typical features of a parallel machine.

  1. A temporal model for Clinical Data Analytics language.

    PubMed

    Safari, Leila; Patrick, Jon D

    2013-01-01

    The proposal of a special purpose language for Clinical Data Analytics (CliniDAL) is presented along with a general model for expressing temporal events in the language. The temporal dimension of clinical data needs to be addressed from at least five different points of view. Firstly, how to attach the knowledge of time based constraints to queries; secondly, how to mine temporal data in different CISs with various data models; thirdly, how to deal with both relative time and absolute time in the query language; fourthly, how to tackle internal time-event dependencies in queries, and finally, how to manage historical time events preserved in the patient's narrative. The temporal elements of the language are defined in Bachus Naur Form (BNF) along with a UML schema. Its use in a designed taxonomy of a five class hierarchy of data analytics tasks shows the solution to problems of time event dependencies in a highly complex cascade of queries needed to evaluate scientific experiments. The issues in using the model in a practical way are discussed as well.

  2. Analytic Model for Self-Excited Plasma Series Resonances

    NASA Astrophysics Data System (ADS)

    Czarnetzki, Uwe; Mussenbrock, Thomas; Brinkmann, Ralf-Peter

    2006-10-01

    Self-excited Plasma Series Resonances (PSR) are observed in capacitve discharges as high frequency oscillations superimposed on the normal RF current. This high-frequency contribution to the current is generated by a series resonance between the capacitve sheath and the inductive and ohmic bulk of the plasma. The non-linearity of the sheath leads to a complex dynamic. The effect is applied e.g. as a diagnostic technique in commercial etch reactors where analysis is performed by a numerical model. Here a simple analytical investigation is introduced. In order to solve the non-linear equations analytically, a series of approximation is necessary. Nevertheless, the basic physics is conserved and excellent agreement with numerical solutions is found. The model provides explicit and simple formula for the current waveform and the spectral range of the oscillations. In particular, the dependence on the discharge parameters is shown. Further, the model gives insight into an additional dissipation channel opened by the high frequency oscillations. With decreasing pressure the ohmic resistance of the bulk is decreasing too, while the amplitude of the PSR oscillations is growing. This results in substantially higher power dissipation.

  3. Optimizing multi-pinhole SPECT geometries using an analytical model

    NASA Astrophysics Data System (ADS)

    Rentmeester, M. C. M.; van der Have, F.; Beekman, F. J.

    2007-05-01

    State-of-the-art multi-pinhole SPECT devices allow for sub-mm resolution imaging of radio-molecule distributions in small laboratory animals. The optimization of multi-pinhole and detector geometries using simulations based on ray-tracing or Monte Carlo algorithms is time-consuming, particularly because many system parameters need to be varied. As an efficient alternative we develop a continuous analytical model of a pinhole SPECT system with a stationary detector set-up, which we apply to focused imaging of a mouse. The model assumes that the multi-pinhole collimator and the detector both have the shape of a spherical layer, and uses analytical expressions for effective pinhole diameters, sensitivity and spatial resolution. For fixed fields-of-view, a pinhole-diameter adapting feedback loop allows for the comparison of the system resolution of different systems at equal system sensitivity, and vice versa. The model predicts that (i) for optimal resolution or sensitivity the collimator layer with pinholes should be placed as closely as possible around the animal given a fixed detector layer, (ii) with high-resolution detectors a resolution improvement up to 31% can be achieved compared to optimized systems, (iii) high-resolution detectors can be placed close to the collimator without significant resolution losses, (iv) interestingly, systems with a physical pinhole diameter of 0 mm can have an excellent resolution when high-resolution detectors are used.

  4. Analytical modeling of turbine wakes in yawed conditions

    NASA Astrophysics Data System (ADS)

    Bastankhah, Majid; Porté-Agel, Fernando

    2016-04-01

    Increasing wind energy production has become a unanimous plan for virtually all the developed countries. In addition to constructing new wind farms, this goal can be achieved by making wind farms more efficient. Control strategies in wind farms, such as manipulating the yaw angle of the turbines, have the potential to make wind farms more efficient. Costly numerical simulations or measurements cannot be, however, employed to assess the viability of this strategy in the numerous different scenarios happening in real wind farms. In this study, we aim to develop an inexpensive and simple analytical model that is able for the first time to predict the whole wake of a yawed turbine with an acceptable accuracy. The proposed analytical model is built upon the simplified version of the Reynolds-averaged Navier-Stokes equations. Apart from the ability of the model to predict wake flows in yawed conditions, it can provide a better understanding of turbine wakes in this complex situation. For example, it can give valuable insights on how the wake deflection varies by changing turbine and incoming flow characteristics, such as the thrust coefficient of the turbine or the ambient turbulence.

  5. Analytic solution of Hubbell's model of local community dynamics.

    PubMed

    McKane, Alan J; Alonso, David; Solé, Ricard V

    2004-02-01

    Recent theoretical approaches to community structure and dynamics reveal that many large-scale features of community structure (such as species-rank distributions and species-area relations) can be explained by a so-called neutral model. Using this approach, species are taken to be equivalent and trophic relations are not taken into account explicitly. Here we provide a general analytic solution to the local community model of Hubbell's neutral theory of biodiversity by recasting it as an urn model, i.e. a Markovian description of states and their transitions. Both stationary and time-dependent distributions are analysed. The stationary distribution-also called the zero-sum multinomial-is given in closed form. An approximate form for the time-dependence is obtained by using an expansion of the master equation. The temporal evolution of the approximate distribution is shown to be a good representation for the true temporal evolution for a large range of parameter values.

  6. A MODEL STUDY OF TRANSVERSE MODE COUPLING INSTABILITY AT NATIONAL SYNCHROTRON LIGHT SOURCE-II (NSLS-II).

    SciTech Connect

    BLEDNYKH, A.; WANG, J.M.

    2005-05-15

    The vertical impedances of the preliminary designs of National Synchrotron Light Source II (NSLS-II) Mini Gap Undulators (MGU) are calculated by means of GdfidL code. The Transverse Mode Coupling Instability (TMCI) thresholds corresponding to these impedances are estimated using an analytically solvable model.

  7. Analytical aerodynamic model of a high alpha research vehicle wind-tunnel model

    NASA Technical Reports Server (NTRS)

    Cao, Jichang; Garrett, Frederick, Jr.; Hoffman, Eric; Stalford, Harold

    1990-01-01

    A 6 DOF analytical aerodynamic model of a high alpha research vehicle is derived. The derivation is based on wind-tunnel model data valid in the altitude-Mach flight envelope centered at 15,000 ft altitude and 0.6 Mach number with Mach range between 0.3 and 0.9. The analytical models of the aerodynamics coefficients are nonlinear functions of alpha with all control variable and other states fixed. Interpolation is required between the parameterized nonlinear functions. The lift and pitching moment coefficients have unsteady flow parts due to the time range of change of angle-of-attack (alpha dot). The analytical models are plotted and compared with their corresponding wind-tunnel data. Piloted simulated maneuvers of the wind-tunnel model are used to evaluate the analytical model. The maneuvers considered are pitch-ups, 360 degree loaded and unloaded rolls, turn reversals, split S's, and level turns. The evaluation finds that (1) the analytical model is a good representation at Mach 0.6, (2) the longitudinal part is good for the Mach range 0.3 to 0.9, and (3) the lateral part is good for Mach numbers between 0.6 and 0.9. The computer simulations show that the storage requirement of the analytical model is about one tenth that of the wind-tunnel model and it runs twice as fast.

  8. Validated Analytical Model of a Pressure Compensation Drip Irrigation Emitter

    NASA Astrophysics Data System (ADS)

    Shamshery, Pulkit; Wang, Ruo-Qian; Taylor, Katherine; Tran, Davis; Winter, Amos

    2015-11-01

    This work is focused on analytically characterizing the behavior of pressure-compensating drip emitters in order to design low-cost, low-power irrigation solutions appropriate for off-grid communities in developing countries. There are 2.5 billion small acreage farmers worldwide who rely solely on their land for sustenance. Drip, compared to flood, irrigation leads to up to 70% reduction in water consumption while increasing yields by 90% - important in countries like India which are quickly running out of water. To design a low-power drip system, there is a need to decrease the pumping pressure requirement at the emitters, as pumping power is the product of pressure and flow rate. To efficiently design such an emitter, the relationship between the fluid-structure interactions that occur in an emitter need to be understood. In this study, a 2D analytical model that captures the behavior of a common drip emitter was developed and validated through experiments. The effects of independently changing the channel depth, channel width, channel length and land height on the performance were studied. The model and the key parametric insights presented have the potential to be optimized in order to guide the design of low-pressure, clog-resistant, pressure-compensating emitters.

  9. Fitting meta-analytic structural equation models with complex datasets.

    PubMed

    Wilson, Sandra Jo; Polanin, Joshua R; Lipsey, Mark W

    2016-06-01

    A modification of the first stage of the standard procedure for two-stage meta-analytic structural equation modeling for use with large complex datasets is presented. This modification addresses two common problems that arise in such meta-analyses: (a) primary studies that provide multiple measures of the same construct and (b) the correlation coefficients that exhibit substantial heterogeneity, some of which obscures the relationships between the constructs of interest or undermines the comparability of the correlations across the cells. One component of this approach is a three-level random effects model capable of synthesizing a pooled correlation matrix with dependent correlation coefficients. Another component is a meta-regression that can be used to generate covariate-adjusted correlation coefficients that reduce the influence of selected unevenly distributed moderator variables. A non-technical presentation of these techniques is given, along with an illustration of the procedures with a meta-analytic dataset. Copyright © 2016 John Wiley & Sons, Ltd.

  10. A Three Level Analytic Model for Alkali Vapor Lasers

    SciTech Connect

    Hager, Gordon D.; Perram, Glen P.

    2010-10-08

    A three level analytic model for optically pumped alkali metal vapor lasers is developed considering the steady-state rate equations for the longitudinally averaged number densities of the ground {sup 2}S{sub 1/2} and first excited {sup 2}P{sub 1/2} and {sup 2}P{sub 3/2} states. The threshold pump intensity includes both the requirements to fully bleach the pump transition and exceed optical losses, typically about 200 W/cm{sup 2}. Slope efficiency depends critically on the fraction of incident photons absorbed and the overlap of pump and resonator modes, approaching the quantum efficiency of 0.95-0.98, depending on alkali atom. For efficient operation, the collisional relaxation between the two upper levels should be fast relative to stimulated emission. By assuming a statistical distribution between the upper levels, the limiting analytic solution for the quasi-two level system is achieved. Application of the model and comparisons to recent laser demonstrations is presented.

  11. 33 CFR 385.33 - Revisions to models and analytical tools.

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... system-wide simulation models and analytical tools used in the evaluation and assessment of projects, and shall propose improvements in system-wide models and analytical tools required for the evaluation and... Incorporating New Information Into the Plan § 385.33 Revisions to models and analytical tools. (a) In...

  12. 33 CFR 385.33 - Revisions to models and analytical tools.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... system-wide simulation models and analytical tools used in the evaluation and assessment of projects, and shall propose improvements in system-wide models and analytical tools required for the evaluation and... Incorporating New Information Into the Plan § 385.33 Revisions to models and analytical tools. (a) In...

  13. An analytically tractable model for community ecology with many species

    NASA Astrophysics Data System (ADS)

    Dickens, Benjamin; Fisher, Charles; Mehta, Pankaj; Pankaj Mehta Biophysics Theory Group Team

    A fundamental problem in community ecology is to understand how ecological processes such as selection, drift, and immigration yield observed patterns in species composition and diversity. Here, we present an analytically tractable, presence-absence (PA) model for community assembly and use it to ask how ecological traits such as the strength of competition, diversity in competition, and stochasticity affect species composition in a community. In our PA model, we treat species as stochastic binary variables that can either be present or absent in a community: species can immigrate into the community from a regional species pool and can go extinct due to competition and stochasticity. Despite its simplicity, the PA model reproduces the qualitative features of more complicated models of community assembly. In agreement with recent work on large, competitive Lotka-Volterra systems, the PA model exhibits distinct ecological behaviors organized around a special (``critical'') point corresponding to Hubbell's neutral theory of biodiversity. Our results suggest that the concepts of ``phases'' and phase diagrams can provide a powerful framework for thinking about community ecology and that the PA model captures the essential ecological dynamics of community assembly. Pm was supported by a Simons Investigator in the Mathematical Modeling of Living Systems and a Sloan Research Fellowship.

  14. Analytical model for active metamaterials with quantum ingredients

    NASA Astrophysics Data System (ADS)

    Chipouline, A.; Sugavanam, S.; Fedotov, V. A.; Nikolaenko, A. E.

    2012-11-01

    We present an analytical model for describing complex dynamics of a hybrid system consisting of resonantly coupled classical resonator and quantum structures. Classical resonators in our model correspond to plasmonic metamaterials of various geometries, as well as other types of nano- and microstructure, the optical responses of which can be described classically. Quantum resonators are represented by atoms or molecules, or their aggregates (for example, quantum dots, carbon nanotubes, dye molecules, polymer or bio-molecules etc), which can be accurately modelled only with the use of the quantum mechanical approach. Our model is based on the set of equations that combines well established density matrix formalism appropriate for quantum systems, coupled with harmonic-oscillator equations ideal for modelling sub-wavelength plasmonic and optical resonators. As a particular example of application of our model, we show that the saturation nonlinearity of carbon nanotubes increases multifold in the resonantly enhanced near field of a metamaterial. In the framework of our model, we discuss the effect of inhomogeneity of the carbon-nanotube layer (bandgap value distribution) on the nonlinearity enhancement.

  15. Quasi-exact solvability of Dirac equation with Lorentz scalar potential

    SciTech Connect

    Ho, C.-L. . E-mail: hcl@mail.tku.edu.tw

    2006-09-15

    We consider exact/quasi-exact solvability of Dirac equation with a Lorentz scalar potential based on factorizability of the equation. Exactly solvable and sl (2)-based quasi-exactly solvable potentials are discussed separately in Cartesian coordinates for a pure Lorentz potential depending only on one spatial dimension, and in spherical coordinates in the presence of a Dirac monopole.

  16. Characterization of uniform scanning proton beams with analytical models

    NASA Astrophysics Data System (ADS)

    Demez, Nebi

    Tissue equivalent phantoms have an important place in radiation therapy planning and delivery. They have been manufactured for use in conventional radiotherapy. Their tissue equivalency for proton beams is currently in active investigation. The Bragg-Kleeman rule was used to calculate water equivalent thickness (WET) for available tissue equivalent phantoms from CIRS (Norfolk, VA, USA). WET's of those phantoms were also measured using proton beams at Hampton University Proton Therapy Institute (HUPTI). WET measurements and calculations are in good agreement within ˜1% accuracy except for high Z phantoms. Proton beams were also characterized with an analytical proton dose calculation model, Proton Loss Model (PLM) [26], to investigate protons interactions in water and those phantoms. Depth-dose and lateral dose profiles of protons in water and in those phantoms were calculated, measured, and compared. Water Equivalent Spreadness (WES) was also investigated for those phantoms using the formula for scattering power ratio. Because WES is independent of incident energy of protons, it is possible to estimate spreadness of protons in different media by just knowing WES. Measurements are usually taken for configuration of the treatment planning system (TPS). This study attempted to achieve commissioning data for uniform scanning proton planning with analytical methods, PLM, which have been verified with published measurements and Monte Carlo calculations. Depth doses and lateral profiles calculated by PLM were compared with measurements via the gamma analysis method. While gamma analysis shows that depth doses are in >90% agreement with measured depth doses, the agreement falls to <80% for some lateral profiles. PLM data were imported into the TPS (PLM-TPS). PLM-TPS was tested with different patient cases. The PLM-TPS treatment plans for 5 prostate cases show acceptable agreement. The Planning Treatment Volume (PTV) coverage was 100 % with PLM-TPS except for one case in

  17. Visual analytics for model selection in time series analysis.

    PubMed

    Bögl, Markus; Aigner, Wolfgang; Filzmoser, Peter; Lammarsch, Tim; Miksch, Silvia; Rind, Alexander

    2013-12-01

    Model selection in time series analysis is a challenging task for domain experts in many application areas such as epidemiology, economy, or environmental sciences. The methodology used for this task demands a close combination of human judgement and automated computation. However, statistical software tools do not adequately support this combination through interactive visual interfaces. We propose a Visual Analytics process to guide domain experts in this task. For this purpose, we developed the TiMoVA prototype that implements this process based on user stories and iterative expert feedback on user experience. The prototype was evaluated by usage scenarios with an example dataset from epidemiology and interviews with two external domain experts in statistics. The insights from the experts' feedback and the usage scenarios show that TiMoVA is able to support domain experts in model selection tasks through interactive visual interfaces with short feedback cycles.

  18. A Double Scattering Analytical Model For Elastic Recoil Detection Analysis

    SciTech Connect

    Barradas, N. P.; Lorenz, K.; Alves, E.; Darakchieva, V.

    2011-06-01

    We present an analytical model for calculation of double scattering in elastic recoil detection measurements. Only events involving the beam particle and the recoil are considered, i.e. 1) an ion scatters off a target element and then produces a recoil, and 2) an ion produces a recoil which then scatters off a target element. Events involving intermediate recoils are not considered, i.e. when the primary ion produces a recoil which then produces a second recoil. If the recoil element is also present in the stopping foil, recoil events in the stopping foil are also calculated. We included the model in the standard code for IBA data analysis NDF, and applied it to the measurement of hydrogen in Si.

  19. An analytical model of dynamic sliding friction during impact

    NASA Astrophysics Data System (ADS)

    Arakawa, Kazuo

    2017-01-01

    Dynamic sliding friction was studied based on the angular velocity of a golf ball during an oblique impact. This study used the analytical model proposed for the dynamic sliding friction on lubricated and non-lubricated inclines. The contact area A and sliding velocity u of the ball during impact were used to describe the dynamic friction force Fd = λAu, where λ is a parameter related to the wear of the contact area. A comparison with experimental results revealed that the model agreed well with the observed changes in the angular velocity during impact, and λAu is qualitatively equivalent to the empirical relationship, μN + μη‧dA/dt, given by the product between the frictional coefficient μ and the contact force N, and the additional term related to factor η‧ for the surface condition and the time derivative of A.

  20. Streaming instability of slime mold amoebae: An analytical model

    NASA Astrophysics Data System (ADS)

    Höfer, Thomas; Maini, Philip K.

    1997-08-01

    During the aggregation of amoebae of the cellular slime mould Dictyostelium, the interaction of chemical waves of the signaling molecule cAMP with cAMP-directed cell movement causes the breakup of a uniform cell layer into branching patterns of cell streams. Recent numerical and experimental investigations emphasize the pivotal role of the cell-density dependence of the chemical wave speed for the occurrence of the streaming instability. A simple, analytically tractable, model of Dictyostelium aggregation is developed to test this idea. The interaction of cAMP waves with cAMP-directed cell movement is studied in the form of coupled dynamics of wave front geometries and cell density. Comparing the resulting explicit instability criterion and dispersion relation for cell streaming with the previous findings of model simulations and numerical stability analyses, a unifying interpretation of the streaming instability as a cAMP wave-driven chemotactic instability is proposed.

  1. Galacticus: A Semi-Analytic Model of Galaxy Formation

    NASA Astrophysics Data System (ADS)

    Benson, Andrew

    2011-08-01

    Galacticus is designed to solve the physics involved in the formation of galaxies within the current standard cosmological framework. It is of a type of model known as “semi-analytic” in which the numerous complex non-linear physics involved are solved using a combination of analytic approximations and empirical calibrations from more detailed, numerical solutions. Models of this type aim to begin with the initial state of the Universe (specified shortly after the Big Bang) and apply physical principles to determine the properties of galaxies in the Universe at later times, including the present day. Typical properties computed include the mass of stars and gas in each galaxy, broad structural properties (e.g. radii, rotation speeds, geometrical shape etc.), dark matter and black hole contents, and observable quantities such as luminosities, chemical composition etc.

  2. An analytical model of dynamic sliding friction during impact

    PubMed Central

    Arakawa, Kazuo

    2017-01-01

    Dynamic sliding friction was studied based on the angular velocity of a golf ball during an oblique impact. This study used the analytical model proposed for the dynamic sliding friction on lubricated and non-lubricated inclines. The contact area A and sliding velocity u of the ball during impact were used to describe the dynamic friction force Fd = λAu, where λ is a parameter related to the wear of the contact area. A comparison with experimental results revealed that the model agreed well with the observed changes in the angular velocity during impact, and λAu is qualitatively equivalent to the empirical relationship, μN + μη′dA/dt, given by the product between the frictional coefficient μ and the contact force N, and the additional term related to factor η′ for the surface condition and the time derivative of A. PMID:28054668

  3. Analytical modelling of regional radiotherapy dose response of lung

    NASA Astrophysics Data System (ADS)

    Lee, Sangkyu; Stroian, Gabriela; Kopek, Neil; AlBahhar, Mahmood; Seuntjens, Jan; El Naqa, Issam

    2012-06-01

    Knowledge of the dose-response of radiation-induced lung disease (RILD) is necessary for optimization of radiotherapy (RT) treatment plans involving thoracic cavity irradiation. This study models the time-dependent relationship between local radiation dose and post-treatment lung tissue damage measured by computed tomography (CT) imaging. Fifty-eight follow-up diagnostic CT scans from 21 non-small-cell lung cancer patients were examined. The extent of RILD was segmented on the follow-up CT images based on the increase of physical density relative to the pre-treatment CT image. The segmented RILD was locally correlated with dose distribution calculated by analytical anisotropic algorithm and the Monte Carlo method to generate the corresponding dose-response curves. The Lyman-Kutcher-Burman (LKB) model was fit to the dose-response curves at six post-RT time periods, and temporal change in the LKB parameters was recorded. In this study, we observed significant correlation between the probability of lung tissue damage and the local dose for 96% of the follow-up studies. Dose-injury correlation at the first three months after RT was significantly different from later follow-up periods in terms of steepness and threshold dose as estimated from the LKB model. Dependence of dose response on superior-inferior tumour position was also observed. The time-dependent analytical modelling of RILD might provide better understanding of the long-term behaviour of the disease and could potentially be applied to improve inverse treatment planning optimization.

  4. Analytical higher-order model for flexible and stretchable sensors

    NASA Astrophysics Data System (ADS)

    Zhang, Yongfang; Zhu, Hongbin; Liu, Cheng; Liu, Xu; Liu, Fuxi; Lü, Yanjun

    2015-03-01

    The stretchable sensor wrapped around a foldable airfoil or embedded inside of it has great potential for use in the monitoring of the structural status of the foldable airfoil. The design methodology is important to the development of the stretchable sensor for status monitoring on the foldable airfoil. According to the requirement of mechanical flexibility of the sensor, the combined use of a layered flexible structural formation and a strain isolation layer is implemented. An analytical higher-order model is proposed to predict the stresses of the strain-isolation layer based on the shear-lag model for the safe design of the flexible and stretchable sensors. The normal stress and shear stress equations in the constructed structure of the sensors are obtained by the proposed model. The stress distribution in the structure is investigated when bending load is applied to the structures. The numerical results show that the proposed model can predict the variation of normal stress and shear stress along the thickness of the strain-isolation (polydimethylsiloxane) layer accurately. The results by the proposed model are in good agreement with the finite element method, in which the normal stress is variable while the shear stress is invariable along the thickness direction of strain-isolation layer. The high-order model is proposed to predict the stresses of the layered structure of the flexible and stretchable sensor for monitoring the status of the foldable airfoil.

  5. Analytically tractable model for community ecology with many species

    NASA Astrophysics Data System (ADS)

    Dickens, Benjamin; Fisher, Charles K.; Mehta, Pankaj

    2016-08-01

    A fundamental problem in community ecology is understanding how ecological processes such as selection, drift, and immigration give rise to observed patterns in species composition and diversity. Here, we analyze a recently introduced, analytically tractable, presence-absence (PA) model for community assembly, and we use it to ask how ecological traits such as the strength of competition, the amount of diversity, and demographic and environmental stochasticity affect species composition in a community. In the PA model, species are treated as stochastic binary variables that can either be present or absent in a community: species can immigrate into the community from a regional species pool and can go extinct due to competition and stochasticity. Building upon previous work, we show that, despite its simplicity, the PA model reproduces the qualitative features of more complicated models of community assembly. In agreement with recent studies of large, competitive Lotka-Volterra systems, the PA model exhibits distinct ecological behaviors organized around a special ("critical") point corresponding to Hubbell's neutral theory of biodiversity. These results suggest that the concepts of ecological "phases" and phase diagrams can provide a powerful framework for thinking about community ecology, and that the PA model captures the essential ecological dynamics of community assembly.

  6. Progressive Learning of Topic Modeling Parameters: A Visual Analytics Framework.

    PubMed

    El-Assady, Mennatallah; Sevastjanova, Rita; Sperrle, Fabian; Keim, Daniel; Collins, Christopher

    2017-08-29

    Topic modeling algorithms are widely used to analyze the thematic composition of text corpora but remain difficult to interpret and adjust. Addressing these limitations, we present a modular visual analytics framework, tackling the understandability and adaptability of topic models through a user-driven reinforcement learning process which does not require a deep understanding of the underlying topic modeling algorithms. Given a document corpus, our approach initializes two algorithm configurations based on a parameter space analysis that enhances document separability. We abstract the model complexity in an interactive visual workspace for exploring the automatic matching results of two models, investigating topic summaries, analyzing parameter distributions, and reviewing documents. The main contribution of our work is an iterative decision-making technique in which users provide a document-based relevance feedback that allows the framework to converge to a user-endorsed topic distribution. We also report feedback from a two-stage study which shows that our technique results in topic model quality improvements on two independent measures.

  7. Analytically tractable model for community ecology with many species.

    PubMed

    Dickens, Benjamin; Fisher, Charles K; Mehta, Pankaj

    2016-08-01

    A fundamental problem in community ecology is understanding how ecological processes such as selection, drift, and immigration give rise to observed patterns in species composition and diversity. Here, we analyze a recently introduced, analytically tractable, presence-absence (PA) model for community assembly, and we use it to ask how ecological traits such as the strength of competition, the amount of diversity, and demographic and environmental stochasticity affect species composition in a community. In the PA model, species are treated as stochastic binary variables that can either be present or absent in a community: species can immigrate into the community from a regional species pool and can go extinct due to competition and stochasticity. Building upon previous work, we show that, despite its simplicity, the PA model reproduces the qualitative features of more complicated models of community assembly. In agreement with recent studies of large, competitive Lotka-Volterra systems, the PA model exhibits distinct ecological behaviors organized around a special ("critical") point corresponding to Hubbell's neutral theory of biodiversity. These results suggest that the concepts of ecological "phases" and phase diagrams can provide a powerful framework for thinking about community ecology, and that the PA model captures the essential ecological dynamics of community assembly.

  8. Random-Effects Models for Meta-Analytic Structural Equation Modeling: Review, Issues, and Illustrations

    ERIC Educational Resources Information Center

    Cheung, Mike W.-L.; Cheung, Shu Fai

    2016-01-01

    Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM.…

  9. Random-Effects Models for Meta-Analytic Structural Equation Modeling: Review, Issues, and Illustrations

    ERIC Educational Resources Information Center

    Cheung, Mike W.-L.; Cheung, Shu Fai

    2016-01-01

    Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM.…

  10. A conditionally exactly solvable generalization of the inverse square root potential

    NASA Astrophysics Data System (ADS)

    Ishkhanyan, A. M.

    2016-11-01

    We present a conditionally exactly solvable singular potential for the one-dimensional Schrödinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general solution of the problem is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. Discussing the bound-state wave functions vanishing both at infinity and in the origin, we derive the exact equation for the energy spectrum which is written using two Hermite functions of non-integer order. In specific auxiliary variables this equation becomes a mathematical equation that does not refer to a specific physical context discussed. In the two-dimensional space of these auxiliary variables the roots of this equation draw a countable infinite set of open curves with hyperbolic asymptotes. We present an analytic description of these curves by a transcendental algebraic equation for the involved variables. The intersections of the curves thus constructed with a certain cubic curve provide a highly accurate description of the energy spectrum.

  11. Analytical model of diffuse reflectance spectrum of skin tissue

    SciTech Connect

    Lisenko, S A; Kugeiko, M M; Firago, V A; Sobchuk, A N

    2014-01-31

    We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions. (biophotonics)

  12. Analytical model of diffuse reflectance spectrum of skin tissue

    NASA Astrophysics Data System (ADS)

    Lisenko, S. A.; Kugeiko, M. M.; Firago, V. A.; Sobchuk, A. N.

    2014-01-01

    We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions.

  13. Analytic model and frequency characteristics of plasma synthetic jet actuator

    NASA Astrophysics Data System (ADS)

    Zong, Hao-hua; Wu, Yun; Li, Ying-hong; Song, Hui-min; Zhang, Zhi-bo; Jia, Min

    2015-02-01

    This paper reports a novel analytic model of a plasma synthetic jet actuator (PSJA), considering both the heat transfer effect and the inertia of the throat gas. Both the whole cycle characteristics and the repetitive working process of PSJA can be predicted with this model. The frequency characteristics of a PSJA with 87 mm3 volume and different orifice diameters are investigated based on the analytic model combined with experiments. In the repetitive working mode, the actuator works initially in the transitional stage with 20 cycles and then in the dynamic balanced stage. During the transitional stage, major performance parameters of PSJA experience stepped growth, while during the dynamic balanced stage, these parameters are characterized by periodic variation. With a constant discharge energy of 6.9 mJ, there exists a saturated frequency of 4 kHz/6 kHz for an orifice diameter of 1 mm/1.5 mm, at which the time-averaged total pressure of the pulsed jet reaches a maximum. Between 0.5 mm and 1.5 mm, a larger orifice diameter leads to a higher saturated frequency due to the reduced jet duration time. As the actuation frequency increases, both the time-averaged cavity temperature and the peak jet velocity initially increase and then remain almost unchanged at 1600 K and 280 m/s, respectively. Besides, with increasing frequency, the mechanical energy incorporated in single pulsed jet, the expelled mass per pulse, and the time-averaged density in the cavity, decline in a stair stepping way, which is caused by the intermittent decrease of refresh stage duration in one period.

  14. Analytic model for coaxial helicity injection in tokamak plasmas

    SciTech Connect

    Weening, R. H.

    2011-12-15

    Using a partial differential equation for the time evolution of the mean-field poloidal magnetic flux that incorporates resistivity {eta} and hyper-resistivity {Lambda} terms, an exact analytic solution is obtained for steady-state coaxial helicity injection (CHI) in force-free large aspect ratio tokamaks. The analytic mean-field Ohm's law model allows for calculation of the tokamak CHI current drive efficiency and the plasma inductances at arbitrary levels of magnetic fluctuations, or dynamo activity. The results of the mean-field model suggest that CHI approaching Ohmic efficiency is only possible in tokamaks when the size of the effective current drive boundary layer, {delta}{identical_to}({Lambda}/{eta}){sup 1/2}, becomes greater than half the size of the plasma, {delta}>a/2, with a the plasma minor radius. The electron thermal diffusivity due to magnetic fluctuation induced transport is obtained from the expression {chi}{sub e}={Lambda}/{mu}{sub 0}d{sub e}{sup 2}, with {mu}{sub 0} the permeability of free space and d{sub e} the electron skin depth, which for typical tokamak fusion plasma parameters is on the order of a millimeter. Thus, the ratio of the energy confinement time to the resistive diffusion time in a tokamak plasma driven by steady-state CHI approaching Ohmic efficiency is shown to be constrained by the relation {tau}{sub E}/{tau}{sub {eta}}<(d{sub e}/a){sup 2}{approx_equal}10{sup -6}. The mean-field model suggests that steady-state CHI can be viewed most simply as a boundary layer of stochastically wandering magnetic field lines.

  15. Maximum likelihood estimation in meta-analytic structural equation modeling.

    PubMed

    Oort, Frans J; Jak, Suzanne

    2016-06-01

    Meta-analytic structural equation modeling (MASEM) involves fitting models to a common population correlation matrix that is estimated on the basis of correlation coefficients that are reported by a number of independent studies. MASEM typically consist of two stages. The method that has been found to perform best in terms of statistical properties is the two-stage structural equation modeling, in which maximum likelihood analysis is used to estimate the common correlation matrix in the first stage, and weighted least squares analysis is used to fit structural equation models to the common correlation matrix in the second stage. In the present paper, we propose an alternative method, ML MASEM, that uses ML estimation throughout. In a simulation study, we use both methods and compare chi-square distributions, bias in parameter estimates, false positive rates, and true positive rates. Both methods appear to yield unbiased parameter estimates and false and true positive rates that are close to the expected values. ML MASEM parameter estimates are found to be significantly less bias than two-stage structural equation modeling estimates, but the differences are very small. The choice between the two methods may therefore be based on other fundamental or practical arguments. Copyright © 2016 John Wiley & Sons, Ltd.

  16. Analytical Modeling of Variable Density Multilayer Insulation for Cryogenic Storage

    NASA Technical Reports Server (NTRS)

    Hedayat, A.; Hastings, L. J.; Brown, T.; Cruit, Wendy (Technical Monitor)

    2001-01-01

    A unique foam/Multilayer Insulation (MLI) combination concept for orbital cryogenic storage was experimentally evaluated at NASA Marshall Space Flight Center (MSFC) using the Multipurpose Hydrogen Test Bed (MHTB). The MLI was designed for an on-orbit storage period of 45 days and included several unique features such as: a variable layer density and larger but fewer perforations for venting during ascent to orbit. Test results with liquid hydrogen indicated that the MLI weight or heat leak is reduced by about half in comparison with standard MLI. The focus of this paper is on analytical modeling of the Variable Density MLI (VD-MLI) on-orbit performance (i.e. vacuum/low pressure environment). The foam/VD-MLI combination model is considered to have five segments. The first segment represents the optional foam layer. The second, third, and fourth segments represent three MLI segments with different layer densities. The last segment is considered to be a shroud that surrounds the last MLI layer. Two approaches are considered. In the first approach, the variable density MLI is modeled layer by layer while in the second approach, a semi-empirical model is applied. Both models account for thermal radiation between shields, gas conduction, and solid conduction through the layer separator materials.

  17. Analytical model of peptide mass cluster centres with applications

    PubMed Central

    Wolski, Witold E; Farrow, Malcolm; Emde, Anne-Katrin; Lehrach, Hans; Lalowski, Maciej; Reinert, Knut

    2006-01-01

    Background The elemental composition of peptides results in formation of distinct, equidistantly spaced clusters across the mass range. The property of peptide mass clustering is used to calibrate peptide mass lists, to identify and remove non-peptide peaks and for data reduction. Results We developed an analytical model of the peptide mass cluster centres. Inputs to the model included, the amino acid frequencies in the sequence database, the average length of the proteins in the database, the cleavage specificity of the proteolytic enzyme used and the cleavage probability. We examined the accuracy of our model by comparing it with the model based on an in silico sequence database digest. To identify the crucial parameters we analysed how the cluster centre location depends on the inputs. The distance to the nearest cluster was used to calibrate mass spectrometric peptide peak-lists and to identify non-peptide peaks. Conclusion The model introduced here enables us to predict the location of the peptide mass cluster centres. It explains how the location of the cluster centres depends on the input parameters. Fast and efficient calibration and filtering of non-peptide peaks is achieved by a distance measure suggested by Wool and Smilansky. PMID:16995952

  18. A visual analytics approach for models of heterogeneous cell populations

    PubMed Central

    2012-01-01

    In recent years, cell population models have become increasingly common. In contrast to classic single cell models, population models allow for the study of cell-to-cell variability, a crucial phenomenon in most populations of primary cells, cancer cells, and stem cells. Unfortunately, tools for in-depth analysis of population models are still missing. This problem originates from the complexity of population models. Particularly important are methods to determine the source of heterogeneity (e.g., genetics or epigenetic differences) and to select potential (bio-)markers. We propose an analysis based on visual analytics to tackle this problem. Our approach combines parallel-coordinates plots, used for a visual assessment of the high-dimensional dependencies, and nonlinear support vector machines, for the quantification of effects. The method can be employed to study qualitative and quantitative differences among cells. To illustrate the different components, we perform a case study using the proapoptotic signal transduction pathway involved in cellular apoptosis. PMID:22651376

  19. A macroscopic analytical model of collaboration in distributed robotic systems.

    PubMed

    Lerman, K; Galstyan, A; Martinoli, A; Ijspeert, A

    2001-01-01

    In this article, we present a macroscopic analytical model of collaboration in a group of reactive robots. The model consists of a series of coupled differential equations that describe the dynamics of group behavior. After presenting the general model, we analyze in detail a case study of collaboration, the stick-pulling experiment, studied experimentally and in simulation by Ijspeert et al. [Autonomous Robots, 11, 149-171]. The robots' task is to pull sticks out of their holes, and it can be successfully achieved only through the collaboration of two robots. There is no explicit communication or coordination between the robots. Unlike microscopic simulations (sensor-based or using a probabilistic numerical model), in which computational time scales with the robot group size, the macroscopic model is computationally efficient, because its solutions are independent of robot group size. Analysis reproduces several qualitative conclusions of Ijspeert et al.: namely, the different dynamical regimes for different values of the ratio of robots to sticks, the existence of optimal control parameters that maximize system performance as a function of group size, and the transition from superlinear to sublinear performance as the number of robots is increased.

  20. Fuzzy modeling of analytical redundancy for sensor failure detection

    SciTech Connect

    Tsai, T.M.; Chou, H.P. )

    1991-01-01

    Failure detection and isolation (FDI) in dynamic systems may be accomplished by testing the consistency of the system via analytically redundant relations. The redundant relation is basically a mathematical model relating system inputs and dissimilar sensor outputs from which information is extracted and subsequently examined for the presence of failure signatures. Performance of the approach is often jeopardized by inherent modeling error and noise interference. To mitigate such effects, techniques such as Kalman filtering, auto-regression-moving-average (ARMA) modeling in conjunction with probability tests are often employed. These conventional techniques treat the stochastic nature of uncertainties in a deterministic manner to generate best-estimated model and sensor outputs by minimizing uncertainties. In this paper, the authors present a different approach by treating the effect of uncertainties with fuzzy numbers. Coefficients in redundant relations derived from first-principle physical models are considered as fuzzy parameters and on-line updated according to system behaviors. Failure detection is accomplished by examining the possibility that a sensor signal occurred in an estimated fuzzy domain. To facilitate failure isolation, individual FDI monitors are designed for each interested sensor.

  1. Model choice considerations and information integration using analytical hierarchy process

    SciTech Connect

    Langenbrunner, James R; Hemez, Francois M; Booker, Jane M; Ross, Timothy J.

    2010-10-15

    Using the theory of information-gap for decision-making under severe uncertainty, it has been shown that model output compared to experimental data contains irrevocable trade-offs between fidelity-to-data, robustness-to-uncertainty and confidence-in-prediction. We illustrate a strategy for information integration by gathering and aggregating all available data, knowledge, theory, experience, similar applications. Such integration of information becomes important when the physics is difficult to model, when observational data are sparse or difficult to measure, or both. To aggregate the available information, we take an inference perspective. Models are not rejected, nor wasted, but can be integrated into a final result. We show an example of information integration using Saaty's Analytic Hierarchy Process (AHP), integrating theory, simulation output and experimental data. We used expert elicitation to determine weights for two models and two experimental data sets, by forming pair-wise comparisons between model output and experimental data. In this way we transform epistemic and/or statistical strength from one field of study into another branch of physical application. The price to pay for utilizing all available knowledge is that inferences drawn for the integrated information must be accounted for and the costs can be considerable. Focusing on inferences and inference uncertainty (IU) is one way to understand complex information.

  2. Star formation in Herschel's Monsters versus semi-analytic models

    NASA Astrophysics Data System (ADS)

    Gruppioni, C.; Calura, F.; Pozzi, F.; Delvecchio, I.; Berta, S.; De Lucia, G.; Fontanot, F.; Franceschini, A.; Marchetti, L.; Menci, N.; Monaco, P.; Vaccari, M.

    2015-08-01

    We present a direct comparison between the observed star formation rate functions (SFRFs) and the state-of-the-art predictions of semi-analytic models (SAMs) of galaxy formation and evolution. We use the PACS Evolutionary Probe Survey and Herschel Multi-tiered Extragalactic Survey data sets in the COSMOS and GOODS-South fields, combined with broad-band photometry from UV to sub-mm, to obtain total (IR+UV) instantaneous star formation rates (SFRs) for individual Herschel galaxies up to z ˜ 4, subtracted of possible active galactic nucleus (AGN) contamination. The comparison with model predictions shows that SAMs broadly reproduce the observed SFRFs up to z ˜ 2, when the observational errors on the SFR are taken into account. However, all the models seem to underpredict the bright end of the SFRF at z ≳ 2. The cause of this underprediction could lie in an improper modelling of several model ingredients, like too strong (AGN or stellar) feedback in the brighter objects or too low fallback of gas, caused by weak feedback and outflows at earlier epochs.

  3. Analytic model for the bispectrum of galaxies in redshift space

    SciTech Connect

    Smith, Robert E.; Sheth, Ravi K.; Scoccimarro, Roman

    2008-07-15

    We develop an analytic theory for the redshift space bispectrum of dark matter, haloes, and galaxies. This is done within the context of the halo model of structure formation, as this allows for the self-consistent inclusion of linear and nonlinear redshift-space distortions and also for the nonlinearity of the halo bias. The model is applicable over a wide range of scales: on the largest scales the predictions reduce to those of the standard perturbation theory (PT); on smaller scales they are determined primarily by the nonlinear virial velocities of galaxies within haloes, and this gives rise to the U-shaped anisotropy in the reduced bispectrum--a finger print of the Finger-Of-God distortions. We then confront the predictions with measurements of the redshift-space bispectrum of dark matter from an ensemble of numerical simulations. On very large scales, k=0.05h Mpc{sup -1}, we find reasonably good agreement between our halo model, PT and the data, to within the errors. On smaller scales, k=0.1h Mpc{sup -1}, the measured bispectra differ from the PT at the level of {approx}10%-20%, especially for colinear triangle configurations. The halo model predictions improve over PT, but are accurate to no better than 10%. On smaller scales k=0.5-1.0h Mpc{sup -1}, our model provides a significant improvement over PT, which breaks down. This implies that studies which use the lowest order PT to extract galaxy bias information are not robust on scales k > or approx. 0.1h Mpc{sup -1}. The analytic and simulation results also indicate that there is no observable scale for which the configuration dependence of the reduced bispectrum is constant--hierarchical models for the higher-order correlation functions in redshift space are unlikely to be useful. It is hoped that our model will facilitate extraction of information from large-scale structure surveys of the Universe, because different galaxy populations are naturally included into our description.

  4. Exactly Solvable Quantum Mechanical Potentials: An Alternative Approach.

    ERIC Educational Resources Information Center

    Pronchik, Jeremy N.; Williams, Brian W.

    2003-01-01

    Describes an alternative approach to finding exactly solvable, one-dimensional quantum mechanical potentials. Differs from the usual approach in that instead of starting with a particular potential and seeking solutions to the related Schrodinger equations, it begins with known solutions to second-order ordinary differential equations and seeks to…

  5. On the solvability of two dimensional semigroup gauge theories

    SciTech Connect

    Varga, Peter

    2010-06-15

    We study the solvability of two dimensional semigroup gauge theories by Migdal's link elimination method. We determine certain conditions that ensure that the partition sum corresponding to the join of two plaquettes depends only on the holonomy around the boundary of the joined plaquettes. These conditions are checked for a few types of semigroups: 0-groups, cyclic, inverse symmetric, and Brandt semigroups.

  6. Exactly Solvable Quantum Mechanical Potentials: An Alternative Approach.

    ERIC Educational Resources Information Center

    Pronchik, Jeremy N.; Williams, Brian W.

    2003-01-01

    Describes an alternative approach to finding exactly solvable, one-dimensional quantum mechanical potentials. Differs from the usual approach in that instead of starting with a particular potential and seeking solutions to the related Schrodinger equations, it begins with known solutions to second-order ordinary differential equations and seeks to…

  7. Explicitly solvable complex Chebyshev approximation problems related to sine polynomials

    NASA Technical Reports Server (NTRS)

    Freund, Roland

    1989-01-01

    Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.

  8. Infinitely extended Kac table of solvable critical dense polymers

    NASA Astrophysics Data System (ADS)

    Pearce, Paul A.; Rasmussen, Jørgen; Villani, Simon P.

    2013-05-01

    Solvable critical dense polymers is a Yang-Baxter integrable model of polymers on the square lattice. It is the first member LM(1,2) of the family of logarithmic minimal models LM(p,p^{\\prime }). The associated logarithmic conformal field theory admits an infinite family of Kac representations labelled by the Kac labels r, s = 1, 2, …. In this paper, we explicitly construct the conjugate boundary conditions on the strip. The boundary operators are labelled by the Kac fusion labels (r, s) = (r, 1)⊗(1, s) and involve a boundary field ξ. Tuning the field ξ appropriately, we solve exactly for the transfer matrix eigenvalues on arbitrary finite-width strips and obtain the conformal spectra using the Euler-Maclaurin formula. The key to the solution is an inversion identity satisfied by the commuting double-row transfer matrices. The transfer matrix eigenvalues are classified by the physical combinatorics of the patterns of zeros in the complex spectral-parameter plane. This yields selection rules for the physically relevant solutions to the inversion identity which takes the form of a decomposition into irreducible blocks corresponding combinatorially to finitized characters given by generalized q-Catalan polynomials. This decomposition is in accord with the decomposition of the Kac characters into irreducible characters. In the scaling limit, we confirm the central charge c = -2 and the Kac formula for the conformal weights \\Delta _{r,s}=\\frac{(2r-s)^2-1}{8} for r, s = 1, 2, 3, … in the infinitely extended Kac table.

  9. Analytic model of aurorally coupled magnetospheric and ionospheric electrostatic potentials

    NASA Technical Reports Server (NTRS)

    Cornwall, John M.

    1993-01-01

    This paper describes modest but significant improvements on earlier studies of electrostatic potential structure in the auroral region, using the adiabatic auroral arc model. With certain simplifying assumptions, new analytic nonlinear solutions fully exhibiting the parametric dependence of potentials on magnetospheric (e.g., cross-tail potential) and ionospheric (e.g., recombination rate) parameters are found. No purely phenomenological parameters are introduced. The results are in reasonable agreement with observed average auroral potential drops, inverted-V scale sizes, and dissipation rates. The dissipation rate is quite comparable to tail energization and transport rates and should have a major effect on tail and magnetospheric dynamics. Various relations between the cross-tail potential and auroral parameters (e.g., total parallel currents and potential drops) are given which can be studied with existing data sets.

  10. Analytical model of a giant magnetostrictive resonance transducer

    NASA Astrophysics Data System (ADS)

    Sheykholeslami, M.; Hojjat, Y.; Ansari, S.; Cinquemani, S.; Ghodsi, M.

    2016-04-01

    Resonance transducers have been widely developed and studied, as they can be profitably used in many application such as liquid atomizing and sonar technology. The active element of these devices can be a giant magnetostrictive material (GMM) that is known to have significant energy density and good performance at high frequencies. The paper introduces an analytical model of GMM transducers to describe their dynamics in different working conditions and to predict any change in their performance. The knowledge of the transducer behavior, especially in operating conditions different from the ideal ones, is helpful in the design and fabrication of highly efficient devices. This transducer is design to properly work in its second mode of vibration and its working frequency is around 8000 Hz. Most interesting parameters of the device, such as quality factor, bandwidth and output strain are obtained from theoretical analysis.

  11. An analytical model of joule heating in piezoresistive microcantilevers.

    PubMed

    Ansari, Mohd Zahid; Cho, Chongdu

    2010-01-01

    The present study investigates Joule heating in piezoresistive microcantilever sensors. Joule heating and thermal deflections are a major source of noise in such sensors. This work uses analytical and numerical techniques to characterise the Joule heating in 4-layer piezoresistive microcantilevers made of silicon and silicon dioxide substrates but with the same U-shaped silicon piezoresistor. A theoretical model for predicting the temperature generated due to Joule heating is developed. The commercial finite element software ANSYS Multiphysics was used to study the effect of electrical potential on temperature and deflection produced in the cantilevers. The effect of piezoresistor width on Joule heating is also studied. Results show that Joule heating strongly depends on the applied potential and width of piezoresistor and that a silicon substrate cantilever has better thermal characteristics than a silicon dioxide cantilever.

  12. High-Performance data flows using analytical models and measurements

    SciTech Connect

    Rao, Nageswara S; Towlsey, D.; Vardoyan, G.; Kettimuthu, R.; Foster, I.; Settlemyer, Bradley

    2016-01-01

    The combination of analytical models and measurements provide practical configurations and parameters to achieve high data transport rates: (a) buffer sizes and number of parallel streams for improved memory and file transfer rates, (b) Hamilton and Scalable TCP congestion control modules for memory transfers in place of default CUBIC, and (c) direct IO mode for Lustre file systems for wide-area transfers. Conventional parameter selection using full sweeps is impractical in many cases since it takes months. By exploiting the unimodality of throughput profiles, we developed the d-w method that significantly reduces the number of measurements needed for parameter identification. This heuristic method was effective in practice in reducing the measurements by about 90% for Lustre and XFS file transfers.

  13. The linear Ising model and its analytic continuation, random walk

    NASA Astrophysics Data System (ADS)

    Lavenda, B. H.

    2004-02-01

    A generalization of Gauss's principle is used to derive the error laws corresponding to Types II and VII distributions in Pearson's classification scheme. Student's r-p.d.f. (Type II) governs the distribution of the internal energy of a uniform, linear chain, Ising model, while the analytic continuation of the uniform exchange energy converts it into a Student t-density (Type VII) for the position of a random walk in a single spatial dimension. Higher-dimensional spaces, corresponding to larger degrees of freedom and generalizations to multidimensional Student r- and t-densities, are obtained by considering independent and identically random variables, having rotationally invariant densities, whose entropies are additive and generating functions are multiplicative.

  14. Analytical model for non-thermal pressure in galaxy clusters

    NASA Astrophysics Data System (ADS)

    Shi, Xun; Komatsu, Eiichiro

    2014-07-01

    Non-thermal pressure in the intracluster gas has been found ubiquitously in numerical simulations, and observed indirectly. In this paper we develop an analytical model for intracluster non-thermal pressure in the virial region of relaxed clusters. We write down and solve a first-order differential equation describing the evolution of non-thermal velocity dispersion. This equation is based on insights gained from observations, numerical simulations, and theory of turbulence. The non-thermal energy is sourced, in a self-similar fashion, by the mass growth of clusters via mergers and accretion, and dissipates with a time-scale determined by the turnover time of the largest turbulence eddies. Our model predicts a radial profile of non-thermal pressure for relaxed clusters. The non-thermal fraction increases with radius, redshift, and cluster mass, in agreement with numerical simulations. The radial dependence is due to a rapid increase of the dissipation time-scale with radii, and the mass and redshift dependence comes from the mass growth history. Combing our model for the non-thermal fraction with the Komatsu-Seljak model for the total pressure, we obtain thermal pressure profiles, and compute the hydrostatic mass bias. We find typically 10 per cent bias for the hydrostatic mass enclosed within r500.

  15. An analytical model of capped turbulent oscillatory bottom boundary layers

    NASA Astrophysics Data System (ADS)

    Shimizu, Kenji

    2010-03-01

    An analytical model of capped turbulent oscillatory bottom boundary layers (BBLs) is proposed using eddy viscosity of a quadratic form. The common definition of friction velocity based on maximum bottom shear stress is found unsatisfactory for BBLs under rotating flows, and a possible extension based on turbulent kinetic energy balance is proposed. The model solutions show that the flow may slip at the top of the boundary layer due to capping by the water surface or stratification, reducing the bottom shear stress, and that the Earth's rotation induces current and bottom shear stress components perpendicular to the interior flow with a phase lag (or lead). Comparisons with field and numerical experiments indicate that the model predicts the essential characteristics of the velocity profiles, although the agreement is rather qualitative due to assumptions of quadratic eddy viscosity with time-independent friction velocity and a well-mixed boundary layer. On the other hand, the predicted linear friction coefficients, phase lead, and veering angle at the bottom agreed with available data with an error of 3%-10%, 5°-10°, and 5°-10°, respectively. As an application of the model, the friction coefficients are used to calculate e-folding decay distances of progressive internal waves with a semidiurnal frequency.

  16. Estimating recharge rates with analytic element models and parameter estimation

    USGS Publications Warehouse

    Dripps, W.R.; Hunt, R.J.; Anderson, M.P.

    2006-01-01

    Quantifying the spatial and temporal distribution of recharge is usually a prerequisite for effective ground water flow modeling. In this study, an analytic element (AE) code (GFLOW) was used with a nonlinear parameter estimation code (UCODE) to quantify the spatial and temporal distribution of recharge using measured base flows as calibration targets. The ease and flexibility of AE model construction and evaluation make this approach well suited for recharge estimation. An AE flow model of an undeveloped watershed in northern Wisconsin was optimized to match median annual base flows at four stream gages for 1996 to 2000 to demonstrate the approach. Initial optimizations that assumed a constant distributed recharge rate provided good matches (within 5%) to most of the annual base flow estimates, but discrepancies of >12% at certain gages suggested that a single value of recharge for the entire watershed is inappropriate. Subsequent optimizations that allowed for spatially distributed recharge zones based on the distribution of vegetation types improved the fit and confirmed that vegetation can influence spatial recharge variability in this watershed. Temporally, the annual recharge values varied >2.5-fold between 1996 and 2000 during which there was an observed 1.7-fold difference in annual precipitation, underscoring the influence of nonclimatic factors on interannual recharge variability for regional flow modeling. The final recharge values compared favorably with more labor-intensive field measurements of recharge and results from studies, supporting the utility of using linked AE-parameter estimation codes for recharge estimation. Copyright ?? 2005 The Author(s).

  17. Analytical Deriving of the Field Capacity through Soil Bundle Model

    NASA Astrophysics Data System (ADS)

    Arnone, E.; Viola, F.; Antinoro, C.; Noto, L. V.

    2015-12-01

    The concept of field capacity as soil hydraulic parameter is widely used in many hydrological applications. Althought its recurring usage, its definition is not univocal. Traditionally, field capacity has been related to the amount of water that remains in the soil after the excess water has drained away and the water downward movement experiences a significant decresase. Quantifying the drainage of excess of water may be vague and several definitions, often subjective, have been proposed. These definitions are based on fixed thresholds either of time, pressure, or flux to which the field capacity condition is associated. The flux-based definition identifies the field capacity as the soil moisture value corresponding to an arbitrary fixed threshold of free drainage flux. Recently, many works have investigated the flux-based definition by varying either the drainage threshold, the geometry setting and mainly the description of the drainage flux. Most of these methods are based on the simulation of the flux through a porous medium by using the Darcy's law or Richard's equation. Using the above-mentioned flux-based definition, in this work we propose an alternative analytical approach for deriving the field capacity based on a bundle-of-tubes model. The pore space of a porous medium is conceptualized as a bundle of capillary tubes of given length of different radii, derived from a known distribution. The drainage from a single capillary tube is given by the analytical solution of the differential equation describing the water height evolution within the capillary tube. This equation is based on the Poiseuille's law and describes the drainage flux with time as a function of tube radius. The drainage process is then integrated for any portion of soil taking into account the tube radius distribution which in turns depends on the soil type. This methodology allows to analytically derive the dynamics of drainage water flux for any soil type and consequently to define the

  18. Analytical model of an Annular Momentum Control Device (AMCD) laboratory test model magnetic bearing actuator

    NASA Technical Reports Server (NTRS)

    Groom, N. J.

    1979-01-01

    An analytical model of an Annular Momentum Control Device (AMCD) laboratory test model magnetic bearing actuator with permanent magnet fluxbiasing is presented. An AMCD consists of a spinning annular rim which is suspended by a noncontacting linear electromagnetic spin motor. The actuator is treated as a lumped-parameter electromechanical system in the development of the model.

  19. An analytical light distribution model in the optical system of a scintillation detector

    NASA Astrophysics Data System (ADS)

    Kuznetsov, Sergey; Skachkov, E. V.; Belyaev, V. N.

    2017-01-01

    The article describes an analytical light distribution model in the optical system of a scintillation detector. The model can be useful for scintillation detector development since it allows to make quick calculations with different parameters. Comparison of the analytical model and Geant4 calculation results has been done. The comparison of the analytical model calculation results and experimental measurements have been done. Both comparisons show model validity and a capability to be used in the research.

  20. Machine learning and cosmological simulations - I. Semi-analytical models

    NASA Astrophysics Data System (ADS)

    Kamdar, Harshil M.; Turk, Matthew J.; Brunner, Robert J.

    2016-01-01

    We present a new exploratory framework to model galaxy formation and evolution in a hierarchical Universe by using machine learning (ML). Our motivations are two-fold: (1) presenting a new, promising technique to study galaxy formation, and (2) quantitatively analysing the extent of the influence of dark matter halo properties on galaxies in the backdrop of semi-analytical models (SAMs). We use the influential Millennium Simulation and the corresponding Munich SAM to train and test various sophisticated ML algorithms (k-Nearest Neighbors, decision trees, random forests, and extremely randomized trees). By using only essential dark matter halo physical properties for haloes of M > 1012 M⊙ and a partial merger tree, our model predicts the hot gas mass, cold gas mass, bulge mass, total stellar mass, black hole mass and cooling radius at z = 0 for each central galaxy in a dark matter halo for the Millennium run. Our results provide a unique and powerful phenomenological framework to explore the galaxy-halo connection that is built upon SAMs and demonstrably place ML as a promising and a computationally efficient tool to study small-scale structure formation.

  1. Analytical thermal model validation for Cassini radioisotope thermoelectric generator

    SciTech Connect

    Lin, E.I.

    1997-12-31

    The Saturn-bound Cassini spacecraft is designed to rely, without precedent, on the waste heat from its three radioisotope thermoelectric generators (RTGs) to warm the propulsion module subsystem, and the RTG end dome temperature is a key determining factor of the amount of waste heat delivered. A previously validated SINDA thermal model of the RTG was the sole guide to understanding its complex thermal behavior, but displayed large discrepancies against some initial thermal development test data. A careful revalidation effort led to significant modifications and adjustments of the model, which result in a doubling of the radiative heat transfer from the heat source support assemblies to the end domes and bring up the end dome and flange temperature predictions to within 2 C of the pertinent test data. The increased inboard end dome temperature has a considerable impact on thermal control of the spacecraft central body. The validation process offers an example of physically-driven analytical model calibration with test data from not only an electrical simulator but also a nuclear-fueled flight unit, and has established the end dome temperatures of a flight RTG where no in-flight or ground-test data existed before.

  2. Analytical modelling for ultrasonic surface mechanical attrition treatment

    NASA Astrophysics Data System (ADS)

    Huang, Guan-Rong; Tsai, W. Y.; Huang, J. C.; Hu, Chin-Kun

    2015-07-01

    The grain refinement, gradient structure, fatigue limit, hardness, and tensile strength of metallic materials can be effectively enhanced by ultrasonic surface mechanical attrition treatment (SMAT), however, never before has SMAT been treated with rigorous analytical modelling such as the connection among the input energy and power and resultant temperature of metallic materials subjected to SMAT. Therefore, a systematic SMAT model is actually needed. In this article, we have calculated the averaged speed, duration time of a cycle, kinetic energy and kinetic energy loss of flying balls in SMAT for structural metallic materials. The connection among the quantities such as the frequency and amplitude of attrition ultrasonic vibration motor, the diameter, mass and density of balls, the sample mass, and the height of chamber have been considered and modelled in details. And we have introduced the one-dimensional heat equation with heat source within uniform-distributed depth in estimating the temperature distribution and heat energy of sample. In this approach, there exists a condition for the frequency of flying balls reaching a steady speed. With these known quantities, we can estimate the strain rate, hardness, and grain size of sample.

  3. Computational and analytical modeling of eye refractive surgery

    NASA Astrophysics Data System (ADS)

    Cabrera, Delia

    As the number of corneal refractive procedures increases annually, concerns about their long-term stability and predictability have become the center of attention in the ophthalmic community. This thesis focuses on developing quantitative biomechanical models of the cornea that will overcome shortcomings of previous models and incorporate new observations of corneal elastic properties. Our intent is to provide a more accurate model of the corneal structure to guide current and future developments. The second chapter shows that neural networks could rapidly prototype practical solutions to obtain a better estimate of the average corneal power using the contrast and image size parameters provided by the topographic systems. After establishing improved measurements of the corneal shape the thesis focuses on the development of various corneal models. The analytical model proposed shows that geometric optics, corneal structural properties and surgical nomograms could be used to gain a better understanding of corneal response to surgical interventions. The predictions of this model are closer to the values provided by the published nomograms and clinical data than that obtained by the traditional geometric model. Three surgical procedures (Ultrafast Laser-Automated Lamellar Keratomileusis, Corneal Transplant and Intrastromal Refractive Keratectomy) were simulated using the finite element method. A new formulation was developed that simulates the changes on corneal curvature after refractive surgery when the stiffness inhomogeneities across the corneal thickness are considered. It has been shown that the predictability of the surgical outcome is improved when the stiffness inhomogeneities and nonlinearities of the deformations are included in the finite element simulations. Moreover, a finite element formulation has been developed first time to characterize the intrastromal refractive keratectomy procedure. An inhomogeneous (small displacements) model was identified as an

  4. Enabling analytical and Modeling Tools for Enhanced Disease Surveillance

    SciTech Connect

    Dawn K. Manley

    2003-04-01

    Early detection, identification, and warning are essential to minimize casualties from a biological attack. For covert attacks, sick people are likely to provide the first indication of an attack. An enhanced medical surveillance system that synthesizes distributed health indicator information and rapidly analyzes the information can dramatically increase the number of lives saved. Current surveillance methods to detect both biological attacks and natural outbreaks are hindered by factors such as distributed ownership of information, incompatible data storage and analysis programs, and patient privacy concerns. Moreover, because data are not widely shared, few data mining algorithms have been tested on and applied to diverse health indicator data. This project addressed both integration of multiple data sources and development and integration of analytical tools for rapid detection of disease outbreaks. As a first prototype, we developed an application to query and display distributed patient records. This application incorporated need-to-know access control and incorporated data from standard commercial databases. We developed and tested two different algorithms for outbreak recognition. The first is a pattern recognition technique that searches for space-time data clusters that may signal a disease outbreak. The second is a genetic algorithm to design and train neural networks (GANN) that we applied toward disease forecasting. We tested these algorithms against influenza, respiratory illness, and Dengue Fever data. Through this LDRD in combination with other internal funding, we delivered a distributed simulation capability to synthesize disparate information and models for earlier recognition and improved decision-making in the event of a biological attack. The architecture incorporates user feedback and control so that a user's decision inputs can impact the scenario outcome as well as integrated security and role-based access-control for communicating between

  5. Exactly solvable chaos in an electromechanical oscillator

    NASA Astrophysics Data System (ADS)

    Owens, Benjamin A. M.; Stahl, Mark T.; Corron, Ned J.; Blakely, Jonathan N.; Illing, Lucas

    2013-09-01

    A novel electromechanical chaotic oscillator is described that admits an exact analytic solution. The oscillator is a hybrid dynamical system with governing equations that include a linear second order ordinary differential equation with negative damping and a discrete switching condition that controls the oscillatory fixed point. The system produces provably chaotic oscillations with a topological structure similar to either the Lorenz butterfly or Rössler's folded-band oscillator depending on the configuration. Exact solutions are written as a linear convolution of a fixed basis pulse and a sequence of discrete symbols. We find close agreement between the exact analytical solutions and the physical oscillations. Waveform return maps for both configurations show equivalence to either a shift map or tent map, proving the chaotic nature of the oscillations.

  6. Simple analytical model of evapotranspiration in the presence of roots.

    PubMed

    Cejas, Cesare M; Hough, L A; Castaing, Jean-Christophe; Frétigny, Christian; Dreyfus, Rémi

    2014-10-01

    Evaporation of water out of a soil involves complicated and well-debated mechanisms. When plant roots are added into the soil, water transfer between the soil and the outside environment is even more complicated. Indeed, plants provide an additional process of water transfer. Water is pumped by the roots, channeled to the leaf surface, and released into the surrounding air by a process called transpiration. Prediction of the evapotranspiration of water over time in the presence of roots helps keep track of the amount of water that remains in the soil. Using a controlled visual setup of a two-dimensional model soil consisting of monodisperse glass beads, we perform experiments on actual roots grown under different relative humidity conditions. We record the total water mass loss in the medium and the position of the evaporating front that forms within the medium. We then develop a simple analytical model that predicts the position of the evaporating front as a function of time as well as the total amount of water that is lost from the medium due to the combined effects of evaporation and transpiration. The model is based on fundamental principles of evaporation fluxes and includes empirical assumptions on the quantity of open stomata in the leaves, where water transpiration occurs. Comparison between the model and experimental results shows excellent prediction of the position of the evaporating front as well as the total mass loss from evapotranspiration in the presence of roots. The model also provides a way to predict the lifetime of a plant.

  7. Simple analytical model of evapotranspiration in the presence of roots

    NASA Astrophysics Data System (ADS)

    Cejas, Cesare M.; Hough, L. A.; Castaing, Jean-Christophe; Frétigny, Christian; Dreyfus, Rémi

    2014-10-01

    Evaporation of water out of a soil involves complicated and well-debated mechanisms. When plant roots are added into the soil, water transfer between the soil and the outside environment is even more complicated. Indeed, plants provide an additional process of water transfer. Water is pumped by the roots, channeled to the leaf surface, and released into the surrounding air by a process called transpiration. Prediction of the evapotranspiration of water over time in the presence of roots helps keep track of the amount of water that remains in the soil. Using a controlled visual setup of a two-dimensional model soil consisting of monodisperse glass beads, we perform experiments on actual roots grown under different relative humidity conditions. We record the total water mass loss in the medium and the position of the evaporating front that forms within the medium. We then develop a simple analytical model that predicts the position of the evaporating front as a function of time as well as the total amount of water that is lost from the medium due to the combined effects of evaporation and transpiration. The model is based on fundamental principles of evaporation fluxes and includes empirical assumptions on the quantity of open stomata in the leaves, where water transpiration occurs. Comparison between the model and experimental results shows excellent prediction of the position of the evaporating front as well as the total mass loss from evapotranspiration in the presence of roots. The model also provides a way to predict the lifetime of a plant.

  8. New analytic solutions for modeling vertical gravity gradient anomalies

    NASA Astrophysics Data System (ADS)

    Kim, Seung-Sep; Wessel, Paul

    2016-05-01

    Modern processing of satellite altimetry for use in marine gravimetry involves computing the along-track slopes of observed sea-surface heights, projecting them into east-west and north-south deflection of the vertical grids, and using Laplace's equation to algebraically obtain a grid of the vertical gravity gradient (VGG). The VGG grid is then integrated via overlapping, flat Earth Fourier transforms to yield a free-air anomaly grid. Because of this integration and associated edge effects, the VGG grid retains more short-wavelength information (e.g., fracture zone and seamount signatures) that is of particular importance for plate tectonic investigations. While modeling of gravity anomalies over arbitrary bodies has long been a standard undertaking, similar modeling of VGG anomalies over oceanic features is not commonplace yet. Here we derive analytic solutions for VGG anomalies over simple bodies and arbitrary 2-D and 3-D sources. We demonstrate their usability in determining mass excess and deficiency across the Mendocino fracture zone (a 2-D feature) and find the best bulk density estimate for Jasper seamount (a 3-D feature). The methodologies used herein are implemented in the Generic Mapping Tools, available from gmt.soest.hawaii.edu.

  9. Analytic model of aurorally coupled magnetospheric and ionospheric electrostatic potentials

    NASA Technical Reports Server (NTRS)

    Cornwall, J. M.

    1994-01-01

    This paper describes modest but significant improvements on earlier studies of electrostatic potential structure in the auroral region using the adiabatic auroral arc model. This model has crucial nonlinearities (connected, for example. with aurorally produced ionization) which have hampered analysis; earlier work has either been linear, which I will show is a poor approximation or, if nonlinear, either numerical or too specialized to study parametric dependencies. With certain simplifying assumptions I find new analytic nonlinear solutions fully exhibiting the parametric dependence of potentials on magnetospheric (e.g.. cross-tail potential) and ionospheric (e.g., recombination rate) parameters. No purely phenomenological parameters are introduced. The results are in reasonable agreement with observed average auroral potential drops, inverted-V scale sizes, and dissipation rates. The dissipation rate is quite comparable to tail energization and transport rates and should have a major effect on tail and magnetospheric dynamics. This paper gives various relations between the cross-tail potential and auroral parameters (e.g., total parallel currents and potential drops) which can be studied with existing data sets.

  10. A physically based analytical model of flood frequency curves

    NASA Astrophysics Data System (ADS)

    Basso, S.; Schirmer, M.; Botter, G.

    2016-09-01

    Predicting magnitude and frequency of floods is a key issue in hydrology, with implications in many fields ranging from river science and geomorphology to the insurance industry. In this paper, a novel physically based approach is proposed to estimate the recurrence intervals of seasonal flow maxima. The method links the extremal distribution of streamflows to the stochastic dynamics of daily discharge, providing an analytical expression of the seasonal flood frequency curve. The parameters involved in the formulation embody climate and landscape attributes of the contributing catchment and can be estimated from daily rainfall and streamflow data. Only one parameter, which is linked to the antecedent wetness condition in the watershed, needs to be calibrated on the observed maxima. The performance of the method is discussed through a set of applications in four rivers featuring heterogeneous daily flow regimes. The model provides reliable estimates of seasonal maximum flows in different climatic settings and is able to capture diverse shapes of flood frequency curves emerging in erratic and persistent flow regimes. The proposed method exploits experimental information on the full range of discharges experienced by rivers. As a consequence, model performances do not deteriorate when the magnitude of events with return times longer than the available sample size is estimated. The approach provides a framework for the prediction of floods based on short data series of rainfall and daily streamflows that may be especially valuable in data scarce regions of the world.

  11. A semi-analytical variable property droplet combustion model

    NASA Astrophysics Data System (ADS)

    Sisti, John

    A multizone droplet burn model is developed to account for changes in the thermal and transport properties as a function of droplet radius. The formulation is semi-analytical---allowing for accurate and computationally efficient estimates of flame structure and burn rates. Zonal thermal and transport properties are computed using the Cantera software and pre-tabulated for rapid evaluation during run-time. Model predictions are compared to experimental measurements of burning n-heptane, ethanol and methanol droplets. An adaptive zone refinement algorithm is developed that minimizes the number of zones required to provide accurate estimates of burn time without excess zones. A sensitivity study of burn rate and flame stand-off with far-field oxygen concentration is conducted with comparisons to experimental data. Overall agreement to data is encouraging with errors typically less than 20% for predictions of burn rates, stand-off ratio and flame temperature for the fuels considered. The quiescent quasi-steady solution is extended to a convective transient solution without the need to solve an eigenvalue solution in time. The time history of the burning droplets show good comparison with experimental data. To further decrease computational cost, the source terms for the transient solution are linearized for an explicit time marching solution. An error convergence study was performed to show a time-step independent solution exists at a reasonable Delta t.

  12. Analytical model for heterogeneous reactions in mixed porous media

    SciTech Connect

    Hatfield, K.; Burris, D.R.; Wolfe, N.L.

    1996-08-01

    The funnel/gate system is a developing technology for passive ground-water plume management and treatment. This technology uses sheet pilings as a funnel to force polluted ground water through a highly permeable zone of reactive porous media (the gate) where contaminants are degraded by biotic or abiotic heterogeneous reactions. This paper presents a new analytical nonequilibrium model for solute transport in saturated, nonhomogeneous or mixed porous media that could assist efforts to design funnel/gate systems and predict their performance. The model incorporates convective/dispersion transport, dissolved constituent decay, surface-mediated degradation, and time-dependent mass transfer between phases. Simulation studies of equilibrium and nonequilibrium transport conditions reveal manifestations of rate-limited degradation when mass-transfer times are longer than system hydraulic residence times, or when surface-mediated reaction rates are faster than solute mass-transfer processes (i.e., sorption, film diffusion, or intraparticle diffusion). For example, steady-state contaminant concentrations will be higher under a nonequilibrium transport scenario than would otherwise be expected when assuming equilibrium conditions. Thus, a funnel/gate system may fail to achieve desired ground-water treatment if the possibility of mass-transfer-limited degradation is not considered.

  13. Analytical examples, measurement models, and classical limit of quantum backflow

    NASA Astrophysics Data System (ADS)

    Yearsley, J. M.; Halliwell, J. J.; Hartshorn, R.; Whitby, A.

    2012-10-01

    We investigate the backflow effect in elementary quantum mechanics—the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. We compute the current and flux for states consisting of superpositions of Gaussian wave packets. These are experimentally realizable but the amount of backflow is small. Inspired by the numerical results of Penz [Penz, Grübl, Kreidl, and Wagner, J. Phys. AJPHAC50305-447010.1088/0305-4470/39/2/012 39, 423 (2006)], we find two nontrivial wave functions whose current at any time may be computed analytically and which have periods of significant backflow, in one case with a backward flux equal to about 70% of the maximum possible backflow, a dimensionless number cbm≈0.04, discovered by Bracken and Melloy [Bracken and Melloy, J. Phys. AJPHAC50305-447010.1088/0305-4470/27/6/040 27, 2197 (1994)]. This number has the unusual property of being independent of ℏ (and also of all other parameters of the model), despite corresponding to an obviously quantum-mechanical effect, and we shed some light on this surprising property by considering the classical limit of backflow. We discuss some specific measurement models in which backflow may be identified in certain measurable probabilities.

  14. The use of analytical models in human-computer interface design

    NASA Technical Reports Server (NTRS)

    Gugerty, Leo

    1991-01-01

    Some of the many analytical models in human-computer interface design that are currently being developed are described. The usefulness of analytical models for human-computer interface design is evaluated. Can the use of analytical models be recommended to interface designers? The answer, based on the empirical research summarized here, is: not at this time. There are too many unanswered questions concerning the validity of models and their ability to meet the practical needs of design organizations.

  15. CTE Solvability, Nonlocal Symmetry and Explicit Solutions of Modified Boussinesq System

    NASA Astrophysics Data System (ADS)

    Ren, Bo; Cheng, Xue-Ping

    2016-07-01

    A consistent tanh expansion (CTE) method is used to study the modified Boussinesq equation. It is proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a nonanto-BT theorem. Furthermore, the nonlocal symmetry for the modified Boussinesq equation is obtained by the Painlevé analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing one auxiliary dependent variable. The finite symmetry transformation related with the nonlocal symemtry is obtained by solving the initial value problem of the prolonged systems. Thanks to the localization process, many interaction solutions among solitons and other complicated waves are computed through similarity reductions. Some special concrete soliton-cnoidal wave interaction behaviors are studied both in analytical and graphical ways. Supported by the National Natural Science Foundation of China under Grant Nos. 11305106 and 11505154

  16. Model Misspecification and Invariance Testing Using Confirmatory Factor Analytic Procedures

    ERIC Educational Resources Information Center

    French, Brian F.; Finch, W. Holmes

    2011-01-01

    Confirmatory factor analytic procedures are routinely implemented to provide evidence of measurement invariance. Current lines of research focus on the accuracy of common analytic steps used in confirmatory factor analysis for invariance testing. However, the few studies that have examined this procedure have done so with perfectly or near…

  17. Model Misspecification and Invariance Testing Using Confirmatory Factor Analytic Procedures

    ERIC Educational Resources Information Center

    French, Brian F.; Finch, W. Holmes

    2011-01-01

    Confirmatory factor analytic procedures are routinely implemented to provide evidence of measurement invariance. Current lines of research focus on the accuracy of common analytic steps used in confirmatory factor analysis for invariance testing. However, the few studies that have examined this procedure have done so with perfectly or near…

  18. Toward making the mean spherical approximation of primitive model electrolytes analytic: An analytic approximation of the MSA screening parameter

    NASA Astrophysics Data System (ADS)

    Gillespie, Dirk

    2011-01-01

    The mean spherical approximation (MSA) for the primitive model of electrolytes provides reasonable estimates of thermodynamic quantities such as the excess chemical potential and screening length. It is especially widely used because of its explicit formulas so that numerically solving equations is minimized. As originally formulated, the MSA screening parameter Γ (akin to the reciprocal of the Debye screening length) does not have an explicit analytic formula; an equation for Γ must be solved numerically. Here, an analytic approximation for Γ is presented whose relative error is generally ≲ 10^{-5}. If more accuracy is desired, one step of an iterative procedure (which also produces an explicit formula for Γ) is shown to give relative errors within machine precision in many cases. Even when ion diameter ratios are ˜10 and ion valences are ˜10, the relative error for the analytic approximation is still ≲ 10^{-3} and for the single iterative substitution it is ≲ 10^{-9}.

  19. An analytical model of rumpling in thermal barrier coatings

    NASA Astrophysics Data System (ADS)

    Balint, D. S.; Hutchinson, J. W.

    2005-04-01

    Multilayer thermal barrier coatings (TBCs) deposited on superalloy turbine blades provide protection from combustion temperatures in excess of 1500 °C. One of the dominant failure modes comprises cracking from undulation growth, or rumpling, of the highly compressed oxide layer that grows between the ceramic top coat and the intermetallic bond coat. In this paper, a mechanistic model providing an analytical approximation of undulation growth is presented for realistic cyclic thermal histories. Thickening, lateral growth straining and high temperature yielding of the oxide layer are taken into account. Undulation growth in TBC systems is highly nonlinear and characterized by more than 20 material and geometric parameters, highlighting the importance of a robust yet computationally efficient model. At temperatures above 600 °C, the bond coat creeps. Thermal expansion mismatch occurs between the superalloy substrate and the oxide layer and, in some systems, the bond coat. In addition, some bond coats, such as PtNiAl, exhibit a martensitic phase transformation accompanied by nearly a 1% linear expansion, giving rise to a large effective mismatch. These two mismatches promote undulation growth. Nonlinear interaction between the stress in the bond coat induced by the constraining effect of the thick substrate and normal tractions applied at the surface of the bond coat by the compressed, undulating oxide layer produces an increment of undulation growth during each thermal cycle, before the stress decays by creep. A series of problems for systems without the ceramic top coat are used to elucidate the mechanics of undulation growth and to replicate trends observed in a series of experiments and in prior finite-element simulations. The model is employed to study for the first time the effect on undulation growth of a shift in the temperature range over which the transformation occurs, as well as the relative importance of the transformation compared to thermal expansion

  20. Flexible Carbon-Use Efficiency across Litter Types and during Decomposition Partly Compensates Nutrient Imbalances—Results from Analytical Stoichiometric Models

    PubMed Central

    Manzoni, Stefano

    2017-01-01

    Mathematical models involving explicit representations of microbial processes have been developed to infer microbial community properties from laboratory and field measurements. While this approach has been used to estimate the kinetic constants related to microbial activity, it has not been fully exploited for inference of stoichiometric traits, such as carbon-use efficiency (CUE). Here, a hierarchy of analytically-solvable mass-balance models of litter carbon (C) and nitrogen (N) dynamics is developed, to infer decomposer CUE from measured C and N contents during litter decomposition. The models are solved in the phase space—expressing litter remaining N as a function of remaining C—rather than in time, thus focusing on the stoichiometric relations during decomposition rather than the kinetics of degradation. This approach leads to explicit formulas that depend on CUE and other microbial properties, which can then be treated as model parameters and retrieved via nonlinear regression. CUE is either assumed time-invariant or as a function of the fraction of remaining litter C as a substitute for time. In all models, CUE tends to increase with increasing litter N availability across a range of litter types. When temporal trends in CUE are considered, CUE increases during decomposition of N-poor litter cohorts, in which decomposers are initially N-limited, but decreases in N-rich litter possibly due to C-limitation. These patterns of flexible CUE that partly compensate stoichiometric imbalances are robust to moderate shifts in decomposer C:N ratio and hold across wide climatic gradients. PMID:28491054

  1. Analysis of structural dynamic data from Skylab. Volume 2: Skylab analytical and test model data

    NASA Technical Reports Server (NTRS)

    Demchak, L.; Harcrow, H.

    1976-01-01

    The orbital configuration test modal data, analytical test correlation modal data, and analytical flight configuration modal data are presented. Tables showing the generalized mass contributions (GMCs) for each of the thirty tests modes are given along with the two dimensional mode shape plots and tables of GMCs for the test correlated analytical modes. The two dimensional mode shape plots for the analytical modes and uncoupled and coupled modes of the orbital flight configuration at three development phases of the model are included.

  2. Analytical models for total dose ionization effects in MOS devices.

    SciTech Connect

    Campbell, Phillip Montgomery; Bogdan, Carolyn W.

    2008-08-01

    MOS devices are susceptible to damage by ionizing radiation due to charge buildup in gate, field and SOI buried oxides. Under positive bias holes created in the gate oxide will transport to the Si / SiO{sub 2} interface creating oxide-trapped charge. As a result of hole transport and trapping, hydrogen is liberated in the oxide which can create interface-trapped charge. The trapped charge will affect the threshold voltage and degrade the channel mobility. Neutralization of oxidetrapped charge by electron tunneling from the silicon and by thermal emission can take place over long periods of time. Neutralization of interface-trapped charge is not observed at room temperature. Analytical models are developed that account for the principal effects of total dose in MOS devices under different gate bias. The intent is to obtain closed-form solutions that can be used in circuit simulation. Expressions are derived for the aging effects of very low dose rate radiation over long time periods.

  3. An analytical model of axial compressor off-design performance

    SciTech Connect

    Camp, T.R.; Horlock, J.H. . Whittle Lab.)

    1994-07-01

    An analysis is presented of the off-design performance of multistage axial-flow compressors. It is based on an analytical solution, valid for small perturbations in operating conditions from the design point, and provides an insight into the effects of choices made during the compressor design process on performance and off-design stage matching. It is shown that the mean design value of stage loading coefficient ([psi] = [Delta]h[sub 0]/U[sup 2]) has a dominant effect on off-design performance, whereas the stage-wise distribution of stage loading coefficient and the design value of flow coefficient have little influence. The powerful effects of variable stator vanes on stage-matching are also demonstrated and these results are shown to agree well with previous work. The slope of the working line of a gas turbine engine, overlaid on overall compressor characteristics, is shown to have a strong effect on the off-design stage-matching through the compressor. The model is also used to analyze design changes to the compressor geometry and to show how errors in estimates of annulus blockage, decided during the design process, have less effect on compressor performance than has previously been thought.

  4. Analytical model of coincidence resolving time in TOF-PET.

    PubMed

    Wieczorek, H; Thon, A; Dey, T; Khanin, V; Rodnyi, P

    2016-06-21

    The coincidence resolving time (CRT) of scintillation detectors is the parameter determining noise reduction in time-of-flight PET. We derive an analytical CRT model based on the statistical distribution of photons for two different prototype scintillators. For the first one, characterized by single exponential decay, CRT is proportional to the decay time and inversely proportional to the number of photons, with a square root dependence on the trigger level. For the second scintillator prototype, characterized by exponential rise and decay, CRT is proportional to the square root of the product of rise time and decay time divided by the doubled number of photons, and it is nearly independent of the trigger level. This theory is verified by measurements of scintillation time constants, light yield and CRT on scintillator sticks. Trapping effects are taken into account by defining an effective decay time. We show that in terms of signal-to-noise ratio, CRT is as important as patient dose, imaging time or PET system sensitivity. The noise reduction effect of better timing resolution is verified and visualized by Monte Carlo simulation of a NEMA image quality phantom.

  5. Using visual analytics model for pattern matching in surveillance data

    NASA Astrophysics Data System (ADS)

    Habibi, Mohammad S.

    2013-03-01

    In a persistent surveillance system huge amount of data is collected continuously and significant details are labeled for future references. In this paper a method to summarize video data as a result of identifying events based on these tagged information is explained, leading to concise description of behavior within a section of extended recordings. An efficient retrieval of various events thus becomes the foundation for determining a pattern in surveillance system observations, both in its extended and fragmented versions. The patterns consisting of spatiotemporal semantic contents are extracted and classified by application of video data mining on generated ontology, and can be matched based on analysts interest and rules set forth for decision making. The proposed extraction and classification method used in this paper uses query by example for retrieving similar events containing relevant features, and is carried out by data aggregation. Since structured data forms majority of surveillance information this Visual Analytics model employs KD-Tree approach to group patterns in variant space and time, thus making it convenient to identify and match any abnormal burst of pattern detected in a surveillance video. Several experimental video were presented to viewers to analyze independently and were compared with the results obtained in this paper to demonstrate the efficiency and effectiveness of the proposed technique.

  6. Analytical model for minority games with evolutionary learning

    NASA Astrophysics Data System (ADS)

    Campos, Daniel; Méndez, Vicenç; Llebot, Josep E.; Hernández, Germán A.

    2010-06-01

    In a recent work [D. Campos, J.E. Llebot, V. Méndez, Theor. Popul. Biol. 74 (2009) 16] we have introduced a biological version of the Evolutionary Minority Game that tries to reproduce the intraspecific competition for limited resources in an ecosystem. In comparison with the complex decision-making mechanisms used in standard Minority Games, only two extremely simple strategies ( juveniles and adults) are accessible to the agents. Complexity is introduced instead through an evolutionary learning rule that allows younger agents to learn taking better decisions. We find that this game shows many of the typical properties found for Evolutionary Minority Games, like self-segregation behavior or the existence of an oscillation phase for a certain range of the parameter values. However, an analytical treatment becomes much easier in our case, taking advantage of the simple strategies considered. Using a model consisting of a simple dynamical system, the phase diagram of the game (which differentiates three phases: adults crowd, juveniles crowd and oscillations) is reproduced.

  7. An analytical study of various telecomminication networks using markov models

    NASA Astrophysics Data System (ADS)

    Ramakrishnan, M.; Jayamani, E.; Ezhumalai, P.

    2015-04-01

    The main aim of this paper is to examine issues relating to the performance of various Telecommunication networks, and applied queuing theory for better design and improved efficiency. Firstly, giving an analytical study of queues deals with quantifying the phenomenon of waiting lines using representative measures of performances, such as average queue length (on average number of customers in the queue), average waiting time in queue (on average time to wait) and average facility utilization (proportion of time the service facility is in use). In the second, using Matlab simulator, summarizes the finding of the investigations, from which and where we obtain results and describing methodology for a) compare the waiting time and average number of messages in the queue in M/M/1 and M/M/2 queues b) Compare the performance of M/M/1 and M/D/1 queues and study the effect of increasing the number of servers on the blocking probability M/M/k/k queue model.

  8. Analytical model of mechanically excited piezoelectric unimorph beams.

    PubMed

    Pillai, Minu A; Ebenezer, D D; Deenadayalan, Ezhilarasi

    2017-08-01

    A model is presented of a composite beam with one elastic and one piezoelectric layer. A reduced set of piezoelectric equations of state that has only the longitudinal components of stress and strain and the transverse components of electric field and charge density is consistently used to include the effect of piezoelectric coupling in all the equations. The equi-potential boundary conditions on the electrodes, the open-circuit condition, and the Gauss condition are satisfied. The position of the neutral axis and the dynamic equilibrium equation are derived after including the effect of piezoelectric coupling. All equations are combined to derive an equation of motion that contains only the displacement and the mechanical excitation. The solution to the equation is expressed in terms of a complete set of functions and an auxiliary function that contains the electric potential. The latter is needed to satisfy piezoelectric boundary conditions at the ends of the beam. The electric potential varies along the length of the beam and has a quadratic variation between the electrodes. Analytical expressions for displacement and potential, and numerical results at low frequencies and in the neighborhood of resonance, are presented for certain sets of boundary conditions.

  9. Analytical model of coincidence resolving time in TOF-PET

    NASA Astrophysics Data System (ADS)

    Wieczorek, H.; Thon, A.; Dey, T.; Khanin, V.; Rodnyi, P.

    2016-06-01

    The coincidence resolving time (CRT) of scintillation detectors is the parameter determining noise reduction in time-of-flight PET. We derive an analytical CRT model based on the statistical distribution of photons for two different prototype scintillators. For the first one, characterized by single exponential decay, CRT is proportional to the decay time and inversely proportional to the number of photons, with a square root dependence on the trigger level. For the second scintillator prototype, characterized by exponential rise and decay, CRT is proportional to the square root of the product of rise time and decay time divided by the doubled number of photons, and it is nearly independent of the trigger level. This theory is verified by measurements of scintillation time constants, light yield and CRT on scintillator sticks. Trapping effects are taken into account by defining an effective decay time. We show that in terms of signal-to-noise ratio, CRT is as important as patient dose, imaging time or PET system sensitivity. The noise reduction effect of better timing resolution is verified and visualized by Monte Carlo simulation of a NEMA image quality phantom.

  10. Numerical and Analytical Modeling of Transit Timing Variations

    NASA Astrophysics Data System (ADS)

    Hadden, Sam; Lithwick, Yoram

    2016-09-01

    We develop and apply methods to extract planet masses and eccentricities from observed transit timing variations (TTVs). First, we derive simple analytic expressions for the TTV that include the effects of both first- and second-order resonances. Second, we use N-body Markov chain Monte Carlo simulations, as well as the analytic formulae, to measure the masses and eccentricities of 10 planets discovered by Kepler that have not previously been analyzed. Most of the 10 planets have low densities. Using the analytic expressions to partially circumvent degeneracies, we measure small eccentricities of a few percent or less.

  11. Numerical and Analytic Studies of Random-Walk Models.

    NASA Astrophysics Data System (ADS)

    Li, Bin

    We begin by recapitulating the universality approach to problems associated with critical systems, and discussing the role that random-walk models play in the study of phase transitions and critical phenomena. As our first numerical simulation project, we perform high-precision Monte Carlo calculations for the exponents of the intersection probability of pairs and triplets of ordinary random walks in 2 dimensions, in order to test the conformal-invariance theory predictions. Our numerical results strongly support the theory. Our second numerical project aims to test the hyperscaling relation dnu = 2 Delta_4-gamma for self-avoiding walks in 2 and 3 dimensions. We apply the pivot method to generate pairs of self-avoiding walks, and then for each pair, using the Karp-Luby algorithm, perform an inner -loop Monte Carlo calculation of the number of different translates of one walk that makes at least one intersection with the other. Applying a least-squares fit to estimate the exponents, we have obtained strong numerical evidence that the hyperscaling relation is true in 3 dimensions. Our great amount of data for walks of unprecedented length(up to 80000 steps), yield a updated value for the end-to-end distance and radius of gyration exponent nu = 0.588 +/- 0.001 (95% confidence limit), which comes out in good agreement with the renormalization -group prediction. In an analytic study of random-walk models, we introduce multi-colored random-walk models and generalize the Symanzik and B.F.S. random-walk representations to the multi-colored case. We prove that the zero-component lambdavarphi^2psi^2 theory can be represented by a two-color mutually -repelling random-walk model, and it becomes the mutually -avoiding walk model in the limit lambda to infty. However, our main concern and major break-through lies in the study of the two-point correlation function for the lambda varphi^2psi^2 theory with N > 0 components. By representing it as a two-color random-walk expansion

  12. An Analytical Model of Wave-Induced Longshore Current Based on Power Law Wave Height Decay.

    DTIC Science & Technology

    1988-01-01

    34I ANALYtTICAL MODEL OF NAVE-INDUCED LON6SHORE CURRENT BASED ON PONE* LAW.. (U) COASTAL ENG INEERING RESEAKNH CENTER VICKSBURG NS J N SMITH ET AL...j . - .L .V . : ; * AN ANALYTICAL MODEL OF WAVE-INDUCED ~ z * LONGSHORE CURRENT BASED ON POWER LAW * - WAVE HEIGHT DECAY by Jane McKee...I_ I IF 31592 11. TITLE (Include Security Classfication) • An Analytical Model of Wave-Induced Longshore Current Based on Power Law . Wave

  13. CD-HPF: New habitability score via data analytic modeling

    NASA Astrophysics Data System (ADS)

    Bora, K.; Saha, S.; Agrawal, S.; Safonova, M.; Routh, S.; Narasimhamurthy, A.

    2016-10-01

    The search for life on the planets outside the Solar System can be broadly classified into the following: looking for Earth-like conditions or the planets similar to the Earth (Earth similarity), and looking for the possibility of life in a form known or unknown to us (habitability). The two frequently used indices, Earth Similarity Index (ESI) and Planetary Habitability Index (PHI), describe heuristic methods to score habitability in the efforts to categorize different exoplanets (or exomoons). ESI, in particular, considers Earth as the reference frame for habitability, and is a quick screening tool to categorize and measure physical similarity of any planetary body with the Earth. The PHI assesses the potential habitability of any given planet, and is based on the essential requirements of known life: presence of a stable and protected substrate, energy, appropriate chemistry and a liquid medium. We propose here a different metric, a Cobb-Douglas Habitability Score (CDHS), based on Cobb-Douglas habitability production function (CD-HPF), which computes the habitability score by using measured and estimated planetary input parameters. As an initial set, we used radius, density, escape velocity and surface temperature of a planet. The values of the input parameters are normalized to the Earth Units (EU). The proposed metric, with exponents accounting for metric elasticity, is endowed with analytical properties that ensure global optima, and scales up to accommodate finitely many input parameters. The model is elastic, and, as we discovered, the standard PHI turns out to be a special case of the CDHS. Computed CDHS scores are fed to K-NN (K-Nearest Neighbor) classification algorithm with probabilistic herding that facilitates the assignment of exoplanets to appropriate classes via supervised feature learning methods, producing granular clusters of habitability. The proposed work describes a decision-theoretical model using the power of convex optimization and

  14. New Numerical Integrators Based on Solvability and Splitting

    DTIC Science & Technology

    2007-11-02

    display a currently valid OMB control number. 1. REPORT DATE 03 JAN 2005 2. REPORT TYPE N/A 3. DATES COVERED - 4. TITLE AND SUBTITLE New...Group Methods And Control Theory Workshop Held on 28 June 2004 - 1 July 2004., The original document contains color images. 14. ABSTRACT 15...Mechanics, NMR spectroscopy, infrared divergences in QED, control theory,... 1.1 Magnus expansion (IV) NEW NUMERICAL INTEGRATORS BASED ON SOLVABILITY AND

  15. Solvability of the master equation for dichotomous flow.

    PubMed

    Balakrishnan, V; Van den Broeck, C

    2002-01-01

    We consider the one-dimensional stochastic flow x=f(x)+g(x)xi(t), where xi(t) is a dichotomous Markov noise, and use a simple procedure to identify the conditions under which the integro-differential equation satisfied by the total probability density P(x,t) of the driven variable can be reduced to a differential equation of finite order. This generalizes the enumeration of the "solvable" cases.

  16. Complex modes and solvability of nonclassical linear systems

    NASA Astrophysics Data System (ADS)

    Caughey, T. K.; Ma, F.

    1993-03-01

    Some basic properties of nonclassical linear systems are examined to determine necessary and sufficient conditions under which nonclassical linear systems can be decoupled or become solvable in n-space. It was found that a necessary and sufficient condition under which a nonclassical system can be decoupled is for the coefficient matrices M, C, and K (where M is the mass matrix, C is the damping matrix, and K is the stiffness matrix) to be diagonalizable and pairwise commutative.

  17. Analytical model of impact disruption of satellites and asteroids

    NASA Astrophysics Data System (ADS)

    Leliwa-Kopystyński, J.; Włodarczyk, I.; Burchell, M. J.

    2016-04-01

    A model of impact disruption of the bodies with sizes from the laboratory scale to that of an order of 100 km is developed. On the lowermost end of the target size the model is based on the numerous laboratory data related to the mass-velocity distribution of the impact produced fragments. On the minor-planets scale the model is supported by the data related to the largest observed craters on small icy satellites and on some asteroids (Leliwa-Kopystynski, J., Burchell, M.J., Lowen, D. [2008]. Icarus 195, 817-826). The model takes into account the target disruption and the dispersion of the impact produced fragments against the intermolecular forces acting on the surfaces of the contacts of the fragments and against self-gravitation of the target. The head-on collisions of non-rotating and non-porous targets and impactors are considered. The impactor delivers kinetic energy but its mass is neglected in comparison to mass of the target. For this simple case the analytical formulae for specific disruption energy as well as for specific energy of formation of the largest craters are found. They depend on a set of parameters. Of these the most important (i.e. with the greatest influence on the final result) are three rather weakly known parameters. They are: (i) The exponent γ in the distribution function of the fragments. (ii) The characteristic velocity v0 that appears in the velocity distribution of the ejected fragments. (iii) The exponent β in the mass-velocity distribution. The influence of the choice of the numerical values of these parameters on the final results has been studied. Another group of parameters contains the relevant material data. They are: (a) The energy σ of breaking of the intermolecular bonds of the target material per unit of the fragment surface and (b) the density ρ of the target. According to our calculations the transition between the strength regime and the gravitational regime is in the range of the target radius from ∼0.4 km to

  18. Determining passive cooling limits in CPV using an analytical thermal model

    NASA Astrophysics Data System (ADS)

    Gualdi, Federico; Arenas, Osvaldo; Vossier, Alexis; Dollet, Alain; Aimez, Vincent; Arès, Richard

    2013-09-01

    We propose an original thermal analytical model aiming to predict the practical limits of passive cooling systems for high concentration photovoltaic modules. The analytical model is described and validated by comparison with a commercial 3D finite element model. The limiting performances of flat plate cooling systems in natural convection are then derived and discussed.

  19. Three-body problem in 3D space: ground state, (quasi)-exact-solvability

    NASA Astrophysics Data System (ADS)

    Turbiner, Alexander V.; Miller, Willard, Jr.; Escobar-Ruiz, Adrian M.

    2017-05-01

    We study aspects of the quantum and classical dynamics of a 3-body system in 3D space with interaction depending only on mutual distances. The study is restricted to solutions in the space of relative motion which are functions of mutual distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories in the classical case are of this type. The quantum (and classical) system for which these states are eigenstates is found and its Hamiltonian is constructed. It corresponds to a three-dimensional quantum particle moving in a curved space with special metric. The kinetic energy of the system has a hidden sl(4, R) Lie (Poisson) algebra structure, alternatively, the hidden algebra h (3) typical for the H 3 Calogero model. We find an exactly solvable three-body generalized harmonic oscillator-type potential as well as a quasi-exactly-solvable three-body sextic polynomial type potential; both models have an extra integral.

  20. Design Protocols and Analytical Strategies that Incorporate Structural Reliability Models

    NASA Technical Reports Server (NTRS)

    Duffy, Stephen F.

    1997-01-01

    Ceramic matrix composites (CMC) and intermetallic materials (e.g., single crystal nickel aluminide) are high performance materials that exhibit attractive mechanical, thermal and chemical properties. These materials are critically important in advancing certain performance aspects of gas turbine engines. From an aerospace engineer's perspective the new generation of ceramic composites and intermetallics offers a significant potential for raising the thrust/weight ratio and reducing NO(x) emissions of gas turbine engines. These aspects have increased interest in utilizing these materials in the hot sections of turbine engines. However, as these materials evolve and their performance characteristics improve a persistent need exists for state-of-the-art analytical methods that predict the response of components fabricated from CMC and intermetallic material systems. This need provided the motivation for the technology developed under this research effort. Continuous ceramic fiber composites exhibit an increase in work of fracture, which allows for "graceful" rather than catastrophic failure. When loaded in the fiber direction, these composites retain substantial strength capacity beyond the initiation of transverse matrix cracking despite the fact that neither of its constituents would exhibit such behavior if tested alone. As additional load is applied beyond first matrix cracking, the matrix tends to break in a series of cracks bridged by the ceramic fibers. Any additional load is born increasingly by the fibers until the ultimate strength of the composite is reached. Thus modeling efforts supported under this research effort have focused on predicting this sort of behavior. For single crystal intermetallics the issues that motivated the technology development involved questions relating to material behavior and component design. Thus the research effort supported by this grant had to determine the statistical nature and source of fracture in a high strength, Ni

  1. Design Protocols and Analytical Strategies that Incorporate Structural Reliability Models

    NASA Technical Reports Server (NTRS)

    Duffy, Stephen F.

    1997-01-01

    Ceramic matrix composites (CMC) and intermetallic materials (e.g., single crystal nickel aluminide) are high performance materials that exhibit attractive mechanical, thermal, and chemical properties. These materials are critically important in advancing certain performance aspects of gas turbine engines. From an aerospace engineers perspective the new generation of ceramic composites and intermetallics offers a significant potential for raising the thrust/weight ratio and reducing NO(sub x) emissions of gas turbine engines. These aspects have increased interest in utilizing these materials in the hot sections of turbine engines. However, as these materials evolve and their performance characteristics improve a persistent need exists for state-of-the-art analytical methods that predict the response of components fabricated from CMC and intermetallic material systems. This need provided the motivation for the technology developed under this research effort. Continuous ceramic fiber composites exhibit an increase in work of fracture, which allows for 'graceful' rather than catastrophic failure. When loaded in the fiber direction these composites retain substantial strength capacity beyond the initiation of transverse matrix cracking despite the fact that neither of its constituents would exhibit such behavior if tested alone. As additional load is applied beyond first matrix cracking, the matrix tends to break in a series of cracks bridged by the ceramic fibers. Any additional load is born increasingly by the fibers until the ultimate strength of the composite is reached. Thus modeling efforts supported under this research effort have focused on predicting this sort of behavior. For single crystal intermetallics the issues that motivated the technology development involved questions relating to material behavior and component design. Thus the research effort supported by this grant had to determine the statistical nature and source of fracture in a high strength, Ni

  2. A genetic algorithm-based job scheduling model for big data analytics.

    PubMed

    Lu, Qinghua; Li, Shanshan; Zhang, Weishan; Zhang, Lei

    Big data analytics (BDA) applications are a new category of software applications that process large amounts of data using scalable parallel processing infrastructure to obtain hidden value. Hadoop is the most mature open-source big data analytics framework, which implements the MapReduce programming model to process big data with MapReduce jobs. Big data analytics jobs are often continuous and not mutually separated. The existing work mainly focuses on executing jobs in sequence, which are often inefficient and consume high energy. In this paper, we propose a genetic algorithm-based job scheduling model for big data analytics applications to improve the efficiency of big data analytics. To implement the job scheduling model, we leverage an estimation module to predict the performance of clusters when executing analytics jobs. We have evaluated the proposed job scheduling model in terms of feasibility and accuracy.

  3. An analytic model for the prediction of the bar temperature in a roughing mill

    NASA Astrophysics Data System (ADS)

    Kim, Jaeboo; Lee, Junghyeung; Hwang, Sang Moo

    2010-06-01

    An on-line model is presented for the prediction of temperature distributions in the bar in the roughing mill of a hot strip mill. The model consists of an analytic model for the prediction of temperature distributions in the inter-stand zone, and a semi-analytic model for the prediction of temperature distributions in the bite zone. The prediction accuracy of the model is examined through comparison with predictions from a finite element model.

  4. An Analytical Model for the Influence of Contact Resistance on Thermoelectric Efficiency

    NASA Astrophysics Data System (ADS)

    Bjørk, Rasmus

    2016-03-01

    An analytical model is presented that can account for both electrical and hot and cold thermal contact resistances when calculating the efficiency of a thermoelectric generator. The model is compared to a numerical model of a thermoelectric leg for 16 different thermoelectric materials, as well as to the analytical models of Ebling et al. (J Electron Mater 39:1376, 2010) and Min and Rowe (J Power Sour 38:253, 1992). The model presented here is shown to accurately calculate the efficiency for all systems and all contact resistances considered, with an average difference in efficiency between the numerical model and the analytical model of -0.07 ± 0.35pp. This makes the model more accurate than previously published models. The maximum absolute difference in efficiency between the analytical model and the numerical model is 1.14pp for all materials and all contact resistances considered.

  5. Solvable (nonrelativistic, classical) n-body problems on the line. II

    NASA Astrophysics Data System (ADS)

    Calogero, F.

    1996-03-01

    A solvable n-body problem is exhibited, which features equations of motion of Newtonian type, mjẍj=Fj, j=1,...,n, with ``forces'' Fj that are linear and quadratic in the particle velocities, Fj=ẋj{∑k=1n[fjk(1)(x) +ẋkfjk(2)(x)]}, and depend highly nonlinearly on the positions xk≡xk(t), k=1,...,n, of the n ``particles'' on the line. Explicit expressions of the functions fjk(i)(x), in terms of elliptic functions, are given; they contain n+4 arbitrary constants, in addition to the n ``masses'' mk and to n arbitrary functions gk(xk). Special cases in which the elliptic functions reduce to trigonometric or rational functions are of course included. The technique whereby this model has been arrived at entails that its initial-value problem is solvable by quadratures [for any n and arbitrary initial data x(0) and ẋ(0)]. A discussion of the actual behavior of the solution, and of special cases, is postponed to future papers.

  6. Quantitative, comprehensive, analytical model for magnetic reconnection in Hall magnetohydrodynamics.

    PubMed

    Simakov, Andrei N; Chacón, L

    2008-09-05

    Dissipation-independent, or "fast", magnetic reconnection has been observed computationally in Hall magnetohydrodynamics (MHD) and predicted analytically in electron MHD. However, a quantitative analytical theory of reconnection valid for arbitrary ion inertial lengths, d{i}, has been lacking and is proposed here for the first time. The theory describes a two-dimensional reconnection diffusion region, provides expressions for reconnection rates, and derives a formal criterion for fast reconnection in terms of dissipation parameters and d{i}. It also confirms the electron MHD prediction that both open and elongated diffusion regions allow fast reconnection, and reveals strong dependence of the reconnection rates on d{i}.

  7. Analytical model for electromagnetic cascades in rotating electric field

    SciTech Connect

    Nerush, E. N.; Bashmakov, V. F.; Kostyukov, I. Yu.

    2011-08-15

    Electromagnetic cascades attract a lot of attention as an important quantum electrodynamics effect that will reveal itself in various electromagnetic field configurations at ultrahigh intensities. We study cascade dynamics in rotating electric field analytically and numerically. The kinetic equations for the electron-positron plasma and gamma-quanta are formulated. The scaling laws are derived and analyzed. For the cascades arising far above the threshold the dependence of the cascade parameters on the field frequency is derived. The spectra of high-energy cascade particles are calculated. The analytical results are verified by numerical simulations.

  8. A two-site bipolaron model for organic magnetoresistance

    NASA Astrophysics Data System (ADS)

    Wagemans, W.; Bloom, F. L.; Bobbert, P. A.; Wohlgenannt, M.; Koopmans, B.

    2008-04-01

    The recently proposed bipolaron model for large "organic magnetoresistance" (OMAR) at room temperature is extended to an analytically solvable two-site scheme. It is shown that even this extremely simplified approach reproduces some of the key features of OMAR, viz., the possibility to have both positive and negative magnetoresistance, as well as its universal line shapes. Specific behavior and limiting cases are discussed. Extensions of the model, to guide future experiments and numerical Monte Carlo studies, are suggested.

  9. Analytical prediction for electromagnetic performance of interior permanent magnet machines based on subdomain model

    NASA Astrophysics Data System (ADS)

    Shin, Kyung-Hun; Park, Hyung-II; Cho, Han-Wook; Choi, Jang-Young

    2017-05-01

    This paper presents an analytical model for the computation of the electromagnetic performance in interior permanent magnet (IPM) machines that accounts for the stator and the complex rotor structure. Using the subdomain method, we propose a simplified analytical model that considers the magnetic properties of the IPM machine. The analytical solutions are derived by solving the field-governing equations in each simple and regular subdomain, i.e., magnet, barrier, air gap, slot opening, and slot, and then applying the boundary conditions to the interfaces between these subdomains. The analytical model accurately accounts for the influence of the interaction between the slots, the relative recoil permeability of the magnets, and the boundary conditions. The magnetic field and electromagnetic performance obtained using the analytical method are compared with those obtained using finite element analysis. Finally, the analytical predictions are compared with the measured data in order to confirm the validity of the methods proposed in this paper.

  10. Random-effects models for meta-analytic structural equation modeling: review, issues, and illustrations.

    PubMed

    Cheung, Mike W-L; Cheung, Shu Fai

    2016-06-01

    Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM. Random-effects models are well known in conventional meta-analysis but are less studied in MASEM. The primary objective of this paper was to address issues related to random-effects models in MASEM. Specifically, we compared two different random-effects models in MASEM-correlation-based MASEM and parameter-based MASEM-and explored their strengths and limitations. Two examples were used to illustrate the similarities and differences between these models. We offered some practical guidelines for choosing between these two models. Future directions for research on random-effects models in MASEM were also discussed. Copyright © 2016 John Wiley & Sons, Ltd.

  11. A Hydro-mechanical Model and Analytical Solutions for Geomechanical Modeling of Carbon Dioxide Geological Sequestration

    SciTech Connect

    Xu, Zhijie; Fang, Yilin; Scheibe, Timothy D.; Bonneville, Alain

    2012-05-15

    We present a hydro-mechanical model for geological sequestration of carbon dioxide. The model considers the poroelastic effects by taking into account the coupling between the geomechanical response and the fluid flow in greater detail. The simplified hydro-mechanical model includes the geomechanical part that relies on the linear elasticity, while the fluid flow is based on the Darcy’s law. Two parts were coupled using the standard linear poroelasticity. Analytical solutions for pressure field were obtained for a typical geological sequestration scenario. The model predicts the temporal and spatial variation of pressure field and effects of permeability and elastic modulus of formation on the fluid pressure distribution.

  12. Modelling a flows in supply chain with analytical models: Case of a chemical industry

    NASA Astrophysics Data System (ADS)

    Benhida, Khalid; Azougagh, Yassine; Elfezazi, Said

    2016-02-01

    This study is interested on the modelling of the logistics flows in a supply chain composed on a production sites and a logistics platform. The contribution of this research is to develop an analytical model (integrated linear programming model), based on a case study of a real company operating in the phosphate field, considering a various constraints in this supply chain to resolve the planning problems for a better decision-making. The objectives of this model is to determine and define the optimal quantities of different products to route, to and from the various entities in the supply chain studied.

  13. Analytical Model of Water Flow in Coal with Active Matrix

    NASA Astrophysics Data System (ADS)

    Siemek, Jakub; Stopa, Jerzy

    2014-12-01

    This paper presents new analytical model of gas-water flow in coal seams in one dimension with emphasis on interactions between water flowing in cleats and coal matrix. Coal as a flowing system, can be viewed as a solid organic material consisting of two flow subsystems: a microporous matrix and a system of interconnected macropores and fractures. Most of gas is accumulated in the microporous matrix, where the primary flow mechanism is diffusion. Fractures and cleats existing in coal play an important role as a transportation system for macro scale flow of water and gas governed by Darcy's law. The coal matrix can imbibe water under capillary forces leading to exchange of mass between fractures and coal matrix. In this paper new partial differential equation for water saturation in fractures has been formulated, respecting mass exchange between coal matrix and fractures. Exact analytical solution has been obtained using the method of characteristics. The final solution has very simple form that may be useful for practical engineering calculations. It was observed that the rate of exchange of mass between the fractures and the coal matrix is governed by an expression which is analogous to the Newton cooling law known from theory of heat exchange, but in present case the mass transfer coefficient depends not only on coal and fluid properties but also on time and position. The constant term of mass transfer coefficient depends on relation between micro porosity and macro porosity of coal, capillary forces, and microporous structure of coal matrix. This term can be expressed theoretically or obtained experimentally. W artykule zaprezentowano nowy model matematyczny przepływu wody i gazu w jednowymiarowej warstwie węglowej z uwzględnieniem wymiany masy między systemem szczelin i matrycą węglową. Węgiel jako system przepływowy traktowany jest jako układ o podwójnej porowatości i przepuszczalności, składający się z mikroporowatej matrycy węglowej oraz z

  14. Quantitative analytical model for magnetic reconnection in hall magnetohydrodynamics

    SciTech Connect

    Simakov, Andrei N

    2008-01-01

    Magnetic reconnection is of fundamental importance for laboratory and naturally occurring plasmas. Reconnection usually develops on time scales which are much shorter than those associated with classical collisional dissipation processes, and which are not fully understood. While such dissipation-independent (or 'fast') reconnection rates have been observed in particle and Hall magnetohydrodynamics (MHD) simulations and predicted analytically in electron MHD, a quantitative analytical theory of fast reconnection valid for arbitrary ion inertial lengths d{sub i} has been lacking. Here we propose such a theory without a guide field. The theory describes two-dimensional magnetic field diffusion regions, provides expressions for the reconnection rates, and derives a formal criterion for fast reconnection in terms of dissipation parameters and di. It also demonstrates that both open X-point and elongated diffusion regions allow dissipation-independent reconnection and reveals a possibility of strong dependence of the reconnection rates on d{sub i}.

  15. A simple analytical aerodynamic model of Langley Winged-Cone Aerospace Plane concept

    NASA Technical Reports Server (NTRS)

    Pamadi, Bandu N.

    1994-01-01

    A simple three DOF analytical aerodynamic model of the Langley Winged-Coned Aerospace Plane concept is presented in a form suitable for simulation, trajectory optimization, and guidance and control studies. The analytical model is especially suitable for methods based on variational calculus. Analytical expressions are presented for lift, drag, and pitching moment coefficients from subsonic to hypersonic Mach numbers and angles of attack up to +/- 20 deg. This analytical model has break points at Mach numbers of 1.0, 1.4, 4.0, and 6.0. Across these Mach number break points, the lift, drag, and pitching moment coefficients are made continuous but their derivatives are not. There are no break points in angle of attack. The effect of control surface deflection is not considered. The present analytical model compares well with the APAS calculations and wind tunnel test data for most angles of attack and Mach numbers.

  16. Simplified analytical model for open-phase operating mode of thyristor-controlled phase angle regulator

    NASA Astrophysics Data System (ADS)

    Astashev, M. G.; Novikov, M. A.; Panfilov, D. I.; Rashitov, P. A.; Fedorova, M. I.

    2015-12-01

    In this paper, an approach to the development of a simplified analytical model for the analysis of electromagnetic processes of a thyristor-controlled phase angle regulator with an individual phase-controlled thyristor switch is considered. The analytical expressions for the calculation of electrical parameters in symmetrical and open-phase operating mode are obtained. With a concrete example, the verification of the developed analytical model is carried out. It is accomplished by means of comparison between current and voltage calculation results when the thyristor-controlled phase angle regulator is in an open-phase operating mode with the simulation results in the MatLab software environment. Adequacy check of the obtained analytical model is carried out by comparison between the analytical calculation and experimental data received from the actual physical model.

  17. The use of analytical models in human-computer interface design

    NASA Technical Reports Server (NTRS)

    Gugerty, Leo

    1993-01-01

    Recently, a large number of human-computer interface (HCI) researchers have investigated building analytical models of the user, which are often implemented as computer models. These models simulate the cognitive processes and task knowledge of the user in ways that allow a researcher or designer to estimate various aspects of an interface's usability, such as when user errors are likely to occur. This information can lead to design improvements. Analytical models can supplement design guidelines by providing designers rigorous ways of analyzing the information-processing requirements of specific tasks (i.e., task analysis). These models offer the potential of improving early designs and replacing some of the early phases of usability testing, thus reducing the cost of interface design. This paper describes some of the many analytical models that are currently being developed and evaluates the usefulness of analytical models for human-computer interface design. This paper will focus on computational, analytical models, such as the GOMS model, rather than less formal, verbal models, because the more exact predictions and task descriptions of computational models may be useful to designers. The paper also discusses some of the practical requirements for using analytical models in complex design organizations such as NASA.

  18. Analytical Model for Chip Formation in Case of Orthogonal Machining Process

    NASA Astrophysics Data System (ADS)

    Salvatore, Ferdinando; Mabrouki, Tarek; Hamdi, Hédi

    2011-01-01

    The present work deals with the presentation of analytical methodology allowing the modelling of chip formation. For that a "decomposition approach", based on assuming that the material removal is the summation of two contributions: ploughing and pure cut was adopted. Moreover, this analytical model was calibrated by a finite element model and experimental data in terms of temperature and forces evolutions. The global aim is to propose to the industrial community, an efficient rapid-execution analytical model concerning the material removal in the case of an orthogonal cutting process.

  19. Solvable critical dense polymers on the cylinder

    NASA Astrophysics Data System (ADS)

    Pearce, Paul A.; Rasmussen, Jørgen; Villani, Simon P.

    2010-02-01

    A lattice model of critical dense polymers is solved exactly on a cylinder with finite circumference. The model is the first member {\\cal LM}(1,2) of the Yang-Baxter integrable series of logarithmic minimal models. The cylinder topology allows for non-contractible loops with fugacity α that wind around the cylinder or for an arbitrary number \\ell of defects that propagate along the full length of the cylinder. Using an enlarged periodic Temperley-Lieb algebra, we set up commuting transfer matrices acting on states whose links are considered distinct with respect to connectivity around the front or back of the cylinder. These transfer matrices satisfy a functional equation in the form of an inversion identity. For even N, this involves a non-diagonalizable braid operator J and an involution R = - (J3 - 12J)/16 = (-1)F with eigenvalues R=(-1)^{\\ell /2} . This is reminiscent of supersymmetry with a pair of defects interpreted as a fermion. The number of defects \\ell thus separates the theory into Ramond (\\ell /2 even), Neveu-Schwarz (\\ell /2 odd) and \\mathbb {Z}_4 (\\ell odd) sectors. For the case of loop fugacity α = 2, the inversion identity is solved exactly sector by sector for the eigenvalues in finite geometry. The eigenvalues are classified according to the physical combinatorics of the patterns of zeros in the complex spectral-parameter plane. This yields selection rules for the physically relevant solutions to the inversion identity. The finite-size corrections are obtained from Euler-Maclaurin formula. In the scaling limit, we obtain the conformal partition functions as sesquilinear forms and confirm the central charge c = - 2 and conformal weights \\Delta,\\bar {\\Delta }=\\Delta_t=(t^2-1)/8 . Here t=\\ell /2 and t=2r-s\\in \\mathbb {N} in the \\ell even sectors with Kac labels r = 1, 2, 3,...;s = 1, 2 while t\\in \\mathbb {Z}-\\frac 12 in the \\ell odd sectors. Strikingly, the \\ell /2 odd sectors exhibit a {\\cal W} -extended symmetry but the

  20. The third exactly solvable hypergeometric quantum-mechanical potential

    NASA Astrophysics Data System (ADS)

    Ishkhanyan, Artur

    2016-07-01

    We introduce the third independent exactly solvable hypergeometric potential, after the Eckart and the Pöschl-Teller potentials, which is proportional to an energy-independent parameter and has a shape that is independent of this parameter. The general solution of the Schrödinger equation for this potential is written through fundamental solutions each of which presents an irreducible combination of two Gauss hypergeometric functions. The potential is an asymmetric step-barrier with variable height and steepness. Discussing the transmission above such a barrier, we derive a compact formula for the reflection coefficient.