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.
Magnetic field barriers in graphene: an analytically solvable model.
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.
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.
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.
Solvable model of a strongly driven micromaser
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.
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.
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.
An exactly solvable model for quantum communications.
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.
Algebraic spin liquid in an exactly solvable spin model
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.'
Solvable models and hidden symmetries in QCD
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.
Solvable model for polymorphic dynamics of biofilaments.
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.
An analytically solvable eigenvalue problem for the linear elasticity equations.
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.
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.
A solvable model for localized adsorption in a Coulomb system
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.
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.
Gegenbauer-solvable quantum chain model
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.
Analytically solvable chaotic oscillator based on a first-order filter
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.
Model for microemulsions: An exactly solvable case
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.
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.
An Exactly Solvable Supersymmetric Model of Semimagic Nuclei
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.
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.
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.
Effective viscosity and dynamics of spreading epithelia: a solvable model.
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.
Solvable model in renormalization group analysis for effective eddy viscosity.
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).
Solvable four-state Landau-Zener model of two interacting qubits with path interference
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.
An exactly solvable, spatial model of mutation accumulation in cancer
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
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.
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.
An exactly solvable model of random site-specific recombinations
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
Neutron-proton correlations in an exactly solvable model
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}
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.
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
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.
Solvable four-state Landau-Zener model of two interacting qubits with path interference
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
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.
Localized Majorana-Like Modes in a Number-Conserving Setting: An Exactly Solvable Model.
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.
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
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.
On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations
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.
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.
Quasi-exactly solvable relativistic soft-core Coulomb models
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.
Isovector Pairing within the so(5) Richardson-Gaudin Exactly Solvable Model
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.
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.
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).
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.
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.
Numerically Solvable Model for Resonant Collisions of Electronswith Diatomic Molecules
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.
Oscillations and chaos in neural networks: an exactly solvable model.
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
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.
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
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.
Exactly solvable spin chain models corresponding to BDI class of topological superconductors.
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.
Exactly solvable spin chain models corresponding to BDI class of topological superconductors
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
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.
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.
A solvable model of axisymmetric and non-axisymmetric droplet bouncing.
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.
Quantum scattering theory in light of an exactly solvable model with rearrangement collisions
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.}
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.
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.
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
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.
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.
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.
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.
Quasi-exactly solvable quasinormal modes
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.
Analytic Modeling of Insurgencies
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... carrots ” x. A dynamic utility-based model is developed in [26] in which the state variables are the fractions of contrarians (supporters of the...Unanticipated Political Revolution," Public Choice, vol. 61, pp. 41-74, 1989. [26] M. P. Atkinson, M. Kress and R. Szechtman, " Carrots , Sticks and Fog
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.
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.
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.
Statistics of avalanches with relaxation and Barkhausen noise: a solvable model.
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.
Metric measures of interparticle interaction in an exactly solvable two-electron model atom
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.
Nonequilibrium phase transition in an exactly solvable driven Ising model with friction.
Hucht, Alfred
2009-12-01
A driven Ising model with friction due to magnetic correlations was proposed by Kadau [Phys. Rev. Lett. 101, 137205 (2008)]. The nonequilibrium phase transition present in this system is investigated in detail using analytical methods as well as Monte Carlo simulations. In the limit of high driving velocities v the model shows mean-field behavior due to dimensional reduction and can be solved exactly for various geometries. The simulations are performed with three different single spin-flip rates: the common Metropolis and Glauber rates as well as a multiplicative rate. Due to the nonequilibrium nature of the model all rates lead to different critical temperatures at v>0, while the exact solution matches the multiplicative rate. Finally, the crossover from Ising to mean-field behavior as function of velocity and system size is analyzed in one and two dimensions.
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.
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.
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 .
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
Energy and angular distributions of detached electrons in a solvable model of ion-atom collisions
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}
Energy and angular distributions of detached electrons in a solvable model of ion-atom collisions
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
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.
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.
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.
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.
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.
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.
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.
Entropy-enthalpy compensation in chemical reactions and adsorption: an exactly solvable model.
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.
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.
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.
Work and information processing in a solvable model of Maxwell’s demon
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
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.
Solvable continuous-time random walk model of the motion of tracer particles through porous media.
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.
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
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.
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.
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.
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.
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.
Solvable models with self-triality in statistical mechanics and field theory
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.
Solvable multistate model of Landau-Zener transitions in cavity QED
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.
Family of exactly solvable models with an ultimate quantum paramagnetic ground state.
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.
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.
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.
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.
Rate of Adaptation in Sexuals and Asexuals: A Solvable Model of the Fisher–Muller Effect
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
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.
Ultrametricity and memory in a solvable model of self-organized criticality
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.
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.
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
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.
Predictive analytics can support the ACO model.
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.
Analytic Model of Reactive Flow
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.
Analytic Model of Reactive Flow
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.
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.
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
Stochastic genetic networks with solvable structures
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.
ANALYTICAL ELEMENT MODELING OF COASTAL AQUIFERS
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; ...
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.
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.
Disturbance accommodating control design for wind turbines using solvability conditions
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
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.
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.
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.
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.
ESTIMATING UNCERTAINITIES IN FACTOR ANALYTIC MODELS
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 ...
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.
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.
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.
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
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 Γ_{E}). 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.
Some analytical models of radiating collapsing spheres
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.
Analytical steam injection model for layered systems
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.
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.
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.
An analytical model of memristors in plants
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
Mission Stream Analysis - Delta Analytic Model. Revision
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
Analytical Modeling of High Rate Processes.
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
Transonic Cascade Measurements to Support Analytical Modeling
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
Analytic Modeling of Severe Vortical Storms.
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
Hidden algebra method (quasi-exact-solvability in quantum mechanics)
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.
Exactly solvable birth and death processes
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.
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.
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.
Analytic Models of Plausible Gravitational Lens Potentials
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.
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.
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.
Analytical modeling of materialized view maintenance algorithms
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.
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.
Analytical model for a vertical buoyant jet
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.
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.
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.
Simple analytic model for astrophysical S factors
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).
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.
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].
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.
ANALYTIC MODELING OF THE MORETON WAVE KINEMATICS
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.
WHAEM: PROGRAM DOCUMENTATION FOR THE WELLHEAD ANALYTIC ELEMENT MODEL
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...
Modeling Biodegradation and Reactive Transport: Analytical and Numerical Models
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.
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.
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.
An analytical model of joint contact.
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.
Analytic wave model of Stark deceleration dynamics
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.
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.
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
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
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.
Project Summary. ANALYTICAL ELEMENT MODELING OF COASTAL AQUIFERS
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; ...
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.
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.
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
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.
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.
Analytic Model For Estimation Of Cold Bulk Metal Forming Simulations
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.
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.
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
Combining Modeling and Gaming for Predictive Analytics
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.
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.
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.
High Fidelity Quantum Gates via Analytically Solvable Pulses
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
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.
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.
Evaluating Child Welfare policies with decision-analytic simulation models
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
Analytic modeling of the subthreshold behavior in MOSFET
NASA Astrophysics Data System (ADS)
Liu, C. W.; Hsieh, T. X.
2000-09-01
An analytic model is derived to describe the bias-dependent behavior of the subthreshold swing in MOSFETs for the uniform channel and the ion-implanted channel, and is compared to two-dimensional simulation, Tsividis' model and Brews' model. This simple analytical model confirms that the subthreshold swing is a function of the gate-source bias and exhibits a global minimum in the weak inversion region. This model is based on Tsividis' current equations and assumes that the surface potential difference between the drain and the source is small for the gate-source voltage below the threshold voltage. This yields a conventional exponential form of the subthreshold current, and the subthreshold swing can be obtained analytically from this current equation.
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
Analytical results for a three-phase traffic model.
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.
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
Analytical model for screening potential CO2 repositories
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.
Analytical Models for Parallel Processing Systems
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
Analytical model for fast-shock ignition
Ghasemi, S. A. Farahbod, A. H.; Sobhanian, S.
2014-07-15
A model and its improvements are introduced for a recently proposed approach to inertial confinement fusion, called fast-shock ignition (FSI). The analysis is based upon the gain models of fast ignition, shock ignition and considerations for the fast electrons penetration into the pre-compressed fuel to examine the formation of an effective central hot spot. Calculations of fast electrons penetration into the dense fuel show that if the initial electron kinetic energy is of the order ∼4.5 MeV, the electrons effectively reach the central part of the fuel. To evaluate more realistically the performance of FSI approach, we have used a quasi-two temperature electron energy distribution function of Strozzi (2012) and fast ignitor energy formula of Bellei (2013) that are consistent with 3D PIC simulations for different values of fast ignitor laser wavelength and coupling efficiency. The general advantages of fast-shock ignition in comparison with the shock ignition can be estimated to be better than 1.3 and it is seen that the best results can be obtained for the fuel mass around 1.5 mg, fast ignitor laser wavelength ∼0.3 micron and the shock ignitor energy weight factor about 0.25.
Analytical Modeling of Reinforced Concrete in Tension
1989-04-01
0,26,6*0/, TODMFE93 COMMON /SOFT/ ISCODE,WWCC,ELWW,GGFF, DDAA TDFE 42 IF (MODEL.EQ.5) READ(IIN,1005) ISCODE,WWCC,ELWW,GGFF, DDAA TDFE 101 1005 FORMAT...15,4F10.0) TDFE1219 COMMON /SOFT/ ISCODE,WWCC,ELWW,GGFF, DDAA MATRT214 WRITE (6,2239) ISCODE,WWCC,ELWW,GGFF, DDAA MATRT244 2239 FORMAT(/38H (8) CODE FOR...ELEMENT WIDTH (ELWW) IF10.5, 5 /38H FRACTURE ENERGY (GGFF) IF10.8, 6 /38H MAXIMUM AGGREGATE SIZE ( DDAA ) ,F10.5) CHANGES IN ELT2D4.F77 IDW=18*ITWO ELT2D438
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…
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.
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.
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.
Combined experimental/analytical modeling of shell/payload structures
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.
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
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.
An analytical model of the HINT performance metric
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.
Analytic model to predict the strength of tendon repairs.
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.
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.
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.
Modeling Analyte Transport and Capture in Porous Bead Sensors
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
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…
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…
FACTOR ANALYTIC MODELS OF CLUSTERED MULTIVARIATE DATA WITH INFORMATIVE CENSORING
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...
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…
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.
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.
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…
Palm: Easing the Burden of Analytical Performance Modeling
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.
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.
Approximate Solvability of Forward-Backward Stochastic Differential Equations
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.
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.
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.
Ground water modeling applications using the analytic element method.
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).
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.
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.
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.
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.
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.
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.
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.
Pitfalls in TDM of antibiotic drugs: analytical and modelling issues.
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.
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.
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.
An analytical model for microsegregation in open and expanding domains
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.
Human performance modeling for system of systems analytics.
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.
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.
Accuracy of analytic model planning in bimaxillary surgery.
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.
AN ANALYTIC RADIATIVE-CONVECTIVE MODEL FOR PLANETARY ATMOSPHERES
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.
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.
Peat pyrolysis and the analytical semi-empirical model
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.
Analytical properties of a three-compartmental dynamical demographic model.
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.
Model and Analytic Processes for Export License Assessments
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
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.
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).
An analytic model for buoyancy resonances in protoplanetary disks
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.
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.
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.
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.
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.
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.
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.
Analytical modeling of glucose biosensors based on carbon nanotubes
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
Analytical model of reactive transport processes with spatially variable coefficients.
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.
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.
Use of groundwater levels with the PULSE analytical model.
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.
A semi-analytical Lagrangian dispersion model in inhomogeneous turbulence
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.
Analytical results on the Beauchemin model of lymphocyte migration
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
Laser satellite constellations for strategic defense - an analytic model
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.
Analytical model of an isolated single-atom electron source.
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.
A two-dimensional analytical model of petroleum vapor intrusion
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
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.
A semi-analytic model of magnetized liner inertial fusion
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.
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.
A workflow learning model to improve geovisual analytics utility
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
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.
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.
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.
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
A hybrid finite-difference and analytic element groundwater model.
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.
Digital forensics: an analytical crime scene procedure model (ACSPM).
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
Analytical and numerical modeling of surface morphologies in thin films
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.
Analytical model for the radio-frequency sheath.
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
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.
Analytical performance models for geologic repositories. Volume 2
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.
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
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.
"Violent Intent Modeling: Incorporating Cultural Knowledge into the Analytical Process
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.
X: A Comprehensive Analytic Model for Parallel Machines
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.
A temporal model for Clinical Data Analytics language.
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.
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.
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.
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.
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.
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.
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.
Fitting meta-analytic structural equation models with complex datasets.
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.
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.
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.
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...
33 CFR 385.33 - Revisions to models and analytical tools.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 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...
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...
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
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.
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.
A Double Scattering Analytical Model For Elastic Recoil Detection Analysis
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.
An analytical model of dynamic sliding friction during impact
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
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.
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.
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.…
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.
Analytical model of diffuse reflectance spectrum of skin tissue
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)
Maximum likelihood estimation in meta-analytic structural equation modeling.
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.
Analytical model of peptide mass cluster centres with applications
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
A macroscopic analytical model of collaboration in distributed robotic systems.
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.
Fuzzy modeling of analytical redundancy for sensor failure detection
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.
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.
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.
Model choice considerations and information integration using analytical hierarchy process
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.
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.
Analytic model for coaxial helicity injection in tokamak plasmas
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.
Quasi-exact solvability of Dirac equation with Lorentz scalar potential
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.
Analytic model for the bispectrum of galaxies in redshift space
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.
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.
High-Performance data flows using analytical models and measurements
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.
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.
An analytical model of joule heating in piezoresistive microcantilevers.
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.
Estimating recharge rates with analytic element models and parameter estimation
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).
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.
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.
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
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.
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.
On the solvability of two dimensional semigroup gauge theories
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.
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…
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.
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.
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.
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
Enabling analytical and Modeling Tools for Enhanced Disease Surveillance
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
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.
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.
Analytical model for heterogeneous reactions in mixed porous media
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.
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.
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.
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.
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.
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.
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…
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.
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}.
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
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.
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.
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
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.
An Analytical Model of Wave-Induced Longshore Current Based on Power Law Wave Height Decay.
1988-01-01
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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
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
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
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
Solvability of the master equation for dichotomous flow.
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.
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.
New Numerical Integrators Based on Solvability and Splitting
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
A genetic algorithm-based job scheduling model for big data analytics.
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.
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.
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}.
Analytical model for electromagnetic cascades in rotating electric field
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.
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.
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.
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.
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.
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
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.
Quantitative analytical model for magnetic reconnection in hall magnetohydrodynamics
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}.
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.
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.
NASA Astrophysics Data System (ADS)
Tiwari, Purushottam; Wang, Xuewen; Darici, Yesim; He, Jin; Uren, Aykut
Surface plasmon resonance (SPR) is a biophysical technique for the quantitative analysis of bimolecular interactions. Correct identification of the binding model is crucial for the interpretation of SPR data. Bivalent SPR model is governed by non-linear differential equations, which, in general, have no analytical solutions. Therefore, an analytical based approach cannot be employed in order to identify this particular model. There exists a unique signature in the bivalent analyte model, existence of an `optimal analyte concentration', which can distinguish this model from other biphasic models. The unambiguous identification and related analysis of the bivalent analyte model is demonstrated by using theoretical simulations and experimentally measured SPR sensorgrams. Experimental SPR sensorgrams were measured by using Biacore T200 instrument available in Biacore Molecular Interaction Shared Resource facility, supported by NIH Grant P30CA51008, at Georgetown University.
IT vendor selection model by using structural equation model & analytical hierarchy process
NASA Astrophysics Data System (ADS)
Maitra, Sarit; Dominic, P. D. D.
2012-11-01
Selecting and evaluating the right vendors is imperative for an organization's global marketplace competitiveness. Improper selection and evaluation of potential vendors can dwarf an organization's supply chain performance. Numerous studies have demonstrated that firms consider multiple criteria when selecting key vendors. This research intends to develop a new hybrid model for vendor selection process with better decision making. The new proposed model provides a suitable tool for assisting decision makers and managers to make the right decisions and select the most suitable vendor. This paper proposes a Hybrid model based on Structural Equation Model (SEM) and Analytical Hierarchy Process (AHP) for long-term strategic vendor selection problems. The five steps framework of the model has been designed after the thorough literature study. The proposed hybrid model will be applied using a real life case study to assess its effectiveness. In addition, What-if analysis technique will be used for model validation purpose.
Analytic Models for Radiation Induced Loss in Optical Fibers II. A Physical Model,
1984-06-01
and identify by Mock number) PIEL GRUP UB.GR. Optical fibers Analytical models Radiation effects 19. ABSTRACT (ConinueII. anl mwr,f fneciua,, and...conditions specified in the derivation of the equations existed during the irradiations. This is because the functional form of the equations is not...tion is not necessarily incorrect. If one assumes a relatively simple form of re- covery as a function of time, such as an exponential recovery, it can
Promoting Active Learning by Practicing the "Self-Assembly" of Model Analytical Instruments
ERIC Educational Resources Information Center
Algar, W. Russ; Krull, Ulrich J.
2010-01-01
In our upper-year instrumental analytical chemistry course, we have developed "cut-and-paste" exercises where students "build" models of analytical instruments from individual schematic images of components. These exercises encourage active learning by students. Instead of trying to memorize diagrams, students are required to think deeply about…
An Analytic Hierarchy Process for School Quality and Inspection: Model Development and Application
ERIC Educational Resources Information Center
Al Qubaisi, Amal; Badri, Masood; Mohaidat, Jihad; Al Dhaheri, Hamad; Yang, Guang; Al Rashedi, Asma; Greer, Kenneth
2016-01-01
Purpose: The purpose of this paper is to develop an analytic hierarchy planning-based framework to establish criteria weights and to develop a school performance system commonly called school inspections. Design/methodology/approach: The analytic hierarchy process (AHP) model uses pairwise comparisons and a measurement scale to generate the…
ERIC Educational Resources Information Center
Budsankom, Prayoonsri; Sawangboon, Tatsirin; Damrongpanit, Suntorapot; Chuensirimongkol, Jariya
2015-01-01
The purpose of the research is to develop and identify the validity of factors affecting higher order thinking skills (HOTS) of students. The thinking skills can be divided into three types: analytical, critical, and creative thinking. This analysis is done by applying the meta-analytic structural equation modeling (MASEM) based on a database of…
Analytical models of optical refraction in the troposphere.
Nener, Brett D; Fowkes, Neville; Borredon, Laurent
2003-05-01
An extremely accurate but simple asymptotic description (with known error) is obtained for the path of a ray propagating over a curved Earth with radial variations in refractive index. The result is sufficiently simple that analytic solutions for the path can be obtained for linear and quadratic index profiles. As well as rendering the inverse problem trivial for these profiles, this formulation shows that images are uniformly magnified in the vertical direction when viewed through a quadratic refractive-index profile. Nonuniform vertical distortions occur for higher-order refractive-index profiles.
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
Comment on ``Coherent states for exactly solvable potentials''
NASA Astrophysics Data System (ADS)
Toutounji, Mohamad
2013-10-01
In Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.69.012102 69, 012102 (2004), Schreecharan, Panigrahi, and Banerji present a general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials, e.g., Morse and Poschl-Teller. I have examined coherent states of the Morse oscillator presented by the authors and have found them to have incorrect mathematical substitutions. As such, this Comment looks at the correctness of two important equations that have led to their Morse oscillator coherent states.
Design Evaluation of Wind Turbine Spline Couplings Using an Analytical Model: Preprint
Guo, Y.; Keller, J.; Wallen, R.; Errichello, R.; Halse, C.; Lambert, S.
2015-02-01
Articulated splines are commonly used in the planetary stage of wind turbine gearboxes for transmitting the driving torque and improving load sharing. Direct measurement of spline loads and performance is extremely challenging because of limited accessibility. This paper presents an analytical model for the analysis of articulated spline coupling designs. For a given torque and shaft misalignment, this analytical model quickly yields insights into relationships between the spline design parameters and resulting loads; bending, contact, and shear stresses; and safety factors considering various heat treatment methods. Comparisons of this analytical model against previously published computational approaches are also presented.
Improvement of the Analytical Model of a Laminated Core Parametric Motor
NASA Astrophysics Data System (ADS)
Tajima, Katsubumi; Sato, Tadashi; Sakamoto, Yoshinori
A laminated core parametric induction motor has desirable features and the planer structure to make it possible to reduce the production cost of the motor by mass production. In the past work, we showed the validity to apply the two-dimensional reluctance network analytical model to the dynamic analysis of the motor while the rotor is driving. In this paper, we investigate the improvement the accuracy of the analytical method of the motor by using new reluctance network analytical model of the motor. In this model, the magnetic circuits of the stator and the rotor are connected by the variable reluctances that are expressed as the function of the rotating angle.
Evaluation of Analytical Modeling Functions for the Phonation Onset Process.
Petermann, Simon; Kniesburges, Stefan; Ziethe, Anke; Schützenberger, Anne; Döllinger, Michael
2016-01-01
The human voice originates from oscillations of the vocal folds in the larynx. The duration of the voice onset (VO), called the voice onset time (VOT), is currently under investigation as a clinical indicator for correct laryngeal functionality. Different analytical approaches for computing the VOT based on endoscopic imaging were compared to determine the most reliable method to quantify automatically the transient vocal fold oscillations during VO. Transnasal endoscopic imaging in combination with a high-speed camera (8000 fps) was applied to visualize the phonation onset process. Two different definitions of VO interval were investigated. Six analytical functions were tested that approximate the envelope of the filtered or unfiltered glottal area waveform (GAW) during phonation onset. A total of 126 recordings from nine healthy males and 210 recordings from 15 healthy females were evaluated. Three criteria were analyzed to determine the most appropriate computation approach: (1) reliability of the fit function for a correct approximation of VO; (2) consistency represented by the standard deviation of VOT; and (3) accuracy of the approximation of VO. The results suggest the computation of VOT by a fourth-order polynomial approximation in the interval between 32.2 and 67.8% of the saturation amplitude of the filtered GAW.
Evaluation of Analytical Modeling Functions for the Phonation Onset Process
Petermann, Simon; Kniesburges, Stefan; Ziethe, Anke; Schützenberger, Anne; Döllinger, Michael
2016-01-01
The human voice originates from oscillations of the vocal folds in the larynx. The duration of the voice onset (VO), called the voice onset time (VOT), is currently under investigation as a clinical indicator for correct laryngeal functionality. Different analytical approaches for computing the VOT based on endoscopic imaging were compared to determine the most reliable method to quantify automatically the transient vocal fold oscillations during VO. Transnasal endoscopic imaging in combination with a high-speed camera (8000 fps) was applied to visualize the phonation onset process. Two different definitions of VO interval were investigated. Six analytical functions were tested that approximate the envelope of the filtered or unfiltered glottal area waveform (GAW) during phonation onset. A total of 126 recordings from nine healthy males and 210 recordings from 15 healthy females were evaluated. Three criteria were analyzed to determine the most appropriate computation approach: (1) reliability of the fit function for a correct approximation of VO; (2) consistency represented by the standard deviation of VOT; and (3) accuracy of the approximation of VO. The results suggest the computation of VOT by a fourth-order polynomial approximation in the interval between 32.2 and 67.8% of the saturation amplitude of the filtered GAW. PMID:27066108
About solvability of some boundary value problems for Poisson equation in a ball
NASA Astrophysics Data System (ADS)
Koshanova, Maira D.; Usmanov, Kairat I.; Turmetov, Batirkhan Kh.
2016-08-01
In the present paper, we study properties of some integro-differential operators of fractional order. As an application of the properties of these operators for Poisson equation we examine questions on solvability of a fractional analogue of the Neumann problem and analogues of periodic boundary value problems for circular domains. The exact conditions for solvability of these problems are found.
Analytical Model for the Thermonuclear Instability in IGNITOR
NASA Astrophysics Data System (ADS)
Cardinali, A.; Sonnino, G.; Coppi, B.
2013-10-01
The non-linear energy balance equation for thermal equilibrium and stability, is analytically and numerically investigated in order to study the thermonuclear instability in the IGNITOR experiment facility. The expressions for the ion and the electron thermal coefficients, introduced in the thermal energy balance equation, are obtained by solving the nonlinear transport equations relevant to several collisional transport regimes (in particular the banana regime). The differential equation for the temperature profile at equilibrium is solved and the resulting profile is compared with the results obtained by a full transport code. The growth of the perturbation in the temperature is analyzed by integrating the equation in time. A scenario is considered where IGNITOR is led to operate in a slightly sub-critical regime by adding a small fraction of 3He to the nominal 50-50 Deuterium-Tritium mixture and heating the plasma by ICRH power. Sponsored in part by the US DOE.
A complex of analytical models for predicting noise in an aircraft cabin
NASA Astrophysics Data System (ADS)
Efimtsov, B. M.; Lazarev, L. A.
2012-07-01
A series of analytical calculated models for predicting the noise in an aircraft cabin is developed: an orthotropic model, a model with discrete frames, a model with discrete stringers, a model with isolated cells, and a model with a cross system of discrete ribs. The analytical solution is constructed on the basis of the method of space harmonic expansion. Vibrations are represented in the form of double trigonometric series. Strict periodicity allows dividing the series into a large number of independent groups, which makes it possible to effectively perform calculations for large fragments of the fuselage in the entire frequency region both for deterministic and random external force fields.
Analytical model and finite element computation of braking torque in electromagnetic retarder
NASA Astrophysics Data System (ADS)
Ye, Lezhi; Yang, Guangzhao; Li, Desheng
2014-12-01
An analytical model has been developed for analyzing the braking torque in electromagnetic retarder by flux tube and armature reaction method. The magnetic field distribution in air gap, the eddy current induced in the rotor and the braking torque are calculated by the developed model. Two-dimensional and three-dimensional finite element models for retarder have also been developed. Results from the analytical model are compared with those from finite element models. The validity of these three models is checked by the comparison of the theoretical predictions and the measurements from an experimental prototype. The influencing factors of braking torque have been studied.
Analytic optical-constant model derived from Tauc-Lorentz and Urbach tail.
Rodríguez-de Marcos, Luis V; Larruquert, Juan I
2016-12-12
Tauc-Lorentz model is commonly used to describe the dielectric constant of amorphous semiconductors as a function of few parameters. However, this model is not fully analytic and presents other mathematical shortcomings. A modified self-consistent model based on the integration of [E'-(E + ia)]-1 functions using Tauc-Lorentz`s ε2 expression as a weight function is presented. This new model is analytic and meets all other mathematical requirements of optical constants. The main difference with TL model stands at photon energies close to or smaller than the bandgap energy. The new model has been satisfactorily tested on SiC optical constants. Additionally, an analytic extension of the new model has been also developed to include the Urbach tail. The complete model has been tested with Si_{3}N_{4} optical constants, and it enables to extend the optical-constant characterization of materials down to zero energy.
Simple analytic QCD model with perturbative QCD behavior at high momenta
Contreras, Carlos; Espinosa, Olivier; Cvetic, Gorazd; Martinez, Hector E.
2010-10-01
Analytic QCD models are those where the QCD running coupling has the physically correct analytic behavior, i.e., no Landau singularities in the Euclidean regime. We present a simple analytic QCD model in which the discontinuity function of the running coupling at high momentum scales is the same as in perturbative QCD (just like in the analytic QCD model of Shirkov and Solovtsov), but at low scales it is replaced by a delta function which parametrizes the unknown behavior there. We require that the running coupling agree to a high degree with the perturbative coupling at high energies, which reduces the number of free parameters of the model from four to one. The remaining parameter is fixed by requiring the reproduction of the correct value of the semihadronic tau decay ratio.
A Path-Analytic Model of Career Indecision.
ERIC Educational Resources Information Center
Hartman, Bruce W.; And Others
1985-01-01
Tested a path model reflecting developmental and chronic types of career indecision on counseling students (N=164) and high school students (N=155). Data from both samples supported the model, confirming the role of trait anxiety in career indecision. (JAC)
PESTAN: Pesticide Analytical Model Version 4.0 User's Guide
The principal objective of this User's Guide to provide essential information on the aspects such as model conceptualization, model theory, assumptions and limitations, determination of input parameters, analysis of results and sensitivity analysis.
Lumb, Matthew P.; Steiner, Myles A.; Geisz, John F.; Walters, Robert J.
2014-11-21
The analytical drift-diffusion formalism is able to accurately simulate a wide range of solar cell architectures and was recently extended to include those with back surface reflectors. However, as solar cells approach the limits of material quality, photon recycling effects become increasingly important in predicting the behavior of these cells. In particular, the minority carrier diffusion length is significantly affected by the photon recycling, with consequences for the solar cell performance. In this paper, we outline an approach to account for photon recycling in the analytical Hovel model and compare analytical model predictions to GaAs-based experimental devices operating close to the fundamental efficiency limit.
Simplified Analytical Model of a Six-Degree-of-Freedom Large-Gap Magnetic Suspension System
NASA Technical Reports Server (NTRS)
Groom, Nelson J.
1997-01-01
A simplified analytical model of a six-degree-of-freedom large-gap magnetic suspension system is presented. The suspended element is a cylindrical permanent magnet that is magnetized in a direction which is perpendicular to its axis of symmetry. The actuators are air core electromagnets mounted in a planar array. The analytical model consists of an open-loop representation of the magnetic suspension system with electromagnet currents as inputs.
Process models: analytical tools for managing industrial energy systems
Howe, S O; Pilati, D A; Balzer, C; Sparrow, F T
1980-01-01
How the process models developed at BNL are used to analyze industrial energy systems is described and illustrated. Following a brief overview of the industry modeling program, the general methodology of process modeling is discussed. The discussion highlights the important concepts, contents, inputs, and outputs of a typical process model. A model of the US pulp and paper industry is then discussed as a specific application of process modeling methodology. Applications addressed with the case study results include projections of energy demand, conservation technology assessment, energy-related tax policies, and sensitivity analysis. A subsequent discussion of these results supports the conclusion that industry process models are versatile and powerful tools for managing industrial energy systems.
Hybrid Analytical and Data-Driven Modeling for Feed-Forward Robot Control †.
Reinhart, René Felix; Shareef, Zeeshan; Steil, Jochen Jakob
2017-02-08
Feed-forward model-based control relies on models of the controlled plant, e.g., in robotics on accurate knowledge of manipulator kinematics or dynamics. However, mechanical and analytical models do not capture all aspects of a plant's intrinsic properties and there remain unmodeled dynamics due to varying parameters, unmodeled friction or soft materials. In this context, machine learning is an alternative suitable technique to extract non-linear plant models from data. However, fully data-based models suffer from inaccuracies as well and are inefficient if they include learning of well known analytical models. This paper thus argues that feed-forward control based on hybrid models comprising an analytical model and a learned error model can significantly improve modeling accuracy. Hybrid modeling here serves the purpose to combine the best of the two modeling worlds. The hybrid modeling methodology is described and the approach is demonstrated for two typical problems in robotics, i.e., inverse kinematics control and computed torque control. The former is performed for a redundant soft robot and the latter for a rigid industrial robot with redundant degrees of freedom, where a complete analytical model is not available for any of the platforms.
Hybrid Analytical and Data-Driven Modeling for Feed-Forward Robot Control †
Reinhart, René Felix; Shareef, Zeeshan; Steil, Jochen Jakob
2017-01-01
Feed-forward model-based control relies on models of the controlled plant, e.g., in robotics on accurate knowledge of manipulator kinematics or dynamics. However, mechanical and analytical models do not capture all aspects of a plant’s intrinsic properties and there remain unmodeled dynamics due to varying parameters, unmodeled friction or soft materials. In this context, machine learning is an alternative suitable technique to extract non-linear plant models from data. However, fully data-based models suffer from inaccuracies as well and are inefficient if they include learning of well known analytical models. This paper thus argues that feed-forward control based on hybrid models comprising an analytical model and a learned error model can significantly improve modeling accuracy. Hybrid modeling here serves the purpose to combine the best of the two modeling worlds. The hybrid modeling methodology is described and the approach is demonstrated for two typical problems in robotics, i.e., inverse kinematics control and computed torque control. The former is performed for a redundant soft robot and the latter for a rigid industrial robot with redundant degrees of freedom, where a complete analytical model is not available for any of the platforms. PMID:28208697
Analytical solutions for extended surface electrochemical fin models
NASA Astrophysics Data System (ADS)
Cassenti, Brice N.; Nelson, George J.; DeGostin, Matthew B.; Peracchio, Aldo A.; Chiu, Wilson K. S.
2014-11-01
Exact solutions were obtained for variations in the potential and the current for three axisymmetric geometries, with positive, negative and zero curvatures, which simulate current transport in fuel cell electrodes. These solutions can be used to assess the influence of geometry on performance for three dimensional electrode microstructures. A solid oxide fuel cell (SOFC) electrode was selected as a test case for these studies. From the exact solutions, simulations of current flow and potential drop for one dimensional networks in SOFC electrodes were performed. Numerical tests demonstrated that surfaces with positive curvature have greater current flow for the same potential drop due to higher current losses through the lateral surface area. The study also showed that zero curvature solutions will be sufficiently accurate for positive or negative curvature geometries for moderate radius changes, but differ significantly from positive or negative curvature solutions for more extreme radius changes. Analytical solutions indicate fundamental differences in geometry and its influence on current flow. Based on the results of the simulations, an approximate solution, based on one non-dimensional parameter, was developed for estimating the effects of extreme changes in cross-section area.
Semi-analytical model for slug test in unconfined aquifers
NASA Astrophysics Data System (ADS)
Mishra, P. K.; Alves Silva, L. P.; Malama, B.
2015-12-01
We present mathematical model which describes three dimensional flow of water during slug test in saturated and unsaturated zone. Following Mishra and Neuman (2010), we consider four-parameter exponential model to describe soil-water characteristics curves. Furthermore, we represent the effect of oscillatory response in highly conductive aquifers as did Malama et al. (2011), correlating the oscillatory change in head inside of the well with the drawdown in the aquifer. We conclude by comparing developed model with existing models for analyzing slug tests.
Improvement of receptor model use in analytical aspect
NASA Astrophysics Data System (ADS)
Wang, Chu-Fang; Chiang, Pen-Chi; Cheng, Man-Ting; Chiang, Hung-Lung
In this study, four certified particle standards including NIST SRM 1648 urban particulate matter, BCR Reference Material No. 176 city waste incineration ash, NIST SRM 2709 San Joaquin soil, and NIST SRM 1633b coal fly ash were used to simulate ambient particulate matter. Twenty-five samples were prepared with the four certified particulate standards. A total of 23 elements were analyzed per sample, 19 by ICP-AES and ICP-MS, three by IC, and one element, Si, by spectrophotometer. Results showed that combining the three IC-analyzed ionic species with the 19 ICP-AES/MS analyzed elements into the CMB model did not improve the source identification significantly. In addition, when all 23 analyzed chemical species per sample were used in the CMB model, they were still not good enough to effectively make the parameters of the CMB model fit the statistical criteria. Some of high variation and low recovery chemical species, i.e. Cd, V, Sb, etc., may have caused poor CMB model simulation. Omitting some poor quality analyzed species (such as relative analysis error >20%) could improve the CMB model simulation. Therefore, high quality chemical species data are important for the CMB model. In addition, co-linearity of source profiles also affects the CMB model; combining the co-linear sources could enhance the solubility of the CMB model. In this study, a two-step procedure was developed for CMB model simulation to improve source identification.
Analytical modeling of irrigation and land use effects on streamflow in semi-arid conditions
NASA Astrophysics Data System (ADS)
Traylor, Jonathan P.; Zlotnik, Vitaly A.
2016-02-01
Availability and uncertainty in input data are the primary constraints of groundwater modeling. Analytical models assimilate the key and important data, but capture the major traits of the watershed. We study a baseflow-dominated stream, Frenchman Creek in southwestern Nebraska, USA, which has experienced large streamflow reductions since the 1960s and is a subject of various actions on water rights appropriation. The new element of the model is simultaneous analytical consideration of groundwater pumping and land use change effects. Analytical stream depletion rate calculations by various methods show that pumping from the 462 irrigation wells in the basin consumed a large amount of baseflow. The simulated streamflow at the outlet of Frenchman Creek with minimal calibration compares favorably with observed streamflow and indicates the viability of an analytical approach to watersheds with limited hydrogeologic data.
NASA Astrophysics Data System (ADS)
Gong, YanJun; Wu, ZhenSen; Wang, MingJun; Cao, YunHua
2010-01-01
We propose an analytical model of Doppler power spectra in backscatter from arbitrary rough convex quadric bodies of revolution (whose lateral surface is a quadric) rotating around axes. In the global Cartesian coordinate system, the analytical model deduced is suitable for general convex quadric body of revolution. Based on this analytical model, the Doppler power spectra of cones, cylinders, paraboloids of revolution, and sphere-cones combination are proposed. We analyze numerically the influence of geometric parameters, aspect angle, wavelength and reflectance of rough surface of the objects on the broadened spectra because of the Doppler effect. This analytical solution may contribute to laser Doppler velocimetry, and remote sensing of ballistic missile that spin.
An Analytical Model for University Identity and Reputation Strategy Work
ERIC Educational Resources Information Center
Steiner, Lars; Sundstrom, Agneta C.; Sammalisto, Kaisu
2013-01-01
Universities face increasing global competition, pressuring them to restructure and find new identities. A multidimensional model: identity, image and reputation of strategic university identity and reputation work is developed. The model includes: organizational identity; employee and student attitudes; symbolic identity; influence from…
Energy demand analytics using coupled technological and economic models
Impacts of a range of policy scenarios on end-use energy demand are examined using a coupling of MARKAL, an energy system model with extensive supply and end-use technological detail, with Inforum LIFT, a large-scale model of the us. economy with inter-industry, government, and c...
On the Development of Parameterized Linear Analytical Longitudinal Airship Models
NASA Technical Reports Server (NTRS)
Kulczycki, Eric A.; Johnson, Joseph R.; Bayard, David S.; Elfes, Alberto; Quadrelli, Marco B.
2008-01-01
In order to explore Titan, a moon of Saturn, airships must be able to traverse the atmosphere autonomously. To achieve this, an accurate model and accurate control of the vehicle must be developed so that it is understood how the airship will react to specific sets of control inputs. This paper explains how longitudinal aircraft stability derivatives can be used with airship parameters to create a linear model of the airship solely by combining geometric and aerodynamic airship data. This method does not require system identification of the vehicle. All of the required data can be derived from computational fluid dynamics and wind tunnel testing. This alternate method of developing dynamic airship models will reduce time and cost. Results are compared to other stable airship dynamic models to validate the methods. Future work will address a lateral airship model using the same methods.
NASA Technical Reports Server (NTRS)
Oglebay, J. C.
1977-01-01
A thermal analytic model for a 30-cm engineering model mercury-ion thruster was developed and calibrated using the experimental test results of tests of a pre-engineering model 30-cm thruster. A series of tests, performed later, simulated a wide range of thermal environments on an operating 30-cm engineering model thruster, which was instrumented to measure the temperature distribution within it. The modified analytic model is described and analytic and experimental results compared for various operating conditions. Based on the comparisons, it is concluded that the analytic model can be used as a preliminary design tool to predict thruster steady-state temperature distributions for stage and mission studies and to define the thermal interface bewteen the thruster and other elements of a spacecraft.
Analytical solutions and moment analysis of chromatographic models for rectangular pulse injections.
Qamar, Shamsul; Abbasi, Javeria N; Javeed, Shumaila; Shah, Munawar; Khan, Farman U; Seidel-Morgenstern, Andreas
2013-11-08
This work focuses on the analysis of two standard liquid chromatographic models, namely the lumped kinetic model and the equilibrium dispersive model. Analytical solutions, obtained by means of Laplace transformation, are derived for rectangular single solute concentration pulses of finite length and breakthrough curves injected under linear conditions. In order to analyze the solute transport behavior by means of the two models, the temporal moments up to fourth order are calculated from the Laplace-transformed solutions. The limiting cases of continuous injection and negligible mass transfer limitations are evaluated. For validation, the analytical solutions are compared with the numerical solutions of models using the discontinuous Galerkin finite element method. Results of different case studies are discussed for linear and nonlinear adsorption isotherms. The discontinuous Galerkin method is employed to obtain moments for both linear and nonlinear models numerically. Analytically and numerically determined concentration profiles and moments were found to be in good agreement.
An analytical model for porous single crystals with ellipsoidal voids
NASA Astrophysics Data System (ADS)
Mbiakop, A.; Constantinescu, A.; Danas, K.
2015-11-01
A rate-(in)dependent constitutive model for porous single crystals with arbitrary crystal anisotropy (e.g., FCC, BCC, HCP, etc.) containing general ellipsoidal voids is developed. The proposed model, denoted as modified variational model (MVAR), is based on the nonlinear variational homogenization method, which makes use of a linear comparison porous material to estimate the response of the nonlinear porous single crystal. Periodic multi-void finite element simulations are used in order to validate the MVAR for a large number of parameters including cubic (FCC, BCC) and hexagonal (HCP) crystal anisotropy, various creep exponents (i.e., nonlinearity), several stress triaxiality ratios, general void shapes and orientations and various porosity levels. The MVAR model, which involves a priori no calibration parameters, is found to be in good agreement with the finite element results for all cases considered in the rate-dependent context. The model is then used in a predictive manner to investigate the complex response of porous single crystals in several cases with strong coupling between the anisotropy of the crystal and the (morphological) anisotropy induced by the shape and orientation of the voids. Finally, a simple way of calibrating the MVAR with just two adjustable parameters is depicted in the rate-independent context so that an excellent agreement with the FE simulation results is obtained. In this last case, this proposed model can be thought as a generalization of the Gurson model in the context of porous single crystals and general ellipsoidal void shapes and orientations.
An analytical model for hydraulic fracturing in shallow bedrock formations.
dos Santos, José Sérgio; Ballestero, Thomas Paul; Pitombeira, Ernesto da Silva
2011-01-01
A theoretical method is proposed to estimate post-fracturing fracture size and transmissivity, and as a test of the methodology, data collected from two wells were used for verification. This method can be employed before hydrofracturing in order to obtain estimates of the potential hydraulic benefits of hydraulic fracturing. Five different pumping test analysis methods were used to evaluate the well hydraulic data. The most effective methods were the Papadopulos-Cooper model (1967), which includes wellbore storage effects, and the Gringarten-Ramey model (1974), known as the single horizontal fracture model. The hydraulic parameters resulting from fitting these models to the field data revealed that as a result of hydraulic fracturing, the transmissivity increased more than 46 times in one well and increased 285 times in the other well. The model developed by dos Santos (2008), which considers horizontal radial fracture propagation from the hydraulically fractured well, was used to estimate potential fracture geometry after hydrofracturing. For the two studied wells, their fractures could have propagated to distances of almost 175 m or more and developed maximum apertures of about 2.20 mm and hydraulic apertures close to 0.30 mm. Fracturing at this site appears to have expanded and propagated existing fractures and not created new fractures. Hydraulic apertures calculated from pumping test analyses closely matched the results obtained from the hydraulic fracturing model. As a result of this model, post-fracturing geometry and resulting post-fracturing well yield can be estimated before the actual hydrofracturing.
Formal analytical modeling of blog content as personal narrative
NASA Astrophysics Data System (ADS)
Coombs, Michael J.; Jaenisch, Holger M.; Handley, James W.
2008-04-01
This paper contrasts two techniques for analyzing blog content and making use of this information to model blog content. One method uses classical text content and analysis presented for human interpretation. The second method relies on a data mined list of descriptive words characterizing the blogs. We examine the use of different data mining tools, Kryltech's "Subject Search Summarizer", Leximancer, and QUEST, to provide orthogonal and independently generated key word lists. These lists are then converted into Data Models, enabling mathematical modeling of blog content.
Schmidt, P J; Emelko, M B; Thompson, M E
2013-05-01
Quantitative microbial risk assessment (QMRA) is a tool to evaluate the potential implications of pathogens in a water supply or other media and is of increasing interest to regulators. In the case of potentially pathogenic protozoa (e.g. Cryptosporidium oocysts and Giardia cysts), it is well known that the methods used to enumerate (oo)cysts in samples of water and other media can have low and highly variable analytical recovery. In these applications, QMRA has evolved from ignoring analytical recovery to addressing it in point-estimates of risk, and then to addressing variation of analytical recovery in Monte Carlo risk assessments. Often, variation of analytical recovery is addressed in exposure assessment by dividing concentration values that were obtained without consideration of analytical recovery by random beta-distributed recovery values. A simple mathematical proof is provided to demonstrate that this conventional approach to address non-constant analytical recovery in drinking water QMRA will lead to overestimation of mean pathogen concentrations. The bias, which can exceed an order of magnitude, is greatest when low analytical recovery values are common. A simulated dataset is analyzed using a diverse set of approaches to obtain distributions representing temporal variation in the oocyst concentration, and mean annual risk is then computed from each concentration distribution using a simple risk model. This illustrative example demonstrates that the bias associated with mishandling non-constant analytical recovery and non-detect samples can cause drinking water systems to be erroneously classified as surpassing risk thresholds.
Analytic model for assessing the thermal performance of scuba divers
NASA Technical Reports Server (NTRS)
Montgomery, L. D.
1974-01-01
A biothermal model with a physically-controlled subsystem and a dynamically-controlled subsystem is developed to simulate the thermoregulatory system of man under immersed conditions. The model is consistent with experimental data for seminude subjects immersed to neck in cool to temperate water and for 'wet-suited' subjects immersed to neck in cold water. Equations are derived for predicting body temperatures under various dive conditions.
Integration of Analytic and Synthetic Biosystem Models and Data
2005-06-01
environment akin to the Electrical Engineering SPICE modeling and simulation package, in which an open environment and standards-based modularity enable an...the Electrical Engineering SPICE modeling and simulation package, in which an open environment and standards-based modularity enable an enormous...was based on the following perceived requirements (excerpted from the white paper): • Heterogeneous Data Access. The Bio- SPICE DMI must support
FIST and the Analytical Hierarchy Process: Comparative Modeling
2013-03-01
counter the insurgency threat (Ferran et al., 2012). Although this article was written 10 years before the FIST model first appeared, it serves as...engagements. The article states that often innovation stems from small budgets. Small budgets force project managers to be more resourceful and exercise...model is not directly mentioned in this article , but the concept is clearly being formed (Ward, 2004). This article is the first installment of a five
Reliability and structural integrity. [analytical model for calculating crack detection probability
NASA Technical Reports Server (NTRS)
Davidson, J. R.
1973-01-01
An analytic model is developed to calculate the reliability of a structure after it is inspected for cracks. The model accounts for the growth of undiscovered cracks between inspections and their effect upon the reliability after subsequent inspections. The model is based upon a differential form of Bayes' Theorem for reliability, and upon fracture mechanics for crack growth.
NASA Astrophysics Data System (ADS)
Vsekhsvyatskaya, I. S.; Evstratova, E. A.; Kalinin, Yu. K.; Romanchuk, A. A.
1989-08-01
A new analytical model is proposed for the distribution of variations of the relative electron-density contrast of large-scale ionospheric inhomogeneities. The model is characterized by other-than-zero skewness and kurtosis. It is shown that the model is applicable in the interval of horizontal dimensions of inhomogeneities from hundreds to thousands of kilometers.
Fitting the Normal-Ogive Factor Analytic Model to Scores on Tests.
ERIC Educational Resources Information Center
Ferrando, Pere J.; Lorenzo-Seva, Urbano
2001-01-01
Describes how the nonlinear factor analytic approach of R. McDonald to the normal ogive curve can be used to factor analyze test scores. Discusses the conditions in which this model is more appropriate than the linear model and illustrates the applicability of both models using an empirical example based on data from 1,769 adolescents who took the…
An analytical channel thermal noise model for deep-submicron MOSFETs with short channel effects
NASA Astrophysics Data System (ADS)
Jeon, Jongwook; Lee, Jong Duk; Park, Byung-Gook; Shin, Hyungcheol
2007-07-01
In this work, an analytical channel thermal noise model for short channel MOSFETs is derived. The transfer function of the noise was derived by following the Tsividis' method. The proposed model takes into account the channel length modulation, velocity saturation, and carrier heating effects in the gradual channel region. Modeling results show good agreements with the measured noise data.
Analytic model for the dynamic Z-pinch
Piriz, A. R. Sun, Y. B.; Tahir, N. A.
2015-06-15
A model is presented for describing the cylindrical implosion of a shock wave driven by an accelerated piston. It is based in the identification of the acceleration of the shocked mass with the acceleration of the piston. The model yields the separate paths of the piston and the shock. In addition, by considering that the shocked region evolves isentropically, the approximate profiles of all the magnitudes in the shocked region are obtained. The application to the dynamic Z-pinch is presented and the results are compared with the well known snowplow and slug models which are also derived as limiting cases of the present model. The snowplow model is seen to yield a trajectory in between those of the shock and the piston. Instead, the neglect of the inertial effects in the slug model is seen to produce a too fast implosion, and the pressure uniformity is shown to lead to an unphysical instantaneous piston stopping when the shock arrives to the axis.
Human performance modeling for system of systems analytics :soldier fatigue.
Lawton, Craig R.; Campbell, James E.; Miller, Dwight Peter
2005-10-01
The military has identified Human Performance Modeling (HPM) as a significant requirement and challenge of future systems modeling and analysis initiatives as can be seen in the Department of Defense's (DoD) Defense Modeling and Simulation Office's (DMSO) Master Plan (DoD 5000.59-P 1995). To this goal, the military is currently spending millions of dollars on programs devoted to HPM in various military contexts. Examples include the Human Performance Modeling Integration (HPMI) program within the Air Force Research Laboratory, which focuses on integrating HPMs with constructive models of systems (e.g. cockpit simulations) and the Navy's Human Performance Center (HPC) established in September 2003. Nearly all of these initiatives focus on the interface between humans and a single system. This is insufficient in the era of highly complex network centric SoS. This report presents research and development in the area of HPM in a system-of-systems (SoS). Specifically, this report addresses modeling soldier fatigue and the potential impacts soldier fatigue can have on SoS performance.
Herrera-May, Agustín L.; Aguilera-Cortés, Luz A.; Plascencia-Mora, Hector; Rodríguez-Morales, Ángel L.; Lu, Jian
2011-01-01
Multilayered microresonators commonly use sensitive coating or piezoelectric layers for detection of mass and gas. Most of these microresonators have a variable cross-section that complicates the prediction of their fundamental resonant frequency (generally of the bending mode) through conventional analytical models. In this paper, we present an analytical model to estimate the first resonant frequency and deflection curve of single-clamped multilayered microresonators with variable cross-section. The analytical model is obtained using the Rayleigh and Macaulay methods, as well as the Euler-Bernoulli beam theory. Our model is applied to two multilayered microresonators with piezoelectric excitation reported in the literature. Both microresonators are composed by layers of seven different materials. The results of our analytical model agree very well with those obtained from finite element models (FEMs) and experimental data. Our analytical model can be used to determine the suitable dimensions of the microresonator’s layers in order to obtain a microresonator that operates at a resonant frequency necessary for a particular application. PMID:22164071
Analytical model of LDMOS with a single step buried oxide layer
NASA Astrophysics Data System (ADS)
Yuan, Song; Duan, Baoxing; Cao, Zhen; Guo, Haijun; Yang, Yintang
2016-09-01
In this paper, a two-dimensional analytical model is established for the Single-Step Buried Oxide SOI structure proposed by the authors. Based on the two-dimensional Poisson equation, the analytic expression of the surface electric field and potential distributions for the device is achieved. In the SBOSOI (Single-Step Buried Oxide Silicon On Insulator) structure, the buried oxide layer thickness changes stepwise along the drift region, and the electric field in the oxide layer also varies with the different buried oxide layer thickness. These variations will modulate the surface electric field distribution through the electric field modulation effects, which makes the surface electric field distribution more uniform. As a result, the breakdown voltage of the device is improved by 60% compared with the conventional SOI structure. To verify the accuracy of the analytical model, the device simulation software ISE TCAD is utilized, the analytical values are in good agreement with the simulation results by the simulation software. The results verified the established two-dimensional analytical model for SBOSOI structure is valid, and it also illustrates the breakdown voltage enhancement by the electric field modulation effect sufficiently. The established analytical models will provide the physical and mathematical basis for further analysis of the new power devices with the patterned buried oxide layer.
Analytical model of LDMOS with a double step buried oxide layer
NASA Astrophysics Data System (ADS)
Yuan, Song; Duan, Baoxing; Cao, Zhen; Guo, Haijun; Yang, Yintang
2016-09-01
In this paper, a two-dimensional analytical model is established for the Buried Oxide Double Step Silicon On Insulator structure proposed by the authors. Based on the two-dimensional Poisson equation, the analytic expressions of the surface electric field and potential distributions for the device are achieved. In the BODS (Buried Oxide Double Step Silicon On Insulator) structure, the buried oxide layer thickness changes stepwise along the drift region, and the positive charge in the drift region can be accumulated at the corner of the step. These accumulated charge function as the space charge in the depleted drift region. At the same time, the electric field in the oxide layer also varies with the different drift region thickness. These variations especially the accumulated charge will modulate the surface electric field distribution through the electric field modulation effects, which makes the surface electric field distribution more uniform. As a result, the breakdown voltage of the device is improved by 30% compared with the conventional SOI structure. To verify the accuracy of the analytical model, the device simulation software ISE TCAD is utilized, the analytical values are in good agreement with the simulation results by the simulation software. That means the established two-dimensional analytical model for BODS structure is valid, and it also illustrates the breakdown voltage enhancement by the electric field modulation effect sufficiently. The established analytical models will provide the physical and mathematical basis for further analysis of the new power devices with the patterned buried oxide layer.
Hypersingularity, electromagnetic edge condition, and an analytic hyperbolic wedge model.
Li, Lifeng
2014-04-01
It is insufficient to consider that hypersingularity is unphysical solely based on energy considerations. With a proper combination of the two degenerate hypersingular modes, the energy-flux edge condition is satisfied. A hyperbolic wedge model is presented that is much simpler than the previous model for the purpose of studying singular characteristics of the edge fields. This model not only reproduces the sharp edge model as the wedge becomes infinitely sharp but also naturally shows how the two degenerate hypersingular modes of the sharp edge model should be combined. In an incidental study of the effect of rounding edges on numerical computation, I show that the converged results for rounded edges do not converge to a fixed value when the radius of curvature tends to zero, if the corresponding sharp edge supports hypersingularity. I also prove that introducing a small amount of absorption loss for the purpose of improving numerical convergence is effective only when the ratio of the real parts of the permittivities of the two media forming the wedge is close to -1. Finally I remark on the possible illposedness of the hypersingularity problem without imposition of the edge condition.
A generalized analytical compliance model for cartwheel flexure hinges
NASA Astrophysics Data System (ADS)
Wu, Jianwei; Cai, Shuai; Cui, Jiwen; Tan, Jiubin
2015-10-01
Normal cartwheel flexure hinge (NCFH) typically consists of two flexible springs crossing at their mid points. These have been used in compliant mechanism applications owing to the large motion range of such hinges. In this paper, a novel generalized cartwheel flexure hinge (GCFH) is proposed by modifying spring number and varying the angle between two springs on the basis of the NCFH. A 6 degrees of freedom (6-DOF) compliance model of the GCFH was derived. Validity of this model was demonstrated using finite element analysis simulation and experimental results on a GCFH with 3 pairs of springs and 70° angle. According to the model, influence of distribution and shape parameters of GCFH on performance was analyzed. Characteristics such as compliance, off-axis/axis compliance ratio, motion precision, and capacity of rotation were determined. Results show that the GCFH can achieve improved performance compared to NCFH with optimized GCFH parameters.
Dynamic test/analysis correlation using reduced analytical models
NASA Technical Reports Server (NTRS)
Mcgowan, Paul E.; Angelucci, A. F.; Javeed, Mehzad
1992-01-01
Test/analysis correlation is an important aspect of the verification of analysis models which are used to predict on-orbit response characteristics of large space structures. This paper presents results of a study using reduced analysis models for performing dynamic test/analysis correlation. The reduced test-analysis model (TAM) has the same number and orientation of DOF as the test measurements. Two reduction methods, static (Guyan) reduction and the Improved Reduced System reduction, are applied to the test/analysis correlation of a laboratory truss structure. Simulated test results and modal test data are used to examine the performance of each method. It is shown that selection of DOF to be retained in the TAM is critical when large structural masses are involved. In addition, the use of modal test results may provide difficulties in TAM accuracy even if a large number of DOF are retained in the TAM.
Dynamic test/analysis correlation using reduced analytical models
NASA Technical Reports Server (NTRS)
Mcgowan, Paul E.; Angelucci, A. Filippo; Javeed, Mehzad
1992-01-01
Test/analysis correlation is an important aspect of the verification of analysis models which are used to predict on-orbit response characteristics of large space structures. This paper presents results of a study using reduced analysis models for performing dynamic test/analysis correlation. The reduced test-analysis model (TAM) has the same number and orientation of DOF as the test measurements. Two reduction methods, static (Guyan) reduction and the Improved Reduced System (IRS) reduction, are applied to the test/analysis correlation of a laboratory truss structure. Simulated test results and modal test data are used to examine the performance of each method. It is shown that selection of DOF to be retained in the TAM is critical when large structural masses are involved. In addition, the use of modal test results may provide difficulties in TAM accuracy even if a large number of DOF are retained in the TAM.
Analytical and numerical models to predict the behavior of unbonded flexible risers under torsion
NASA Astrophysics Data System (ADS)
Ren, Shao-fei; Xue, Hong-xiang; Tang, Wen-yong
2016-04-01
This paper presents analytical and numerical models to predict the behavior of unbonded flexible risers under torsion. The analytical model takes local bending and torsion of tensile armor wires into consideration, and equilibrium equations of forces and displacements of layers are deduced. The numerical model includes lay angle, cross-sectional profiles of carcass, pressure armor layer and contact between layers. Abaqus/Explicit quasi-static simulation and mass scaling are adopted to avoid convergence problem and excessive computation time caused by geometric and contact nonlinearities. Results show that local bending and torsion of helical strips may have great influence on torsional stiffness, but stress related to bending and torsion is negligible; the presentation of anti-friction tapes may have great influence both on torsional stiffness and stress; hysteresis of torsion-twist relationship under cyclic loading is obtained by numerical model, which cannot be predicted by analytical model because of the ignorance of friction between layers.
Analytic model for assessing thermal performance of SCUBA divers
NASA Technical Reports Server (NTRS)
Montgomery, L. D.
1975-01-01
To assist design of adequate protective clothing, mathematical model of man's thermoregulatory system has been developed so that body thermal responses under immersed conditions can be predicted accurately. Experimental data encompassed wide range of water temperatures, protective clothing, breathing-gas mixtures, and durations of immersion.
Analytical models integrated with satellite images for optimized pest management
Technology Transfer Automated Retrieval System (TEKTRAN)
The global field protection (GFP) was developed to protect and optimize pest management resources integrating satellite images for precise field demarcation with physical models of controlled release devices of pesticides to protect large fields. The GFP was implemented using a graphical user interf...
Material characteristics for an analytic hypervelocity impact performance model
NASA Astrophysics Data System (ADS)
Miller, Joshua; Ryan, Shannon
2015-06-01
A performance model has recently been developed to describe the evolution of a hypervelocity impact of a threat with a dual-wall, Whipple shield. The Whipple shield uses an initial sacrificial wall to initiate threat fragmentation and melt before the debris expands over a void and is subsequently arrested by the second wall in front of a critical component. As such, understanding the initial interaction of the threat particle and the sacrificial wall is crucial to modeling the overall shield performance. Among the key material parameters that must be defined for the threat particle and sacrificial wall are the equilibrium shock wave states and tensile response to vacuum exposure. This paper documents the work performed to obtain the necessary material characteristics and a description of the fragmentation of the threat needed for the performance model. The results from the use of these quantities within the model are compared here with hydrodynamic simulations and available experimental records that have sought to characterize these parameters.
V/STOL shaft propulsion system analytical performance model
NASA Technical Reports Server (NTRS)
Sulkoske, R. A.; Tucker, R. N.; Holmes, J. E.
1977-01-01
Several classes of system performance simulations of V/STOL propulsion systems are presented. A digital simulation approach for a typical system (a propulsion system made up of three engines, shafts and gearbox, and remote lift fan) is given with a description of the general philosophy, solution options and model flexibility.
A Meta-Analytic Review of Behavior Modeling Training
ERIC Educational Resources Information Center
Taylor, Paul J.; Russ-Eft, Darlene F.; Chan, Daniel W. L.
2005-01-01
A meta-analysis of 117 studies evaluated the effects of behavior modeling training (BMT) on 6 training outcomes, across characteristics of training design. BMT effects were largest for learning outcomes, smaller for job behavior, and smaller still for results outcomes. Although BMT effects on declarative knowledge decayed over time, training…
Integrability of the Rabi Model
Braak, D.
2011-09-02
The Rabi model is a paradigm for interacting quantum systems. It couples a bosonic mode to the smallest possible quantum model, a two-level system. I present the analytical solution which allows us to consider the question of integrability for quantum systems that do not possess a classical limit. A criterion for quantum integrability is proposed which shows that the Rabi model is integrable due to the presence of a discrete symmetry. Moreover, I introduce a generalization with no symmetries; the generalized Rabi model is the first example of a nonintegrable but exactly solvable system.
Analytical modeling of squeeze air film damping of biomimetic MEMS directional microphone
NASA Astrophysics Data System (ADS)
Ishfaque, Asif; Kim, Byungki
2016-08-01
Squeeze air film damping is introduced in microelectromechanical systems due to the motion of the fluid between two closely spaced oscillating micro-structures. The literature is abundant with different analytical models to address the squeeze air film damping effects, however, there is a lack of work in modeling the practical sensors like directional microphones. Here, we derive an analytical model of squeeze air film damping of first two fundamental vibration modes, namely, rocking and bending modes, of a directional microphone inspired from the fly Ormia ochracea's ear anatomy. A modified Reynolds equation that includes compressibility and rarefaction effects is used in the analysis. Pressure distribution under the vibrating diaphragm is derived by using Green's function. From mathematical modeling of the fly's inspired mechanical model, we infer that bringing the damping ratios of both modes in the critical damping range enhance the directional sensitivity cues. The microphone parameters are varied in derived damping formulas to bring the damping ratios in the vicinity of critical damping, and to show the usefulness of the analytical model in tuning the damping ratios of both modes. The accuracy of analytical damping results are also verified by finite element method (FEM) using ANSYS. The FEM results are in full compliance with the analytical results.
NASA Technical Reports Server (NTRS)
Gedge, M. R.
1979-01-01
Analytical models were developed to study the effect of flow contraction and screening on inflow distortions to identify qualitative design criteria. Results of the study are that: (1) static testing distortions are due to atmospheric turbulence, nacelle boundary layer, exhaust flow reingestion, flow over stand, ground plane, and engine casing; (2) flow contraction suppresses, initially, turbulent axial velocity distortions and magnifies turbulent transverse velocity distortions; (3) perforated plate and gauze screens suppress axial components of velocity distortions to a degree determined by the screen pressure loss coefficient; (4) honeycomb screen suppress transverse components of velocity distortions to a degree determined by the length to diameter ratio of the honeycomb; (5) acoustic transmission loss of perforated plate is controlled by the reactance of its acoustic impedance; (6) acoustic transmission loss of honeycomb screens is negligible; and (7) a model for the direction change due to a corner between honeycomb panels compares favorably with measured data.
An analytical model for in situ extraction of organic vapors
Roy, W.R.; Griffin, R.A.
1991-01-01
This paper introduces a simple convective-flow model that can be used as a screening tool and for conducting sensitivity analyses for in situ vapor extraction of organic compounds from porous media. An assumption basic to this model was that the total mass of volatile organic chemicals (VOC) exists in three forms: as vapors, in the soil solution, and adsorbed to soil particles. The equilibrium partitioning between the vapor-liquid phase was described by Henry's law constants (K(H)) and between the liquid-soil phase by soil adsorption constants (K(d)) derived from soil organic carbon-water partition coefficients (K(oc)). The model was used to assess the extractability of 36 VOCs from a hypothetical site. Most of the VOCs appeared to be removable from soil by this technology, although modeling results suggested that rates for the alcohols and ketones may be very slow. In general, rates for weakly adsorbed compounds (K(oc) < 100 mL/g) were significantly higher when K(H) was greater than 10-4 atm??m3??mol-1. When K(oc) was greater than about 100 mL/g, the rates of extraction were sensitive to the amount of organic carbon present in the soil. The air permeability of the soil material (k) was a critical factor. In situ extraction needs careful evaluation when k is less than 10 millidarcies to determine its applicability. An increase in the vacuum applied to an extraction well accelerated removal rates but the diameter of the well had little effect. However, an increase in the length of the well screen open to the contaminated zone significantly affected removal rates, especially in low-permeability materials.This paper introduces a simple convective-flow model that can be used as a screening tool and for conducting sensitivity analyses for in situ vapor extraction of organic compounds from porous media. An assumption basic to this model was that the total mass of volatile organic chemicals (VOC) exists in three forms: as vapors, in the soil solution, and adsorbed to soil
An Analytic Model Of Thermal Drift In Piezoresistive Microcantilever Sensors
Loui, A; Elhadj, S; Sirbuly, D J; McCall, S K; Hart, B R; Ratto, T V
2009-08-26
A closed form semi-empirical model has been developed to understand the physical origins of thermal drift in piezoresistive microcantilever sensors. The two-component model describes both the effects of temperature-related bending and heat dissipation on the piezoresistance. The temperature-related bending component is based on the Euler-Bernoulli theory of elastic deformation applied to a multilayer cantilever. The heat dissipation component is based on energy conservation per unit time for a piezoresistive cantilever in a Wheatstone bridge circuit, representing a balance between electrical power input and heat dissipation into the environment. Conduction and convection are found to be the primary mechanisms of heat transfer, and the dependence of these effects on the thermal conductivity, temperature, and flow rate of the gaseous environment is described. The thermal boundary layer value which defines the length scale of the heat dissipation phenomenon is treated as an empirical fitting parameter. Using the model, it is found that the cantilever heat dissipation is unaffected by the presence of a thin polymer coating, therefore the residual thermal drift in the differential response of a coated and uncoated cantilever is the result of non-identical temperature-related bending. Differential response data shows that residual drift is eliminated under isothermal laboratory conditions but not the unregulated and variable conditions that exist in the outdoor environment (i.e., the field). The two-component model is then validated by simulating the thermal drifts of an uncoated and a coated piezoresistive cantilever under field conditions over a 24 hour period using only meteorological data as input.
Analytical and scale model research aimed at improved hangglider design
NASA Technical Reports Server (NTRS)
Kroo, I.; Chang, L. S.
1979-01-01
Research consisted of a theoretical analysis which attempts to predict aerodynamic characteristics using lifting surface theory and finite-element structural analysis as well as an experimental investigation using 1/5 scale elastically similar models in the NASA Ames 2m x 3m (7' x 10') wind tunnel. Experimental data were compared with theoretical results in the development of a computer program which may be used in the design and evaluation of ultralight gliders.
Simplified analytical dynamic model for a parallel prosthetic elbow.
Mendoza-Vazquez, Rafael; Escudero-Uribe, Apolo Z; Fernandez-Mulia, Raul
2007-01-01
A three degree of freedom elbow prosthesis impelled by linear actuators disposed in parallel is modeled by the Lagrange-Euler method. The method proposes to replace a parallel mechanism with an equivalent serial topology with the purpose of calculating the Lagrangian, however the parallel topology is used for the calculus of forces and torques. The result is a simplification in the mathematical analysis without an important loss in precision.
Analytical Modeling of Medium Access Control Protocols in Wireless Networks
2006-03-01
provide the basic functionalities that are common to any com - puter network. The proposed modeling framework focuses on the interactions between the...colleagues I had the pleasure to meet at the Computer Com - munication Research Group (CCRG). In particular, I would like to thank Marco Spohn, Re- nato...Brazil), the Baskin Chair of Com - puter Engineering at UCSC, the National Science Foundation under Grant CNS-0435522, the UCOP CLC under Grant SC-05
An analytical model of self-starting thermoacoustic engines
NASA Astrophysics Data System (ADS)
Benavides, Efrýn Moreno
2006-06-01
This paper presents a theoretical model of thermoacoustic engines. It aims for a better physical understanding of the power production of these devices. The main idea that supports the work is that the power output emerges from a thermodynamic cycle. The fluid near the heat exchangers is assumed to follow a thermodynamic cycle such as in a closed chamber of a Stirling reciprocating engine. This analogy between thermoacoustic engines and Stirling reciprocating engines introduces a lumped element in the model as the closed chamber of the Stirling engine. In the analogy, the boundaries of this lumped element are the pistons of the chamber, and the kinematical mechanism of the reciprocating engine is the acoustic process in the pipes. The position of the pistons is fixed by studying the longitudinal heat transfer process and the mass conservation. The set of equations obtained can be solved by using the mathematical limit that represents the actual small movement of the pistons. The result is four linear algebraic equations that can be easily solved in several practical cases. One outcome of this approach is the selection of a few dimensionless design parameters useful for any configuration of the engine. Another outcome is a simplified method of calculating the initial power around a self-starting point of a thermoacoustic engine. Finally, the threshold of several thermoacoustic devices is calculated with the present model and compared with the experimental results reported in the scientific literature.
Semi-analytical modeling of the NIO1 source
Cazzador, M.; Cavenago, M.; Serianni, G.; Veltri, P.
2015-04-08
NIO1 is a compact and versatile negative ion source, with a total current of 130 mA accelerated to 60 keV. Negative ions are created inside the plasma, which is inductively coupled to an external rf cylindrical coil operating in the range of 2 ± 0.2 MHz. The plasma is confined in the source chamber (a 50 mm radius cylinder) by a multipole magnetic field and the ions are extracted through a 3x3 matrix of apertures. The use of cesium, to enhance the negative ion production by H{sub 0} bombardment of the surfaces, is foreseen in a second stage of the operation, so that at present time the source is operating in pure volume configuration. This paper presents a model aimed to describe the main physical phenomena occurring in the source, focusing on the rf coupling with the plasma and the evolution of plasma parameters in the source. With respect to more sophisticated models of negative ion sources here we aimed to develop a fast tool capable of qualitatively describing the response of the system to variations in the basic operating parameters. The findings of this models is finally compared with the first experimental results of NIO1.
An Analytic Model of Close-Range Blast Fragment Loading
NASA Astrophysics Data System (ADS)
Rottenkolber, Ernst; Arnold, Werner
2006-07-01
The effects of blast-fragmentation warheads need to be carefully characterized in a variety of applications like passive and active vehicle protection or hard target defeat and TBM defense. With these applications in mind, we have developed a collection of tools called FI-BLAST (Fast Interface for Blast-Fragment Load Analysis of Structures). In the present paper we describe the essential part of these tools, namely the close range blast-fragment model. The meaning of "close range" is here defined as the standoff to a charge at which blast effects can inflict serious damage on massive structures. In order to quantify our model's range of validity, examples of measured and calculated momentum of bare and confined charges are given in the present paper. Short (L/D = 0.5) and long (L/D = 5) cylindrical charges are included as well as spherical charges. The presented examples demonstrate that the model gives reasonable results in the intended domains of application.
International Space Station Microgravity Analytical Model Correlation And Update
NASA Technical Reports Server (NTRS)
DelBasso, Steve; Laible, Michael; OKeefe, Edmund; Scheer, Steven A.
2003-01-01
The acceleration environment aboard the completed International Space Station (ISS) is a key resource for scientific and technological endeavors. Hardware verification activIties and early measurements indicate that the ISS is well on the way of meeting these "Assembly Complete" "microgravity" provisions, however, the simulation models that compute these accelerations have, to date, lacked the high degree of empirical validation typical of standard aerospace industry practices. Assembly stage, on-orbit measurements are used to address this shortcoming and to develop higher confidence in the simulation models. The Phase I correlation results show the analyses to be consistently conservative, producing higher than measured levels. The 25 to 30% greater quasi-steady computations are deemed acceptable for verification. Updates are made to localized structural dynamic and vibroacoustic parameters that reduce responses in selected one-third octave bands by almost 50%. These models are then used for the Assembly Complete verification analysis which concludes that the ISS vehicle meets the ISS microgravity requirements with minor reservations. Two of the sixteen rack are marginally non-compliant in the quasi-steady regime, and operational constraints are needed on the U. S. Lab and ESA APM vacuum resource vents, and the Russian Resistive Exercise Device in the structural dynamic regime.
Analytical model of range-Doppler image of rough rotating cones
NASA Astrophysics Data System (ADS)
Luo, Long-gang; Wu, Zhen-sen; Liao, Run-gui
2013-09-01
The technique of laser range-Doppler image has get growing attentions from aerospace and national defense experts. Recently, in laser range-Doppler image system, laser scatter feature has been used for target ranging and orientation. Laser range-Doppler image can identify the moving components of the aeroplane, and detect the moving disk and sphere. Meanwhile, it is also widely used in detection of the moving gesture of the aerospace, discover of the target micro-motion and the measurement of the local fluid velocity. The laser range-Doppler image of target is the pulse laser scatter feature of the rotating target, which can reflect the shape, attitude and surface material of the target. For instance, detection of the flight gesture of target, identification of the warhead, the rotation of structures in a target, and the target torsional state. An analytical model of laser range-Doppler image of cones rotating around their axes is proposed in this paper. The analytical model can provide the effects of geometric parameters, the roughness of the surface, attitude and pulse duration on laser range-Doppler image. This analytical model can degenerate into the analytical model of Doppler spectra for plane waves. The influences of geometry parameters and attitude are analyzed numerically by using the analytical model. The results indicate that the laser range-Doppler image of cone can show the information about geometrical shape and attitude of target. Combining the theory and measurements, the analytical model can be used for identifying physical parameters and geometrical parameters of cone. This analytical solution may contribute to the laser Doppler velocimetry and ladar applications.
Analytical, Experimental, and Modelling Studies of Lunar and Terrestrial Rocks
NASA Technical Reports Server (NTRS)
Haskin, Larry A.
1997-01-01
The goal of our research has been to understand the paths and the processes of planetary evolution that produced planetary surface materials as we find them. Most of our work has been on lunar materials and processes. We have done studies that obtain geological knowledge from detailed examination of regolith materials and we have reported implications for future sample-collecting and on-surface robotic sensing missions. Our approach has been to study a suite of materials that we have chosen in order to answer specific geologic questions. We continue this work under NAG5-4172. The foundation of our work has been the study of materials with precise chemical and petrographic analyses, emphasizing analysis for trace chemical elements. We have used quantitative models as tests to account for the chemical compositions and mineralogical properties of the materials in terms of regolith processes and igneous processes. We have done experiments as needed to provide values for geochemical parameters used in the models. Our models take explicitly into account the physical as well as the chemical processes that produced or modified the materials. Our approach to planetary geoscience owes much to our experience in terrestrial geoscience, where samples can be collected in field context and sampling sites revisited if necessary. Through studies of terrestrial analog materials, we have tested our ideas about the origins of lunar materials. We have been mainly concerned with the materials of the lunar highland regolith, their properties, their modes of origin, their provenance, and how to extrapolate from their characteristics to learn about the origin and evolution of the Moon's early igneous crust. From this work a modified model for the Moon's structure and evolution is emerging, one of globally asymmetric differentiation of the crust and mantle to produce a crust consisting mainly of ferroan and magnesian igneous rocks containing on average 70-80% plagioclase, with a large
Analytical modeling and experimental validation of a V-shape piezoelectric ultrasonic transducer
NASA Astrophysics Data System (ADS)
Li, Xiaoniu; Yao, Zhiyuan
2016-07-01
In this paper, an analytical model of a V-shape piezoelectric ultrasonic transducer is presented. The V-shape piezoelectric ultrasonic transducer has been widely applied to the piezoelectric actuator (ultrasonic motor), ultrasonic aided fabrication, sensor, and energy harvesting device. The V-shape piezoelectric ultrasonic transducer consists of two Langevin-type transducers connected together through a coupling point with a certain coupling angle. Considering the longitudinal and lateral movements of a single beam, the symmetrical and asymmetrical modals of the V-shape piezoelectric ultrasonic transducer are calculated. By using Hamilton-Lagrange equations, the electromechanical coupling model of the V-shape piezoelectric ultrasonic transducer is proposed. The influence of the coupling angle and cross-section on modal characteristics and electromechanical coupling coefficient are analyzed by the analytical model. A prototype of the V-shape piezoelectric ultrasonic transducer is fabricated, and the results of the experiments are in good agreement with the analytical model.
Analytical models of calcium binding in a calcium channel
Liu, Jinn-Liang; Eisenberg, Bob
2014-08-21
The anomalous mole fraction effect of L-type calcium channels is analyzed using a Fermi like distribution with the experimental data of Almers and McCleskey [J. Physiol. 353, 585 (1984)] and the atomic resolution model of Lipkind and Fozzard [Biochemistry 40, 6786 (2001)] of the selectivity filter of the channel. Much of the analysis is algebraic, independent of differential equations. The Fermi distribution is derived from the configuration entropy of ions and water molecules with different sizes, different valences, and interstitial voids between particles. It allows us to calculate potentials and distances (between the binding ion and the oxygen ions of the glutamate side chains) directly from the experimental data using algebraic formulas. The spatial resolution of these results is comparable with those of molecular models, but of course the accuracy is no better than that implied by the experimental data. The glutamate side chains in our model are flexible enough to accommodate different types of binding ions in different bath conditions. The binding curves of Na{sup +} and Ca{sup 2+} for [CaCl{sub 2}] ranging from 10{sup −8} to 10{sup −2} M with a fixed 32 mM background [NaCl] are shown to agree with published Monte Carlo simulations. The Poisson-Fermi differential equation—that includes both steric and correlation effects—is then used to obtain the spatial profiles of energy, concentration, and dielectric coefficient from the solvent region to the filter. The energy profiles of ions are shown to depend sensitively on the steric energy that is not taken into account in the classical rate theory. We improve the rate theory by introducing a steric energy that lumps the effects of excluded volumes of all ions and water molecules and empty spaces between particles created by Lennard-Jones type and electrostatic forces. We show that the energy landscape varies significantly with bath concentrations. The energy landscape is not constant.
Leasing vs. owning a medical office: an analytical model.
Tolbert, Samuel H; Wood, Carol P
2007-01-01
Physicians often face a major financial dilemma: To lease or own their medical office. This article takes a set of typical assumptions for a real estate market and analyzes the capital costs, cash flow, and investment implications of the option of leasing a medical office versus owning a similar property. The paper analyzes the financial aspects of each option and the impact on net physician income and potential return-on-investment. A model for analysis is presented that can be used by practitioners who advise physicians in such decision-making.
Analytics For Distracted Driver Behavior Modeling in Dilemma Zone
Li, Jan-Mou; Malikopoulos, Andreas; Thakur, Gautam; Vatsavai, Raju
2014-01-01
In this paper, we present the results obtained and insights gained through the analysis of TRB contest data. We used exploratory analysis, regression, and clustering models for gaining insights into the driver behavior in a dilemma zone while driving under distraction. While simple exploratory analysis showed the distinguishing driver behavior patterns among different popu- lation groups in the dilemma zone, regression analysis showed statically signification relationships between groups of variables. In addition to analyzing the contest data, we have also looked into the possible impact of distracted driving on the fuel economy.
Three-phase CFD analytical modeling of blood flow.
Jung, J.; Hassanein, A.; Mathematics and Computer Science
2008-01-01
The behavior of blood cells in disturbed flow regions of arteries has significant relevance for understanding atherogenesis. However, their distribution with red blood cells (RBCs) and leukocytes is not so well studied and understood. Our three-phase computational fluid dynamics approach including plasma, RBCs, and leukocytes was used to numerically simulate the local hemodynamics in such a flow regime. This model has tracked the wall shear stress (WSS), phase distributions, and flow patterns for each phase in a concentrated suspension shear flow of blood. Unlike other computational approaches, this approach does not require dispersion coefficients as an input. The non-Newtonian viscosity model was applied to a wide physiological range of hematocrits, including low shear rates. The migration and segregation of blood cells in disturbed flow regions were computed, and the results compared favorably with available experimental data. The predicted higher leukocyte concentration was correlated with relatively low WSS near the stenosis having a high WSS. This behavior was attributed to flow-dependent interactions of the leukocytes with RBCs in pulsatile flow. This three-phase hemodynamic analysis may have application to vulnerable plaque formation in arteries with in vivo complex flow conditions.
Semi-analytical modelling of positive corona discharge in air
NASA Astrophysics Data System (ADS)
Pontiga, Francisco; Yanallah, Khelifa; Chen, Junhong
2013-09-01
Semianalytical approximate solutions of the spatial distribution of electric field and electron and ion densities have been obtained by solving Poisson's equations and the continuity equations for the charged species along the Laplacian field lines. The need to iterate for the correct value of space charge on the corona electrode has been eliminated by using the corona current distribution over the grounded plane derived by Deutsch, which predicts a cos m θ law similar to Warburg's law. Based on the results of the approximated model, a parametric study of the influence of gas pressure, the corona wire radius, and the inter-electrode wire-plate separation has been carried out. Also, the approximate solutions of the electron number density has been combined with a simplified plasma chemistry model in order to compute the ozone density generated by the corona discharge in the presence of a gas flow. This work was supported by the Consejeria de Innovacion, Ciencia y Empresa (Junta de Andalucia) and by the Ministerio de Ciencia e Innovacion, Spain, within the European Regional Development Fund contracts FQM-4983 and FIS2011-25161.
Development of an analytical model for organic-fluid fouling
Panchal, C.B.; Watkinson, A.P.
1994-10-01
The research goal of this project is to determine ways to effectively mitigate fouling in organic fluids: hydrocarbons and derived fluids. The fouling research focuses on the development of methodology for determining threshold conditions for fouling. Initially, fluid containing chemicals known to produce foulant is analyzed; subsequently, fouling of industrial fluids is investigated. The fouling model developed for determining the effects of physical parameters is the subject of this report. The fouling model is developed on the premise that the chemical reaction for generation of precursor can take place in the bulk fluid, in the thermal-boundary layer, or at the fluid/wall interface, depending upon the interactive effects of fluid dynamics, heat and mass transfer, and the controlling chemical reaction. In the analysis, the experimental data are examined for fouling deposition of polyperoxide produced by autoxidation of indene in kerosene. The effects of fluid and wall temperatures for two flow geometries are analyzed. The results show that the relative effects of physical parameters on the fouling rate differ for the three fouling mechanisms. Therefore, to apply the closed-flow-loop data to industrial conditions, the controlling mechanism must be identified.
Analytical modeling of structure-soil systems for lunar bases
NASA Technical Reports Server (NTRS)
Macari-Pasqualino, Jose Emir
1989-01-01
The study of the behavior of granular materials in a reduced gravity environment and under low effective stresses became a subject of great interest in the mid 1960's when NASA's Surveyor missions to the Moon began the first extraterrestrial investigation and it was found that Lunar soils exhibited properties quite unlike those on Earth. This subject gained interest during the years of the Apollo missions and more recently due to NASA's plans for future exploration and colonization of Moon and Mars. It has since been clear that a good understanding of the mechanical properties of granular materials under reduced gravity and at low effective stress levels is of paramount importance for the design and construction of surface and buried structures on these bodies. In order to achieve such an understanding it is desirable to develop a set of constitutive equations that describes the response of such materials as they are subjected to tractions and displacements. This presentation examines issues associated with conducting experiments on highly nonlinear granular materials under high and low effective stresses. The friction and dilatancy properties which affect the behavior of granular soils with low cohesion values are assessed. In order to simulate the highly nonlinear strength and stress-strain behavior of soils at low as well as high effective stresses, a versatile isotropic, pressure sensitive, third stress invariant dependent, cone-cap elasto-plastic constitutive model was proposed. The integration of the constitutive relations is performed via a fully implicit Backward Euler technique known as the Closest Point Projection Method. The model was implemented into a finite element code in order to study nonlinear boundary value problems associated with homogeneous as well as nonhomogeneous deformations at low as well as high effective stresses. The effect of gravity (self-weight) on the stress-strain-strength response of these materials is evaluated. The calibration
Fatigue of notched fiber composite laminates. Part 1: Analytical model
NASA Technical Reports Server (NTRS)
Mclaughlin, P. V., Jr.; Kulkarni, S. V.; Huang, S. N.; Rosen, B. W.
1975-01-01
A description is given of a semi-empirical, deterministic analysis for prediction and correlation of fatigue crack growth, residual strength, and fatigue lifetime for fiber composite laminates containing notches (holes). The failure model used for the analysis is based upon composite heterogeneous behavior and experimentally observed failure modes under both static and fatigue loading. The analysis is consistent with the wearout philosophy. Axial cracking and transverse cracking failure modes are treated together in the analysis. Cracking off-axis is handled by making a modification to the axial cracking analysis. The analysis predicts notched laminate failure from unidirectional material fatique properties using constant strain laminate analysis techniques. For multidirectional laminates, it is necessary to know lamina fatique behavior under axial normal stress, transverse normal stress and axial shear stress. Examples of the analysis method are given.
An analytic radiative transfer model for a coupled atmosphere and leaf canopy
NASA Technical Reports Server (NTRS)
Liang, Shunlin; Strahler, Alan H.
1995-01-01
A new analytical radiative transfer model of a leaf canopy is developed that approximates multiple-scattering radiance by a four-stream formulation. The canopy model is coupled to a homogeneous atmospheric model as well as a non-Lambertian lower boundary soil surface. The same four-stream formulation is also used for the calculation of multiple scattering in the atmosphere. Comparisons of radiance derived from the four-stream model with those calculated by an iterative numerical solution of the radiative transfer equation show that the analytic model has a very high accuracy, even with a turbid atmosphere and a very dense canopy in which multiple scattering dominates. Because the coupling of canopy and atmospheric models fully accommodates anisotropic surface reflectance and atmospheric scattering and its effect on directional radiance, the model is especially useful for application to directional radiance and measurements obtained by remote sensing. Retrieval of biophysical parameters using this model is under investigation.
Mechanistic analytical models for long-distance seed dispersal by wind.
Katul, G G; Porporato, A; Nathan, R; Siqueira, M; Soons, M B; Poggi, D; Horn, H S; Levin, S A
2005-09-01
We introduce an analytical model, the Wald analytical long-distance dispersal (WALD) model, for estimating dispersal kernels of wind-dispersed seeds and their escape probability from the canopy. The model is based on simplifications to well-established three-dimensional Lagrangian stochastic approaches for turbulent scalar transport resulting in a two-parameter Wald (or inverse Gaussian) distribution. Unlike commonly used phenomenological models, WALD's parameters can be estimated from the key factors affecting wind dispersal--wind statistics, seed release height, and seed terminal velocity--determined independently of dispersal data. WALD's asymptotic power-law tail has an exponent of -3/2, a limiting value verified by a meta-analysis for a wide variety of measured dispersal kernels and larger than the exponent of the bivariate Student t-test (2Dt). We tested WALD using three dispersal data sets on forest trees, heathland shrubs, and grassland forbs and compared WALD's performance with that of other analytical mechanistic models (revised versions of the tilted Gaussian Plume model and the advection-diffusion equation), revealing fairest agreement between WALD predictions and measurements. Analytical mechanistic models, such as WALD, combine the advantages of simplicity and mechanistic understanding and are valuable tools for modeling large-scale, long-term plant population dynamics.
A Bayesian Multi-Level Factor Analytic Model of Consumer Price Sensitivities across Categories
ERIC Educational Resources Information Center
Duvvuri, Sri Devi; Gruca, Thomas S.
2010-01-01
Identifying price sensitive consumers is an important problem in marketing. We develop a Bayesian multi-level factor analytic model of the covariation among household-level price sensitivities across product categories that are substitutes. Based on a multivariate probit model of category incidence, this framework also allows the researcher to…
ERIC Educational Resources Information Center
Cheung, Mike W. L.; Chan, Wai
2009-01-01
Structural equation modeling (SEM) is widely used as a statistical framework to test complex models in behavioral and social sciences. When the number of publications increases, there is a need to systematically synthesize them. Methodology of synthesizing findings in the context of SEM is known as meta-analytic SEM (MASEM). Although correlation…
Goals and Characteristics of Long-Term Care Programs: An Analytic Model.
ERIC Educational Resources Information Center
Braun, Kathryn L.; Rose, Charles L.
1989-01-01
Used medico-social analytic model to compare five long-term care programs: Skilled Nursing Facility-Intermediate Care Facility (SNF-ICF) homes, ICF homes, foster homes, day hospitals, and home care. Identified similarities and differences among programs. Preliminary findings suggest that model is useful in the evaluation and design of long-term…
Analytic models of ducted turbomachinery tone noise sources. Volume 1: Analysis
NASA Technical Reports Server (NTRS)
Clark, T. L.; Ganz, U. W.; Graf, G. A.; Westall, J. S.
1974-01-01
The analytic models developed for computing the periodic sound pressure of subsonic fans and compressors in an infinite, hardwall annular duct with uniform flow are described. The basic sound-generating mechanism is the scattering into sound waves of velocity disturbances appearing to the rotor or stator blades as a series of harmonic gusts. The models include component interactions and rotor alone.
Several advances in the analytic element method have been made to enhance its performance and facilitate three-dimensional ground-water flow modeling in a regional aquifer setting. First, a new public domain modular code (ModAEM) has been developed for modeling ground-water flow ...
Tang, Sanyi; Xiao, Yanni
2007-12-01
The purpose of this article is to provide the analytical solutions of one-compartment models with Michaelis-Menten elimination kinetics for three different inputs (single intravenous dose, multiple-dose bolus injection and constant). All analytical solutions obtained in present paper can be described by the well defined Lambert W function which can be easily implemented in most mathematical softwares such as Matlab and Maple. These results will play an important role in fitting the Michaelis-Menten parameters and in designing a dosing regimen to maintain steady-state plasma concentrations. In particular, the analytical periodic solution for multi-dose inputs is also given, and we note that the maximum and minimum values of the periodic solution depends on the Michaelis-Menten parameters, dose and time interval of drug administration. In practice, it is important to maintain a concentration above the minimum therapeutic level at all times without exceeding the minimum toxic concentration. Therefore, the one-compartment model with therapeutic window is proposed, and further the existence of periodic solution, analytical expression and its period are analyzed. The analytical formula of period plays a key role in designing a dose regimen to maintain the plasma concentration within a specified range over long periods of therapy. Finally, the completely analytical solution for the constant input rate is derived and discussed which depends on the relations between constant input rate and maximum rate of change of concentration.
anQCD: Fortran programs for couplings at complex momenta in various analytic QCD models
NASA Astrophysics Data System (ADS)
Ayala, César; Cvetič, Gorazd
2016-02-01
We provide three Fortran programs which evaluate the QCD analytic (holomorphic) couplings Aν(Q2) for complex or real squared momenta Q2. These couplings are holomorphic analogs of the powers a(Q2)ν of the underlying perturbative QCD (pQCD) coupling a(Q2) ≡αs(Q2) / π, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2 δanQCD), and Massive Perturbation Theory (MPT). The index ν can be noninteger. The provided programs do basically the same job as the Mathematica package anQCD.m published by us previously (Ayala and Cvetič, 2015), but are now written in Fortran.
Analytical two-dimensional model of solar cell current-voltage characteristics
NASA Astrophysics Data System (ADS)
Caldararu, F.; Caldararu, M.; Nan, S.; Nicolaescu, D.; Vasile, S.
1991-06-01
This paper describes an analytical two-dimensional model for pn junction solar cell I-V characteristic. In order to solve the two-dimensional equations for the minority carrier concentration the Laplace transformation method is used. The model eliminates Hovel's assumptions concerning a one-dimensional model and provides an I-V characteristic that is simpler than those derived from the one-dimensional model. The method can be extended to any other device with two-dimensional symmetry.
An analytic model for redshift-space distortions
NASA Astrophysics Data System (ADS)
Wang, Lile; Reid, Beth; White, Martin
2014-01-01
Understanding the formation and evolution of large-scale structure is a central problem in cosmology and enables precise tests of General Relativity on cosmological scales and constraints on dark energy. An essential ingredient is an accurate description of the pairwise velocities of biased tracers of the matter field. In this paper, we compute the first and second moments of the pairwise velocity distribution by extending the convolution Lagrangian perturbation theory (CLPT) formalism of Carlson et al. Our predictions outperform standard perturbation theory calculations in many cases when compared to statistics measured in N-body simulations. We combine the CLPT predictions of real-space clustering and velocity statistics in the Gaussian streaming model of Reid & White to obtain predictions for the monopole and quadrupole correlation functions accurate to 2 and 4 per cent, respectively, down to <25 h-1 Mpc for haloes hosting the massive galaxies observed by SDSS-III BOSS. We also discuss contours of the 2D correlation function and clustering `wedges'. We generalize the scheme to cross-correlation functions.
Global sensitivity analysis of analytical vibroacoustic transmission models
NASA Astrophysics Data System (ADS)
Christen, Jean-Loup; Ichchou, Mohamed; Troclet, Bernard; Bareille, Olivier; Ouisse, Morvan
2016-04-01
Noise reduction issues arise in many engineering problems. One typical vibroacoustic problem is the transmission loss (TL) optimisation and control. The TL depends mainly on the mechanical parameters of the considered media. At early stages of the design, such parameters are not well known. Decision making tools are therefore needed to tackle this issue. In this paper, we consider the use of the Fourier Amplitude Sensitivity Test (FAST) for the analysis of the impact of mechanical parameters on features of interest. FAST is implemented with several structural configurations. FAST method is used to estimate the relative influence of the model parameters while assuming some uncertainty or variability on their values. The method offers a way to synthesize the results of a multiparametric analysis with large variability. Results are presented for transmission loss of isotropic, orthotropic and sandwich plates excited by a diffuse field on one side. Qualitative trends found to agree with the physical expectation. Design rules can then be set up for vibroacoustic indicators. The case of a sandwich plate is taken as an example of the use of this method inside an optimisation process and for uncertainty quantification.
Analytical model of rotor wake aerodynamics in ground effect
NASA Technical Reports Server (NTRS)
Saberi, H. A.
1983-01-01
The model and the computer program developed provides the velocity, location, and circulation of the tip vortices of a two-blade helicopter in and out of the ground effect. Comparison of the theoretical results with some experimental measurements for the location of the wake indicate that there is excellent accuracy in the vicinity of the rotor and fair amount of accuracy far from it. Having the location of the wake at all times enables us to compute the history of the velocity and the location of any point in the flow. The main goal of out study, induced velocity at the rotor, can also be calculated in addition to stream lines and streak lines. Since the wake location close to the rotor is known more accurately than at other places, the calculated induced velocity over the disc should be a good estimate of the real induced velocity, with the exception of the blade location, because each blade was replaced only by a vortex line. Because no experimental measurements of the wake close to the ground were available to us, quantitative evaluation of the theoretical wake was not possible. But qualitatively we have been able to show excellent agreement. Comparison of flow visualization with out results has indicated the location of the ground vortex is estimated excellently. Also the flow field in hover is well represented.
A Simple Analytical Model for Rocky Planet Interiors
NASA Astrophysics Data System (ADS)
Zeng, Li; Jacobsen, Stein B.
2017-03-01
This work aims to explore the scaling relations among rocky exoplanets. The assumption that the internal gravity increases linearly in the core and stays constant in the mantle is tested against numerical simulations, and a simple model is constructed, applicable to rocky exoplanets of CMF (core mass fraction) = 0.2–0.35 and mass = 0.1–30 M ⊕. Various scaling relations are derived: (1) CMF ≈ CRF2 (core radius fraction squared), (2) {P}{typical}∼ {g}s2 (typical interior pressure scales as surface gravity squared), (3) energy released in core formation is ∼ \\tfrac{1}{10} the total gravitational energy, (4) effective heat capacity of the mantle ≈ ≤ft(\\tfrac{{M}p}{{M}\\oplus }\\right)× 7.5× {10}27 J K‑1, (5) moment of inertia ≈ \\tfrac{1}{3}{M}p{R}p2. These relations, though approximate, are handy for quick use owing to their simplicity and lucidity, and provide insights into the interior structures of those exoplanets.
Measurement strategy and analytic model to determine firing pin force
NASA Astrophysics Data System (ADS)
Lesenciuc, Ioan; Suciu, Cornel
2016-12-01
As illustrated in literature, ballistics is a branch of theoretical mechanics, which studies the construction and working principles of firearms and ammunition, their effects, as well as the motions of projectiles and bullets1. Criminalistics identification, as part of judiciary identification represents an activity aimed at finding common traits of different objects, objectives, phenomena and beings, but more importantly, traits that differentiate each of them from similar ones2-4. In judicial ballistics, in the case of rifled firearms it is relatively simple for experts to identify the used weapon from traces left on the projectile, as the rifling of the barrel leaves imprints on the bullet, which remain approximately identical even after the respective weapon is fired 100 times with the same barrel. However, in the case of smoothbore firearms, their identification becomes much more complicated. As the firing cap suffers alterations from being hit by the firing pin, determination of the force generated during impact creates the premises for determining the type of firearm used to shoot the respective cartridge. The present paper proposes a simple impact model that can be used to evaluate the force generated by the firing pin during its impact with the firing cap. The present research clearly showed that each rifle, by the combination of the three investigated parameters (impact force maximum value, its variation diagram, and impact time) leave a unique trace. Application of such a method in ballistics can create the perspectives for formulating clear conclusions that eliminate possible judicial errors in this field.
Exactly Solvable Hierarchical Optimization Problem Related to Percolation
NASA Astrophysics Data System (ADS)
Fink, Thomas M.; Ball, Robin C.
1996-04-01
We consider a sequence of elementary decisions which must be made in light of successive information learned. A key feature is that the decisions must balance the reduction of immediate cost against learning information and hence securing a wider range of future options-a conflict which motivates us to attach a value to information. We analytically derive an optimal decision policy; while each individual decision is elementary, the solution to the collective problem, which may be interpreted as a novel percolation model, exhibits a phase transition and finite size scaling.
Comprehensive analytical model for CW laser induced heat in turbid media
Erkol, Hakan; Nouizi, Farouk; Luk, Alex; Unlu, Mehmet Burcin; Gulsen, Gultekin
2015-01-01
In this work, we present a new analytical approach to model continuous wave laser induced temperature in highly homogeneous turbid media. First, the diffusion equation is used to model light transport and a comprehensive solution is derived analytically by obtaining a special Greens’ function. Next, the time-dependent bio-heat equation is used to describe the induced heat increase and propagation within the medium. The bio-heat equation is solved analytically utilizing the separation of variables technique. Our theoretical model is successfully validated using numerical simulations and experimental studies with agarose phantoms and ex-vivo chicken breast samples. The encouraging results show that our method can be implemented as a simulation tool to determine important laser parameters that govern the magnitude of temperature rise within homogenous biological tissue or organs. PMID:26698736
Comprehensive analytical model for CW laser induced heat in turbid media.
Erkol, Hakan; Nouizi, Farouk; Luk, Alex; Unlu, Mehmet Burcin; Gulsen, Gultekin
2015-11-30
In this work, we present a new analytical approach to model continuous wave laser induced temperature in highly homogeneous turbid media. First, the diffusion equation is used to model light transport and a comprehensive solution is derived analytically by obtaining a special Greens' function. Next, the time-dependent bio-heat equation is used to describe the induced heat increase and propagation within the medium. The bio-heat equation is solved analytically utilizing the separation of variables technique. Our theoretical model is successfully validated using numerical simulations and experimental studies with agarose phantoms and ex-vivo chicken breast samples. The encouraging results show that our method can be implemented as a simulation tool to determine important laser parameters that govern the magnitude of temperature rise within homogenous biological tissue or organs.
Evaluation of higher order PMD effects using Jones matrix analytical models: a comparative study
NASA Astrophysics Data System (ADS)
Ferreira, M. F.
2006-04-01
A comparative study among the Jones matrix analytical models with high-order PMD is presented. The models that make use of an exponential expansion arrested up to second order or consider the dispersion vector as a Taylor series expansion do not give good results in the approximation of high-order PMD effects, because of the nonlimited behavior with respect to frequency of the modulus of their dispersion vectors. On the other hand, the analytical model which describes the dispersion vector as rotating on a circumference in the Stokes space is found to be the most accurate. Moreover, it can be used to obtain an analytical expression of the pulse broadening, which is often chosen as a quality-system parameter.
Analytical and numerical modeling of non-collinear shear wave mixing at an imperfect interface
NASA Astrophysics Data System (ADS)
Zhang, Ziyin; Nagy, Peter B.; Hassan, Waled
2016-02-01
Non-collinear shear wave mixing at an imperfect interface between two solids can be exploited for nonlinear ultrasonic assessment of bond quality. In this study we developed two analytical models for nonlinear imperfect interfaces. The first model uses a finite nonlinear interfacial stiffness representation of an imperfect interface of vanishing thickness, while the second model relies on a thin nonlinear interphase layer to represent an imperfect interface region. The second model is actually a derivative of the first model obtained by calculating the equivalent interfacial stiffness of a thin isotropic nonlinear interphase layer in the quasi-static approximation. The predictions of both analytical models were numerically verified by comparison to COMSOL finite element simulations. These models can accurately predict the excess nonlinearity caused by interface imperfections based on the strength of the reflected and transmitted mixed longitudinal waves produced by them under non-collinear shear wave interrogation.
Computational and analytical modeling of cationic lipid-DNA complexes.
Farago, Oded; Grønbech-Jensen, Niels
2007-05-01
We present a theoretical study of the physical properties of cationic lipid-DNA (CL-DNA) complexes--a promising synthetically based nonviral carrier of DNA for gene therapy. The study is based on a coarse-grained molecular model, which is used in Monte Carlo simulations of mesoscopically large systems over timescales long enough to address experimental reality. In the present work, we focus on the statistical-mechanical behavior of lamellar complexes, which in Monte Carlo simulations self-assemble spontaneously from a disordered random initial state. We measure the DNA-interaxial spacing, d(DNA), and the local cationic area charge density, sigma(M), for a wide range of values of the parameter (c) representing the fraction of cationic lipids. For weakly charged complexes (low values of (c)), we find that d(DNA) has a linear dependence on (c)(-1), which is in excellent agreement with x-ray diffraction experimental data. We also observe, in qualitative agreement with previous Poisson-Boltzmann calculations of the system, large fluctuations in the local area charge density with a pronounced minimum of sigma(M) halfway between adjacent DNA molecules. For highly-charged complexes (large (c)), we find moderate charge density fluctuations and observe deviations from linear dependence of d(DNA) on (c)(-1). This last result, together with other findings such as the decrease in the effective stretching modulus of the complex and the increased rate at which pores are formed in the complex membranes, are indicative of the gradual loss of mechanical stability of the complex, which occurs when (c) becomes large. We suggest that this may be the origin of the recently observed enhanced transfection efficiency of lamellar CL-DNA complexes at high charge densities, because the completion of the transfection process requires the disassembly of the complex and the release of the DNA into the cytoplasm. Some of the structural properties of the system are also predicted by a continuum
Analytical model of a five degree of freedom magnetic suspension and positioning system
NASA Technical Reports Server (NTRS)
Groom, Nelson J.
1989-01-01
An analytical model of a five degree of freedom magnetic suspension and positioning system is presented. The suspended element is a cylinder which is composed of permanent magnet material and the magnetic actuators are air core electromagnets mounted in a planar array. The analytical model consists of an open loop representation of the suspension and positioning system with electromagnet currents as inputs and displacements and rates in inertial coordinates as outputs. The uncontrolled degree of freedom is rotation about the long axis of the suspended cylinder.
NASA Technical Reports Server (NTRS)
Fuller, C. R.
1986-01-01
A simplified analytical model of transmission of noise into the interior of propeller-driven aircraft has been developed. The analysis includes directivity and relative phase effects of the propeller noise sources, and leads to a closed form solution for the coupled motion between the interior and exterior fields via the shell (fuselage) vibrational response. Various situations commonly encountered in considering sound transmission into aircraft fuselages are investigated analytically and the results obtained are compared to measurements in real aircraft. In general the model has proved successful in identifying basic mechanisms behind noise transmission phenomena.
Analytical model of the temperature dependent properties of microresonators immersed in a gas
Ilin, E. A.; Kehrbusch, J.; Radzio, B.; Oesterschulze, E.
2011-02-01
A comprehensive theoretical model of microresonators immersed in a viscous gas of varying temperature is presented and verified by experiments. Analytical expressions for both the temperature dependent resonant frequency and quality factor of the first flexural eigenmode were derived extending Sader's theory of viscous damping to small temperature variations. The model provides useful implications for the thermal stabilization of microresonators immersed in a gas as well as for the reduction in the influence of the temperature dependent gas properties on the resonant frequency. Finally, an analytical expression is deduced for the mass detection capability of a microresonator that undergoes temperature variations.
Hanaki, Nobuyuki; Jacquemet, Nicolas; Luchini, Stéphane; Zylbersztejn, Adam
2016-01-01
Dominance solvability is one of the most straightforward solution concepts in game theory. It is based on two principles: dominance (according to which players always use their dominant strategy) and iterated dominance (according to which players always act as if others apply the principle of dominance). However, existing experimental evidence questions the empirical accuracy of dominance solvability. In this study, we study the relationships between the key facets of dominance solvability and two cognitive skills, cognitive reflection, and fluid intelligence. We provide evidence that the behaviors in accordance with dominance and one-step iterated dominance are both predicted by one's fluid intelligence rather than cognitive reflection. Individual cognitive skills, however, only explain a small fraction of the observed failure of dominance solvability. The accuracy of theoretical predictions on strategic decision making thus not only depends on individual cognitive characteristics, but also, perhaps more importantly, on the decision making environment itself. PMID:27559324
Hanaki, Nobuyuki; Jacquemet, Nicolas; Luchini, Stéphane; Zylbersztejn, Adam
2016-01-01
Dominance solvability is one of the most straightforward solution concepts in game theory. It is based on two principles: dominance (according to which players always use their dominant strategy) and iterated dominance (according to which players always act as if others apply the principle of dominance). However, existing experimental evidence questions the empirical accuracy of dominance solvability. In this study, we study the relationships between the key facets of dominance solvability and two cognitive skills, cognitive reflection, and fluid intelligence. We provide evidence that the behaviors in accordance with dominance and one-step iterated dominance are both predicted by one's fluid intelligence rather than cognitive reflection. Individual cognitive skills, however, only explain a small fraction of the observed failure of dominance solvability. The accuracy of theoretical predictions on strategic decision making thus not only depends on individual cognitive characteristics, but also, perhaps more importantly, on the decision making environment itself.
NASA Astrophysics Data System (ADS)
Wang, Xi; Yang, Bintang; Yu, Hu; Gao, Yulong
2017-04-01
The impulse excitation of mechanism causes transient vibration. In order to achieve adaptive transient vibration control, a method which can exactly model the response need to be proposed. This paper presents an analytical model to obtain the response of the primary system attached with dynamic vibration absorber (DVA) under impulse excitation. The impulse excitation which can be divided into single-impulse excitation and multi-impulse excitation is simplified as sinusoidal wave to establish the analytical model. To decouple the differential governing equations, a transform matrix is applied to convert the response from the physical coordinate to model coordinate. Therefore, the analytical response in the physical coordinate can be obtained by inverse transformation. The numerical Runge-Kutta method and experimental tests have demonstrated the effectiveness of the analytical model proposed. The wavelet of the response indicates that the transient vibration consists of components with multiple frequencies, and it shows that the modeling results coincide with the experiments. The optimizing simulations based on genetic algorithm and experimental tests demonstrate that the transient vibration of the primary system can be decreased by changing the stiffness of the DVA. The results presented in this paper are the foundations for us to develop the adaptive transient vibration absorber in the future.
On Improving Analytical Models of Cosmic Reionization for Matching Numerical Simulations
Kaurov, Alexander A.
2016-01-01
The methods for studying the epoch of cosmic reionization vary from full radiative transfer simulations to purely analytical models. While numerical approaches are computationally expensive and are not suitable for generating many mock catalogs, analytical methods are based on assumptions and approximations. We explore the interconnection between both methods. First, we ask how the analytical framework of excursion set formalism can be used for statistical analysis of numerical simulations and visual representation of the morphology of ionization fronts. Second, we explore the methods of training the analytical model on a given numerical simulation. We present a new code which emerged from this study. Its main application is to match the analytical model with a numerical simulation. Then, it allows one to generate mock reionization catalogs with volumes exceeding the original simulation quickly and computationally inexpensively, meanwhile reproducing large scale statistical properties. These mock catalogs are particularly useful for CMB polarization and 21cm experiments, where large volumes are required to simulate the observed signal.
On Improving Analytical Models of Cosmic Reionization for Matching Numerical Simulation
NASA Astrophysics Data System (ADS)
Kaurov, Alexander A.
2016-11-01
The methods for studying the epoch of cosmic reionization vary from full radiative transfer simulations to purely analytical models. While numerical approaches are computationally expensive and are not suitable for generating many mock catalogs, analytical methods are based on assumptions and approximations. We explore the interconnection between both methods. First, we ask how the analytical framework of excursion set formalism can be used for statistical analysis of numerical simulations and visual representation of the morphology of ionization fronts. Second, we explore the methods of training the analytical model on a given numerical simulation. We present a new code which emerged from this study. Its main application is to match the analytical model with a numerical simulation. Then, it allows one to generate mock reionization catalogs with volumes exceeding the original simulation quickly and computationally inexpensively, meanwhile reproducing large-scale statistical properties. These mock catalogs are particularly useful for cosmic microwave background polarization and 21 cm experiments, where large volumes are required to simulate the observed signal.
Analytical model for thin-film SOI PIN-diode leakage current
NASA Astrophysics Data System (ADS)
Schmidt, Andrei; Dreiner, Stefan; Vogt, Holger; Goehlich, Andreas; Paschen, Uwe
2017-04-01
An analytical model for the thin-film silicon-on-insulator pin-diode leakage current is presented. Particularly the back-gate potential influence on the leakage current is addressed. The two-dimensional Poisson equation is simplified and then solved including the influence of the back-gate potential. Subsequently the analytical model is verified by comparison with numerical simulation and measurements. For the verification of the model the dependence on the back-gate potential, reverse voltage, device geometry, doping concentration and -polarity is considered. In this procedure the interface recombination velocity is used as fitting parameter. The model verification shows an accurate modeling of the leakage current at full depletion in combination with a back-gate potential dependence. The usage of the model is limited to back-gate and reverse potentials close to full depletion state of the pin-diode.
Towards an Analytical Age-Dependent Model of Contrast Sensitivity Functions for an Ageing Society
Joulan, Karine; Brémond, Roland
2015-01-01
The Contrast Sensitivity Function (CSF) describes how the visibility of a grating depends on the stimulus spatial frequency. Many published CSF data have demonstrated that contrast sensitivity declines with age. However, an age-dependent analytical model of the CSF is not available to date. In this paper, we propose such an analytical CSF model based on visual mechanisms, taking into account the age factor. To this end, we have extended an existing model from Barten (1999), taking into account the dependencies of this model's optical and physiological parameters on age. Age-dependent models of the cones and ganglion cells densities, the optical and neural MTF, and optical and neural noise are proposed, based on published data. The proposed age-dependent CSF is finally tested against available experimental data, with fair results. Such an age-dependent model may be beneficial when designing real-time age-dependent image coding and display applications. PMID:26078994
ERIC Educational Resources Information Center
Saengprom, Narumon; Erawan, Waraporn; Damrongpanit, Suntonrapot; Sakulku, Jaruwan
2015-01-01
The purposes of this study were 1) Compare analytical thinking ability by testing the same sets of students 5 times 2) Develop and verify whether analytical thinking ability of students corresponds to second-order growth curve factors model. Samples were 1,093 eighth-grade students. The results revealed that 1) Analytical thinking ability scores…
Frankle, S.C.; Fitzgerald, D.H.; Hutson, R.L.; Macek, R.J.; Wilkinson, C.A.
1992-12-31
A comparison of 800-MeV proton beam spill measurements at the Los Alamos Meson Physics Facility (LAMPF) with analytical model calculations of neutron dose equivalent rates (DER) show agreement within factors of 2-3 for simple shielding geometries. The DER estimates were based on a modified Moyer model for transverse angles and a Monte Carlo based forward angle model described in the proceeding paper.
Analytic models for the density of a ground-state spinor condensate
NASA Astrophysics Data System (ADS)
Gautam, Sandeep; Adhikari, S. K.
2015-08-01
We demonstrate that the ground state of a trapped spin-1 and spin-2 spinor ferromagnetic Bose-Einstein condensate (BEC) can be well approximated by a single decoupled Gross-Pitaevskii (GP) equation. Useful analytic models for the ground-state densities of ferromagnetic BECs are obtained from the Thomas-Fermi approximation (TFA) to this decoupled equation. Similarly, for the ground states of spin-1 antiferromagnetic and spin-2 antiferromagnetic and cyclic BECs, some of the spin-component densities are zero, which reduces the coupled GP equation to a simple reduced form. Analytic models for ground-state densities are also obtained for antiferromagnetic and cyclic BECs from the TFA to the respective reduced GP equations. The analytic densities are illustrated and compared with the full numerical solution of the GP equation with realistic experimental parameters.
Pérez-Andújar, Angélica; Zhang, Rui; Newhauser, Wayne
2013-12-15
Purpose: Stray neutron radiation is of concern after radiation therapy, especially in children, because of the high risk it might carry for secondary cancers. Several previous studies predicted the stray neutron exposure from proton therapy, mostly using Monte Carlo simulations. Promising attempts to develop analytical models have also been reported, but these were limited to only a few proton beam energies. The purpose of this study was to develop an analytical model to predict leakage neutron equivalent dose from passively scattered proton beams in the 100-250-MeV interval.Methods: To develop and validate the analytical model, the authors used values of equivalent dose per therapeutic absorbed dose (H/D) predicted with Monte Carlo simulations. The authors also characterized the behavior of the mean neutron radiation-weighting factor, w{sub R}, as a function of depth in a water phantom and distance from the beam central axis.Results: The simulated and analytical predictions agreed well. On average, the percentage difference between the analytical model and the Monte Carlo simulations was 10% for the energies and positions studied. The authors found that w{sub R} was highest at the shallowest depth and decreased with depth until around 10 cm, where it started to increase slowly with depth. This was consistent among all energies.Conclusion: Simple analytical methods are promising alternatives to complex and slow Monte Carlo simulations to predict H/D values. The authors' results also provide improved understanding of the behavior of w{sub R} which strongly depends on depth, but is nearly independent of lateral distance from the beam central axis.
An Exact Solvable Model of Rocket Dynamics in Atmosphere
ERIC Educational Resources Information Center
Rodrigues, H.; Pinho, M. O.; Portes, D., Jr.; Santiago, A.
2009-01-01
In basic physics courses at undergraduate level, the dynamics of self-propelled bodies is presented as an example of momentum conservation law applied to systems with time-varying mass. However, is often studied the simple situation of free motion or the motion under the action of a constant gravitational field. In this work, we investigate the…
Learning from noisy data: An exactly solvable model
NASA Astrophysics Data System (ADS)
Biehl, Michael; Riegler, Peter; Stechert, Martin
1995-11-01
Exact results are derived for the learning of a linearly separable rule with a single-layer perceptron. We consider two sources of noise in the training data: the random inversion of the example outputs and weight noise in the teacher network. In both scenarios, we investigate on-line learning schemes that utilize only the latest in a sequence of uncorrelated random examples for an update of the student weights. We study Hebbian learning as well as on-line algorithms that achieve an optimal decrease of the generalization error. The latter realize an asymptotic decay of the generalization error that coincides, apart from prefactors, with the one found for off-line schemes.
Nastac, L.; Stefanescu, D.M. . Dept. of Metallurgical and Materials Engineering)
1993-09-01
Existing models for solute redistribution (microsegregation) during solidification were reviewed. There are no analytical models that take into account limited diffusion in both the liquid and the solid phases. A new analytical mathematical model for solute redistribution was developed. Diffusion in liquid and in solid was considered. This model does not require a prescribed movement of the interface. It can be used for one-dimensional (1-D) (plate), two-dimensional (cylinder), or three-dimensional (3-D) (sphere) calculations. Thus, it is possible to calculate microsegregation at the level of primary or secondary arm spacing for columnar dendrites or for equiaxed dendrites. The solution was compared with calculations based on existing models, as well as with some available experimental data for the segregation of base elements in as cast Al-4.9 wt pct Cu, INCONEL 718, 625, and plain carbon (0.13 wt pct C) steel.
Simulation of reactive geochemical transport in groundwater using a semi-analytical screening model
NASA Astrophysics Data System (ADS)
McNab, Walt W.
1997-10-01
A reactive geochemical transport model, based on a semi-analytical solution to the advective-dispersive transport equation in two dimensions, is developed as a screening tool for evaluating the impact of reactive contaminants on aquifer hydrogeochemistry. Because the model utilizes an analytical solution to the transport equation, it is less computationally intensive than models based on numerical transport schemes, is faster, and it is not subject to numerical dispersion effects. Although the assumptions used to construct the model preclude consideration of reactions between the aqueous and solid phases, thermodynamic mineral saturation indices are calculated to provide qualitative insight into such reactions. Test problems involving acid mine drainage and hydrocarbon biodegradation signatures illustrate the utility of the model in simulating essential hydrogeochemical phenomena.
Analytic Sensitivities for Shape Optimization in Equivalent Plate Structural Wing Models
NASA Technical Reports Server (NTRS)
Livne, Eli
1994-01-01
Equivalent plate modeling techniques based on Ritz analysis with simple polynomials prove to be efficient tools for structural modeling of wings in the preliminary design stage. Accuracy problems are encountered, however, when these models are used to obtain finite difference behavior sensitivities with respect to planform shape. The accuracy problems are associated with the poor numerical conditioning of static and eigenvalue equations. As higher-order polynomials are being used to Improve the analysis itself, the more sensitive is the finite difference derivative to the step size used. This article describes a formulation of wing equivalent plate modeling in which it is simple to obtain analytic, explicit expressions for stiffness and mass matrix elements without the need to perform numerical integration. This formulation leads naturally to analytic expressions for the derivatives of displacements, stresses, and natural frequencies with respect to shape design variables. This article examines the accuracy of finite difference derivatives compared with the analytic derivatives, and shows that In some cases it is impossible to obtain any information of value by finite differences. Analytic sensitivities, in this case, are still sufficiently accurate for design optimization.
The Effectiveness of CBL Model to Improve Analytical Thinking Skills the Students of Sport Science
ERIC Educational Resources Information Center
Sudibyo, Elok; Jatmiko, Budi; Widodo, Wahono
2016-01-01
Sport science undergraduate education, one of which purposes is to produce an analyst in sport. However, generally analytical thinking skills of sport science's students is still relatively very low in the context of sport. This study aimed to describe the effectiveness of Physics Learning Model in Sport Context, Context Based Learning (CBL)…
Noble gas encapsulation into carbon nanotubes: Predictions from analytical model and DFT studies
NASA Astrophysics Data System (ADS)
Balasubramani, Sree Ganesh; Singh, Devendra; Swathi, R. S.
2014-11-01
The energetics for the interaction of the noble gas atoms with the carbon nanotubes (CNTs) are investigated using an analytical model and density functional theory calculations. Encapsulation of the noble gas atoms, He, Ne, Ar, Kr, and Xe into CNTs of various chiralities is studied in detail using an analytical model, developed earlier by Hill and co-workers. The constrained motion of the noble gas atoms along the axes of the CNTs as well as the off-axis motion are discussed. Analyses of the forces, interaction energies, acceptance and suction energies for the encapsulation enable us to predict the optimal CNTs that can encapsulate each of the noble gas atoms. We find that CNTs of radii 2.98 - 4.20 Å (chiral indices, (5,4), (6,4), (9,1), (6,6), and (9,3)) can efficiently encapsulate the He, Ne, Ar, Kr, and Xe atoms, respectively. Endohedral adsorption of all the noble gas atoms is preferred over exohedral adsorption on various CNTs. The results obtained using the analytical model are subsequently compared with the calculations performed with the dispersion-including density functional theory at the M06 - 2X level using a triple-zeta basis set and good qualitative agreement is found. The analytical model is however found to be computationally cheap as the equations can be numerically programmed and the results obtained in comparatively very less time.
An Analytical Framework for Evaluating E-Commerce Business Models and Strategies.
ERIC Educational Resources Information Center
Lee, Chung-Shing
2001-01-01
Considers electronic commerce as a paradigm shift, or a disruptive innovation, and presents an analytical framework based on the theories of transaction costs and switching costs. Topics include business transformation process; scale effect; scope effect; new sources of revenue; and e-commerce value creation model and strategy. (LRW)
Noble gas encapsulation into carbon nanotubes: Predictions from analytical model and DFT studies
Balasubramani, Sree Ganesh; Singh, Devendra; Swathi, R. S.
2014-11-14
The energetics for the interaction of the noble gas atoms with the carbon nanotubes (CNTs) are investigated using an analytical model and density functional theory calculations. Encapsulation of the noble gas atoms, He, Ne, Ar, Kr, and Xe into CNTs of various chiralities is studied in detail using an analytical model, developed earlier by Hill and co-workers. The constrained motion of the noble gas atoms along the axes of the CNTs as well as the off-axis motion are discussed. Analyses of the forces, interaction energies, acceptance and suction energies for the encapsulation enable us to predict the optimal CNTs that can encapsulate each of the noble gas atoms. We find that CNTs of radii 2.98 − 4.20 Å (chiral indices, (5,4), (6,4), (9,1), (6,6), and (9,3)) can efficiently encapsulate the He, Ne, Ar, Kr, and Xe atoms, respectively. Endohedral adsorption of all the noble gas atoms is preferred over exohedral adsorption on various CNTs. The results obtained using the analytical model are subsequently compared with the calculations performed with the dispersion-including density functional theory at the M06 − 2X level using a triple-zeta basis set and good qualitative agreement is found. The analytical model is however found to be computationally cheap as the equations can be numerically programmed and the results obtained in comparatively very less time.
An analytic model of toroidal half-wave oscillations: Implication on plasma density estimates
NASA Astrophysics Data System (ADS)
Bulusu, Jayashree; Sinha, A. K.; Vichare, Geeta
2015-06-01
The developed analytic model for toroidal oscillations under infinitely conducting ionosphere ("Rigid-end") has been extended to "Free-end" case when the conjugate ionospheres are infinitely resistive. The present direct analytic model (DAM) is the only analytic model that provides the field line structures of electric and magnetic field oscillations associated with the "Free-end" toroidal wave for generalized plasma distribution characterized by the power law ρ = ρo(ro/r)m, where m is the density index and r is the geocentric distance to the position of interest on the field line. This is important because different regions in the magnetosphere are characterized by different m. Significant improvement over standard WKB solution and an excellent agreement with the numerical exact solution (NES) affirms validity and advancement of DAM. In addition, we estimate the equatorial ion number density (assuming H+ atom as the only species) using DAM, NES, and standard WKB for Rigid-end as well as Free-end case and illustrate their respective implications in computing ion number density. It is seen that WKB method overestimates the equatorial ion density under Rigid-end condition and underestimates the same under Free-end condition. The density estimates through DAM are far more accurate than those computed through WKB. The earlier analytic estimates of ion number density were restricted to m = 6, whereas DAM can account for generalized m while reproducing the density for m = 6 as envisaged by earlier models.
ERIC Educational Resources Information Center
Calvert, Carol Elaine
2014-01-01
This case study relates to distance learning students on open access courses. It demonstrates the use of predictive analytics to generate a model of the probabilities of success and retention at different points, or milestones, in a student journey. A core set of explanatory variables has been established and their varying relative importance at…
Erratum: A Simple, Analytical Model of Collisionless Magnetic Reconnection in a Pair Plasma
NASA Technical Reports Server (NTRS)
Hesse, Michael; Zenitani, Seiji; Kuznetsova, Masha; Klimas, Alex
2011-01-01
The following describes a list of errata in our paper, "A simple, analytical model of collisionless magnetic reconnection in a pair plasma." It supersedes an earlier erratum. We recently discovered an error in the derivation of the outflow-to-inflow density ratio.
Bao, Jie; Xu, Zhijie; Fang, Yilin
2015-04-01
A hydro-mechanical model with analytical solutions including pressure evolution and geomechanical deformation for geological CO2 injection and sequestration were introduced in our previous work. However, the reliability and accuracy of the hydro-mechanical model and the companion analytical solution are uncertain because of the assumptions and simplifications in the analytical model, though it was validated by a few example cases. This study introduce the method to efficiently measure the accuracy of the analytical model, and specify the acceptable input parameters range that can guarantee the accuracy and reliability of the analytical solution. A coupled hydro-geomechanical subsurface transport simulator STOMP was adopted as a reference to justify the reliability of the hydro-mechanical model and the analytical solution. A quasi-Monte Carlo sampling method was applied to efficiently sample the input parameter space.
Analytic Modeling of Pressurization and Cryogenic Propellant Conditions for Lunar Landing Vehicle
NASA Technical Reports Server (NTRS)
Corpening, Jeremy
2010-01-01
This slide presentation reviews the development, validation and application of the model to the Lunar Landing Vehicle. The model named, Computational Propellant and Pressurization Program -- One Dimensional (CPPPO), is used to model in this case cryogenic propellant conditions of the Altair Lunar lander. The validation of CPPPO was accomplished via comparison to an existing analytic model (i.e., ROCETS), flight experiment and ground experiments. The model was used to the Lunar Landing Vehicle perform a parametric analysis on pressurant conditions and to examine the results of unequal tank pressurization and draining for multiple tank designs.
Lee, Ping I
2011-10-10
The purpose of this review is to provide an overview of approximate analytical solutions to the general moving boundary diffusion problems encountered during the release of a dispersed drug from matrix systems. Starting from the theoretical basis of the Higuchi equation and its subsequent improvement and refinement, available approximate analytical solutions for the more complicated cases involving heterogeneous matrix, boundary layer effect, finite release medium, surface erosion, and finite dissolution rate are also discussed. Among various modeling approaches, the pseudo-steady state assumption employed in deriving the Higuchi equation and related approximate analytical solutions appears to yield reasonably accurate results in describing the early stage release of a dispersed drug from matrices of different geometries whenever the initial drug loading (A) is much larger than the drug solubility (C(s)) in the matrix (or A≫C(s)). However, when the drug loading is not in great excess of the drug solubility (i.e. low A/C(s) values) or when the drug loading approaches the drug solubility (A→C(s)) which occurs often with drugs of high aqueous solubility, approximate analytical solutions based on the pseudo-steady state assumption tend to fail, with the Higuchi equation for planar geometry exhibiting a 11.38% error as compared with the exact solution. In contrast, approximate analytical solutions to this problem without making the pseudo-steady state assumption, based on either the double-integration refinement of the heat balance integral method or the direct simplification of available exact analytical solutions, show close agreement with the exact solutions in different geometries, particularly in the case of low A/C(s) values or drug loading approaching the drug solubility (A→C(s)). However, the double-integration heat balance integral approach is generally more useful in obtaining approximate analytical solutions especially when exact solutions are not
An analytic, entraining jet model for a stellar outflow in a stratified environment
NASA Astrophysics Data System (ADS)
Raga, A. C.
2016-10-01
We present a model of a steady, entraining, isothermal jet embedded in a stratified environment. This model is appropriate for describing Herbig-Haro (HH) jets in the outer boundaries of molecular clouds. The model has a straightfoward analytic solution which permits an evaluation of the slowing down of the outflow due to the entrainment of environmental material. The solution indicates that the outflow lobe travelling into regions of lower pressure might or might not be slowed down (depending on the parameters of the flow) before leaving the molecular cloud. On the other hand, the outflow lobe travelling into regions of increasing environmental pressure is likely to be slowed down quite drastically regardless of the flow parameters. The analytic model presented in this paper gives simple recipes for calculating the slowing down of the two outflow lobes.
Semi-analytical model for quasi-double-layer surface electrode ion traps
NASA Astrophysics Data System (ADS)
Zhang, Jian; Chen, Shuming; Wang, Yaohua
2016-11-01
To realize scale quantum processors, the surface-electrode ion trap is an effective scaling approach, including single-layer, double-layer, and quasi-double-layer traps. To calculate critical trap parameters such as the trap center and trap depth, the finite element method (FEM) simulation was widely used, however, it is always time consuming. Moreover, the FEM simulation is also incapable of exhibiting the direct relationship between the geometry dimension and these parameters. To eliminate the problems above, House and Madsen et al. have respectively provided analytic models for single-layer traps and double-layer traps. In this paper, we propose a semi-analytical model for quasi-double-layer traps. This model can be applied to calculate the important parameters above of the ion trap in the trap design process. With this model, we can quickly and precisely find the optimum geometry design for trap electrodes in various cases.
Rolland, N; Larson, D J; Geiser, B P; Duguay, S; Vurpillot, F; Blavette, D
2015-12-01
An analytical model describing the field evaporation dynamics of a tip made of a thin layer deposited on a substrate is presented in this paper. The difference in evaporation field between the materials is taken into account in this approach in which the tip shape is modeled at a mesoscopic scale. It was found that the non-existence of sharp edge on the surface is a sufficient condition to derive the morphological evolution during successive evaporation of the layers. This modeling gives an instantaneous and smooth analytical representation of the surface that shows good agreement with finite difference simulations results, and a specific regime of evaporation was highlighted when the substrate is a low evaporation field phase. In addition, the model makes it possible to calculate theoretically the tip analyzed volume, potentially opening up new horizons for atom probe tomographic reconstruction.
Analytical solutions of moisture flow equations and their numerical evaluation
Gibbs, A.G.
1981-04-01
The role of analytical solutions of idealized moisture flow problems is discussed. Some different formulations of the moisture flow problem are reviewed. A number of different analytical solutions are summarized, including the case of idealized coupled moisture and heat flow. The evaluation of special functions which commonly arise in analytical solutions is discussed, including some pitfalls in the evaluation of expressions involving combinations of special functions. Finally, perturbation theory methods are summarized which can be used to obtain good approximate analytical solutions to problems which are too complicated to solve exactly, but which are close to an analytically solvable problem.
The analytic model of a laser-accelerated plasma target and its stability
NASA Astrophysics Data System (ADS)
Khudik, V.; Yi, S. A.; Siemon, C.; Shvets, G.
2014-01-01
A self-consistent kinetic theory of a laser-accelerated plasma target with distributed electron/ion densities is developed. The simplified model assumes that after an initial transition period the bulk of cold ions are uniformly accelerated by the self-consistent electric field generated by hot electrons trapped in combined ponderomotive and electrostatic potentials. Several distinct target regions (non-neutral ion tail, non-neutral electron sheath, and neutral plasma bulk) are identified and analytically described. It is shown analytically that such laser-accelerated finite-thickness target is susceptible to Rayleigh-Taylor (RT) instability. Particle-in-cell simulations of the seeded perturbations of the plasma target reveal that, for ultra-relativistic laser intensities, the growth rate of the RT instability is depressed from the analytic estimates.
An analytical model for decaying swirl flow and heat transfer inside a tube
Wu, H.Y.; Cheng, H.E.; Shuai, R.J.; Zhou, Q.T.
2000-02-01
Decaying swirl flow can enhance the heat transfer inside a tube. For the decaying swirl flow of which maximum tangential velocity is located in the immediate vicinity of the wall, an analytical model based on the fluid theorem about the moment of momentum is proposed for the local maximum tangential velocity, local friction factor, and local Nusselt number in this paper. The analytical solutions compare favorably with the experimental data. Influences of the Reynolds number, wall roughness and initial tangential-to-axial velocity ratio on the decaying characteristics of the friction factor and Nusselt number have been analyzed. The analytical results show that the swirl flow decays more rapidly at the initial segment; for same conditions, the friction factor decays more severely than the Nusselt number; relative to the values of the nonswirl flow, the friction factor increases more intensely than the Nusselt number.
2D analytical modeling of a wholly superconducting synchronous reluctance motor
NASA Astrophysics Data System (ADS)
Malé, G.; Lubin, T.; Mezani, S.; Lévêque, J.
2011-03-01
An analytical computation of the magnetic field distribution in a wholly superconducting synchronous reluctance motor is proposed. The stator of the studied motor consists of three-phase HTS armature windings fed by AC currents. The rotor is made with HTS bulks which have a nearly diamagnetic behavior under zero field cooling. The electromagnetic torque is obtained by the interaction between the rotating magnetic field created by the HTS windings and the HTS bulks. The proposed analytical model is based on the resolution of Laplace's and Poisson's equations (by the separation-of-variables technique) for each sub-domain, i.e. stator windings, air-gap, holes between HTS bulks and exterior iron shield. For the study, the HTS bulks are considered as perfect diamagnetic materials. The boundary and continuity conditions between the sub-domains yield to the global solution. Magnetic field distributions and electromagnetic torque obtained by the analytical method are compared with those obtained from finite element analyses.
The analytic model of a laser-accelerated plasma target and its stability
Khudik, V. Yi, S. A.; Siemon, C.; Shvets, G.
2014-01-15
A self-consistent kinetic theory of a laser-accelerated plasma target with distributed electron/ion densities is developed. The simplified model assumes that after an initial transition period the bulk of cold ions are uniformly accelerated by the self-consistent electric field generated by hot electrons trapped in combined ponderomotive and electrostatic potentials. Several distinct target regions (non-neutral ion tail, non-neutral electron sheath, and neutral plasma bulk) are identified and analytically described. It is shown analytically that such laser-accelerated finite-thickness target is susceptible to Rayleigh-Taylor (RT) instability. Particle-in-cell simulations of the seeded perturbations of the plasma target reveal that, for ultra-relativistic laser intensities, the growth rate of the RT instability is depressed from the analytic estimates.