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.
Time Fractional Diffusion Equations and Analytical Solvable Models
NASA Astrophysics Data System (ADS)
Bakalis, Evangelos; Zerbetto, Francesco
2016-08-01
The anomalous diffusion of a particle that moves in complex environments is analytically studied by means of the time fractional diffusion equation. The influence on the dynamics of a random moving particle caused by a uniform external field is taken into account. We extract analytical solutions in terms either of the Mittag-Leffler functions or of the M- Wright function for the probability distribution, for the velocity autocorrelation function as well as for the mean and the mean square displacement. Discussion of the applicability of the model to real systems is made in order to provide new insight of the medium from the analysis of the motion of a particle embedded in it.
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.
Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes
NASA Astrophysics Data System (ADS)
Jo, Hang-Hyun; Perotti, Juan I.; Kaski, Kimmo; Kertész, János
2014-01-01
Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects, we devise an analytically solvable model of susceptible-infected spreading dynamics in infinite systems for arbitrary inter-event time distributions and for the whole time range. Our model is stationary from the beginning, and the role of the lower bound of inter-event times is explicitly considered. The exact solution shows that for early and intermediate times, the burstiness accelerates the spreading as compared to a Poisson-like process with the same mean and same lower bound of inter-event times. Such behavior is opposite for late-time dynamics in finite systems, where the power-law distribution of inter-event times results in a slower and algebraic convergence to a fully infected state in contrast to the exponential decay of the Poisson-like process. We also provide an intuitive argument for the exponent characterizing algebraic convergence.
Solvable Models of Correlated Particles
NASA Astrophysics Data System (ADS)
Ha, Zachary Nyong-Chol
The Heisenberg spin chain with inverse-square exchange (ISE) has recently been introduced and has elevated general interest in the models with ISE. It has been known for a long time that the model is directly related to the random matrix theory. Recently, the matrix model in two -dimensional quantum gravity has also been shown to be related to the ISE model. In this thesis we show that the Bethe -ansatz-solvable, nearest-neighbor-exchange (NNE) models and the ISE model share a striking structure called the "string". Chapter 1 is a review of the Bethe ansatz, the "strings", and the ISE models. In Chapter 2 the "string" structure of one-dimensional Hubbard model eigenstates is studied numerically and is used to show the validity of thermodynamic Bethe ansatz equations (TBAE). We, furthermore, solve TBAE in a strong coupling expansion series form and obtain the thermodynamic potential which agrees with the known high temperature expansion series. We also calculate various thermodynamic quantities using our solution and provide some new features of the strongly correlated one -dimensional Hubbard model. In Chapter 3 a one-dimensional quantum N-body system of either fermions or bosons with SU(n) "spins" (or colors in particle physics language) interacting via inverse-square exchange is presented. A class of eigenstates of both the continuum and lattice version of the model Hamiltonians is constructed in terms of the Jastrow-product wave function. The class of states we construct corresponds to the ground state and the low-energy excitations of the model that can be described by the effective harmonic fluid Hamiltonian. By expanding the energy about the ground state, we find the harmonic fluid parameters (i.e., the charge, spin velocities, etc.) explicitly. The correlation exponent and the compressibility are also found. As expected, the general harmonic relation (i.e., v_ {S} = (v_{N}v_{J })^{1/2) is satisfied among the charge and the spin velocities. In Chapter 4, an
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.
Exactly solvable interacting spin-ice vertex model.
Ferreira, Anderson A; Alcaraz, Francisco C
2006-07-01
A special family of solvable five-vertex model is introduced on a square lattice. In addition to the usual nearest-neighbor interactions, the vertices defining the model also interact along one of the diagonals of the lattice. This family of models includes in a special limit the standard six-vertex model. The exact solution of these models is an application of the matrix product ansatz introduced recently and applied successfully in the solution of quantum chains. The phase diagram and the free energy of the models are calculated in the thermodynamic limit. The models exhibit massless phases, and our analytical and numerical analyses indicate that such phases are governed by a conformal field theory with central charge c=1 and continuously varying critical exponents.
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. PMID:24240277
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.
A solvable blob-model for magnetized plasmas
NASA Astrophysics Data System (ADS)
Pécseli, H. L.; Sortland, D. S.; Garcia, O. E.
2016-11-01
A simple analytically solvable model for blobs in magnetized plasmas is proposed. The model gives results for a scaling of the blob velocity and acceleration with varying plasma parameters. Limiting cases are considered: one where the plasma motion is strictly perpendicular to an externally imposed toroidal magnetic field, and one where the electrons can move along magnetic field lines to compensate partly the collective electric fields. For these limiting cases, the model predicts scaling laws for the dependence of the blob velocities and accelerations with varying plasma density, temperature and magnetic field strength. Also the scaling with the dominant ion mass is derived. The analysis is completed by including the effects of collisions between ions and neutrals.
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 template coexistence in protocells
NASA Astrophysics Data System (ADS)
Fontanari, J. F.; Serva, M.
2013-02-01
Compartmentalization of self-replicating molecules (templates) in protocells is a necessary step towards the evolution of modern cells. However, coexistence between distinct template types inside a protocell can be achieved only if there is a selective pressure favoring protocells with a mixed template composition. Here we study analytically a group selection model for the coexistence between two template types using the diffusion approximation of population genetics. The model combines competition at the template and protocell levels as well as genetic drift inside protocells. At the steady state, we find a continuous phase transition separating the coexistence and segregation regimes, with the order parameter vanishing linearly with the distance to the critical point. In addition, we derive explicit analytical expressions for the critical steady-state probability density of protocell compositions.
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.
Exactly solvable models for atom-molecule Hamiltonians.
Dukelsky, J; Dussel, G G; Esebbag, C; Pittel, S
2004-07-30
We present a family of exactly solvable generalizations of the Jaynes-Cummings model involving the interaction of an ensemble of SU(2) or SU(1,1) quasispins with a single boson field. They are obtained from the trigonometric Richardson-Gaudin models by replacing one of the SU(2) or SU(1,1) degrees of freedom by an ideal boson. The application to a system of bosonic atoms and molecules is reported.
Solvable model of mechanical unfolding of biopolymers
NASA Astrophysics Data System (ADS)
Jacobs, Donald; Livesay, Dennis; Vorov, Oleg
2010-03-01
We present exact analytical results for a hairpin to coil transition induced through mechanical pulling of dsDNA or peptides (beta-hairpin) within a distance constraint model [1], taking into account geometry of conformations. Starting from ab initio considerations, the configuration partition function is calculated exactly. Among other thermodynamic response functions, an expression for the end-to-end extension as a function of the applied force at a given temperature is derived. Our theoretical results agree well with data from single-molecule stretching experiments [2]. The employed method is general, and promises to remain a tractable computational approach when applied to larger, more complicated macromolecules. This work is supported by NIH R01 GM073082.[4pt] [1] O.K. Vorov, D.R. Livesay and D.J. Jacobs, ENTROPY, v.10 (3) 285-308 (2008).[0pt] [2] O.K. Vorov, D.R. Livesay and D.J. Jacobs, to be subm. to Phys. Rev. Lett., in preparation.
Novel solvable variants of the goldfish many-body model
NASA Astrophysics Data System (ADS)
Bruschi, M.; Calogero, F.
2006-02-01
A recent technique to identify solvable many-body problems in two-dimensional space yields, via a new twist, new many-body problems of "goldfish" type. Some of these models are isochronous, namely their generic solutions are completely periodic with a fixed period (independent of the initial data). The investigation of the behavior of some of these isochronous systems in the vicinity of their equilibrium configurations yields some amusing diophantine relations.
Exactly solvable relativistic model with the anomalous interaction
NASA Astrophysics Data System (ADS)
Ferraro, Elena; Messina, Antonino; Nikitin, A. G.
2010-04-01
A special class of Dirac-Pauli equations with time-like vector potentials of an external field is investigated. An exactly solvable relativistic model describing the anomalous interaction of a neutral Dirac fermion with a cylindrically symmetric external electromagnetic field is presented. The related external field is a superposition of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line current. In the nonrelativistic approximation the considered model is reduced to the integrable Pron’ko-Stroganov model.
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.
Stochastic TDHF in an exactly solvable model
NASA Astrophysics Data System (ADS)
Lacombe, L.; Suraud, E.; Reinhard, P.-G.; Dinh, P. M.
2016-10-01
We apply in a schematic model a theory beyond mean-field, namely Stochastic Time-Dependent Hartree-Fock (STDHF), which includes dynamical electron-electron collisions on top of an incoherent ensemble of mean-field states by occasional 2-particle-2-hole (2 p 2 h) jumps. The model considered here is inspired by a Lipkin-Meshkov-Glick model of Ω particles distributed into two bands of energy and coupled by a two-body interaction. Such a model can be exactly solved (numerically though) for small Ω. It therefore allows a direct comparison of STDHF and the exact propagation. The systematic impact of the model parameters as the density of states, the excitation energy and the bandwidth is presented and discussed. The time evolution of the STDHF compares fairly well with the exact entropy, as soon as the excitation energy is sufficiently large to allow 2 p 2 h transitions. Limitations concerning low energy excitations and memory effects are also discussed.
Gegenbauer-solvable quantum chain model
NASA Astrophysics Data System (ADS)
Znojil, Miloslav
2010-11-01
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≠H†. We managed to (i) start from elementary secular equation G(N,a,En)=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 Θ≠I, (iv) construct eligible metrics in closed forms ordered by increasing nondiagonality, and (v) interpret the model as a smeared N-site lattice.
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
NASA Astrophysics Data System (ADS)
Corron, Ned J.; Cooper, Roy M.; Blakely, Jonathan N.
2016-02-01
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.
Analytically solvable chaotic oscillator based on a first-order filter.
Corron, Ned J; Cooper, Roy M; Blakely, Jonathan N
2016-02-01
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.
Analytically solvable chaotic oscillator based on a first-order filter.
Corron, Ned J; Cooper, Roy M; Blakely, Jonathan N
2016-02-01
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. PMID:26931585
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.
Exactly solvable PT -symmetric models in two dimensions
NASA Astrophysics Data System (ADS)
Agarwal, Kaustubh S.; Pathak, Rajeev K.; Joglekar, Yogesh N.
2015-11-01
Non-Hermitian, PT -symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly solvable, two-dimensional, PT potentials for a non-relativistic particle confined in a circular geometry. We show that the PT -symmetry threshold can be tuned by introducing a second gain-loss potential or its Hermitian counterpart. Our results explicitly demonstrate that PT breaking in two dimensions has a rich phase diagram, with multiple re-entrant PT -symmetric phases.
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.
Fundamental cycle of a periodic box ball system and solvable lattice models
NASA Astrophysics Data System (ADS)
Mada, Jun; Idzumi, Makoto; Tokihiro, Tetsuji
2006-05-01
We investigate the fundamental cycle of a periodic box-ball system (PBBS) from a relation between the PBBS and a solvable lattice model. We show that the fundamental cycle of the PBBS is obtained from eigenvalues of the transfer matrix of the solvable lattice model.
3-state Hamiltonians associated to solvable 33-vertex models
NASA Astrophysics Data System (ADS)
Crampé, N.; Frappat, L.; Ragoucy, E.; Vanicat, M.
2016-09-01
Using the nested coordinate Bethe ansatz, we study 3-state Hamiltonians with 33 non-vanishing entries, or 33-vertex models, where only one global charge with degenerate eigenvalues exists and each site possesses three internal degrees of freedom. In the context of Markovian processes, they correspond to diffusing particles with two possible internal states which may be exchanged during the diffusion (transmutation). The first step of the nested coordinate Bethe ansatz is performed providing the eigenvalues in terms of rapidities. We give the constraints ensuring the consistency of the computations. These rapidities also satisfy Bethe equations involving 4 × 4 R-matrices, solutions of the Yang-Baxter equation which implies new constraints on the models. We solve them allowing us to list all the solvable 33-vertex models.
Topological order in an exactly solvable 3D spin model
Bravyi, Sergey; Leemhuis, Bernhard; Terhal, Barbara M.
2011-04-15
Research highlights: RHtriangle We study exactly solvable spin model with six-qubit nearest neighbor interactions on a 3D face centered cubic lattice. RHtriangle The ground space of the model exhibits topological quantum order. RHtriangle Elementary excitations can be geometrically described as the corners of rectangular-shaped membranes. RHtriangle The ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. RHtriangle Logical operators acting on the encoded qubits are described in terms of closed strings and closed membranes. - Abstract: We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest-neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order. The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes. We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on {Omega}(R{sup 2}) qubits. Composite particles that consist of two monopoles (dipoles) and four monopoles (quadrupoles) can be described as end-points of strings. The peculiar feature of the model is that dipole-type strings are rigid, that is, such strings must be aligned with face-diagonals of the lattice. For periodic boundary conditions the ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. We describe a complete set of logical operators acting on the encoded qubits in terms of closed strings and closed membranes.
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.
Solvable Models with Massless Light-Front Fermions
NASA Astrophysics Data System (ADS)
Martinovic̆, L'ubomír; Grangé, Pierre
2015-09-01
Two-dimensional models with massless fermions (Thirring model, Thirring-Wess and Schwinger model, among others) have been solved exactly a long time ago in the conventional (space-like) form of field theory and in some cases also in the conformal field theoretical approach. However, solutions in the light-front form of the theory have not been obtained so far. The primary obstacle is the apparent difficulty with light-front quantization of free massless fermions, where one half of the fermionic degrees of freedom seems to "disappear" due to the structure of a non-dynamical constraint equation. We shall show a simple way how the missing degree of freedom can be recovered as the massless limit of the massive solution of the constraint. This opens the door to the genuine light front solution of the above models since their solvability is related to free Heisenberg fields, which are the true dynamical variables in these models. In the present contribution, we give an operator solution of the light front Thirring model, including the correct form of the interacting quantum currents and of the Hamiltonian. A few remarks on the light-front Thirring-Wess models are also added. Simplifications and clarity of the light-front formalism turn out to be quite remarkable.
Another New Solvable Many-Body Model of Goldfish Type
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2012-07-01
A new solvable many-body problem is identified. It is characterized by nonlinear Newtonian equations of motion (''acceleration equal force'') featuring one-body and two-body velocity-dependent forces ''of goldfish type'' which determine the motion of an arbitrary number N of unit-mass point-particles in a plane. The N (generally complex) values z_{n}( t) at time t of the N coordinates of these moving particles are given by the N eigenvalues of a time-dependent N× N matrix U( t) explicitly known in terms of the 2N initial data z_{n}( 0) and dot{z}_{n}(0) . This model comes in two different variants, one featuring 3 arbitrary coupling constants, the other only 2; for special values of these parameters all solutions are completely periodic with the same period independent of the initial data (''isochrony''); for other special values of these parameters this property holds up to corrections vanishing exponentially as t→ ∞ (''asymptotic isochrony''). Other isochronous variants of these models are also reported. Alternative formulations, obtained by changing the dependent variables from the N zeros of a monic polynomial of degree N to its N coefficients, are also exhibited. Some mathematical findings implied by some of these results - such as Diophantine properties of the zeros of certain polynomials - are outlined, but their analysis is postponed to a separate paper.
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}
Minimal cooling speed for glass transition in a simple solvable energy landscape model
NASA Astrophysics Data System (ADS)
Toledo-Marín, J. Quetzalcóatl; Castillo, Isaac Pérez; Naumis, Gerardo G.
2016-06-01
The minimal cooling speed required to form a glass is obtained for a simple solvable energy landscape model. The model, made from a two-level system modified to include the topology of the energy landscape, is able to capture either a glass transition or a crystallization depending on the cooling rate. In this setup, the minimal cooling speed to achieve glass formation is then found to be related with the crystallization relaxation time, energy barrier and with the thermal history. In particular, we obtain that the thermal history encodes small fluctuations around the equilibrium population which are exponentially amplified near the glass transition, which mathematically corresponds to the boundary layer of the master equation. The change in the glass transition temperature is also found as a function of the cooling rate. Finally, to verify our analytical results, a kinetic Monte Carlo simulation was implemented.
Novel solvable extensions of the goldfish many-body model
NASA Astrophysics Data System (ADS)
Calogero, F.; Iona, S.
2005-10-01
A novel solvable extension of the goldfish N-body problem is presented. Its Newtonian equations of motion read ζ̈n=2aζ\\dot nζn+2∑m =1,m≠nN(ζ\\dot n-aζn2)(ζ\\dot m-aζm2)/(ζn-ζm), n =1,…,N, where a is an arbitrary (nonvanishing) constant and the rest of the notation is self-evident. The isochronous version of this model is characterized by the Newtonian equations of motion ζ̈n-3iω\\zdot n-2ω2zn=2a(\\zdot n-iωzn)zn+2∑m =1,m≠nN(\\zdot n-iωzn-azn2)(\\zdot m-iωzm-azm2)/(zn-zm), n =1,…,N, where ω is an arbitrary positive constant and the points zn(t) move now necessarily in the complex z-plane. The generic solution of this second model is completely periodic with a period Tk=kT which is an integer multiple k (not larger than N!, indeed generally much smaller) of the basic period T =2π/ω and which is independent of the initial data (for sufficiently small, but otherwise arbitrary, changes of such data). These many-body models have an intriguing variety of equilibrium configurations (genuine: with no two particles sitting at the same place), but only for small values of N (N =2,3,4 for the first model, N =2,3,4,5 for the second). Other versions of these models are also discussed. The study of the behavior of the second, isochronous model around its equilibrium configurations yields some amusing diophantine results.
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.
Exactly solvable model of a highly efficient thermoelectric engine.
Horvat, Martin; Prosen, Tomaz; Casati, Giulio
2009-07-01
We propose a simple classical dynamical model of a thermoelectric (or thermochemical) heat engine based on a pair of ideal gas containers connected by two unequal scattering channels. The model is solved analytically and it is shown that a suitable combination of parameters can be chosen such that the engine operates at Carnot's efficiency. PMID:19658636
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.
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.
Solvable structures of a simple model of earthquakes
NASA Astrophysics Data System (ADS)
Białecki, Mariusz
2016-01-01
This paper propose an extension of Random Domino Automaton by introducing extra parameter related to a very short-distance interactions between clusters which allows to isolate influence two mechanisms of clusters grow, namely enlarging and coalescence. In this setting statistically stationary state under assumption of independence of clusters is investigated and respective set of equations is derived. Moreover, a special solvable case is studied in detail and it is shown how to derive Motzkin numbers out of the automaton for a family of parameters without considering a limit.
Exactly solvable two-state quantum model for a pulse of hyperbolic-tangent shape
NASA Astrophysics Data System (ADS)
Simeonov, Lachezar S.; Vitanov, Nikolay V.
2014-04-01
We present an analytically exactly solvable two-state quantum model, in which the coupling has a hyperbolic-tangent temporal shape and the frequency detuning is constant. The exact solution is expressed in terms of associated Legendre functions. An interesting feature of this model is that the excitation probability does not vanish, except for zero pulse area or zero detuning; this feature is attributed to the asymmetric pulse shape. Two limiting cases are considered. When the coupling rises very slowly, it is nearly linear and the tanh model reduces to the shark model introduced earlier. When the coupling rises very quickly, the tanh model reduces to the Rabi model, which assumes a rectangular pulse shape and hence a sudden switch on. Because of its practical significance, we have elaborated the asymptotics of the solution in the Rabi limit, and we have derived the next terms in the asymptotic expansion, which deliver the corrections to the amplitude and the phase of the Rabi oscillations due to the finite rise time of the coupling.
An exactly solvable coarse-grained model for species diversity
NASA Astrophysics Data System (ADS)
Suweis, Samir; Rinaldo, Andrea; Maritan, Amos
2012-07-01
We present novel analytical results concerning ecosystem species diversity that stem from a proposed coarse-grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing both theoretical results from ecological neutral theory and empirical evidence on species diversity preservation. The neutral model of biodiversity deals with ecosystems at the same trophic level, where per capita vital rates are assumed to be species independent. Closed-form analytical solutions for the neutral theory are obtained within a coarse-grained model, where the only input is the species persistence time distribution. Our results pertain to: the probability distribution function of the number of species in the ecosystem, both in transient and in stationary states; the n-point connected time correlation function; and the survival probability, defined as the distribution of time spans to local extinction for a species randomly sampled from the community. Analytical predictions are also tested on empirical data from an estuarine fish ecosystem. We find that emerging properties of the ecosystem are very robust and do not depend on specific details of the model, with implications for biodiversity and conservation biology.
Exactly solvable model for the QCD tricritical endpoint
Bugaev, K. A.
2008-09-15
An inclusion of temperature and chemical-potential-dependent surface-tension in the gas of quark-gluon bags model resolves a long-standing problem of a unified description of the first-and second-order phase transition with the crossover. The suggested model has an exact analytical solution and allows one to rigorously study the vicinity of the critical endpoint of the deconfinement phase transition. It is found that, at the curve of a zero surface-tension coefficient, there must exist the surface-induced phase transition of the seond or higher order. The present model predicts that the critical endpoint of quantum chromodynamics is the tricritical endpoint.
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
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
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.
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.
NASA Technical Reports Server (NTRS)
1984-01-01
A system-level design and analysis model was developed. This model was conceived to have several key elements: a solar pond thermodynamic performance model, a power generation subsystem model, and an economic analysis element. The basic approach was to create these elements or modules and refine them on an individual basis yet retain the capability to easily couple them into a full system design model. This building block approach allows for maximum flexibility and substitution of refined descriptions as the technology develops. A general overview of interconnecting these subsystem models is presented. The primary program control element will perform the administrative functions of data input, data output, information storage and transfer, and sequential calling of the subsystem models. From the point of view of the requirements of a system design model, a power conversion subsystem model was developed. The goal of the effort was a preliminary subsystem model compatible with the solar pond subsystem model so that a first order system simulation analysis could be performed.
Analytically solvable driven time-dependent two-level quantum systems
NASA Astrophysics Data System (ADS)
Barnes, Edwin; Das Sarma, Sankar
2013-03-01
Analytical solutions to the time-dependent Schrodinger equation describing a driven two-level system are invaluable to many areas of physics, but they are also extremely rare. Here, we present a simple algorithm based on a type of partial reverse-engineering that generates an unlimited number of exact analytical solutions for a general time-dependent Hamiltonian. We demonstrate this method by presenting several new exact solutions that are particularly relevant to qubit control in quantum computing applications. We further show that our formalism easily generates analytical control protocols for performing sweeps across energy level anti-crossings that execute perfect Landau-Zener interferometry and rapid adiabatic passage near the quantum speed limit. Work supported by LPS-CMTC, CNAM and IARPA
Solvable model for many-quark systems in QCD Hamiltonians
Yepez-Martinez, Tochtli; Hess, P. O.; Civitarese, O.
2010-04-15
Motivated by a canonical QCD Hamiltonian, we propose an effective Hamiltonian to represent an arbitrary number of quarks in hadronic bags. The structure of the effective Hamiltonian is discussed and the BCS-type solutions that may represent constituent quarks are presented. The single-particle orbitals are chosen as three-dimensional harmonic oscillators, and we discuss a class of exact solutions that can be obtained when a subset of single-particle basis states is restricted to include a certain number of orbital excitations. The general problem, which includes all possible orbital states, can also be solved by combining analytical and numerical methods.
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.
Weak solvability via bipotential method for contact models with nonmonotone boundary conditions
NASA Astrophysics Data System (ADS)
Costea, Nicuşor; Csirik, Mihály; Varga, Csaba
2015-10-01
We consider a general mathematical model which describes the contact between a body and a foundation, under the small deformations hypothesis. The behavior of the material is modeled by a monotone constitutive law, while on the potential contact zone nonmonotone boundary conditions are imposed. We propose a variational formulation in terms of bipotentials, whose unknown is a pair consisting of the displacement field and the Cauchy stress field. The existence of weak solutions is proved using a recent result due to Costea and Varga (Topol Methods Nonlinear Anal 41:39-67, 2013) concerning the solvability of nonlinear hemivariational inequality systems.
Thermodynamics of an exactly solvable confining quark model
NASA Astrophysics Data System (ADS)
Mintz, Bruno W.
2016-04-01
The grand partition function of a model of confined quarks is exactly calculated at arbitrary temperatures and quark chemical potentials. The model is inspired by a version of QCD where the usual (perturbative) BRST symmetry is broken in the infrared, while possessing a quark mass function compatible with nonperturbative analyses of lattice simulations and Dyson-Schwinger equations. Even though the model is defined at tree level, we show that it produces a non-trivial and stable thermodynamic behaviour at any temperature or chemical potential. Results for the pressure, the entropy and the trace anomaly as a function of the temperature are qualitatively compatible with the effect of non-perturbative interactions as observed in lattice simulations. The finite density thermodynamics is also shown to contain non-trivial features, being far away from an ideal gas picture.
Thermodynamics of an exactly solvable confining quark model
NASA Astrophysics Data System (ADS)
Guimaraes, M. S.; Mintz, B. W.; Palhares, L. F.
2015-10-01
The grand partition function of a model of confined quarks is exactly calculated at arbitrary temperatures and quark chemical potentials. The model is inspired by a version of QCD with a soft breaking of the Becchi-Rouet-Stora-Tyutin symmetry and possesses a quark mass function compatible with nonperturbative analyses of lattice simulations and Dyson-Schwinger equations. Even though the model is defined at tree level, we show that it produces a nontrivial and stable thermodynamic behavior at any temperature or chemical potential. Results for the pressure, the entropy and the trace anomaly as a function of the temperature are qualitatively compatible with the effect of nonperturbative interactions as observed in lattice simulations. The finite density thermodynamics is also shown to contain nontrivial features, being far away from an ideal gas picture.
Tree-like structure of eternal inflation: A solvable model
NASA Astrophysics Data System (ADS)
Harlow, Daniel; Shenker, Stephen H.; Stanford, Douglas; Susskind, Leonard
2012-03-01
In this paper we introduce a simple discrete stochastic model of eternal inflation that shares many of the most important features of the continuum theory as it is now understood. The model allows us to construct a multiverse and rigorously analyze its properties. Although simple and easy to solve, it has a rich mathematical structure underlying it. Despite the discreteness of the space-time the theory exhibits an unexpected nonperturbative analog of conformal symmetry that acts on the boundary of the geometry. The symmetry is rooted in the mathematical properties of trees, p-adic numbers, and ultrametric spaces; and in the physical property of detailed balance. We provide self-contained elementary explanations of the unfamiliar mathematical concepts, which have also appeared in the study of the p-adic string. The symmetry acts on a huge collection of very low-dimensional “multiverse fields” that are not associated with the usual perturbative degrees of freedom. They are connected with the late-time statistical distribution of bubble-universes in the multiverse. The conformal symmetry which acts on the multiverse fields is broken by the existence of terminal decays—to hats or crunches—but in a particularly simple way. We interpret this symmetry breaking as giving rise to an arrow of time. The model is used to calculate statistical correlations at late time and to discuss the measure problem. We show that the natural cutoff in the model is the analog of the so-called light-cone-time cutoff. Applying the model to the problem of the cosmological constant, we find agreement with earlier work.
Solvable Model for Chimera States of Coupled Oscillators
NASA Astrophysics Data System (ADS)
Abrams, Daniel M.; Mirollo, Rennie; Strogatz, Steven H.; Wiley, Daniel A.
2008-08-01
Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.
Solvable model for chimera states of coupled oscillators.
Abrams, Daniel M; Mirollo, Rennie; Strogatz, Steven H; Wiley, Daniel A
2008-08-22
Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.
On the solvability of a mathematical model for prion proliferation
NASA Astrophysics Data System (ADS)
Simonett, Gieri; Walker, Christoph
2006-12-01
We show that a model describing the interaction between normal and infectious prion proteins admits global solutions. More precisely, supposing the involved degradation rates to be bounded, we prove global existence and uniqueness of classical solutions. Based on this existence theory, we provide sufficient conditions for the existence of global weak solutions in the case of unbounded splitting rates. Moreover, we prove global stability of the disease-free steady state.
An exactly solvable model of hierarchical self-assembly.
Dudowicz, Jacek; Douglas, Jack F; Freed, Karl F
2009-06-14
Many living and nonliving structures in the natural world form by hierarchical organization, but physical theories that describe this type of organization are scarce. To address this problem, a model of equilibrium self-assembly is formulated in which dynamically associating species organize into hierarchical structures that preserve their shape at each stage of assembly. In particular, we consider symmetric m-gons that associate at their vertices into Sierpinski gasket structures involving the hierarchical association of triangles, squares, hexagons, etc., at their corner vertices, thereby leading to fractal structures after many generations of assembly. This rather idealized model of hierarchical assembly yields an infinite sequence of self-assembly transitions as the morphology progressively organizes to higher levels of the hierarchy, and these structures coexists at dynamic equilibrium, as found in real hierarchically self-assembling systems such as amyloid fiber forming proteins. Moreover, the transition sharpness progressively grows with increasing m, corresponding to larger and larger loops in the assembled structures. Calculations are provided for several basic thermodynamic properties (including the order parameters for assembly for each stage of the hierarchy, average mass of clusters, specific heat, transition sharpness, etc.) that are required for characterizing the interaction parameters governing this type of self-assembly and for elucidating other basic qualitative aspects of these systems. Our idealized model of hierarchical assembly gives many insights into this ubiquitous type of self-organization process. PMID:19530788
An exactly solvable model of hierarchical self-assembly
NASA Astrophysics Data System (ADS)
Dudowicz, Jacek; Douglas, Jack F.; Freed, Karl F.
2009-06-01
Many living and nonliving structures in the natural world form by hierarchical organization, but physical theories that describe this type of organization are scarce. To address this problem, a model of equilibrium self-assembly is formulated in which dynamically associating species organize into hierarchical structures that preserve their shape at each stage of assembly. In particular, we consider symmetric m-gons that associate at their vertices into Sierpinski gasket structures involving the hierarchical association of triangles, squares, hexagons, etc., at their corner vertices, thereby leading to fractal structures after many generations of assembly. This rather idealized model of hierarchical assembly yields an infinite sequence of self-assembly transitions as the morphology progressively organizes to higher levels of the hierarchy, and these structures coexists at dynamic equilibrium, as found in real hierarchically self-assembling systems such as amyloid fiber forming proteins. Moreover, the transition sharpness progressively grows with increasing m, corresponding to larger and larger loops in the assembled structures. Calculations are provided for several basic thermodynamic properties (including the order parameters for assembly for each stage of the hierarchy, average mass of clusters, specific heat, transition sharpness, etc.) that are required for characterizing the interaction parameters governing this type of self-assembly and for elucidating other basic qualitative aspects of these systems. Our idealized model of hierarchical assembly gives many insights into this ubiquitous type of self-organization process.
Weak solvability of irregularized model of viscoelastisity with memory
NASA Astrophysics Data System (ADS)
Zvyagin, Victor; Orlov, Vladimir
2016-08-01
In the present paper we establish the existence of weak solutions of the initial-boundary value problem for equations of a viscoelastic model of fluid with memory along the trajectories of the velocity field. We use approximation-topological method which involves replacement of the given problem by operator equation, an approximation of equation in a weak sense, and the application of topological degree theory which allows to establish the existence of solutions on the base of a priori estimates and passing to the limit statements.
Exactly solvable time-dependent models of two interacting two-level systems
NASA Astrophysics Data System (ADS)
Grimaudo, R.; Messina, A.; Nakazato, H.
2016-08-01
Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional subdynamics. Each of the subdynamics is shown to be brought into an exactly solvable form by appropriately engineering the magnetic fields and thus we obtain an exact time evolution of the compound system. Several physically relevant and interesting quantities are evaluated exactly to disclose intriguing phenomena in such a system.
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
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 Model for Impurity Scattering at the Edge of the ν = 2 / 3 FQH State
NASA Astrophysics Data System (ADS)
Heinrich, Chris; Levin, Michael
We present an exactly solvable model for impurity scattering on the edge of a ν = 2 / 3 FQH state that is valid in the strong scattering limit. For this model we obtain exact mode expansions for the charge density and current operators, as well as the exact low energy spectrum. Importantly, we find that the low energy theory of the model consists of decoupled and counterpropagating charge and neutral modes, agreeing with the earlier work of Kane, Fisher, and Polchinski. Unlike the previous derivation, which relied on perturbative renormalization group arguments, our approach allows us to derive the emergence of decoupled charge and neutral modes from a microscopic model which is initially far from the decoupled fixed point.
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.
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
An exactly solvable model for a strongly spin-orbit-coupled nanowire quantum dot
NASA Astrophysics Data System (ADS)
Li, Rui; Wu, Lian-Ao; Hu, Xuedong; You, J. Q.
In the presence of spin-orbit coupling, quantum models for semiconductor materials are generally not exactly solvable. As a result, understanding of the strong spin-orbit coupling effects in these systems remains incomplete. Here we develop a method to solve exactly the one-dimensional hard-wall quantum dot problem for a single electron in the presence of a strong spin-orbit coupling and a finite magnetic field. This method allows us to obtain the exact eigenenergies and eigenstates for the single electron. With the help of this solution, we demonstrate unique effects from the strong spin-orbit coupling in a semiconductor quantum dot, in particular the anisotropy of the electron g-factor and its tunability. We thank financial support by NNSF China, NBRP China, NSAF China, Basque Country government, Spanish MICINN, US ARO, and US NSF-PIF.
A solvable toy model for tachyon condensation in string field theory
NASA Astrophysics Data System (ADS)
Zwiebach, Barton
2000-09-01
The lump solution of phi3 field theory provides a toy model for unstable D-branes of bosonic string theory. The field theory living on this lump is itself a cubic field theory involving a tachyon, two additional scalar fields, and a scalar field continuum. Its action can be written explicitly because the fluctuation spectrum of the lump turns out to be governed by a solvable Schroedinger equation; the l = 3 case of a series of reflectionless potentials. We study the multiscalar tachyon potential both exactly and in the level expansion, obtaining insight into issues of convergence, branches of the solution space, and the mechanism for removal of states after condensation. In particular we find an interpretation for the puzzling finite domain of definition of string field marginal parameters.
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.
Isotropic Brownian motions over complex fields as a solvable model for May-Wigner stability analysis
NASA Astrophysics Data System (ADS)
Ipsen, J. R.; Schomerus, H.
2016-09-01
We consider matrix-valued stochastic processes known as isotropic Brownian motions, and show that these can be solved exactly over complex fields. While these processes appear in a variety of questions in mathematical physics, our main motivation is their relation to a May-Wigner-like stability analysis, for which we obtain a stability phase diagram. The exact results establish the full joint probability distribution of the finite-time Lyapunov exponents, and may be used as a starting point for a more detailed analysis of the stability-instability phase transition. Our derivations rest on an explicit formulation of a Fokker-Planck equation for the Lyapunov exponents. This formulation happens to coincide with an exactly solvable class of models of the Calgero-Sutherland type, originally encountered for a model of phase-coherent transport. The exact solution over complex fields describes a determinantal point process of biorthogonal type similar to recent results for products of random matrices, and is also closely related to Hermitian matrix models with an external source.
NASA Astrophysics Data System (ADS)
Ng, Ka Ki; Chan, Wai Soen; Yu, Kin Wah
2015-03-01
Motivated by the need of seismic base isolation, we have proposed a strategy to design vibration isolation systems to achieve near-zero amplitude vibration under external excitations over a broad frequency band. The strategy combines two ideas from previous works: (i) zeros assignment for broadband epsilon-near-zero metamaterials [Sun, and Yu (2012)]; and (ii) the localization of vibrational modes in graded elastic networks [Xiao, Yakubo, and Yu (2006)]. Firstly, we aim to assign zeros (anti-resonance frequencies) over an operating frequency band. Starting from an exactly solvable model of zigzag diatomic chains, we demonstrate a one-to-one correspondence between the zeros and one type of the masses after solving the models. Hence, the zeros can be assigned at will by tuning the masses. Secondly, in order to achieve further vibrational suppression by gradon localization, a band overlapping picture is applied to tune the rest of the masses to an optimal value. The results can be generalized to 2D and 3D structures for more realistic applications.
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.
A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons
NASA Astrophysics Data System (ADS)
Hibberd, K. E.; Dunning, C.; Links, J.
2006-08-01
We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrödinger operators. For the solution we derive here the potential of the Schrödinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PT-symmetric wavefunctions defined on a contour in the complex plane.
Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces
NASA Astrophysics Data System (ADS)
Bihun, Oksana; Calogero, Francesco
2013-10-01
The class of solvable many-body problems ''of goldfish type'' is extended by including (the additional presence of) three-body forces. The solvable N-body problems thereby identified are characterized by Newtonian equations of motion featuring 19 arbitrary ''coupling constants''. Restrictions on these constants are identified which cause these systems - or appropriate variants of them - to be isochronous or asymptotically isochronous, i.e. all their solutions to be periodic with a fixed period (independent of the initial data) or to have this property up to contributions vanishing exponentially as t→ ∞.
Hasegawa, Hideo
2011-07-01
Responses of small open oscillator systems to applied external forces have been studied with the use of an exactly solvable classical Caldeira-Leggett model in which a harmonic oscillator (system) is coupled to finite N-body oscillators (bath) with an identical frequency (ω(n) = ω(o) for n = 1 to N). We have derived exact expressions for positions, momenta, and energy of the system in nonequilibrium states and for work performed by applied forces. A detailed study has been made on an analytical method for canonical averages of physical quantities over the initial equilibrium state, which is much superior to numerical averages commonly adopted in simulations of small systems. The calculated energy of the system which is strongly coupled to a finite bath is fluctuating but nondissipative. It has been shown that the Jarzynski equality is valid in nondissipative nonergodic open oscillator systems regardless of the rate of applied ramp force. PMID:21867150
A solvable model for fermion masses on a warped 6D world with the extra 2D sphere
NASA Astrophysics Data System (ADS)
Kokado, Akira; Saito, Takesi
2015-03-01
In a warped 6D world with an extra two-dimensional sphere, we propose an exactly solvable model for fermion masses with zero mode. The warp factor is given by ϕ(θ, φ) = sin θcos φ, which is a solution to the 6D Einstein equation with the bulk cosmological constant Λ and the energy-momentum tensor of the bulk matter fields. Our model provides another possibility of obtaining fermion zero mode, rather than traditional model based on Dirac's monopole.
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2004-06-01
A simple approach is discussed which associates to (solvable) matrix equations (solvable) dynamical systems, generally interpretable as (interesting) many-body problems, possibly involving auxiliary dependent variables in addition to those identifying the positions of the moving particles. We then focus on cases in which the auxiliary variables can be altogether eliminated, reobtaining thereby (via this unified approach) well-known solvable many-body problems, and moreover a (solvable) extension of the "goldfish" model.
Statistics of avalanches with relaxation and Barkhausen noise: A solvable model
NASA Astrophysics Data System (ADS)
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.
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.
Micheletti, Cristian; Cecconi, Fabio; Flammini, Alessandro; Maritan, Amos
2002-08-01
An exactly solvable model based on the topology of a protein native state is applied to identify bottlenecks and key sites for the folding of human immunodeficiency virus type 1 (HIV-1) protease. The predicted sites are found to correlate well with clinical data on resistance to Food and Drug Administration-approved drugs. It has been observed that the effects of drug therapy are to induce multiple mutations on the protease. The sites where such mutations occur correlate well with those involved in folding bottlenecks identified through the deterministic procedure proposed in this study. The high statistical significance of the observed correlations suggests that the approach may be promisingly used in conjunction with traditional techniques to identify candidate locations for drug attacks.
Tilles, Paulo F C; Petrovskii, Sergei V
2016-07-01
Patterns of individual animal movement have been a focus of considerable attention recently. Of particular interest is a question how different macroscopic properties of animal dispersal result from the stochastic processes occurring on the microscale of the individual behavior. In this paper, we perform a comprehensive analytical study of a model where the animal changes the movement velocity as a result of its behavioral response to environmental stochasticity. The stochasticity is assumed to manifest itself through certain signals, and the animal modifies its velocity as a response to the signals. We consider two different cases, i.e. where the change in the velocity is or is not correlated to its current value. We show that in both cases the early, transient stage of the animal movement is super-diffusive, i.e. ballistic. The large-time asymptotic behavior appears to be diffusive in the uncorrelated case but super-ballistic in the correlated case. We also calculate analytically the dispersal kernel of the movement and show that, whilst it converge to a normal distribution in the large-time limit, it possesses a fatter tail during the transient stage, i.e. at early and intermediate time. Since the transients are known to be highly relevant in ecology, our findings may indicate that the fat tails and superdiffusive spread that are sometimes observed in the movement data may be a feature of the transitional dynamics rather than an inherent property of the animal movement. PMID:26650504
Child abduction murder: the impact of forensic evidence on solvability.
Brown, Katherine M; Keppel, Robert D
2012-03-01
This study examined 733 child abduction murders (CAMs) occurring from 1968 to 2002 to explore the influence of forensic evidence on case solvability in CAM investigations. It was hypothesized that the presence of forensic evidence connecting the offender to the crime would enhance case solvability in murder investigations of abducted children. This study examined the impact of CAM of different types of forensic evidence and the impact of the summed total of forensic evidence items on case solvability by controlling for victim age, victim race, victim gender, and victim-offender relationship. Time and distance theoretical predictors were also included. Binomial logistic regression models were used to determine whether forensic evidence was a critical solvability factor in murder investigations of abducted children. This research indicated that, while forensic evidence increased case solvability, the impact of forensic evidence on solvability was not as important as other solvability factors examined.
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)
Shvartsburg, Aleksandr B.
1998-03-01
An analysis is made of propagation of electromagnetic waves in media which are nonstationary because of relaxation of the refractive index. A series of models of oscillatory and transient regimes of such relaxation is developed. Several characteristic times are used in these models and exact analytic solutions of the Maxwell equations can be obtained for these regimes. In contrast to the traditional approaches, the exact solutions are obtained without assuming smallness or slowness of temporal variations of the parameters of the medium and these solutions are valid even when the characteristic relaxation time is comparable with the period of oscillations of the wave field. A nonstationary generalisation of the Fresnel formulae is derived. It is shown that waves reflected from a nonstationary surface experience amplitude and frequency modulation, and the modulation effect is localised in an interval of the order of one relaxation time. It is shown that a short broadband perturbation pulse forms in the reflected wave and that this pulse contains one or several oscillations of the field. It should be possible to use nonstationary broadening of the spectrum of a probe wave reflected from a surface perturbed by a powerful laser pulse in estimating the relaxation times of fast optical processes.
A hidden analytic structure of the Rabi model
Moroz, Alexander
2014-01-15
The Rabi model describes the simplest interaction between a cavity mode with a frequency ω{sub c} and a two-level system with a resonance frequency ω{sub 0}. It is shown here that the spectrum of the Rabi model coincides with the support of the discrete Stieltjes integral measure in the orthogonality relations of recently introduced orthogonal polynomials. The exactly solvable limit of the Rabi model corresponding to Δ=ω{sub 0}/(2ω{sub c})=0, which describes a displaced harmonic oscillator, is characterized by the discrete Charlier polynomials in normalized energy ϵ, which are orthogonal on an equidistant lattice. A non-zero value of Δ leads to non-classical discrete orthogonal polynomials ϕ{sub k}(ϵ) and induces a deformation of the underlying equidistant lattice. The results provide a basis for a novel analytic method of solving the Rabi model. The number of ca. 1350 calculable energy levels per parity subspace obtained in double precision (cca 16 digits) by an elementary stepping algorithm is up to two orders of magnitude higher than is possible to obtain by Braak’s solution. Any first n eigenvalues of the Rabi model arranged in increasing order can be determined as zeros of ϕ{sub N}(ϵ) of at least the degree N=n+n{sub t}. The value of n{sub t}>0, which is slowly increasing with n, depends on the required precision. For instance, n{sub t}≃26 for n=1000 and dimensionless interaction constant κ=0.2, if double precision is required. Given that the sequence of the lth zeros x{sub nl}’s of ϕ{sub n}(ϵ)’s defines a monotonically decreasing discrete flow with increasing n, the Rabi model is indistinguishable from an algebraically solvable model in any finite precision. Although we can rigorously prove our results only for dimensionless interaction constant κ<1, numerics and exactly solvable example suggest that the main conclusions remain to be valid also for κ≥1. -- Highlights: •A significantly simplified analytic solution of the Rabi model
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.
NASA Astrophysics Data System (ADS)
Erokhin, N. S.; Zakharov, V. E.; Zol'nikova, N. N.; Mikhailovskaya, L. A.
2015-02-01
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.
Exactly solvable model for nonlinear light-matter interaction in an arbitrary time-dependent field
Brown, J. M.; Lotti, A.; Teleki, A.; Kolesik, M.
2011-12-15
Exact analytic expressions are derived for the dipole moment and nonlinear current of a one-dimensional quantum particle subject to a short-range attractive potential and an arbitrary time-dependent electric field. An efficient algorithm for the current evaluation is described and a robust implementation suitable for numerical simulations is demonstrated.
Kinjo, Ken; Uchibe, Eiji; Doya, Kenji
2013-01-01
Linearly solvable Markov Decision Process (LMDP) is a class of optimal control problem in which the Bellman's equation can be converted into a linear equation by an exponential transformation of the state value function (Todorov, 2009b). In an LMDP, the optimal value function and the corresponding control policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunction problem in a continuous state using the knowledge of the system dynamics and the action, state, and terminal cost functions. In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in which the dynamics of the body and the environment have to be learned from experience. We first perform a simulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynamics model on the derived the action policy. The result shows that a crude linear approximation of the non-linear dynamics can still allow solution of the task, despite with a higher total cost. We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robot platform. The state is given by the position and the size of a battery in its camera view and two neck joint angles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servo controller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state cost functions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics model performed equivalently with the optimal linear quadratic regulator (LQR). In the non-quadratic task, the LMDP controller with a linear dynamics model showed the best performance. The results demonstrate the usefulness of the LMDP framework in real robot control even when simple linear models are used for dynamics learning. PMID:23576983
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.
NASA Astrophysics Data System (ADS)
Strekalov, M. L.
2013-11-01
A theoretical study has been made on the non-stationary phenomena in the relaxation of highly vibrationally excited molecules under laser radiation giving rise to these molecules. An exact analytical solution to the master equation has been obtained in terms of Meixner polynomials with regard to VV and VT processes. The time-dependent vibrational distribution is used to obtain analytical expressions for the mean number of photons, stored on the vibrational degrees of freedom and transferred to a thermal bath. Using the latter result, an explicit expression is given for the average energy transfer as a function of time. Its dependence on the partial pressure of absorbing molecules has also been established.
NASA Astrophysics Data System (ADS)
Sasaki, Ryu; Znojil, Miloslav
2016-11-01
Exact solvability (ES) of one-dimensional quantum potentials V(x) is a vague concept. We propose that beyond its most conventional range the ES status should also be attributed to many less common interaction models for which the wave functions remain piecewise proportional to special functions. The claim is supported by constructive analysis of a toy model V(x) =-{g}2\\exp (-| x| ). The detailed description of the related bound-state and scattering solutions of the Schrödinger equation is provided in terms of Bessel functions which are properly matched in the origin.
ANALYTIC MODELING OF STARSHADES
Cash, Webster
2011-09-01
External occulters, otherwise known as starshades, have been proposed as a solution to one of the highest priority yet technically vexing problems facing astrophysics-the direct imaging and characterization of terrestrial planets around other stars. New apodization functions, developed over the past few years, now enable starshades of just a few tens of meters diameter to occult central stars so efficiently that the orbiting exoplanets can be revealed and other high-contrast imaging challenges addressed. In this paper, an analytic approach to the analysis of these apodization functions is presented. It is used to develop a tolerance analysis suitable for use in designing practical starshades. The results provide a mathematical basis for understanding starshades and a quantitative approach to setting tolerances.
An exactly solvable model of an oscillator with nonlinear coupling and zeros of Bessel functions
NASA Technical Reports Server (NTRS)
Dodonov, V. V.; Klimov, A. B.
1993-01-01
We consider an oscillator model with nonpolynomial interaction. The model admits exact solutions for two situations: for energy eigenvalues in terms of zeros of Bessel functions, that were considered as functions of the continuous index; and for the corresponding eigenstates in terms of Lommel polynomials.
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.
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.
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.
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. PMID:27627271
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
Jacquin, Hugo; Shakhnovich, Eugene; Cocco, Simona; Monasson, Rémi
2016-01-01
Inverse statistical approaches to determine protein structure and function from Multiple Sequence Alignments (MSA) are emerging as powerful tools in computational biology. However the underlying assumptions of the relationship between the inferred effective Potts Hamiltonian and real protein structure and energetics remain untested so far. Here we use lattice protein model (LP) to benchmark those inverse statistical approaches. We build MSA of highly stable sequences in target LP structures, and infer the effective pairwise Potts Hamiltonians from those MSA. We find that inferred Potts Hamiltonians reproduce many important aspects of ‘true’ LP structures and energetics. Careful analysis reveals that effective pairwise couplings in inferred Potts Hamiltonians depend not only on the energetics of the native structure but also on competing folds; in particular, the coupling values reflect both positive design (stabilization of native conformation) and negative design (destabilization of competing folds). In addition to providing detailed structural information, the inferred Potts models used as protein Hamiltonian for design of new sequences are able to generate with high probability completely new sequences with the desired folds, which is not possible using independent-site models. Those are remarkable results as the effective LP Hamiltonians used to generate MSA are not simple pairwise models due to the competition between the folds. Our findings elucidate the reasons for the success of inverse approaches to the modelling of proteins from sequence data, and their limitations. PMID:27177270
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.
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2004-12-01
We take advantage of the simple approach, recently discussed, which associates to (solvable) matrix equations (solvable) dynamical systems interpretable as (interesting) many-body problems, possibly involving auxiliary dependent variables in addition to those identifying the positions of the moving particles. Starting from a solvable matrix evolution equation, we obtain the corresponding many-body model and note that in one case the auxiliary variables can be altogether eliminated, obtaining thereby an (also Hamiltonian) extension of the "goldfish" model. The solvability of this novel model, and of its isochronous variant, is exhibited. A related, as well solvable, model, is also introduced, as well as its isochronous variant. Finally, the small oscillations of the isochronous models around their equilibrium configurations are investigated, and from their isochronicity certain diophantine relations are evinced.
Explore or Exploit? A Generic Model and an Exactly Solvable Case
NASA Astrophysics Data System (ADS)
Gueudré, Thomas; Dobrinevski, Alexander; Bouchaud, Jean-Philippe
2014-02-01
Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a stylized model for these exploration-exploitation situations, including population or economic growth, portfolio optimization, evolutionary dynamics, or the problem of optimal pinning of vortices or dislocations in disordered materials. We find the exact growth rate of this model for treelike geometries and prove the existence of an optimal migration rate in this case. Numerical simulations in the one-dimensional case confirm the generic existence of an optimum.
ERIC Educational Resources Information Center
Burke, Lisa A.; Saks, Alan M.
2009-01-01
Decades have been spent studying training transfer in organizational environments in recognition of a transfer problem in organizations. Theoretical models of various antecedents, empirical studies of transfer interventions, and studies of best practices have all been advanced to address this continued problem. Yet a solution may not be so…
Double-semion topological order from exactly solvable quantum dimer models
NASA Astrophysics Data System (ADS)
Qi, Yang; Gu, Zheng-Cheng; Yao, Hong
2015-10-01
We construct a generalized quantum dimer model on two-dimensional nonbipartite lattices, including the triangular lattice, the star lattice, and the kagome lattice. At the Rokhsar-Kivelson (RK) point, we obtain its exact ground states that are shown to be a fully gapped quantum spin liquid with the double-semion topological order. The ground-state wave function of such a model at the RK point is a superposition of dimer configurations with a nonlocal sign structure determined by counting the number of loops in the transition graph. We explicitly demonstrate the double-semion topological order in the ground states by showing the semionic statistics of monomer excitations. We also discuss possible implications of such double-semion resonating valence bond states to candidate quantum spin-liquid systems discovered experimentally and numerically in the past few years.
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.
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.
Exactly solvable antiferromagnetic Blume-Capel model on a sawtooth chain.
Guo, Yan-Ping; Liu, Zhong-Qiang; Xu, Yu-Liang; Kong, Xiang-Mu
2016-05-01
The geometrically frustrated spin-1 Blume-Capel model on an infinite sawtooth chain is exactly solved by the transfer matrix method. The magnetization, ground-state phase diagram, magnetocaloric properties, and specific heat of the system are investigated. The results indicate that: (i) Magnetization plateaus appear at zero temperature. Their number depends on the sign of the crystal field D. For D≥0 there are two magnetization plateaus; however, for D<0 five plateaus exist. At a finite temperature, thermal excitation will destroy these plateaus completely. (ii) Phase transition between any two long-range-ordered ground states, whose spin configurations are given in phase diagram, is the first-order one. The macroscopic degeneracy of the ground states described by the entropy only exists at phase coexistence points. (iii) As temperature approaches zero, magnetocaloric properties and entropy change sharply near phase coexistence points. (iv) The crossovers of the specific heat from a single-peak structure to double-peak ones can signal the phase coexistence points in ground-state phase diagram. PMID:27300873
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.
Exactly solvable antiferromagnetic Blume-Capel model on a sawtooth chain
NASA Astrophysics Data System (ADS)
Guo, Yan-Ping; Liu, Zhong-Qiang; Xu, Yu-Liang; Kong, Xiang-Mu
2016-05-01
The geometrically frustrated spin-1 Blume-Capel model on an infinite sawtooth chain is exactly solved by the transfer matrix method. The magnetization, ground-state phase diagram, magnetocaloric properties, and specific heat of the system are investigated. The results indicate that: (i) Magnetization plateaus appear at zero temperature. Their number depends on the sign of the crystal field D . For D ≥0 there are two magnetization plateaus; however, for D <0 five plateaus exist. At a finite temperature, thermal excitation will destroy these plateaus completely. (ii) Phase transition between any two long-range-ordered ground states, whose spin configurations are given in phase diagram, is the first-order one. The macroscopic degeneracy of the ground states described by the entropy only exists at phase coexistence points. (iii) As temperature approaches zero, magnetocaloric properties and entropy change sharply near phase coexistence points. (iv) The crossovers of the specific heat from a single-peak structure to double-peak ones can signal the phase coexistence points in ground-state phase diagram.
Solvable groups and a shear construction
NASA Astrophysics Data System (ADS)
Freibert, Marco; Swann, Andrew
2016-08-01
The twist construction is a geometric model of T-duality that includes constructions of nilmanifolds from tori. This paper shows how one-dimensional foliations on manifolds may be used in a shear construction, which in algebraic form builds certain solvable Lie groups from Abelian ones. We discuss other examples of geometric structures that may be obtained from the shear construction.
Analytical model for ramp compression
NASA Astrophysics Data System (ADS)
Xue, Quanxi; Jiang, Shaoen; Wang, Zhebin; Wang, Feng; Hu, Yun; Ding, Yongkun
2016-08-01
An analytical ramp compression model for condensed matter, which can provide explicit solutions for isentropic compression flow fields, is reported. A ramp compression experiment can be easily designed according to the capability of the loading source using this model. Specifically, important parameters, such as the maximum isentropic region width, material properties, profile of the pressure pulse, and the pressure pulse duration can be reasonably allocated or chosen. To demonstrate and study this model, laser-direct-driven ramp compression experiments and code simulation are performed successively, and the factors influencing the accuracy of the model are studied. The application and simulation show that this model can be used as guidance in the design of a ramp compression experiment. However, it is verified that further optimization work is required for a precise experimental design.
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
Yao, Hong; Lee, Dung-Hai
2011-08-19
We introduce an exactly solvable SU(2)-invariant spin-1/2 model with exotic spin excitations. With time reversal symmetry (TRS), the ground state is a spin liquid with gapless or gapped spin-1 but fermionic excitations. When TRS is broken, the resulting spin liquid exhibits deconfined vortex excitations which carry spin-1/2 and obey non-Abelian statistics. We show that this SU(2) invariant non-Abelian spin liquid exhibits the spin quantum Hall effect with quantized spin Hall conductivity σ(xy)(s)=ℏ/2π, and that the spin response is effectively described by the SO(3) level-1 Chern-Simons theory at low energy. We further propose that a SU(2) level-2 Chern-Simons theory is the effective field theory describing the topological structure of the non-Abelian SU(2) invariant spin liquid.
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.
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.
NASA Astrophysics Data System (ADS)
Schuck, Peter; Tohyama, Mitsuru
2016-04-01
The Bogoliubov-Born-Green-Kirkwood-Yvon or time-dependent density matrix (TDDM) hierarchy of equations for higher density matrices is truncated at the three-body level in approximating the three-body correlation function by a quadratic form of two-body ones, closing the equations in this way. The procedure is discussed in detail and it is shown in nontrivial model cases that the approximate inclusion of three-body correlation functions is very important to obtain precise results. A small amplitude approximation of this time-dependent nonlinear equation for the two-body correlation function is performed (STDDM*-b) and it is shown that the one-body sector of this generalized nonlinear second random phase approximation (RPA) equation is equivalent to the self-consistent RPA (SCRPA) approach which had been derived previously by different techniques. It is discussed in which way SCRPA also contains the three-body correlations. TDDM and SCRPA are tested versus exactly solvable model cases.
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; ...
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.
Stochastic genetic networks with solvable structures
NASA Astrophysics Data System (ADS)
Lipan, Ovidiu
2014-12-01
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.
Goldfishing: A new solvable many-body problem
NASA Astrophysics Data System (ADS)
Bruschi, M.; Calogero, F.
2006-10-01
A recent technique allows one to identify and investigate solvable dynamical systems naturally interpretable as classical many-body problems, being characterized by equations of motion of Newtonian type (generally in two-dimensional space). In this paper we tersely review results previously obtained in this manner and present novel findings of this kind: mainly solvable variants of the goldfish many-body model, including models that feature isochronous classes of completely periodic solutions. Different formulations of these models are presented. The behavior of one of these isochronous dynamical systems in the neighborhood of its equilibrium configuration is investigated, and in this manner some remarkable Diophantine findings are obtained.
Acoustic detection and ranging using solvable chaos
NASA Astrophysics Data System (ADS)
Corron, Ned J.; Stahl, Mark T.; Chase Harrison, R.; Blakely, Jonathan N.
2013-06-01
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 in the presence of noise and interference from a second chaotic emitter are presented to demonstrate the viability of the approach.
Acoustic detection and ranging using solvable chaos.
Corron, Ned J; Stahl, Mark T; Harrison, R Chase; Blakely, Jonathan N
2013-06-01
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 in the presence of noise and interference from a second chaotic emitter are presented to demonstrate the viability of the approach. PMID:23822484
Analytic gain in probabilistic decompression sickness models.
Howle, Laurens E
2013-11-01
Decompression sickness (DCS) is a disease known to be related to inert gas bubble formation originating from gases dissolved in body tissues. Probabilistic DCS models, which employ survival and hazard functions, are optimized by fitting model parameters to experimental dive data. In the work reported here, I develop methods to find the survival function gain parameter analytically, thus removing it from the fitting process. I show that the number of iterations required for model optimization is significantly reduced. The analytic gain method substantially improves the condition number of the Hessian matrix which reduces the model confidence intervals by more than an order of magnitude. PMID:24209920
Analytic gain in probabilistic decompression sickness models.
Howle, Laurens E
2013-11-01
Decompression sickness (DCS) is a disease known to be related to inert gas bubble formation originating from gases dissolved in body tissues. Probabilistic DCS models, which employ survival and hazard functions, are optimized by fitting model parameters to experimental dive data. In the work reported here, I develop methods to find the survival function gain parameter analytically, thus removing it from the fitting process. I show that the number of iterations required for model optimization is significantly reduced. The analytic gain method substantially improves the condition number of the Hessian matrix which reduces the model confidence intervals by more than an order of magnitude.
Knowledge Generation Model for Visual Analytics.
Sacha, Dominik; Stoffel, Andreas; Stoffel, Florian; Kwon, Bum Chul; Ellis, Geoffrey; Keim, Daniel A
2014-12-01
Visual analytics enables us to analyze huge information spaces in order to support complex decision making and data exploration. Humans play a central role in generating knowledge from the snippets of evidence emerging from visual data analysis. Although prior research provides frameworks that generalize this process, their scope is often narrowly focused so they do not encompass different perspectives at different levels. This paper proposes a knowledge generation model for visual analytics that ties together these diverse frameworks, yet retains previously developed models (e.g., KDD process) to describe individual segments of the overall visual analytic processes. To test its utility, a real world visual analytics system is compared against the model, demonstrating that the knowledge generation process model provides a useful guideline when developing and evaluating such systems. The model is used to effectively compare different data analysis systems. Furthermore, the model provides a common language and description of visual analytic processes, which can be used for communication between researchers. At the end, our model reflects areas of research that future researchers can embark on. PMID:26356874
Knowledge Generation Model for Visual Analytics.
Sacha, Dominik; Stoffel, Andreas; Stoffel, Florian; Kwon, Bum Chul; Ellis, Geoffrey; Keim, Daniel A
2014-12-01
Visual analytics enables us to analyze huge information spaces in order to support complex decision making and data exploration. Humans play a central role in generating knowledge from the snippets of evidence emerging from visual data analysis. Although prior research provides frameworks that generalize this process, their scope is often narrowly focused so they do not encompass different perspectives at different levels. This paper proposes a knowledge generation model for visual analytics that ties together these diverse frameworks, yet retains previously developed models (e.g., KDD process) to describe individual segments of the overall visual analytic processes. To test its utility, a real world visual analytics system is compared against the model, demonstrating that the knowledge generation process model provides a useful guideline when developing and evaluating such systems. The model is used to effectively compare different data analysis systems. Furthermore, the model provides a common language and description of visual analytic processes, which can be used for communication between researchers. At the end, our model reflects areas of research that future researchers can embark on.
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.
An analytic model for the Phobos surface
NASA Technical Reports Server (NTRS)
Duxbury, Thomas C.
1991-01-01
Analytic expressions are derived to model the surface topography and the normal to the surface of Phobos. The analytic expressions are comprised of a spherical harmonic expansion for the global figure of Phobos, augmented by addition terms for the large crater Stickney and other craters. Over 300 craters were measured in more than 100 Viking Orbiter images to produce the model. In general, the largest craters were measured since they have a significant effect on topography. The topographic model derived has a global spatial and topographic accuracy ranging from about 100 m in areas having the highest resolution and convergent, stereo coverage, up to 500 m in the poorest areas.
An analytic model for the PHOBOS surface
NASA Astrophysics Data System (ADS)
Duxbury, T. C.
1991-02-01
Analytic expressions are derived to model the surface topography and the normal to the surface of Phobos. The analytic expressions are comprised of a spherical harmonic expansion for the global figure of Phobos, augmented by addition terms for the large crater Stickney and other craters. Over 300 craters were measured in more than 100 Viking Orbiter images to produce the model. In general, the largest craters were measured since they have a significant effect on topography. The topographic model derived has a global spatial and topographic accuracy ranging from about 100 m in areas having the highest resolution and convergent, stereo coverage, up to 500 m in the poorest areas.
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.
Exactly Solvable su(N) Mixed Spin Ladders
NASA Astrophysics Data System (ADS)
Batchelor, M. T.; de Gier, J.; Maslen, M.
2001-02-01
It is shown that solvable mixed spin ladder models can be constructed from su(N) permutators. Heisenberg rung interactions appear as chemical potential terms in the Bethe Ansatz solution. Explicit examples given are a mixed spin-1/2 spin-1 ladder, a mixed spin-1/2 spin-{3/2} ladder and a spin-1 ladder with biquadratic interactions.
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.
Lienert, Matthias
2015-04-15
The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e., a map from (space-time){sup N} to a spin space. This concept was originally proposed by Dirac as the basis of relativistic quantum mechanics. In such a view, interaction potentials are mathematically inconsistent. This fact motivates the search for new mechanisms for relativistic interactions. In this paper, we explore the idea that relativistic interaction can be described by boundary conditions on the set of coincidence points of two particles in space-time. This extends ideas from zero-range physics to a relativistic setting. We illustrate the idea at the simplest model which still possesses essential physical properties like Lorentz invariance and a positive definite density: two-time equations for massless Dirac particles in 1 + 1 dimensions. In order to deal with a spatio-temporally non-trivial domain, a necessity in the multi-time picture, we develop a new method to prove existence and uniqueness of classical solutions: a generalized version of the method of characteristics. Both mathematical and physical considerations are combined to precisely formulate and answer the questions of probability conservation, Lorentz invariance, interaction, and antisymmetry.
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 modeling for microwave and optical metasurfaces
NASA Astrophysics Data System (ADS)
Monti, Alessio; Soric, Jason; Alù, Andrea; Toscano, Alessandro; Bilotti, Filiberto
2016-06-01
A metasurface is an artificial structure composed by an ultrathin surface textured at a subwavelength scale. In the last years, metasurfaces have been revealed to be particularly useful in the design of electromagnetic scattering cancellation devices operating at microwave and optical frequencies. In this contribution we summarize our results about the analytical modelling of microwave and optical metasurfaces composed, respectively, by patterned metallic surfaces and arrays of plasmonic nanoparticles. The analytical results are compared with the numerical ones obtained with a proper set of full-wave simulations showing an excellent agreement.
Analytical model of internally coupled ears.
Vossen, Christine; Christensen-Dalsgaard, Jakob; van Hemmen, J Leo
2010-08-01
Lizards and many birds possess a specialized hearing mechanism: internally coupled ears where the tympanic membranes connect through a large mouth cavity so that the vibrations of the tympanic membranes influence each other. This coupling enhances the phase differences and creates amplitude differences in the tympanic membrane vibrations. Both cues show strong directionality. The work presented herein sets out the derivation of a three dimensional analytical model of internally coupled ears that allows for calculation of a complete vibration profile of the membranes. The analytical model additionally provides the opportunity to incorporate the effect of the asymmetrically attached columella, which leads to the activation of higher membrane vibration modes. Incorporating this effect, the analytical model can explain measurements taken from the tympanic membrane of a living lizard, for example, data demonstrating an asymmetrical spatial pattern of membrane vibration. As the analytical calculations show, the internally coupled ears increase the directional response, appearing in large directional internal amplitude differences (iAD) and in large internal time differences (iTD). Numerical simulations of the eigenfunctions in an exemplary, realistically reconstructed mouth cavity further estimate the effects of its complex geometry.
Analytical model of internally coupled ears.
Vossen, Christine; Christensen-Dalsgaard, Jakob; van Hemmen, J Leo
2010-08-01
Lizards and many birds possess a specialized hearing mechanism: internally coupled ears where the tympanic membranes connect through a large mouth cavity so that the vibrations of the tympanic membranes influence each other. This coupling enhances the phase differences and creates amplitude differences in the tympanic membrane vibrations. Both cues show strong directionality. The work presented herein sets out the derivation of a three dimensional analytical model of internally coupled ears that allows for calculation of a complete vibration profile of the membranes. The analytical model additionally provides the opportunity to incorporate the effect of the asymmetrically attached columella, which leads to the activation of higher membrane vibration modes. Incorporating this effect, the analytical model can explain measurements taken from the tympanic membrane of a living lizard, for example, data demonstrating an asymmetrical spatial pattern of membrane vibration. As the analytical calculations show, the internally coupled ears increase the directional response, appearing in large directional internal amplitude differences (iAD) and in large internal time differences (iTD). Numerical simulations of the eigenfunctions in an exemplary, realistically reconstructed mouth cavity further estimate the effects of its complex geometry. PMID:20707461
On solvable Dirac equation with polynomial potentials
Stachowiak, Tomasz
2011-01-15
One-dimensional Dirac equation is analyzed with regard to the existence of exact (or closed-form) solutions for polynomial potentials. The notion of Liouvillian functions is used to define solvability, and it is shown that except for the linear potentials the equation in question is not solvable.
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.
Some analytical models of anisotropic strange stars
NASA Astrophysics Data System (ADS)
Murad, Mohammad Hassan
2016-01-01
Over the years of the concept of local isotropy has become a too stringent condition in modeling relativistic self-gravitating objects. Taking local anisotropy into consideration, in this work, some analytical models of relativistic anisotropic charged strange stars have been developed. The Einstein-Maxwell gravitational field equations have been solved with a particular form of one of the metric potentials. The radial pressure and the energy density have been assumed to follow the usual linear equation of state of strange quark matter, the MIT bag model.
A Class of Solvable Impulse Control Problems
Alvarez, Luis H. R.
2004-05-15
We consider a class of stochastic impulse control problems where the controlled process evolves according to a linear, regular, and time homogeneous diffusion. We state a set of easily verifiable sufficient conditions under which the problem is explicitly solvable. We also state an algebraic equation from which the optimal impulse boundary can be determined and, given this threshold, we present the value of the optimal policy interms of the minimal increasing r-excessive mapping for the controlled diffusion. We also consider the comparative static properties of the optimal policy and state a set of typically satisfied conditions under which increased volatility unambiguously increases the value of the optimal policy and expands the continuation region where exercising the irreversible policy is suboptimal. We also illustrate our results explicitly in two models based on geometric Brownian motion.
Flatland Position-Dependent-Mass: Polar Coordinates, Separability and Exact Solvability
NASA Astrophysics Data System (ADS)
Mazharimousavi, S. Habib; Mustafa, Omar
2010-10-01
The kinetic energy operator with position-dependent-mass in plane polar coordinates is obtained. The separability of the corresponding Schrödinger equation is discussed. A hypothetical toy model is reported and two exactly solvable examples are studied.
Analytical Solution of Traffic Cellular Automata Model
NASA Astrophysics Data System (ADS)
Lo, Shih-Ching; Hsu, Chia-Hung
2009-08-01
Complex traffic system seems to be simulated successfully by cellular automaton (CA) models. Various models are developed to understand single-lane traffic, multilane traffic, lane-changing behavior and network traffic situations. However, the result of CA simulation can only be obtained after massive microscopic computation. Although, the mean field theory (MFT) has been studied to be the approximation of CA model, the MFT can only applied to the simple CA rules or small value of parameters. In this study, we simulate traffic flow by the NaSch model under different combination of parameters, which are maximal speed, dawdling probability and density. After that, the position of critical density, the slope of free-flow and congested regime are observed and modeled due to the simulated data. Finally, the coefficients of the model will be calibrated by the simulated data and the analytical solution of traffic CA is obtained.
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.
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.
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.
Channel capacities of an exactly solvable spin-star system
NASA Astrophysics Data System (ADS)
Arshed, Nigum; Toor, A. H.; Lidar, Daniel A.
2010-06-01
We calculate the entanglement-assisted and -unassisted channel capacities of an exactly solvable spin star system, which models the quantum dephasing channel. The capacities for this non-Markovian model exhibit a strong dependence on the coupling strengths of the bath spins with the system, the bath temperature, and the number of bath spins. For equal couplings and bath frequencies, the channel becomes periodically noiseless.
Channel capacities of an exactly solvable spin-star system
Arshed, Nigum; Toor, A. H.; Lidar, Daniel A.
2010-06-15
We calculate the entanglement-assisted and -unassisted channel capacities of an exactly solvable spin star system, which models the quantum dephasing channel. The capacities for this non-Markovian model exhibit a strong dependence on the coupling strengths of the bath spins with the system, the bath temperature, and the number of bath spins. For equal couplings and bath frequencies, the channel becomes periodically noiseless.
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 continuation" of = 2 minimal model
NASA Astrophysics Data System (ADS)
Sugawara, Yuji
2014-04-01
In this paper we discuss what theory should be identified as the "analytic continuation" with N rArr -N of the {mathcal N}=2 minimal model with the central charge hat {c} = 1 - frac {2}{N}. We clarify how the elliptic genus of the expected model is written in terms of holomorphic linear combinations of the "modular completions" introduced in [T. Eguchi and Y. Sugawara, JHEP 1103, 107 (2011)] in the SL(2)_{N+2}/U(1) supercoset theory. We further discuss how this model could be interpreted as a kind of model of the SL(2)_{N+2}/U(1) supercoset in the (widetilde {{R}},widetilde {R}) sector, in which only the discrete spectrum appears in the torus partition function and the potential IR divergence due to the non-compactness of the target space is removed. We also briefly discuss possible definitions of the sectors with other spin structures.
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.
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.
Representations of filtered solvable Lie algebras
Panov, Alexander N
2012-01-31
The representation theory of filtered solvable Lie algebras is constructed. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found. Bibliography: 9 titles.
Symmetrized quartic polynomial oscillators and their partial exact solvability
NASA Astrophysics Data System (ADS)
Znojil, Miloslav
2016-04-01
Sextic polynomial oscillator is probably the best known quantum system which is partially exactly alias quasi-exactly solvable (QES), i.e., which possesses closed-form, elementary-function bound states ψ (x) at certain couplings and energies. In contrast, the apparently simpler and phenomenologically more important quartic polynomial oscillator is not QES. A resolution of the paradox is proposed: The one-dimensional Schrödinger equation is shown QES after the analyticity-violating symmetrization V (x) = A | x | + Bx2 + C | x|3 +x4 of the quartic polynomial potential.
Analytical models for complex swirling flows
NASA Astrophysics Data System (ADS)
Borissov, A.; Hussain, V.
1996-11-01
We develops a new class of analytical solutions of the Navier-Stokes equations for swirling flows, and suggests ways to predict and control such flows occurring in various technological applications. We view momentum accumulation on the axis as a key feature of swirling flows and consider vortex-sink flows on curved axisymmetric surfaces with an axial flow. We show that these solutions model swirling flows in a cylindrical can, whirlpools, tornadoes, and cosmic swirling jets. The singularity of these solutions on the flow axis is removed by matching them with near-axis Schlichting and Long's swirling jets. The matched solutions model flows with very complex patterns, consisting of up to seven separation regions with recirculatory 'bubbles' and vortex rings. We apply the matched solutions for computing flows in the Ranque-Hilsch tube, in the meniscus of electrosprays, in vortex breakdown, and in an industrial vortex burner. The simple analytical solutions allow a clear understanding of how different control parameters affect the flow and guide selection of optimal parameter values for desired flow features. These solutions permit extension to other problems (such as heat transfer and chemical reaction) and have the potential of being significantly useful for further detailed investigation by direct or large-eddy numerical simulations as well as laboratory experimentation.
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.
Analytical modeling of the steady radiative shock
NASA Astrophysics Data System (ADS)
Boireau, L.; Bouquet, S.; Michaut, C.; Clique, C.
2006-06-01
In a paper dated 2000 [1], a fully analytical theory of the radiative shock has been presented. This early model had been used to design [2] radiative shock experiments at the Laboratory for the Use of Intense Lasers (LULI) [3 5]. It became obvious from numerical simulations [6, 7] that this model had to be improved in order to accurately recover experiments. In this communication, we present a new theory in which the ionization rates in the unshocked (bar{Z_1}) and shocked (bar{Z_2} neq bar{Z_1}) material, respectively, are included. Associated changes in excitation energy are also taken into account. We study the influence of these effects on the compression and temperature in the shocked medium.
Radiative Torques: Analytical Model And Basic Properties
NASA Astrophysics Data System (ADS)
Hoang, Thiem; Lazarian, A.
2007-05-01
We attempt to get a physical insight into grain alignment processes by studying basic properties of radiative torques (RATs). For this purpose we consider a simple toy model of a helical grain that reproduces well the basic features of RATs. The model grain consists of a reflecting spheroidal body with a reflecting mirror attached at an angle to it. Being very simple, the model allows analytical description of RATs that act upon it. We show a good correspondence of RATs obtained for this model and those of irregular grains calculated by DDSCAT. Our analysis of the role of different torque components for grain alignment reveals that one of the three RAT components does not affect the alignment, but induces only for grain precession. The other two components provide a generic alignment with grain long axes perpendicular to the light radiation, if the radiation dominates the grain precession, and perpendicular to magnetic field, otherwise. The latter coincides with the famous predictions of the Davis-Greenstein process, but our model does not invoke paramagnetic relaxation. In addition, we find that a substantial part of grains subjected to RATs gets aligned with low angular momentum, which testifies, that most of the grains in diffuse interstellar medium do not rotate fast, i.e. rotate with thermal or even sub-thermal velocities. For the radiation-dominated environments, we find that the alignment can take place on the time scale much shorter than the time of gaseous damping of grain rotation.
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.
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.
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.
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...
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.
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.
Radiative torques: analytical model and basic properties
NASA Astrophysics Data System (ADS)
Lazarian, A.; Hoang, Thiem
2007-07-01
We attempt to get a physical insight into grain alignment processes by studying basic properties of radiative torques (RATs). For this purpose we consider a simple toy model of a helical grain that reproduces well the basic features of RATs. The model grain consists of a spheroidal body with a mirror attached at an angle to it. Being very simple, the model allows analytical description of RATs that act upon it. We show a good correspondence of RATs obtained for this model and those of irregular grains calculated by DDSCAT. Our analysis of the role of different torque components for grain alignment reveals that one of the three RAT components does not affect the alignment, but induces only for grain precession. The other two components provide a generic alignment with grain long axes perpendicular to the radiation direction, if the radiation dominates the grain precession, and perpendicular to magnetic field, otherwise. The latter coincides with the famous predictions of the Davis-Greenstein process, but our model does not invoke paramagnetic relaxation. In fact, we identify a narrow range of angles between the radiation beam and the magnetic field, for which the alignment is opposite to the Davis-Greenstein predictions. This range is likely to vanish, however, in the presence of thermal wobbling of grains. In addition, we find that a substantial part of grains subjected to RATs gets aligned with low angular momentum, which testifies that most of the grains in diffuse interstellar medium do not rotate fast, that is, rotate with thermal or even subthermal velocities. This tendency of RATs to decrease grain angular velocity as a result of the RAT alignment decreases the degree of polarization, by decreasing the degree of internal alignment, that is, the alignment of angular momentum with the grain axes. For the radiation-dominated environments, we find that the alignment can take place on the time-scale much shorter than the time of gaseous damping of grain rotation
Hidden algebra method (quasi-exact-solvability in quantum mechanics)
Turbiner, A. |
1996-02-01
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 {ital N}-body problems ass ociated with an existence of the hidden algebra {ital sl}{sub {ital N}} is discussed extensively. {copyright} {ital 1996 American Institute of Physics.}
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
Analytical solution of a model for complex food webs
NASA Astrophysics Data System (ADS)
Camacho, Juan; Guimerà, Roger; Amaral, Luís A.
2002-03-01
We investigate numerically and analytically a recently proposed model for food webs [Nature 404, 180 (2000)] in the limit of large web sizes and sparse interaction matrices. We obtain analytical expressions for several quantities with ecological interest, in particular, the probability distributions for the number of prey and the number of predators. We find that these distributions have fast-decaying exponential and Gaussian tails, respectively. We also find that our analytical expressions are robust to changes in the details of the model.
Information entropy of conditionally exactly solvable potentials
Dutta, D.; Roy, P.
2011-03-15
We evaluate Shannon entropy for the position and momentum eigenstates of some conditionally exactly solvable potentials which are isospectral to harmonic oscillator and whose solutions are given in terms of exceptional orthogonal polynomials. The Bialynicki-Birula-Mycielski inequality has also been tested for a number of states.
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; ...
Magnetization plateaux in Bethe ansatz solvable spin-S ladders
NASA Astrophysics Data System (ADS)
Maslen, M.; Batchelor, M.; de Gier, J.
2003-07-01
We examine the properties of the Bethe ansatz solvable two- and three-leg spin-S ladders. These models include Heisenberg rung interactions of arbitrary strength and thus capture the physics of the spin-S Heisenberg ladders for strong rung coupling. The discrete values derived for the magnetization plateaux are seen to fit with the general prediction based on the Lieb-Schultz-Mattis theorem. We examine the magnetic phase diagram of the spin-1 ladder in detail and find an extended magnetization plateau at the fractional value
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.
Demonstration of detection and ranging using solvable chaos
NASA Astrophysics Data System (ADS)
Corron, Ned J.; Stahl, Mark T.; Blakely, Jonathan N.
2013-05-01
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.
Fast Analytical Methods for Macroscopic Electrostatic Models in Biomolecular Simulations*
Xu, Zhenli; Cai, Wei
2013-01-01
We review recent developments of fast analytical methods for macroscopic electrostatic calculations in biological applications, including the Poisson–Boltzmann (PB) and the generalized Born models for electrostatic solvation energy. The focus is on analytical approaches for hybrid solvation models, especially the image charge method for a spherical cavity, and also the generalized Born theory as an approximation to the PB model. This review places much emphasis on the mathematical details behind these methods. PMID:23745011
Relationship between supersymmetry and solvable potentials
NASA Astrophysics Data System (ADS)
Cooper, Fred; Ginocchio, Joseph N.; Khare, Avinash
1987-10-01
We investigate whether a general class of solvable potentials, the Natanzon potentials (those potentials whose solutions are hypergeometric functions), and their supersymmetric partner potentials are related by a discrete reparametrization invariance called ``shape invariance'' discovered by Genden- shtein. We present evidence that this is not the case in general. Instead we find that the Natanzon class of potentials is not the most general class of solvable potentials but instead belongs to a wider class of potentials generated by supersymmetry and factorization whose eigenfunctions are sums of hypergeometric functions. The series of Hamiltonians, together with the corresponding supersymmetric charges form the graded Lie algebra sl(1/1)⊗SU(2). We also present a strategy for solving, in a limited domain, the discrete reparametrization invariance equations connected with ``shape invariance.''
Solvable rational extensions of the isotonic oscillator
Grandati, Yves
2011-08-15
Highlights: > We obtain in a new way the solvable rational extensions of the isotonic oscillator. > The method is systematic without resorting to any ansatz. > We use a generalization of the SUSY quantum partnership to excited states. > They are regularized by specific discrete symmetries of the potential. > The proof of the shape invariance of the extensions is direct. - Abstract: Combining recent results on rational solutions of the Riccati-Schroedinger equations for shape invariant potentials to the finite difference Baecklund algorithm and specific symmetries of the isotonic potential, we show that it is possible to generate the three infinite sets (L1, L2 and L3 families) of regular rational solvable extensions of this potential in a very direct and transparent way.
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.
Combined experimental/analytical modeling using component mode synthesis
Martinez, D.R.; Carne, T.G.; Gregory, D.L.; Miller, A.K.
1984-01-01
This study evaluates the accuracy of computed model frequencies and mode shapes obtained from a combined experimental/analytical model for a simple beam structure. The structure was divided into two subsystems, and one subsystem was tested to obtain its free-free modes. Using a Component Mode Synthesis (CMS) technique, the experimental model data base for one subsystem was directly coupled with a finite element model of the other subsystem to create an experimental/analytical model of the total structure. Both the translational and rotational elements of the residual flexibilities and mode shapes at the interface of the experimental subsystem were measured and used in the coupling. The modal frequencies and mode shapes obtained for the combined experimental/analytical model are compared to those for a reference finite element model of the entire structure. The sensitivity of the CMS model predictions to errors in the modal parameters and residual flexibilities, which are required to define a subsystem, is also examined.
Analytical solutions and genuine multipartite entanglement of the three-qubit Dicke model
NASA Astrophysics Data System (ADS)
Zhang, Yu-Yu; Chen, Xiang-You; He, Shu; Chen, Qing-Hu
2016-07-01
We present analytical solutions to three qubits and a single-mode cavity coupling system beyond the rotating-wave approximation (RWA). The zeroth-order approximation, equivalent to the adiabatic approximation, works well for arbitrary coupling strength for small qubit frequency. The first-order approximation, called the generalized rotating-wave approximation (GRWA), produces an effective solvable Hamiltonian with the same form as the ordinary RWA one and exhibits substantial improvements of energy levels over the RWA even on resonance. Based on these analytical eigensolutions, we study both the bipartite entanglement and genuine multipartite entanglement (GME). The dynamics of these two kinds of entanglements using the GRWA are consistent with the numerical exact ones. Interestingly, the well-known sudden death of entanglement occurs in the bipartite entanglement dynamics but not in the GME dynamics.
Experimental and analytical generic space station dynamic models
NASA Technical Reports Server (NTRS)
Belvin, W. K.; Edighoffer, H. H.
1986-01-01
A dynamic model used for verification of analytical and experimental methods is documented. The model consists of five substructures to simulate the multibody, low frequency nature of large space structures. Design considerations which led to a fundamental vibration frequency of less than one Hz are described. Finite element analysis used to predict the vibration modes and frequencies of the experimental model is presented. In addition, modeling of cable suspension effects using prestressed vibration analysis is described. Details of the expermental and analytical models are included to permit replication of the study. Results of the modal vibration tests and analysis are presented in a separate document.
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.
Retardation analytical model to extend service life
NASA Technical Reports Server (NTRS)
Matejczyk, J.
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 is discussed. Future Research plans are outlined.
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.
Combined experimental/analytical modeling using component mode synthesis
Martinez, D.R.; Carne, T.G.; Gregory, D.L.; Miller, A.K.
1984-04-01
This study evaluates the accuracy of computed modal frequencies and mode shapes obtained from a combined experimental/analytical model for a simple beam structure. The structure was divided into two subsystems and one subsystem was tested to obtain its free-free modes. Using a Component Mode Synthesis (CMS) technique, the experimental modal data base for one subsystem was directly coupled with a finite element model of the other subsystem to create an experimental/analytical model of the total structure. Both the translational and rotational elements of the residual flexibilities and mode shapes at the interface of the experimental subsystem were measured and used in the coupling. The modal frequencies and mode shapes obtained for the combined experimental/analytical model are compared to those for a reference finite element model of the entire structure. The sensitivity of the CMS model predictions to errors in the modal parameters and residual flexibilities, which are required to define a subsystem, is also examined.
An analytic model of high solidity vertical axis windmills
NASA Astrophysics Data System (ADS)
Carothers, R. G.; Bragg, G. M.
By introducing an induced cross flow to the conventional flow models used for vertical-axis windmills an analytic model for high solidity rotors is developed. Results as predicted by the model are compared with those determined from wind tunnel tests.
Analytic modeling of a spray diffusion flame
NASA Technical Reports Server (NTRS)
Harsha, P. T.; Edelman, R. B.
1984-01-01
A detailed model for a spray diffusion flame is described. The model is based on the boundary layer form of the equations of motion, with droplet transport accounted for using a discretized droplet size distribution function. Interphase transport of mass and energy are accounted for, with a flame-sheet model used to describe the combustion process on a droplet scale. Near dynamic equilibrium is assumed for the description of droplet transport; droplets can diffuse relative to the gas phase. Gas-phase mixing is accounted for using a two-equation turbulence model; buoyancy effects are included, with a temperature fluctuation equation used to account for buoyancy effects on turbulence structure. Thermal radiation from gas-phase CO2 and H2O is included. Gas-phase chemical kinetics are modeled using a 20-reaction, 10-species version of the advanced quasi-global chemical kinetics formulation. Results are compared with data for a vaporizing Freon spray and a pentane spray flame. It is shown that the computational approach provides a reasonably valid picture of the overall development of a spray diffusion flame, and, furthermore, provides a useful tool for the parametric examination of the spray combustion process.
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 barrage attack model. Final report, January 1986-January 1989
St Ledger, J.W.; Naegeli, R.E.; Dowden, N.A.
1989-01-01
An analytic model is developed for a nuclear barrage attack, assuming weapons with no aiming error and a cookie-cutter damage function. The model is then extended with approximations for the effects of aiming error and distance damage sigma. The final result is a fast running model which calculates probability of damage for a barrage attack. The probability of damage is accurate to within seven percent or better, for weapon reliabilities of 50 to 100 percent, distance damage sigmas of 0.5 or less, and zero to very large circular error probabilities. FORTRAN 77 coding is included in the report for the analytic model and for a numerical model used to check the analytic results.
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 and numerical modeling for flexible pipes
NASA Astrophysics Data System (ADS)
Wang, Wei; Chen, Geng
2011-12-01
The unbonded flexible pipe of eight layers, in which all the layers except the carcass layer are assumed to have isotropic properties, has been analyzed. Specifically, the carcass layer shows the orthotropic characteristics. The effective elastic moduli of the carcass layer have been developed in terms of the influence of deformation to stiffness. With consideration of the effective elastic moduli, the structure can be properly analyzed. Also the relative movements of tendons and relative displacements of wires in helical armour layer have been investigated. A three-dimensional nonlinear finite element model has been presented to predict the response of flexible pipes under axial force and torque. Further, the friction and contact of interlayer have been considered. Comparison between the finite element model and experimental results obtained in literature has been given and discussed, which might provide practical and technical support for the application of unbonded flexible pipes.
Evaluation of the WIND System atmospheric models: An analytic approach
Fast, J.D.
1991-11-25
An analytic approach was used in this study to test the logic, coding, and the theoretical limits of the WIND System atmospheric models for the Savannah River Plant. In this method, dose or concentration estimates predicted by the models were compared to the analytic solutions to evaluate their performance. The results from AREA EVACUATION and PLTFF/PLUME were very nearly identical to the analytic solutions they are based on and the evaluation procedure demonstrated that these models were able to reproduce the theoretical characteristics of a puff or a plume. The dose or concentration predicted by PLTFF/PLUME was always within 1% of the analytic solution. Differences between the dose predicted by 2DPUF and its analytic solution were substantially greater than those associated with PUFF/PLUME, but were usually smaller than 6%. This behavior was expected because PUFF/PLUME solves a form of the analytic solution for a single puff, and 2DPUF performs an integration over a period of time for several puffs to obtain the dose. Relatively large differences between the dose predicted by 2DPUF and its analytic solution were found to occur close to the source under stable atmospheric conditions. WIND System users should be aware of these situations in which the assumptions of the System atmospheric models may be violated so that dose predictions can be interpreted correctly. The WIND System atmospheric models are similar to many other dispersion codes used by the EPA, NRC, and DOE. If the quality of the source term and meteorological data is high, relatively accurate and timely forecasts for emergency response situations can be made by the WIND System atmospheric models.
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 model for fast-shock ignition
NASA Astrophysics Data System (ADS)
Ghasemi, S. A.; Farahbod, A. H.; Sobhanian, S.
2014-07-01
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 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.
Coherent states for exactly solvable potentials
Shreecharan, T.; Panigrahi, Prasanta K.; Banerji, J.
2004-01-01
A general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials, e.g., Morse and Poeschl-Teller, is given. The method, a priori, is potential independent and connects with earlier developed ones, including the oscillator-based approaches for coherent states and their generalizations. This approach can be straightforwardly extended to construct more general coherent states for the quantum-mechanical potential problems, such as the nonlinear coherent states for the oscillators. The time evolution properties of some of these coherent states show revival and fractional revival, as manifested in the autocorrelation functions, as well as, in the quantum carpet structures.
A New Class of Solvable Many-Body Problems
NASA Astrophysics Data System (ADS)
Calogero, Francesco; Yi, Ge
2012-10-01
A new class of solvable N-body problems is identified. They describe N unit-mass point particles whose time-evolution, generally taking place in the complex plane, is characterized by Newtonian equations of motion ''of goldfish type'' (acceleration equal force, with specific velocity-dependent one-body and two-body forces) featuring several arbitrary coupling constants. The corresponding initial-value problems are solved by finding the eigenvalues of a time-dependent N×N matrix U(t) explicitly defined in terms of the initial positions and velocities of the N particles. Some of these models are asymptotically isochronous, i.e. in the remote future they become completely periodic with a period T independent of the initial data (up to exponentially vanishing corrections). Alternative formulations of these models, obtained by changing the dependent variables from the N zero! s of a monic polynomial of degree N to its N coefficients, are also exhibited.
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.
Solvability of a boundary value problem at resonance.
Guezane-Lakoud, A; Khaldi, R; Kılıçman, A
2016-01-01
This paper concerns the solvability of a nonlinear fractional boundary value problem at resonance. By using fixed point theorems we prove that the perturbed problem has a solution, then by some ideas from analysis we show that the original problem is solvable. An example is given to illustrate the obatined results. PMID:27652077
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 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.
Scattering amplitudes for multi-indexed extensions of solvable potentials
Ho, C.-L.; Lee, J.-C.; Sasaki, R.
2014-04-15
New solvable one-dimensional quantum mechanical scattering problems are presented. They are obtained from known solvable potentials by multiple Darboux transformations in terms of virtual and pseudo virtual wavefunctions. The same method applied to confining potentials, e.g. Pöschl–Teller and the radial oscillator potentials, has generated the multi-indexed Jacobi and Laguerre polynomials. Simple multi-indexed formulas are derived for the transmission and reflection amplitudes of several solvable potentials. -- Highlights: •Scattering amplitudes calculated for infinitely many new solvable potentials. •New scattering potentials obtained by deforming six known solvable potentials. •Multiple Darboux transformations in terms of (pseudo) virtual states employed. •Scattering amplitudes checked to obey the shape invariance relation. •Errors in scattering amplitudes of some undeformed potentials in the literature corrected.
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 new analytical model for wind farm power prediction
NASA Astrophysics Data System (ADS)
Niayifar, Amin; Porte-Agel, Fernando
2015-04-01
In this study, a new analytical approach is presented and validated to predict wind farm power production. The new model assumes a Gaussian distribution for the velocity deficit in the wake which has been recently proposed by Bastankhah and Porté-Agel (2014). To estimate the velocity deficit in the wake, this model needs the local wake growth rate parameter which is calculated based on the local turbulence intensity in the wind farm. The interaction of the wakes is modeled by use of the velocity deficit superposition principle. Finally, the power curve is used to estimate the power production from the wind turbines. The wind farm model is compared to large-eddy simulation (LES) data of Horns Rev wind farm for a wide range of wind directions. Reasonable agreement between the proposed analytical model and LES data is obtained. This prediction is substantially better than the one obtained with common wind farm softwares such as WAsP.
LETTER TO THE EDITOR: Exactly solvable quantum spin tubes and ladders
NASA Astrophysics Data System (ADS)
Batchelor, M. T.; Maslen, M.
1999-08-01
We find families of integrable n-leg spin- 1/2 ladders and tubes with general isotropic exchange interactions between spins. These models are equivalent to su(N) spin chains with N = 2n. Arbitrary rung interactions in the spin tubes and ladders induce chemical potentials in the equivalent spin chains. The potentials are n-dependent and differ for the tube and ladder models. The models are solvable by means of nested Bethe ansatze.
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...
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.
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…
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.
Analytical model of plasma-chemical etching in planar reactor
NASA Astrophysics Data System (ADS)
Veselov, D. S.; Bakun, A. D.; Voronov, Yu A.; Kireev, V. Yu; Vasileva, O. V.
2016-09-01
The paper discusses an analytical model of plasma-chemical etching in planar diode- type reactor. Analytical expressions of etch rate and etch anisotropy were obtained. It is shown that etch anisotropy increases with increasing the ion current and ion energy. At the same time, etch selectivity of processed material decreases as compared with the mask. Etch rate decreases with the distance from the centre axis of the reactor. To decrease the loading effect, it is necessary to reduce the wafer temperature and pressure in the reactor, as well as increase the gas flow rate through the reactor.
Improvements to the analytical linescan model for SEM metrology
NASA Astrophysics Data System (ADS)
Mack, Chris A.; Bunday, Benjamin D.
2016-03-01
Critical dimension scanning electron microscope (CD-SEM) metrology has long used empirical approaches to determine edge locations. While such solutions are very flexible, physics-based models offer the potential for improved accuracy and precision for specific applications. Here, Monte Carlo simulation is used to generate theoretical linescans from single step and line/space targets in order to build a physics-based analytical model, including the presence of bottom footing and top corner rounding. The resulting analytical linescan model fits the Monte Carlo simulation results for different feature heights, widths, pitches, sidewall angles, bottom footing, and top corner rounding. This model has also been successfully applied to asymetric features such as sidewall spacers encountered in self-aligned double patterning.
Analytical modeling of thermoluminescent albedo detectors for neutron dosimetry.
Glickstein, S S
1983-02-01
In order to gain an in-depth understanding of the neutron physics of a 6LiF TLD when used as an albedo neutron dosimeter, an analytical model was developed to simulate the response of a 6LiF chip. The analytical model was used to examine the sensitivity of the albedo TLD response to incident monoenergetic neutrons and to evaluate a multiple chip TLD neutron dosimeter. Contrary to initial experimental studies, which were hampered by statistical uncertainties, the analytical evaluation revealed that a three-energy-group detector could not reliably measure the dose equivalent to personnel exposed to multiple neutron spectra. The analysis clearly illustrates that there may be order of magnitude errors in the measured neutron dose if the dosimeter has not been calibrated for the same flux spectrum to which it is exposed. As a result of this analysis, it was concluded that, for personnel neutron monitoring, a present TLD badge must be calibrated for the neutron spectrum into which the badge is to be introduced. The analytical model used in this study can readily be adopted for evaluating other possible detectors and shield material that might be proposed in the future as suitable for use in neutron dosimetry applications. PMID:6826377
Analytical Model For Fluid Dynamics In A Microgravity Environment
NASA Technical Reports Server (NTRS)
Naumann, Robert J.
1995-01-01
Report presents analytical approximation methodology for providing coupled fluid-flow, heat, and mass-transfer equations in microgravity environment. Experimental engineering estimates accurate to within factor of 2 made quickly and easily, eliminating need for time-consuming and costly numerical modeling. Any proposed experiment reviewed to see how it would perform in microgravity environment. Model applied in commercial setting for preliminary design of low-Grashoff/Rayleigh-number experiments.
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.
Analytical network-averaging of the tube model:. Rubber elasticity
NASA Astrophysics Data System (ADS)
Khiêm, Vu Ngoc; Itskov, Mikhail
2016-10-01
In this paper, a micromechanical model for rubber elasticity is proposed on the basis of analytical network-averaging of the tube model and by applying a closed-form of the Rayleigh exact distribution function for non-Gaussian chains. This closed-form is derived by considering the polymer chain as a coarse-grained model on the basis of the quantum mechanical solution for finitely extensible dumbbells (Ilg et al., 2000). The proposed model includes very few physically motivated material constants and demonstrates good agreement with experimental data on biaxial tension as well as simple shear tests.
Analytical Expressions for the REM Model of Recognition Memory
Montenegro, Maximiliano; Myung, Jay I.; Pitt, Mark A.
2014-01-01
An inordinate amount of computation is required to evaluate predictions of simulation-based models. Following Myung et al (2007), we derived an analytic form expression of the REM model of recognition memory using a Fourier transform technique, which greatly reduces the time required to perform model simulations. The accuracy of the derivation is verified by showing a close correspondence between its predictions and those reported in Shiffrin and Steyvers (1997). The derivation also shows that REM’s predictions depend upon the vector length parameter, and that model parameters are not identifiable unless one of the parameters is fixed. PMID:25089060
Comprehensive analytical model to characterize randomness in optical waveguides.
Zhou, Junhe; Gallion, Philippe
2016-04-01
In this paper, the coupled mode theory (CMT) is used to derive the corresponding stochastic differential equations (SDEs) for the modal amplitude evolution inside optical waveguides with random refractive index variations. Based on the SDEs, the ordinary differential equations (ODEs) are derived to analyze the statistics of the modal amplitudes, such as the optical power and power variations as well as the power correlation coefficients between the different modal powers. These ODEs can be solved analytically and therefore, it greatly simplifies the analysis. It is demonstrated that the ODEs for the power evolution of the modes are in excellent agreement with the Marcuse' coupled power model. The higher order statistics, such as the power variations and power correlation coefficients, which are not exactly analyzed in the Marcuse' model, are discussed afterwards. Monte-Carlo simulations are performed to demonstrate the validity of the analytical model.
Analytical Modeling for the Grating Eddy Current Displacement Sensors
NASA Astrophysics Data System (ADS)
Lv, Chunfeng; Tao, Wei; Lei, Huaming; Jiang, Yingying; Zhao, Hui
2015-02-01
As a new type of displacement sensor, grating eddy current displacement sensor (GECDS) combines traditional eddy current sensors and grating structure in one. The GECDS performs a wide range displacement measurement without precision reduction. This paper proposes an analytical modeling approach for the GECDS. The solution model is established in the Cartesian coordinate system, and the solving domain is limited to finite extents by using the truncated region eigenfunction expansion method. Based on the second order vector potential, expressions for the electromagnetic field as well as coil impedance related to the displacement can be expressed in closed-form. Theoretical results are then confirmed by experiments, which prove the suitability and effectiveness of the analytical modeling approach.
An analytical pressure-transient model for complex reservoir scenarios
NASA Astrophysics Data System (ADS)
Gomes, Edmond; Ambastha, Anil K.
1994-10-01
Reservoir deposition occurs through long periods of time, thus most reservoirs are heterogeneous in nature. The presence of various zones and layers of different rock and fluid properties is the usual circumstance in petroleum reservoirs. A secondary recovery operation, such as steam-flooding, results in a composite reservoir situation because of the presence of zones of different fluid properties. Because of reservoir heterogeneity and gravity override effects, fluid boundaries separating two zones may have complicated or irregular shapes. The purpose of this paper is to develop a new analytical pressure-transient model which can accommodate complex reservoir scenarios resulting from reservoir heterogeneity and from thermal recovery or other fluid-injection operations. Mathematically, our analytical model considers such complex situations as a generalized eigenvalue system resulting in a system of linear equations. Computational difficulties faced, validation approach of the new model, and an application for complex reservoir scenarios are discussed.
The Quasi-Exactly Solvable Problems in Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Liu, Li-Yan; Hao, Qing-Hai
2014-06-01
We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein—Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the general form of the potential, we present several examples to give the specific forms. In the examples, we show for special parameters the harmonic potential plus Coulomb potential, Killingbeck potential and a quartic potential plus Cornell potential are quasi-exactly solvable potentials.
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.
Analytical Model for Thermal Elastoplastic Stresses of Functionally Graded Materials
Zhai, P. C.; Chen, G.; Liu, L. S.; Fang, C.; Zhang, Q. J.
2008-02-15
A modification analytical model is presented for the thermal elastoplastic stresses of functionally graded materials subjected to thermal loading. The presented model follows the analytical scheme presented by Y. L. Shen and S. Suresh [6]. In the present model, the functionally graded materials are considered as multilayered materials. Each layer consists of metal and ceramic with different volume fraction. The ceramic layer and the FGM interlayers are considered as elastic brittle materials. The metal layer is considered as elastic-perfectly plastic ductile materials. Closed-form solutions for different characteristic temperature for thermal loading are presented as a function of the structure geometries and the thermomechanical properties of the materials. A main advance of the present model is that the possibility of the initial and spread of plasticity from the two sides of the ductile layers taken into account. Comparing the analytical results with the results from the finite element analysis, the thermal stresses and deformation from the present model are in good agreement with the numerical ones.
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.
A New Analytical Model for Trans-Relativistic Particle Acceleration
NASA Astrophysics Data System (ADS)
Becker, Peter A.
2011-01-01
Most existing analytical models describing the second-order Fermi acceleration of relativistic particles due to collisions with MHD waves assume that the injected seed particles are already highly relativistic, despite the fact that the most prevalent source of particles is usually the local thermal background, which is typically a non-relativistic gas. This presents a problem because the momentum dependence of the momentum diffusion coefficient describing the interaction between the particles and the MHD waves is qualitatively different in the non-relativistic and highly relativistic limits. Since the existing analytical models are not able to address this situation, workers have had to rely on numerical simulations to obtain particle spectra describing the trans-relativistic case. In this work we present the first analytical solution to the global, trans-relativistic problem, obtained by using a hybrid form for the momentum diffusion coefficient, given by the sum of the two asymptotic forms. The model also incorporates the appropriate momentum dependence for the particle escape timescale, and the effect of synchrotron and inverse-Compton losses, which are critical for establishing the location of the high-energy cutoff in the particle spectrum. The results can be used to model the acceleration of particles in AGN and solar environments, and can also be used to compute the spectra of the associated synchrotron and inverse-Compton emission. Applications of both types are discussed.
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.
Analytic solution of a five-direction radiation transport model
Cramer, S.N.
1988-01-01
In order to test certain spatial and angular dependent Monte Carlo biasing techniques, a one-dimensional, one energy, two-media, five-direction radiation transport model has been devised for which an analytic solution exists. Although this solution is too long to be conveniently expressed in an explicit form, it can be easily evaluated on the smallest of computers. This solution is discussed in this paper. 1 ref.
Progress on Analytical Modeling of Coherent Electron Cooling
Wang, G.; Blaskiewicz, M.; Litvinenko, V.; Webb, S.
2010-05-23
We report recent progresses on analytical studies of Coherent Electron Cooling. The phase space electron beam distribution obtained from the 1D FEL amplifier is applied to an infinite electron plasma model and the electron density evolution inside the kicker is derived. We also investigate the velocity modulation in the modulator and obtain a closed form solution for the current density evolution for infinite homogeneous electron plasma.
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.
Optimization of Analytical Potentials for Coarse-Grained Biopolymer Models.
Mereghetti, Paolo; Maccari, Giuseppe; Spampinato, Giulia Lia Beatrice; Tozzini, Valentina
2016-08-25
The increasing trend in the recent literature on coarse grained (CG) models testifies their impact in the study of complex systems. However, the CG model landscape is variegated: even considering a given resolution level, the force fields are very heterogeneous and optimized with very different parametrization procedures. Along the road for standardization of CG models for biopolymers, here we describe a strategy to aid building and optimization of statistics based analytical force fields and its implementation in the software package AsParaGS (Assisted Parameterization platform for coarse Grained modelS). Our method is based on the use and optimization of analytical potentials, optimized by targeting internal variables statistical distributions by means of the combination of different algorithms (i.e., relative entropy driven stochastic exploration of the parameter space and iterative Boltzmann inversion). This allows designing a custom model that endows the force field terms with a physically sound meaning. Furthermore, the level of transferability and accuracy can be tuned through the choice of statistical data set composition. The method-illustrated by means of applications to helical polypeptides-also involves the analysis of two and three variable distributions, and allows handling issues related to the FF term correlations. AsParaGS is interfaced with general-purpose molecular dynamics codes and currently implements the "minimalist" subclass of CG models (i.e., one bead per amino acid, Cα based). Extensions to nucleic acids and different levels of coarse graining are in the course. PMID:27150459
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.
A new analytical model for wind farm power prediction
NASA Astrophysics Data System (ADS)
Niayifar, Amin; Porté-Agel, Fernando
2015-06-01
In this study, a new analytical approach is presented and validated to predict wind farm power production. The new model is an extension of the recently proposed by Bastankhah and Porté-Agel for a single wake. It assumes a self-similar Gaussian shape of the velocity deficit and satisfies conservation of mass and momentum. To estimate the velocity deficit in the wake, this model needs the local wake growth rate parameter which is calculated based on the local turbulence intensity in the wind farm. The interaction of the wakes is modeled by use of the velocity deficit superposition principle. Finally, the power curve is used to estimate the power production from the wind turbines. The wind farm model is compared to large-eddy simulation (LES) data and measurments of Horns Rev wind farm for a wide range of wind directions. Reasonable agreement between the proposed analytical model, LES data and measurments is obtained. This prediction is also found to be substantially better than the one obtained with a commonly used wind farm wake model.
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.
An Analytical Thermal Model for Autonomous Soaring Research
NASA Technical Reports Server (NTRS)
Allen, Michael
2006-01-01
A viewgraph presentation describing an analytical thermal model used to enable research on autonomous soaring for a small UAV aircraft is given. The topics include: 1) Purpose; 2) Approach; 3) SURFRAD Data; 4) Convective Layer Thickness; 5) Surface Heat Budget; 6) Surface Virtual Potential Temperature Flux; 7) Convective Scaling Velocity; 8) Other Calculations; 9) Yearly trends; 10) Scale Factors; 11) Scale Factor Test Matrix; 12) Statistical Model; 13) Updraft Strength Calculation; 14) Updraft Diameter; 15) Updraft Shape; 16) Smoothed Updraft Shape; 17) Updraft Spacing; 18) Environment Sink; 19) Updraft Lifespan; 20) Autonomous Soaring Research; 21) Planned Flight Test; and 22) Mixing Ratio.
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.
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 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.
Analytical probabilistic modeling for radiation therapy treatment planning
NASA Astrophysics Data System (ADS)
Bangert, Mark; Hennig, Philipp; Oelfke, Uwe
2013-08-01
This paper introduces the concept of analytical probabilistic modeling (APM) to quantify uncertainties in quality indicators of radiation therapy treatment plans. Assuming Gaussian probability densities over the input parameters of the treatment plan quality indicators, APM enables the calculation of the moments of the induced probability density over the treatment plan quality indicators by analytical integration. This paper focuses on analytical probabilistic dose calculation algorithms and the implications of APM regarding treatment planning. We derive closed-form expressions for the expectation value and the (co)variance of (1) intensity-modulated photon and proton dose distributions based on a pencil beam algorithm and (2) the standard quadratic objective function used in inverse planning. Complex correlation models of high dimensional uncertain input parameters and the different nature of random and systematic uncertainties in fractionated radiation therapy are explicitly incorporated into APM. APM variance calculations on phantom data sets show that the correlation assumptions and the difference of random and systematic uncertainties of the input parameters have a crucial impact on the uncertainty of the resulting dose. The derivations regarding the quadratic objective function show that APM has the potential to enable robust planning at almost the same computational cost like conventional inverse planning after a single probabilistic dose calculation. Beneficial applications of APM in the context of radiation therapy treatment planning are feasible.
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.
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.
Universal analytic model for tunnel FET circuit simulation
NASA Astrophysics Data System (ADS)
Lu, Hao; Esseni, David; Seabaugh, Alan
2015-06-01
A simple analytic model based on the Kane-Sze formula is used to describe the current-voltage characteristics of tunnel field-effect transistors (TFETs). This model captures the unique features of the TFET including the decrease in subthreshold swing with drain current and the superlinear onset of the output characteristic. The model also captures the ambipolar current characteristic at negative gate-source bias and the negative differential resistance for negative drain-source biases. A simple empirical capacitance model is also included to enable circuit simulation. The model has fairly general validity and is not specific to a particular TFET geometry. Good agreement is shown with published atomistic simulations of an InAs double-gate TFET with gate perpendicular to the tunnel junction and with numerical simulations of a broken-gap AlGaSb/InAs TFET with gate in parallel with the tunnel junction.
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 for self-heating in nanowire geometries
NASA Astrophysics Data System (ADS)
Hunley, D. Patrick; Johnson, Stephen L.; Flores, Roel L.; Sundararajan, Abhishek; Strachan, Douglas R.
2013-06-01
An analytical closed form diffusive model is developed of Joule heating in a device consisting of a nanowire connected to two contacts on a substrate. This analytical model is compared to finite-element simulations and demonstrates excellent agreement over a wider range of system parameters in comparison to other recent models, with particularly large improvements in cases when the width of the nanowire is less than the thermal healing length of the contacts and when the thermal resistance of the contact is appreciable relative to the thermal resistance of the nanowire. The success of this model is due to more accurately accounting for the heat spreading within the contact region of a device and below the nanowire into a substrate. The heat spreading is achieved by matching the linear heat flow near the nanowire interfaces with a radially symmetric spreading solution through an interpolation function. Additional features of this model are the ability to incorporate contact resistances that may be present at the nanowire-contact interfaces, as well as accommodating materials with a linear temperature-dependent electrical resistivity.
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.
2015-01-01
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. PMID:26064648
Analytical model for contaminant mass removal by air sparging
Rabideau, A.J.; Blayden, J.M.
1998-12-31
An analytical model was developed to predict the removal of volatile organic compounds (VOCs) from ground water by air sparging (AS). The model treats the air sparging zone as a completely mixed reactor subject to the removal of dissolved contaminants by volatilization, advection, and first-order decay. Nonequilibrium desorption is approximated as a first-order mass transfer process. The model reproduces the tailing and rebound behavior often observed at AS sites, and would normally require the estimation of three site-specific parameters. Dimensional analysis demonstrates that predicting tailing can be interpreted in terms of kinetic desorption or diffusion of aqueous phase contaminants into discrete air channels. Related work is ongoing to test the model against field data.
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.
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.
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 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.
Particle in a field of two centers in prolate spheroidal coordinates: integrability and solvability
NASA Astrophysics Data System (ADS)
Miller, Willard, Jr.; Turbiner, Alexander V.
2014-05-01
We analyze one particle, two-center quantum problems which admit separation of variables in prolate spheroidal coordinates, a natural restriction satisfied by the H_2^+ molecular ion. The symmetry operator is constructed explicitly. We give the details of the Hamiltonian reduction of the 3D system to a 2D system with modified potential that is separable in elliptic coordinates. The potentials for which there is double-periodicity of the Schrödinger operator in the space of prolate spheroidal coordinates, including one for the H_2^+ molecular ion, are indicated. We study possible potentials that admit exact-solvability is as well as all models known to us with the (quasi)-exact-solvability property for the separation equations. We find deep connections between second-order superintegrable and conformally superintegrable systems and these tractable problems. In particular we derive a general four-parameter expression for a model potential that is always exactly-solvable and integrable and is conformally superintegrable for some parameter choices.
A workflow learning model to improve geovisual analytics utility.
Roth, Robert E; Maceachren, Alan M; McCabe, Craig A
2009-01-01
INTRODUCTION: This paper describes the design and implementation of the G-EX Portal Learn Module, a web-based, geocollaborative application for organizing and distributing digital learning artifacts. G-EX falls into the broader context of geovisual analytics, a new research area with the goal of supporting visually-mediated reasoning about large, multivariate, spatiotemporal information. Because this information is unprecedented in amount and complexity, GIScientists are tasked with the development of new tools and techniques to make sense of it. Our research addresses the challenge of implementing these geovisual analytics tools and techniques in a useful manner. OBJECTIVES: The objective of this paper is to develop and implement a method for improving the utility of geovisual analytics software. The success of software is measured by its usability (i.e., how easy the software is to use?) and utility (i.e., how useful the software is). The usability and utility of software can be improved by refining the software, increasing user knowledge about the software, or both. It is difficult to achieve transparent usability (i.e., software that is immediately usable without training) of geovisual analytics software because of the inherent complexity of the included tools and techniques. In these situations, improving user knowledge about the software through the provision of learning artifacts is as important, if not more so, than iterative refinement of the software itself. Therefore, our approach to improving utility is focused on educating the user. METHODOLOGY: The research reported here was completed in two steps. First, we developed a model for learning about geovisual analytics software. Many existing digital learning models assist only with use of the software to complete a specific task and provide limited assistance with its actual application. To move beyond task-oriented learning about software use, we propose a process-oriented approach to learning based on
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.
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
Improved analytical model for residual stress prediction in orthogonal cutting
NASA Astrophysics Data System (ADS)
Qi, Zhaoxu; Li, Bin; Xiong, Liangshan
2014-09-01
The analytical model of residual stress in orthogonal cutting proposed by Jiann is an important tool for residual stress prediction in orthogonal cutting. In application of the model, a problem of low precision of the surface residual stress prediction is found. By theoretical analysis, several shortages of Jiann's model are picked out, including: inappropriate boundary conditions, unreasonable calculation method of thermal stress, ignorance of stress constraint and cyclic loading algorithm. These shortages may directly lead to the low precision of the surface residual stress prediction. To eliminate these shortages and make the prediction more accurate, an improved model is proposed. In this model, a new contact boundary condition between tool and workpiece is used to make it in accord with the real cutting process; an improved calculation method of thermal stress is adopted; a stress constraint is added according to the volumeconstancy of plastic deformation; and the accumulative effect of the stresses during cyclic loading is considered. At last, an experiment for measuring residual stress in cutting AISI 1045 steel is conducted. Also, Jiann's model and the improved model are simulated under the same conditions with cutting experiment. The comparisons show that the surface residual stresses predicted by the improved model is closer to the experimental results than the results predicted by Jiann's model.
"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.
An analytical model of accretion onto white dwarfs
NASA Astrophysics Data System (ADS)
Ospina, N.; Hernanz, M.
2013-05-01
The analytical model of Frank et al. (2002) has been used to investigate the structure of the accretion stream onto white dwarfs (WD). In particular, the post-shock region (temperature, density and gas velocity distributions) and X-ray spectrum emitted by this region. We have obtained the temperature, density and gas velocity distributions of the emission region for different masses of white dwarfs and at different positions in the shock coordinate. Also, we calculated the emitted spectrum for different WD masses and at different positions of the shock with the principal objective of study the accretion at different points of the emission region.
Analytical Jacobian Calculation in RT Model Including Polarization Effect
NASA Astrophysics Data System (ADS)
Okabayashi, Y.; Yoshida, Y.; Ota, Y.
2014-12-01
The greenhouse gas observing satellite "GOSAT" launched in January 2009 has been observing global distribution of CO2 and CH4. The TANSO-FTS mounted on GOSAT measures the two polarized components (called "P" and "S") of short wavelength infrared (SWIR) spectrum reflected from the earth's surface. In NIES, column-averaged dry air mole fraction of CO2 and CH4 (XCO2 and XCH4) are retrieved from SWIR spectra. However, the observed polarization information is not effectively utilized in the retrieval process due to the large computational cost of a vector RT model, instead the polarization synthesized spectra and a scalar RT model are used in the operational processing. An optical path length modification due to aerosol scattering is known as the major error source for XCO2 and XCH4 retrieval from SWIR spectra. Because the aerosol scattering changes polarization state of light, more accurate or additional aerosol information is expected by using the observed polarization spectra effectively in the retrieval process, which improves the retrieval accuracy of XCO2 and XCH4. In addition, for information content analysis, sensitivity analysis and error analysis, Jacobian matrix is important onto retrieval algorithm design before analyses for actual observed data. However, in the case of using RT model including polarization effect in retrieval process, the computational cost of Jacobian matrix calculations in maximum a posteriori retrieval is significantly large. Efficient calculation of analytical Jacobian is necessary. As a first step, we are implementing an analytical Jacobian calculation function to the vector RT model "Pstar". RT scheme of Pstar is based on hybrid method comprising the discrete ordinate and matrix operator methods. The reflection/transmission matrices and source vectors are obtained for each vertical layer through the discrete ordinate solution, and the vertically inhomogeneous system is constructed using the matrix operator method. Because the delta
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
Shear mechanical properties of the spleen: experiment and analytical modelling.
Nicolle, S; Noguer, L; Palierne, J-F
2012-05-01
This paper aims at providing the first shear mechanical properties of spleen tissue. Rheometric tests on porcine splenic tissues were performed in the linear and nonlinear regime, revealing a weak frequency dependence of the dynamic moduli in linear regime and a distinct strain-hardening effect in nonlinear regime. These behaviours are typical of soft tissues such as kidney and liver, with however a less pronounced strain-hardening for the spleen. An analytical model based on power laws is then proposed to describe the general shear viscoelastic behaviour of the spleen. PMID:22498291
An analytic model for flow reversal in divertor plasmas
Cooke, P.I.H.; Prinja, A.K.
1987-04-01
An analytic model is developed and used to study the phenomenon of flow reversal which is observed in two-dimensional simulations of divertor plasmas. The effect is shown to be caused by the radial spread of neutral particles emitted from the divertor target which can lead to a strong peaking of the ionization source at certain radial locations. The results indicate that flow reversal over a portion of the width of the scrape-off layer is inevitable in high recycling conditions. Implications for impurity transport and particle removal in reactors are discussed.
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.
Experimental, numerical and analytical models of mantle starting plumes
NASA Astrophysics Data System (ADS)
Coulliette, D. L.; Loper, D. E.
1995-12-01
The results of a combined experimental, numerical and analytical investigation of starting thermal plumes are described, to obtain a better perspective on plumes within the Earth's mantle. Thermal plumes were generated experimentally in a tank of corn syrup by means of an electrical heater. Viscosity ratios of 400, 30 000, and 10 8 were generated by varying the temperature of the tank. Plumes for the smaller ratios had the traditional 'balloon-on-astring' shape, but that at the highest ratio had a novel morphology. The plume heads in the first two cases were observed to rise at roughly a constant speed, in contrast to most previous studies which found the plume heads to accelerate. Loss of buoyancy from the plume head owing to heat loss is believed to be responsible for this difference. Starting plumes were simulated numerically using an axisymmetric, finite-element code to solve the Boussinesq equations at finite Prandtl numbers. The constant rise speed observed experimentally was confirmed by the numerical simulation for the viscosity ratios of 400 and 30 000, but numerical instability prevented simulation of the case with a viscosity ratio of 10 8. There was very good agreement between the experimental and numerical rise speeds. An analytical model was developed which reduces to previous models in limiting cases. This parameterization gives better agreement with the experimental and numerical results than does any previous model.
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.
Analytical model of signal amplification in silicon waveguides
NASA Astrophysics Data System (ADS)
Meng, Fan; Yu, Chong-Xiu; Yuan, Jin-Hui
2012-07-01
In this paper, an analytical model to investigate the parametric amplification (PA) and the PA + stimulated Raman scattering (SRS) in silicon waveguides is put forward. When two pump signals are employed, the PA bandwidth of the probe signal is so large that the Raman contribution has to be considered. When Raman contribution fraction f is set to be 0, only the PA occurs to amplify the probe signal, and when f is set to be 0.043, the PA and the SRS amplify the probe signal at the same time. The signal amplifications of both single and dual pump schemes are investigated by using this model. With this model, three main affecting factors, i.e., zero dispersion wavelength (ZDWL), third-order dispersion (TOD), and fourth-order dispersion (FOD), are discussed in detail.
Urban stormwater management planning with analytical probabilistic models
Adams, B.J.
2000-07-01
Understanding how to properly manage urban stormwater is a critical concern to civil and environmental engineers the world over. Mismanagement of stormwater and urban runoff results in flooding, erosion, and water quality problems. In an effort to develop better management techniques, engineers have come to rely on computer simulation and advanced mathematical modeling techniques to help plan and predict water system performance. This important book outlines a new method that uses probability tools to model how stormwater behaves and interacts in a combined- or single-system municipal water system. Complete with sample problems and case studies illustrating how concepts really work, the book presents a cost-effective, easy-to-master approach to analytical modeling of stormwater management systems.
A Mechanistic Stochastic Ricker Model: Analytical and Numerical Investigations
NASA Astrophysics Data System (ADS)
Gadrich, Tamar; Katriel, Guy
The Ricker model is one of the simplest and most widely-used ecological models displaying complex nonlinear dynamics. We study a discrete-time population model, which is derived from simple assumptions concerning individual organisms’ behavior, using the “site-based” approach, developed by Brännström, Broomhead, Johansson and Sumpter. In the large-population limit the model converges to the Ricker model, and can thus be considered a mechanistic version of the Ricker model, derived from basic ecological principles, and taking into account the demographic stochasticity inherent to finite populations. We employ several analytical and precise numerical methods to study the model, showing how each approach contributes to understanding the model’s dynamics. Expressing the model as a Markov chain, we employ the concept of quasi-stationary distributions, which are computed numerically, and used to examine the interaction between complex deterministic dynamics and demographic stochasticity, as well as to calculate mean times to extinction. A Gaussian Markov chain approximation is used to obtain quantitative asymptotic approximations for the size of fluctuations of the stochastic model’s time series around the deterministic trajectory, and for the correlations between successive fluctuations. Results of these approximations are compared to results obtained from quasi-stationary distributions and from direct simulations, and are shown to be in good agreement.
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.
Stochastic analytical modeling of the biodegradation of steady plumes
NASA Astrophysics Data System (ADS)
Zarlenga, A.; Fiori, A.
2014-02-01
We present a stochastic analytical framework to assess the contaminant concentration of a steady plume undergoing biodegradation. The method is focused on heterogeneous formations, and it embeds both fringe and core degradation. The Lagrangian concentration approach of Fiori (2001) was employed, which is suited for describing the interplay between the large scale advection caused by heterogeneity and the local dispersion processes. The principal scope of the model is to provide a relatively simple tool for a quick assessment of the contamination level in aquifers, as function of a few relevant, physically based dimensionless parameters. The solution of the analytical model is relatively simple and generalizes previous approaches developed for homogeneous formations. It is found that heterogeneity generally enhances mixing and degradation; in fact, the plume shear and distortion operated by the complex, heterogeneous velocity field facilitates local dispersion in diluting the contaminant and mixing it with the electron acceptor. The decay of the electron donor concentration, and so the plume length, is proportional to the transverse pore-scale dispersivity, which is indeed the parameter ruling mixing and hence degradation. While the theoretical plume length is controlled by the fringe processes, the core degradation may determine a significant decay of concentration along the mean flow direction, thus affecting the length of the plume. The method is applied to the crude oil contamination event at the Bemijdi site, Minnesota (USA).
Analytical inverse model for multicomponent soil vapor extraction
Ho, C.K.
1998-06-01
In the past decade, soil vapor extraction has become a popular method for remediating sites contaminated with volatile organic chemicals (VOCs) and nonaqueous phase liquids (NAPLs). An analytical model has been developed to predict in-situ compositions and contaminant volumes from early monitoring of effluent gas concentrations of individual species during multicomponent soil vapor extraction. The model exploits the wave-like propagation of the evaporation fronts of individual species to present analytical expressions for the in-situ compositions, contaminant volumes, effluent concentrations, and recovery rates during discrete time intervals. The efficiency of soil vapor extraction systems also can be determined. Comparison of this theory to a previous experiment of through-flow venting of benzene, toluene, and o-xylene yielded excellent agreement. This suggests that if effluent concentrations of individual species are monitored in the field during soil vapor extraction operations, only minimal data are required at early times to yield predictions of in-situ compositions and contaminant volumes, as well as subsequent effluent concentrations and recovery rates.
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.
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
Streaming instability of slime mold amoebae: An analytical model
NASA Astrophysics Data System (ADS)
Höfer, Thomas; Maini, Philip K.
1997-08-01
During the aggregation of amoebae of the cellular slime mould Dictyostelium, the interaction of chemical waves of the signaling molecule cAMP with cAMP-directed cell movement causes the breakup of a uniform cell layer into branching patterns of cell streams. Recent numerical and experimental investigations emphasize the pivotal role of the cell-density dependence of the chemical wave speed for the occurrence of the streaming instability. A simple, analytically tractable, model of Dictyostelium aggregation is developed to test this idea. The interaction of cAMP waves with cAMP-directed cell movement is studied in the form of coupled dynamics of wave front geometries and cell density. Comparing the resulting explicit instability criterion and dispersion relation for cell streaming with the previous findings of model simulations and numerical stability analyses, a unifying interpretation of the streaming instability as a cAMP wave-driven chemotactic instability is proposed.
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.
Visual analytics for model selection in time series analysis.
Bögl, Markus; Aigner, Wolfgang; Filzmoser, Peter; Lammarsch, Tim; Miksch, Silvia; Rind, Alexander
2013-12-01
Model selection in time series analysis is a challenging task for domain experts in many application areas such as epidemiology, economy, or environmental sciences. The methodology used for this task demands a close combination of human judgement and automated computation. However, statistical software tools do not adequately support this combination through interactive visual interfaces. We propose a Visual Analytics process to guide domain experts in this task. For this purpose, we developed the TiMoVA prototype that implements this process based on user stories and iterative expert feedback on user experience. The prototype was evaluated by usage scenarios with an example dataset from epidemiology and interviews with two external domain experts in statistics. The insights from the experts' feedback and the usage scenarios show that TiMoVA is able to support domain experts in model selection tasks through interactive visual interfaces with short feedback cycles.
Strong field coherent control of molecular torsions—Analytical models
Ashwell, Benjamin A.; Ramakrishna, S.; Seideman, Tamar
2015-08-14
We introduce analytical models of torsional alignment by moderately intense laser pulses that are applicable to the limiting cases of the torsional barrier heights. Using these models, we explore in detail the role that the laser intensity and pulse duration play in coherent torsional dynamics, addressing both experimental and theoretical concerns. Our results suggest strategies for minimizing the risk of off-resonant ionization, noting the qualitative differences between the case of torsional alignment subject to a field-free torsional barrier and that of torsional alignment of a barrier-less system (equivalent to a 2D rigid rotor). We also investigate several interesting torsional phenomena, including the onset of impulsive alignment of torsions, field-driven oscillations in quantum number space, and the disappearance of an alignment upper bound observed for a rigid rotor in the impulsive torsional alignment limit.
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.
Analytical higher-order model for flexible and stretchable sensors
NASA Astrophysics Data System (ADS)
Zhang, Yongfang; Zhu, Hongbin; Liu, Cheng; Liu, Xu; Liu, Fuxi; Lü, Yanjun
2015-03-01
The stretchable sensor wrapped around a foldable airfoil or embedded inside of it has great potential for use in the monitoring of the structural status of the foldable airfoil. The design methodology is important to the development of the stretchable sensor for status monitoring on the foldable airfoil. According to the requirement of mechanical flexibility of the sensor, the combined use of a layered flexible structural formation and a strain isolation layer is implemented. An analytical higher-order model is proposed to predict the stresses of the strain-isolation layer based on the shear-lag model for the safe design of the flexible and stretchable sensors. The normal stress and shear stress equations in the constructed structure of the sensors are obtained by the proposed model. The stress distribution in the structure is investigated when bending load is applied to the structures. The numerical results show that the proposed model can predict the variation of normal stress and shear stress along the thickness of the strain-isolation (polydimethylsiloxane) layer accurately. The results by the proposed model are in good agreement with the finite element method, in which the normal stress is variable while the shear stress is invariable along the thickness direction of strain-isolation layer. The high-order model is proposed to predict the stresses of the layered structure of the flexible and stretchable sensor for monitoring the status of the foldable airfoil.
Analytically tractable model for community ecology with many species.
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. PMID:27627348
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.
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.
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)
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 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 semi-analytic dynamical friction model for cored galaxies
NASA Astrophysics Data System (ADS)
Petts, J. A.; Read, J. I.; Gualandris, A.
2016-11-01
We present a dynamical friction model based on Chandrasekhar's formula that reproduces the fast inspiral and stalling experienced by satellites orbiting galaxies with a large constant density core. We show that the fast inspiral phase does not owe to resonance. Rather, it owes to the background velocity distribution function for the constant density core being dissimilar from the usually assumed Maxwellian distribution. Using the correct background velocity distribution function and our semi-analytic model from previous work, we are able to correctly reproduce the infall rate in both cored and cusped potentials. However, in the case of large cores, our model is no longer able to correctly capture core-stalling. We show that this stalling owes to the tidal radius of the satellite approaching the size of the core. By switching off dynamical friction when rt(r) = r (where rt is the tidal radius at the satellite's position), we arrive at a model which reproduces the N-body results remarkably well. Since the tidal radius can be very large for constant density background distributions, our model recovers the result that stalling can occur for Ms/Menc ≪ 1, where Ms and Menc are the mass of the satellite and the enclosed galaxy mass, respectively. Finally, we include the contribution to dynamical friction that comes from stars moving faster than the satellite. This next-to-leading order effect becomes the dominant driver of inspiral near the core region, prior to stalling.
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.
A semi-analytic dynamical friction model for cored galaxies
NASA Astrophysics Data System (ADS)
Petts, J. A.; Read, J. I.; Gualandris, A.
2016-08-01
We present a dynamical friction model based on Chandrasekhar's formula that reproduces the fast inspiral and stalling experienced by satellites orbiting galaxies with a large constant density core. We show that the fast inspiral phase does not owe to resonance. Rather, it owes to the background velocity distribution function for the constant density core being dissimilar from the usually-assumed Maxwellian distribution. Using the correct background velocity distribution function and the semi-analytic model from Petts et al. (2015), we are able to correctly reproduce the infall rate in both cored and cusped potentials. However, in the case of large cores, our model is no longer able to correctly capture core-stalling. We show that this stalling owes to the tidal radius of the satellite approaching the size of the core. By switching off dynamical friction when rt(r) = r (where rt is the tidal radius at the satellite's position) we arrive at a model which reproduces the N-body results remarkably well. Since the tidal radius can be very large for constant density background distributions, our model recovers the result that stalling can occur for Ms/Menc ≪ 1, where Ms and Menc are the mass of the satellite and the enclosed galaxy mass, respectively. Finally, we include the contribution to dynamical friction that comes from stars moving faster than the satellite. This next-to-leading order effect becomes the dominant driver of inspiral near the core region, prior to stalling.
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.
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.
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.
Analytical modeling and vibration analysis of internally cracked rectangular plates
NASA Astrophysics Data System (ADS)
Joshi, P. V.; Jain, N. K.; Ramtekkar, G. D.
2014-10-01
This study proposes an analytical model for nonlinear vibrations in a cracked rectangular isotropic plate containing a single and two perpendicular internal cracks located at the center of the plate. The two cracks are in the form of continuous line with each parallel to one of the edges of the plate. The equation of motion for isotropic cracked plate, based on classical plate theory is modified to accommodate the effect of internal cracks using the Line Spring Model. Berger's formulation for in-plane forces makes the model nonlinear. Galerkin's method used with three different boundary conditions transforms the equation into time dependent modal functions. The natural frequencies of the cracked plate are calculated for various crack lengths in case of a single crack and for various crack length ratio for the two cracks. The effect of the location of the part through crack(s) along the thickness of the plate on natural frequencies is studied considering appropriate crack compliance coefficients. It is thus deduced that the natural frequencies are maximally affected when the crack(s) are internal crack(s) symmetric about the mid-plane of the plate and are minimally affected when the crack(s) are surface crack(s), for all the three boundary conditions considered. It is also shown that crack parallel to the longer side of the plate affect the vibration characteristics more as compared to crack parallel to the shorter side. Further the application of method of multiple scales gives the nonlinear amplitudes for different aspect ratios of the cracked plate. The analytical results obtained for surface crack(s) are also assessed with FEM results. The FEM formulation is carried out in ANSYS.
Hydrogeologic role of geologic structures. Part 2: analytical models
NASA Astrophysics Data System (ADS)
Levens, Russell L.; Williams, Roy E.; Ralston, Dale R.
1994-04-01
This paper is the second of two papers that address the influence of geologic structures on ground water flow at various scales in fractured rocks. The ultimate purpose of this research is to investigate the feasibility of grouting preferentially permeable zones as a strategy to minimize the production of acid mine drainage in underground hard rock mines in which the major permeability is structure and fracture controlled. The aim of grouting is to reduce permeability around mined-out openings, to minimize the rate of inflow of ground water into such openings via the structurally controlled preferentially permeable pathways. A series of hydraulic stress tests were conducted to help characterize the role of geologic structures in controlling the ground water flow system in the vicinity of the Bunker Hill Mine in north Idaho. The results of these tests indicate that most of the ground water that flows from the underground drillholes used for hydraulic stress testing is derived from a few discrete, structurally produced fracture zones that are more or less connected through smaller-scale fractures. Four types of analytical models are considered as a means of analyzing the results of multiple drillhole hydraulic stress tests, as follows: cross-hole equivalent porous media; double-porosity equivalent porous media; a solution to flow in and around a single vertical fracture; leaky equivalent porous media, partial penetration. The estimation of hydraulic coefficients in complex fractured rock environments involves the combined application of a number of deterministic analytical models. The models to be used are selected dependent on the location of the drawdown observations relative to the water-producing zone and the length of the test. The result of the tests can be related to the permeability hierarchy discussed in our first paper.
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.
Two novel classes of solvable many-body problems of goldfish type with constraints
NASA Astrophysics Data System (ADS)
Calogero, F.; Gómez-Ullate, D.
2007-05-01
Two novel classes of many-body models with nonlinear interactions 'of goldfish type' are introduced. They are solvable provided the initial data satisfy a single constraint (in one case; in the other, two constraints), i.e., for such initial data the solution of their initial-value problem can be achieved via algebraic operations, such as finding the eigenvalues of given matrices or equivalently the zeros of known polynomials. Entirely isochronous versions of some of these models are also exhibited, i.e., versions of these models whose nonsingular solutions are all completely periodic with the same period.
An updated analytic model for attenuation by the intergalactic medium
NASA Astrophysics Data System (ADS)
Inoue, Akio K.; Shimizu, Ikkoh; Iwata, Ikuru; Tanaka, Masayuki
2014-08-01
We present an updated version of the so-called Madau model for attenuation of the radiation from distant objects by intergalactic neutral hydrogen. First, we derive the distribution function of intergalactic absorbers from the latest observational statistics of the Lyα forest, Lyman-limit systems and damped Lyα systems. The distribution function reproduces the observed redshift evolution of the Lyα depression and the mean-free path of the Lyman continuum excellently and simultaneously. We then derive a set of analytic functions describing the mean intergalactic attenuation curve for objects at z > 0.5. The new model predicts less (or more) Lyα attenuation for z ≃ 3-5 (z > 6) sources through the usual broad-band filters relative to the original Madau model. This may cause a systematic difference in the photometric redshift estimates, which is, however, still small: about 0.05. Finally, we find a more than 0.5 mag overestimation of Lyman-continuum attenuation in the original Madau model at z > 3, which causes a significant overcorrection against direct observations of the Lyman continuum of galaxies.
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).
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.
Analytic model of aurorally coupled magnetospheric and ionospheric electrostatic potentials
NASA Astrophysics Data System (ADS)
Cornwall, John M.
1993-09-01
This paper describes modest but significant improvements on earlier studies of electrostatic potential structure in the auroral region, using the adiabatic auroral arc model. With certain simplifying assumptions, new analytic nonlinear solutions fully exhibiting the parametric dependence of potentials on magnetospheric (e.g., cross-tail potential) and ionospheric (e.g., recombination rate) parameters are found. No purely phenomenological parameters are introduced. The results are in reasonable agreement with observed average auroral potential drops, inverted-V scale sizes, and dissipation rates. The dissipation rate is quite comparable to tail energization and transport rates and should have a major effect on tail and magnetospheric dynamics. Various relations between the cross-tail potential and auroral parameters (e.g., total parallel currents and potential drops) are given which can be studied with existing data sets.
A simplified analytical random walk model for proton dose calculation
NASA Astrophysics Data System (ADS)
Yao, Weiguang; Merchant, Thomas E.; Farr, Jonathan B.
2016-10-01
We propose an analytical random walk model for proton dose calculation in a laterally homogeneous medium. A formula for the spatial fluence distribution of primary protons is derived. The variance of the spatial distribution is in the form of a distance-squared law of the angular distribution. To improve the accuracy of dose calculation in the Bragg peak region, the energy spectrum of the protons is used. The accuracy is validated against Monte Carlo simulation in water phantoms with either air gaps or a slab of bone inserted. The algorithm accurately reflects the dose dependence on the depth of the bone and can deal with small-field dosimetry. We further applied the algorithm to patients’ cases in the highly heterogeneous head and pelvis sites and used a gamma test to show the reasonable accuracy of the algorithm in these sites. Our algorithm is fast for clinical use.
On t-local solvability of inverse scattering problems in two-dimensional layered media
NASA Astrophysics Data System (ADS)
Baev, A. V.
2015-06-01
The solvability of two-dimensional inverse scattering problems for the Klein-Gordon equation and the Dirac system in a time-local formulation is analyzed in the framework of the Galerkin method. A necessary and sufficient condition for the unique solvability of these problems is obtained in the form of an energy conservation law. It is shown that the inverse problems are solvable only in the class of potentials for which the stationary Navier-Stokes equation is solvable.
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
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.
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.
Analytical thermal model validation for Cassini radioisotope thermoelectric generator
Lin, E.I.
1997-12-31
The Saturn-bound Cassini spacecraft is designed to rely, without precedent, on the waste heat from its three radioisotope thermoelectric generators (RTGs) to warm the propulsion module subsystem, and the RTG end dome temperature is a key determining factor of the amount of waste heat delivered. A previously validated SINDA thermal model of the RTG was the sole guide to understanding its complex thermal behavior, but displayed large discrepancies against some initial thermal development test data. A careful revalidation effort led to significant modifications and adjustments of the model, which result in a doubling of the radiative heat transfer from the heat source support assemblies to the end domes and bring up the end dome and flange temperature predictions to within 2 C of the pertinent test data. The increased inboard end dome temperature has a considerable impact on thermal control of the spacecraft central body. The validation process offers an example of physically-driven analytical model calibration with test data from not only an electrical simulator but also a nuclear-fueled flight unit, and has established the end dome temperatures of a flight RTG where no in-flight or ground-test data existed before.
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.
A SPICE model for a phase-change memory cell based on the analytical conductivity model
NASA Astrophysics Data System (ADS)
Yiqun, Wei; Xinnan, Lin; Yuchao, Jia; Xiaole, Cui; Jin, He; Xing, Zhang
2012-11-01
By way of periphery circuit design of the phase-change memory, it is necessary to present an accurate compact model of a phase-change memory cell for the circuit simulation. Compared with the present model, the model presented in this work includes an analytical conductivity model, which is deduced by means of the carrier transport theory instead of the fitting model based on the measurement. In addition, this model includes an analytical temperature model based on the 1D heat-transfer equation and the phase-transition dynamic model based on the JMA equation to simulate the phase-change process. The above models for phase-change memory are integrated by using Verilog-A language, and results show that this model is able to simulate the I-V characteristics and the programming characteristics accurately.
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.
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. PMID:25375532
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 flux saturation in sediment transport.
Pähtz, Thomas; Parteli, Eric J R; Kok, Jasper F; Herrmann, Hans J
2014-05-01
The transport of sediment by a fluid along the surface is responsible for dune formation, dust entrainment, and a rich diversity of patterns on the bottom of oceans, rivers, and planetary surfaces. Most previous models of sediment transport have focused on the equilibrium (or saturated) particle flux. However, the morphodynamics of sediment landscapes emerging due to surface transport of sediment is controlled by situations out of equilibrium. In particular, it is controlled by the saturation length characterizing the distance it takes for the particle flux to reach a new equilibrium after a change in flow conditions. The saturation of mass density of particles entrained into transport and the relaxation of particle and fluid velocities constitute the main relevant relaxation mechanisms leading to saturation of the sediment flux. Here we present a theoretical model for sediment transport which, for the first time, accounts for both these relaxation mechanisms and for the different types of sediment entrainment prevailing under different environmental conditions. Our analytical treatment allows us to derive a closed expression for the saturation length of sediment flux, which is general and thus can be applied under different physical conditions.
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 Modeling of Neural Tissue: I. A Spherical Bidomain.
Schwartz, Benjamin L; Chauhan, Munish; Sadleir, Rosalind J
2016-12-01
Presented here is a model of neural tissue in a conductive medium stimulated by externally injected currents. The tissue is described as a conductively isotropic bidomain, i.e. comprised of intra and extracellular regions that occupy the same space, as well as the membrane that divides them, and the injection currents are described as a pair of source and sink points. The problem is solved in three spatial dimensions and defined in spherical coordinates [Formula: see text]. The system of coupled partial differential equations is solved by recasting the problem to be in terms of the membrane and a monodomain, interpreted as a weighted average of the intra and extracellular domains. The membrane and monodomain are defined by the scalar Helmholtz and Laplace equations, respectively, which are both separable in spherical coordinates. Product solutions are thus assumed and given through certain transcendental functions. From these electrical potentials, analytic expressions for current density are derived and from those fields the magnetic flux density is calculated. Numerical examples are considered wherein the interstitial conductivity is varied, as well as the limiting case of the problem simplifying to two dimensions due to azimuthal independence. Finally, future modeling work is discussed. PMID:27613652
INCAS: an analytical model to describe displacement cascades
NASA Astrophysics Data System (ADS)
Jumel, Stéphanie; Claude Van-Duysen, Jean
2004-07-01
REVE (REactor for Virtual Experiments) is an international project aimed at developing tools to simulate neutron irradiation effects in Light Water Reactor materials (Fe, Ni or Zr-based alloys). One of the important steps of the project is to characterise the displacement cascades induced by neutrons. Accordingly, the Department of Material Studies of Electricité de France developed an analytical model based on the binary collision approximation. This model, called INCAS (INtegration of CAScades), was devised to be applied on pure elements; however, it can also be used on diluted alloys (reactor pressure vessel steels, etc.) or alloys composed of atoms with close atomic numbers (stainless steels, etc.). INCAS describes displacement cascades by taking into account the nuclear collisions and electronic interactions undergone by the moving atoms. In particular, it enables to determine the mean number of sub-cascades induced by a PKA (depending on its energy) as well as the mean energy dissipated in each of them. The experimental validation of INCAS requires a large effort and could not be carried out in the framework of the study. However, it was verified that INCAS results are in conformity with those obtained from other approaches. As a first application, INCAS was applied to determine the sub-cascade spectrum induced in iron by the neutron spectrum corresponding to the central channel of the High Flux Irradiation Reactor of Oak Ridge National Laboratory.
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.
Explicitly solvable complex Chebyshev approximation problems related to sine polynomials
NASA Technical Reports Server (NTRS)
Freund, Roland
1989-01-01
Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.
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…
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…
33 CFR 385.33 - Revisions to models and analytical tools.
Code of Federal Regulations, 2010 CFR
2010-07-01
... analytical tools. 385.33 Section 385.33 Navigation and Navigable Waters CORPS OF ENGINEERS, DEPARTMENT OF THE... Incorporating New Information Into the Plan § 385.33 Revisions to models and analytical tools. (a) In carrying... and other analytical tools for conducting analyses for the planning, design, construction,...
Analytical models for total dose ionization effects in MOS devices.
Campbell, Phillip Montgomery; Bogdan, Carolyn W.
2008-08-01
MOS devices are susceptible to damage by ionizing radiation due to charge buildup in gate, field and SOI buried oxides. Under positive bias holes created in the gate oxide will transport to the Si / SiO{sub 2} interface creating oxide-trapped charge. As a result of hole transport and trapping, hydrogen is liberated in the oxide which can create interface-trapped charge. The trapped charge will affect the threshold voltage and degrade the channel mobility. Neutralization of oxidetrapped charge by electron tunneling from the silicon and by thermal emission can take place over long periods of time. Neutralization of interface-trapped charge is not observed at room temperature. Analytical models are developed that account for the principal effects of total dose in MOS devices under different gate bias. The intent is to obtain closed-form solutions that can be used in circuit simulation. Expressions are derived for the aging effects of very low dose rate radiation over long time periods.
Analytical description of scale-dependent topology. A toy model
NASA Astrophysics Data System (ADS)
Seriu, Masafumi
1993-12-01
Based on a (2+1)-dimensional toy model, we present one analytical description of the scale-dependent effective topology of the space-time foam. We describe it in terms of a scattering cross-section. We begin by preparing a two-dimensional space with one topological handle, regarding it as the most elementary building block for the foam-like structure. We then calculate the scattering cross-section of a scalar field on this space. We investigate, how the scattering cross-section changes depending on the variety of topologies as well as the incident energy scale. We also investigate how a twist of the handle affects the cross-section. We find out a systematic topology-dependence and a twist effect in the cross-section. We also try to sketch briefly some basic points of the topological approximation procedure in terms of the homology group. Present address: Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Pune 411007, India
Analytical model for minority games with evolutionary learning
NASA Astrophysics Data System (ADS)
Campos, Daniel; Méndez, Vicenç; Llebot, Josep E.; Hernández, Germán A.
2010-06-01
In a recent work [D. Campos, J.E. Llebot, V. Méndez, Theor. Popul. Biol. 74 (2009) 16] we have introduced a biological version of the Evolutionary Minority Game that tries to reproduce the intraspecific competition for limited resources in an ecosystem. In comparison with the complex decision-making mechanisms used in standard Minority Games, only two extremely simple strategies ( juveniles and adults) are accessible to the agents. Complexity is introduced instead through an evolutionary learning rule that allows younger agents to learn taking better decisions. We find that this game shows many of the typical properties found for Evolutionary Minority Games, like self-segregation behavior or the existence of an oscillation phase for a certain range of the parameter values. However, an analytical treatment becomes much easier in our case, taking advantage of the simple strategies considered. Using a model consisting of a simple dynamical system, the phase diagram of the game (which differentiates three phases: adults crowd, juveniles crowd and oscillations) is reproduced.
Analytical model of coincidence resolving time in TOF-PET
NASA Astrophysics Data System (ADS)
Wieczorek, H.; Thon, A.; Dey, T.; Khanin, V.; Rodnyi, P.
2016-06-01
The coincidence resolving time (CRT) of scintillation detectors is the parameter determining noise reduction in time-of-flight PET. We derive an analytical CRT model based on the statistical distribution of photons for two different prototype scintillators. For the first one, characterized by single exponential decay, CRT is proportional to the decay time and inversely proportional to the number of photons, with a square root dependence on the trigger level. For the second scintillator prototype, characterized by exponential rise and decay, CRT is proportional to the square root of the product of rise time and decay time divided by the doubled number of photons, and it is nearly independent of the trigger level. This theory is verified by measurements of scintillation time constants, light yield and CRT on scintillator sticks. Trapping effects are taken into account by defining an effective decay time. We show that in terms of signal-to-noise ratio, CRT is as important as patient dose, imaging time or PET system sensitivity. The noise reduction effect of better timing resolution is verified and visualized by Monte Carlo simulation of a NEMA image quality phantom.
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.
Analysis of structural dynamic data from Skylab. Volume 2: Skylab analytical and test model data
NASA Technical Reports Server (NTRS)
Demchak, L.; Harcrow, H.
1976-01-01
The orbital configuration test modal data, analytical test correlation modal data, and analytical flight configuration modal data are presented. Tables showing the generalized mass contributions (GMCs) for each of the thirty tests modes are given along with the two dimensional mode shape plots and tables of GMCs for the test correlated analytical modes. The two dimensional mode shape plots for the analytical modes and uncoupled and coupled modes of the orbital flight configuration at three development phases of the model are included.
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
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
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... 33 Navigation and Navigable Waters 3 2011-07-01 2011-07-01 false Revisions to models and... Incorporating New Information Into the Plan § 385.33 Revisions to models and analytical tools. (a) In...
CTE Solvability, Nonlocal Symmetry and Explicit Solutions of Modified Boussinesq System
NASA Astrophysics Data System (ADS)
Ren, Bo; Cheng, Xue-Ping
2016-07-01
A consistent tanh expansion (CTE) method is used to study the modified Boussinesq equation. It is proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a nonanto-BT theorem. Furthermore, the nonlocal symmetry for the modified Boussinesq equation is obtained by the Painlevé analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing one auxiliary dependent variable. The finite symmetry transformation related with the nonlocal symemtry is obtained by solving the initial value problem of the prolonged systems. Thanks to the localization process, many interaction solutions among solitons and other complicated waves are computed through similarity reductions. Some special concrete soliton-cnoidal wave interaction behaviors are studied both in analytical and graphical ways. Supported by the National Natural Science Foundation of China under Grant Nos. 11305106 and 11505154
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
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.
Liquid contact resonance AFM: analytical models, experiments, and limitations
NASA Astrophysics Data System (ADS)
Parlak, Zehra; Tu, Qing; Zauscher, Stefan
2014-11-01
Contact resonance AFM (CR-AFM) is a scanning probe microscopy technique that utilizes the contact resonances of the AFM cantilever for concurrent imaging of topography and surface stiffness. The technique has not been used in liquid until recently due to analytical and experimental difficulties, associated with viscous damping of cantilever vibrations and fluid loading effects. To address these difficulties, (i) an analytical approach for contact resonances in liquid is developed, and (ii) direct excitation of the contact resonances is demonstrated by actuating the cantilever directly in a magnetic field. By implementing the analytical approach and the direct actuation through magnetic particles, quantitative stiffness imaging on surfaces with a wide range of stiffness can be achieved in liquid with soft cantilevers and low contact forces.
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.
Kostanyan, Artak E
2015-08-01
In closed-loop recycling (CLR) chromatography, the effluent from the outlet of a column is directly returned into the column through the sample feed line and continuously recycled until the required separation is reached. To select optimal operating conditions for the separation of a given feed mixture, an appropriate mathematical description of the process is required. This work is concerned with the analysis of models for the CLR separations. Due to the effect of counteracting mechanisms on separation of solutes, analytical solutions of the models could be helpful to understand and optimize chromatographic processes. The objective of this work was to develop analytical expressions to describe the CLR counter-current (liquid-liquid) chromatography (CCC). The equilibrium dispersion and cell models were used to describe the transport and separation of solutes inside a CLR CCC column. The Laplace transformation is applied to solve the model equations. Several possible CLR chromatography methods for the binary and complex mixture separations are simulated.
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 model for analytical performance prediction of hypervapotron
Baxi, C.B.; Falter, H.
1992-07-01
A hypervapotron is a water-cooled device which combines the advantages of finned surfaces with the large heat transfer rates possible during boiling heat transfer. Hypervapotrons have been used as beam dumps in the past and plans are under way to use them for divertor cooling in the Joint European Torus (JET). Experiments at JET have shows that a surface heat flux of 25 MW/m{sup 2} can be achieved in hypervapotrons. This performance makes such a device very attractive for cooling of divertor of the International Thermonuclear Experimental Reactor (ITER). This paper presents an analytical method to predict the thermal performance of the hypervapotrons. Preliminary results show an excellent agreement between experimental results and analytical prediction over a wide range of flow velocities, pressures, subcooling temperatures and heat fluxes. This paper also presents the predicted performance of hypervapotron made of materials other than copper. After further development and verification, the analytical method could be used for optimizing designs and performance prediction.
A simple analytical aerodynamic model of Langley Winged-Cone Aerospace Plane concept
NASA Astrophysics Data System (ADS)
Pamadi, Bandu N.
1994-10-01
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.
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.
NASA Astrophysics Data System (ADS)
Astashev, M. G.; Novikov, M. A.; Panfilov, D. I.; Rashitov, P. A.; Fedorova, M. I.
2015-12-01
In this paper, an approach to the development of a simplified analytical model for the analysis of electromagnetic processes of a thyristor-controlled phase angle regulator with an individual phase-controlled thyristor switch is considered. The analytical expressions for the calculation of electrical parameters in symmetrical and open-phase operating mode are obtained. With a concrete example, the verification of the developed analytical model is carried out. It is accomplished by means of comparison between current and voltage calculation results when the thyristor-controlled phase angle regulator is in an open-phase operating mode with the simulation results in the MatLab software environment. Adequacy check of the obtained analytical model is carried out by comparison between the analytical calculation and experimental data received from the actual physical model.
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.
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.
Analytical models of helical wind-type astrophysical flows
NASA Technical Reports Server (NTRS)
Tsinganos, K.; Vlastou-Tsinganos, G.
1988-01-01
Three classes of analytic solutions of the basic hydrodynamic equations assumed to govern plasma flow in the atmosphere of a rotating astrophysical object are presented. Attention is focused on the balance of the inertial and gravitational forces with suitable pressure gradients in the presence of rotation. The solutions are written in terms of dimensionless physical parameters in order to facilitate their direct application to specific astrophysical flows, such as winds from massive premain sequence objects and T Tauri stars, and bipolar flows in young stellar objects.
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…
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…
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…
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
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.
Hunt, R.J.; Anderson, M.P.; Kelson, V.A.
1998-01-01
This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.
Analytic Expressions for the BCDMEM Model of Recognition Memory
Myung, Jay I.; Montenegro, Maximiliano; Pitt, Mark A.
2007-01-01
We introduce a Fourier Transformation technique that enables one to derive closed-form expressions of performance measures (e.g., hit and false alarm rates) of simulation-based models of recognition memory. Application of the technique is demonstrated using the bind cue decide model of episodic memory (BCDMEM; Dennis & Humphreys, 2001). In addition to reducing the time required to test the model, which for models like BCDMEM can be excessive, asymptotic expressions of the measures reveal heretofore unknown properties of the model, such as model predictions being dependent on vector length. PMID:18516213
The Word Problem for Solvable Lie Algebras and Groups
NASA Astrophysics Data System (ADS)
Kharlampovich, O. G.
1990-02-01
The variety of groups Z\\mathfrak{N}_2\\mathfrak{A} is given by the identity \\displaystyle \\lbrack\\lbrack x_1,\\,x_2\\rbrack,\\,\\lbrack x_3,\\,x_4\\rbrack,\\,\\lbrack x_5,\\, x_6\\rbrack,\\, x_7\\rbrack = 1,and the analogous variety of Lie algebras is given by the identity \\displaystyle (x_1x_2)(x_3x_4)(x_5x_6)x_7=0.Previously the author proved the unsolvability of the word problem for any variety of groups (respectively: Lie algebras) containing Z\\mathfrak{N}_2\\mathfrak{A}, and its solvability for any subvariety of \\mathfrak{N}_2\\mathfrak{A}. Here the word problem is investigated in varieties of Lie algebras over a field of characteristic zero and in varieties of groups contained in Z\\mathfrak{N}_2\\mathfrak{A}. It is proved that in the lattice of subvarieties of Z\\mathfrak{N}_2\\mathfrak{A} there exist arbitrary long chains in which the varieties with solvable and unsolvable word problems alternate. In particular, the variety Z\\mathfrak{N}_2\\mathfrak{A}\\cap\\mathfrak{N}_2\\mathfrak{N}_c has a solvable word problem for any c, while the variety \\mathfrak{Y}_2, given within Z\\mathfrak{N}_2\\mathfrak{A} by the identity \\displaystyle \\lbrack\\lbrack x_1,\\,\\dots,\\,x_{2c+2}\\rbrack,\\,\\lbrack y_1,\\,\\dots,\\,y_{2c+2}\\rbrack,\\lbrack z_1,\\,\\dots,\\,z_{2c}\\rbrack\\rbrack = 1,in the case of groups and by the identity \\displaystyle (x_1\\dotsb x_{2c+2})(y_1\\dotsb y_{2c+2})(z_1\\dotsb z_{2c})=0in the case of Lie algebras, has an unsolvable word problem. It is also proved that in Z\\mathfrak{N}_2\\mathfrak{A} there exists an infinite series of minimal varieties with an unsolvable word problem, i.e. varieties whose proper subvarieties all have solvable word problems.Bibliography: 17 titles.
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.
A two-dimensional analytical model for short channel junctionless double-gate MOSFETs
NASA Astrophysics Data System (ADS)
Jiang, Chunsheng; Liang, Renrong; Wang, Jing; Xu, Jun
2015-05-01
A physics-based analytical model of electrostatic potential for short-channel junctionless double-gate MOSFETs (JLDGMTs) operated in the subthreshold regime is proposed, in which the full two-dimensional (2-D) Poisson's equation is solved in channel region by a method of series expansion similar to Green's function. The expression of the proposed electrostatic potential is completely rigorous and explicit. Based on this expression, analytical models of threshold voltage, subthreshold swing, and subthreshold drain current for JLDGMTs were derived. Subthreshold behavior was studied in detail by changing different device parameters and bias conditions, including doping concentration, channel thickness, gate length, gate oxide thickness, drain voltage, and gate voltage. Results predicted by all the analytical models agree well with numerical solutions from the 2-D simulator. These analytical models can be used to investigate the operating mechanisms of nanoscale JLDGMTs and to optimize their device performance.
Team mental models: techniques, methods, and analytic approaches.
Langan-Fox, J; Code, S; Langfield-Smith, K
2000-01-01
Effective team functioning requires the existence of a shared or team mental model among members of a team. However, the best method for measuring team mental models is unclear. Methods reported vary in terms of how mental model content is elicited and analyzed or represented. We review the strengths and weaknesses of vatrious methods that have been used to elicit, represent, and analyze individual and team mental models and provide recommendations for method selection and development. We describe the nature of mental models and review techniques that have been used to elicit and represent them. We focus on a case study on selecting a method to examine team mental models in industry. The processes involved in the selection and development of an appropriate method for eliciting, representing, and analyzing team mental models are described. The criteria for method selection were (a) applicability to the problem under investigation; (b) practical considerations - suitability for collecting data from the targeted research sample; and (c) theoretical rationale - the assumption that associative networks in memory are a basis for the development of mental models. We provide an evaluation of the method matched to the research problem and make recommendations for future research. The practical applications of this research include the provision of a technique for analyzing team mental models in organizations, the development of methods and processes for eliciting a mental model from research participants in their normal work environment, and a survey of available methodologies for mental model research.
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.
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.
On loop equations in KdV exactly solvable string theory
Dalley, S. . Joseph Henry Labs.)
1992-05-10
In this paper, the non-perturbative behavior of macroscopic loop amplitudes in the exactly solvable string theories based on the KdV hierarchies is considered. Loop equations are presented for the real non-perturbative solutions living on the spectral half-line, allowed by the most general string equation ({bar P}, Q) = Q, where {bar P} generates scale transformations. In general the end of the half-line (the wall) is a non-perturbative parameter whose role is that of boundary cosmological constant. The properties are compared with the perturbative behavior and solutions of (P,Q) = 1. Detailed arguments are given for the (2,2m {minus} 1) models while generalization to the other (p,q) minimal models and c = 1 is briefly addressed.
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.
Automated refinement and inference of analytical models for metabolic networks
Schmidt, Michael D; Vallabhajosyula, Ravishankar R; Jenkins, Jerry W; Hood, Jonathan E; Soni, Abhishek S; Wikswo, John P; Lipson, Hod
2013-01-01
The reverse engineering of metabolic networks from experimental data is traditionally a labor-intensive task requiring a priori systems knowledge. Using a proven model as a test system, we demonstrate an automated method to simplify this process by modifying an existing or related model – suggesting nonlinear terms and structural modifications – or even constructing a new model that agrees with the system’s time-series observations. In certain cases, this method can identify the full dynamical model from scratch without prior knowledge or structural assumptions. The algorithm selects between multiple candidate models by designing experiments to make their predictions disagree. We performed computational experiments to analyze a nonlinear seven-dimensional model of yeast glycolytic oscillations. This approach corrected mistakes reliably in both approximated and overspecified models. The method performed well to high levels of noise for most states, could identify the correct model de novo, and make better predictions than ordinary parametric regression and neural network models. We identified an invariant quantity in the model, which accurately derived kinetics and the numerical sensitivity coefficients of the system. Finally, we compared the system to dynamic flux estimation and discussed the scaling and application of this methodology to automated experiment design and control in biological systems in real-time. PMID:21832805
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.
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...
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…
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.
Rozet, E; Rudaz, S; Marini, R D; Ziémons, E; Boulanger, B; Hubert, Ph
2011-09-30
Evaluation of analytical results reliability is of core importance as crucial decisions are taken with them. From the various methodologies to evaluate the fitness of purpose of analytical methods, overall measurement uncertainty estimation is more and more applied. Overall measurement uncertainty allows to combine simultaneously the remaining systematic influences to the random sources of uncertainty and allows assessing the reliability of results generated by analytical methods. However there are various interpretations on how to estimate overall measurement uncertainty, and thus various models for estimating it. Each model together with its assumptions has great impacts on the risks to abusively declare that analytical methods are suitable for their intended purpose. This review paper aims at (i) summarizing the various models used to estimate overall measurement uncertainty, (ii) provide their pros and cons, (iii) review the main areas of application and (iv) as a conclusion provide some recommendations when evaluating overall measurement uncertainty.
Health Informatics for Neonatal Intensive Care Units: An Analytical Modeling Perspective.
Khazaei, Hamzeh; Mench-Bressan, Nadja; McGregor, Carolyn; Pugh, James Edward
2015-01-01
The effective use of data within intensive care units (ICUs) has great potential to create new cloud-based health analytics solutions for disease prevention or earlier condition onset detection. The Artemis project aims to achieve the above goals in the area of neonatal ICUs (NICU). In this paper, we proposed an analytical model for the Artemis cloud project which will be deployed at McMaster Children's Hospital in Hamilton. We collect not only physiological data but also the infusion pumps data that are attached to NICU beds. Using the proposed analytical model, we predict the amount of storage, memory, and computation power required for the system. Capacity planning and tradeoff analysis would be more accurate and systematic by applying the proposed analytical model in this paper. Numerical results are obtained using real inputs acquired from McMaster Children's Hospital and a pilot deployment of the system at The Hospital for Sick Children (SickKids) in Toronto. PMID:27170907
Health Informatics for Neonatal Intensive Care Units: An Analytical Modeling Perspective.
Khazaei, Hamzeh; Mench-Bressan, Nadja; McGregor, Carolyn; Pugh, James Edward
2015-01-01
The effective use of data within intensive care units (ICUs) has great potential to create new cloud-based health analytics solutions for disease prevention or earlier condition onset detection. The Artemis project aims to achieve the above goals in the area of neonatal ICUs (NICU). In this paper, we proposed an analytical model for the Artemis cloud project which will be deployed at McMaster Children's Hospital in Hamilton. We collect not only physiological data but also the infusion pumps data that are attached to NICU beds. Using the proposed analytical model, we predict the amount of storage, memory, and computation power required for the system. Capacity planning and tradeoff analysis would be more accurate and systematic by applying the proposed analytical model in this paper. Numerical results are obtained using real inputs acquired from McMaster Children's Hospital and a pilot deployment of the system at The Hospital for Sick Children (SickKids) in Toronto.
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.
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.
Analytical model and performance data for a cylindrical parabolic collector
Ford, F.M.; Stewart, W.E. Jr.
1980-01-01
Concentrating solar collectors provide higher fluid temperatures than flat-plate, an important advantage in many applications. The parabolic cylinder is one of the most popular types of concentrating collectors because of its relatively simple construction and tracking configuration. A mathematical model was developed for one such collector in order to predict thermal efficiency as a function of solar insolation. An experiment was then devised in an attempt to verify this model. Discrepancies between predicted and observed values are discussed, and suggestions are made for improving the model and the experimental procedure.
Analytical model of the combustion of multicomponent solid propellants
NASA Technical Reports Server (NTRS)
Cohen, N. S.; Price, C. F.; Strand, L. D.
1977-01-01
Multiple flame models derived for simple composite propellants are extended to describe the combustion of propellants containing multimodal particle sizes, mixed oxidizers and monopropellant binders. Models combining the component contributions to propellant surface structure, flame structure and energy distribution are based in part upon experimental observations and in part upon hypotheses constrained to provide reasonable agreement with measured burning rate characteristics. The methods employed consist of superposition, interaction and iteration. The computerized model is applied to explain the effects of multiple ingredients and to discuss burning rate tailoring problems of current interest.
Analytic toy model for the innermost stable circular orbit shift
NASA Astrophysics Data System (ADS)
Hod, Shahar
2013-01-01
A simple black-hole-ring system is proposed as a toy model for the two-body problem in general relativity. This toy-model yields the fractional shift ΔΩisco/Ωisco=(29)/(812)η in the Schwarzschild ISCO (innermost stable circular orbit) frequency, where η≡m/Mir≪1 is the dimensionless ratio between the mass of the particle and the irreducible mass of the black hole. Our model suggests that the second-order spin-orbit interaction between the black hole and the orbiting particle (the dragging of inertial frames) is the main element determining the observed value of the ISCO shift.
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.
An analytic solution to the Monod-Wyman-Changeux model and all parameters in this model.
Zhou, G; Ho, P S; van Holde, K E
1989-01-01
Starting from the Monod-Wyman-Changeux (MWC) model (Monod, J., J. Wyman, and J. P. Changeux. 1965. J. Mol. Biol. 12:88-118), we obtain an analytical expression for the slope of the Hill plot at any ligand concentration. Furthermore, we derive an equation satisfied by the ligand concentration at the position of maximum slope. From these results, we derive a set of formulas which allow determination of the parameters of the MWC model (kR, C, and L) from the value of the Hill coefficient, nH, the ligand concentration at the position of maximum slope [( A]0), and the value of nu/(n-nu) at this point. We then outline procedures for utilizing these equations to provide a "best fit" of the MWC model to the experimental data, and to obtain a refined set of the parameters. Finally, we demonstrate the applicability of the technique by analysis of oxygen binding data for Octopus hemocyanin. PMID:2713440
Recent Analytical and Numerical Results for The Navier-Stokes-Voigt Model and Related Models
NASA Astrophysics Data System (ADS)
Larios, Adam; Titi, Edriss; Petersen, Mark; Wingate, Beth
2010-11-01
The equations which govern the motions of fluids are notoriously difficult to handle both mathematically and computationally. Recently, a new approach to these equations, known as the Voigt-regularization, has been investigated as both a numerical and analytical regularization for the 3D Navier-Stokes equations, the Euler equations, and related fluid models. This inviscid regularization is related to the alpha-models of turbulent flow; however, it overcomes many of the problems present in those models. I will discuss recent work on the Voigt-regularization, as well as a new criterion for the finite-time blow-up of the Euler equations based on their Voigt-regularization. Time permitting, I will discuss some numerical results, as well as applications of this technique to the Magnetohydrodynamic (MHD) equations and various equations of ocean dynamics.
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.
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.
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.
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.
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…
A Meta-Analytic Investigation of Fiedler's Contingency Model of Leadership Effectiveness.
ERIC Educational Resources Information Center
Strube, Michael J.; Garcia, Joseph E.
According to Fiedler's Contingency Model of Leadership Effectiveness, group performance is a function of the leader-situation interaction. A review of past validations has found several problems associated with the model. Meta-analytic techniques were applied to the Contingency Model in order to assess the validation evidence quantitatively. The…
Simple analytical model of evapotranspiration in the presence of roots
NASA Astrophysics Data System (ADS)
Cejas, Cesare; Castaing, Jean-Christophe; Hough, Larry; Fretigny, Christian; Dreyfus, Remi; Compass Team
2015-03-01
Water is essential for plant growth. The loss of water via evaporation in soil remains to be an important limiting factor for root growth and consists of well-debated mechanisms. The presence of a plant also provides an additional pathway for water transport in the form of transpiration. Prediction of total evapotranspiration flux permits estimation of the remaining quantity of water in the soil. Using a controlled visual 2D model set-up, we perform evaporation experiments with real root systems under different relative humidity conditions. We use the results on mass loss and evaporation front positions to develop a simple model, based on basic principles of evaporation flux, which predicts the position of the evaporating front and the total mass of water that is lost from the evapotranspiration of water out of the granular medium. The model also helps predict the lifetime of the plant - an important application in agriculture.
Analytical and experimental study of control effort associated with model reference adaptive control
NASA Technical Reports Server (NTRS)
Messer, R. S.; Haftka, R. T.; Cudney, H. H.
1992-01-01
Numerical simulation results presently obtained for the performance of model reference adaptive control (MRAC) are experimentally verified, with a view to accounting for differences between the plant and the reference model after the control function has been brought to bear. MRAC is both experimentally and analytically applied to a single-degree-of-freedom system, as well as analytically to a MIMO system having controlled differences between the reference model and the plant. The control effort is noted to be sensitive to differences between the plant and the reference model.
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.
Time dependent turbulence modeling and analytical theories of turbulence
NASA Technical Reports Server (NTRS)
Rubinstein, R.
1993-01-01
By simplifying the direct interaction approximation (DIA) for turbulent shear flow, time dependent formulas are derived for the Reynolds stresses which can be included in two equation models. The Green's function is treated phenomenologically, however, following Smith and Yakhot, we insist on the short and long time limits required by DIA. For small strain rates, perturbative evaluation of the correlation function yields a time dependent theory which includes normal stress effects in simple shear flows. From this standpoint, the phenomenological Launder-Reece-Rodi model is obtained by replacing the Green's function by its long time limit. Eddy damping corrections to short time behavior initiate too quickly in this model; in contrast, the present theory exhibits strong suppression of eddy damping at short times. A time dependent theory for large strain rates is proposed in which large scales are governed by rapid distortion theory while small scales are governed by Kolmogorov inertial range dynamics. At short times and large strain rates, the theory closely matches rapid distortion theory, but at long times it relaxes to an eddy damping model.
Canonical Correlation Analysis as a General Analytical Model.
ERIC Educational Resources Information Center
Fan, Xitao
This paper focuses on three aspects related to the conceptualization and application of canonical correlation analysis as a dominant statistical model: (1) partial canonical correlation analysis and its application in statistical testing; (2) the relation between canonical correlation analysis and discriminant analysis; and (3) the relation…
A Factor Analytic Model of College Student Development.
ERIC Educational Resources Information Center
Lavelle, Ellen; Rickord, Bill
This research study reports the results of an attempt to build a model of individual differences in undergraduate student development based on factor analysis of a wide range of students' beliefs and behaviors. An 127-item inventory named the Dakota Inventory of Student Orientations was administered to 738 male and female undergraduate students in…
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...
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 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.
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
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 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.
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.
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 analytical model for a class of processor-memory interconnection networks
Conterno, R.; Melen, R.
1987-11-01
The performance of a delta interconnection network for multiprocessors is evaluated in a circuit switching environment. An error is pointed out in previous literature and an exact analytical model is given for regeneration systems, where a connection request is considered lost if not immediately granted. An approximated numerical method is suggested for the correction of the analytical results, which gave outputs in very good agreement with the simulation of real systems where requests are maintained.
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.
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 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 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.
Analytical models of calcium binding in a calcium channel
NASA Astrophysics Data System (ADS)
Liu, Jinn-Liang; Eisenberg, Bob
2014-08-01
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+ and Ca2+ for [CaCl2] ranging from 10-8 to 10-2 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.
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.
Loop quantum cosmology in Bianchi type I models: Analytical investigation
Chiou, D.-W.
2007-01-15
The comprehensive formulation for loop quantum cosmology in the spatially flat, isotropic model was recently constructed. In this paper, the methods are extended to the anisotropic Bianchi I cosmology. Both the precursor and the improved strategies are applied and the expected results are established: (i) the scalar field again serves as an internal clock and is treated as emergent time; (ii) the total Hamiltonian constraint is derived by imposing the fundamental discreteness and gives the evolution as a difference equation; and (iii) the physical Hilbert space, Dirac observables, and semiclassical states are constructed rigorously. It is also shown that the state in the kinematical Hilbert space associated with the classical singularity is decoupled in the difference evolution equation, indicating that the big bounce may take place when any of the area scales undergoes the vanishing behavior. The investigation affirms the robustness of the framework used in the isotropic model by enlarging its domain of validity and provides foundations to conduct the detailed numerical analysis.
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.
Analytical modeling and experimental characterization of chemotaxis in Serratia marcescens
NASA Astrophysics Data System (ADS)
Zhuang, Jiang; Wei, Guopeng; Wright Carlsen, Rika; Edwards, Matthew R.; Marculescu, Radu; Bogdan, Paul; Sitti, Metin
2014-05-01
This paper presents a modeling and experimental framework to characterize the chemotaxis of Serratia marcescens (S. marcescens) relying on two-dimensional and three-dimensional tracking of individual bacteria. Previous studies mainly characterized bacterial chemotaxis based on population density analysis. Instead, this study focuses on single-cell tracking and measuring the chemotactic drift velocity VC from the biased tumble rate of individual bacteria on exposure to a concentration gradient of l-aspartate. The chemotactic response of S. marcescens is quantified over a range of concentration gradients (10-3 to 5 mM/mm) and average concentrations (0.5×10-3 to 2.5 mM). Through the analysis of a large number of bacterial swimming trajectories, the tumble rate is found to have a significant bias with respect to the swimming direction. We also verify the relative gradient sensing mechanism in the chemotaxis of S. marcescens by measuring the change of VC with the average concentration and the gradient. The applied full pathway model with fitted parameters matches the experimental data. Finally, we show that our measurements based on individual bacteria lead to the determination of the motility coefficient μ (7.25×10-6 cm2/s) of a population. The experimental characterization and simulation results for the chemotaxis of this bacterial species contribute towards using S. marcescens in chemically controlled biohybrid systems.
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 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 modeling of circuit aerodynamics in the new NASA Lewis Altitude Wind Tunnel
NASA Technical Reports Server (NTRS)
Towne, C. E.; Povinelli, L. A.; Kunik, W. G.; Muramoti, K. K.; Hughes, C. E.; Levy, R.
1985-01-01
Rehabilitation and extention of the capability of the altitude wind tunnel (AWT) was analyzed. The analytical modelling program involves the use of advanced axisymmetric and three dimensional viscous analyses to compute the flow through the various AWT components. Results for the analytical modelling of the high speed leg aerodynamics are presented; these include: an evaluation of the flow quality at the entrance to the test section, an investigation of the effects of test section bleed for different model blockages, and an examination of three dimensional effects in the diffuser due to reentry flow and due to the change in cross sectional shape of the exhaust scoop.
Analytical modeling of circuit aerodynamics in the new NASA Lewis wind tunnel
NASA Technical Reports Server (NTRS)
Towne, C. E.; Povinelli, L. A.; Kunik, W. G.; Muramoto, K. K.; Hughes, C. E.; Levy, R.
1985-01-01
Rehabilitation and extention of the capability of the altitude wind tunnel (AWT) was analyzed. The analytical modeling program involves the use of advanced axisymmetric and three dimensional viscous analyses to compute the flow through the various AWT components. Results for the analytical modeling of the high speed leg aerodynamics are presented; these include: an evaluation of the flow quality at the entrance to the test section, an investigation of the effects of test section bleed for different model blockages, and an examination of three dimensional effects in the diffuser due to reentry flow and due to the change in cross sectional shape of the exhaust scoop.
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
Analytical solution for two-phase flow in a wellbore using the drift-flux model
Pan, L.; Webb, S.W.; Oldenburg, C.M.
2011-11-01
This paper presents analytical solutions for steady-state, compressible two-phase flow through a wellbore under isothermal conditions using the drift flux conceptual model. Although only applicable to highly idealized systems, the analytical solutions are useful for verifying numerical simulation capabilities that can handle much more complicated systems, and can be used in their own right for gaining insight about two-phase flow processes in wells. The analytical solutions are obtained by solving the mixture momentum equation of steady-state, two-phase flow with an assumption that the two phases are immiscible. These analytical solutions describe the steady-state behavior of two-phase flow in the wellbore, including profiles of phase saturation, phase velocities, and pressure gradients, as affected by the total mass flow rate, phase mass fraction, and drift velocity (i.e., the slip between two phases). Close matching between the analytical solutions and numerical solutions for a hypothetical CO{sub 2} leakage problem as well as to field data from a CO{sub 2} production well indicates that the analytical solution is capable of capturing the major features of steady-state two-phase flow through an open wellbore, and that the related assumptions and simplifications are justified for many actual systems. In addition, we demonstrate the utility of the analytical solution to evaluate how the bottomhole pressure in a well in which CO{sub 2} is leaking upward responds to the mass flow rate of CO{sub 2}-water mixture.
Analytical and Numerical Modeling of Strongly Rotating Rarefied Gas Flows
NASA Astrophysics Data System (ADS)
Pradhan, Sahadev; Kumaran, Viswanathan
2015-11-01
Centrifugal gas separation processes effect separation by utilizing the difference in the mole fraction in a high speed rotating cylinder caused by the difference in molecular mass, and consequently the centrifugal force density. These have been widely used in isotope separation because chemical separation methods cannot be used to separate isotopes of the same chemical species. More recently, centrifugal separation has also been explored for the separation of gases such as carbon dioxide and methane. The efficiency of separation is critically dependent on the secondary flow generated due to temperature gradients at the cylinder wall or due to inserts, and it is important to formulate accurate models for this secondary flow. The widely used Onsager model for secondary flow is restricted to very long cylinders where the length is large compared to the diameter, the limit of high stratification parameter, where the gas is restricted to a thin layer near the wall of the cylinder, and it assumes that there is no mass difference in the two species while calculating the secondary flow. There are two objectives of the present analysis of the rarefied gas flow in a rotating cylinder. The first is to remove the restriction of high stratification parameter, and to generalize the solutions to low rotation speeds where the stratification parameter may be O(1), and to apply for dissimilar gases considering the difference in molecular mass of the two species. Secondly, we would like to compare the predictions with molecular simulations based on the direct simulation Monte Carlo (DSMC) method for rarefied gas flows, in order to quantify the errors resulting from the approximations at different aspect ratios, Reynolds number and stratification parameter.
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.
33 CFR 385.33 - Revisions to models and analytical tools.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 33 Navigation and Navigable Waters 3 2014-07-01 2014-07-01 false Revisions to models and... Incorporating New Information Into the Plan § 385.33 Revisions to models and analytical tools. (a) In carrying... Management District, and other non-Federal sponsors shall rely on the best available science including...
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…
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. PMID:16224691
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…
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.
Meta-Analytic Structural Equation Modeling (MASEM): Comparison of the Multivariate Methods
ERIC Educational Resources Information Center
Zhang, Ying
2011-01-01
Meta-analytic Structural Equation Modeling (MASEM) has drawn interest from many researchers recently. In doing MASEM, researchers usually first synthesize correlation matrices across studies using meta-analysis techniques and then analyze the pooled correlation matrix using structural equation modeling techniques. Several multivariate methods of…
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 ...
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…
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.
Analytic modeling of soot nucleation under fuel rich conditions
NASA Technical Reports Server (NTRS)
Yang, C. H.
1983-01-01
The objective of the present research is to construct a soot nucleation model according to a proposed chemical kinetic scheme to delineate quantitatively the nucleation mechanism in the soot formation process. Instead of following the traditional views which generally associate sooting with the homogeneous nucleation process in phase transformation or polymerization, we choose a chemical kinetic approach. In our proposed scheme the number of carbon atoms in the intermediate species between the fuel molecule and soot nuclei is continuously increased by radical additions. The number of hydrogen atoms in the intermediate species on the other hand is steadily decreased by radical dehydrogenation. When the number of carbon atoms in each of the intermediate molecules has exceeded a certain limit and the number of hydrogen atoms has fallen below a certain level, they may coagulate with one and another to form a larger molecule which is regarded as the initial soot nuclei in the present theory. Further coagulation and surface growth of the nuclei will lead to observable soot particles.
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.
Analytical model of infiltration under constant-concentration boundary conditions
NASA Astrophysics Data System (ADS)
Triadis, D.; Broadbridge, P.
2010-03-01
Known integrable models for 1D flow in unsaturated soil have a rescaled soil water diffusivity that is either constant or proportional to C(C - 1)/(C - Θ)2, where Θ is the degree of saturation and C > 1 is constant. With a wider more realistic range of hydraulic conductivity functions than has been used in this context before, a formal series solution is developed for infiltration, subject to constant-concentration boundary conditions. A readily programmed iteration algorithm, applicable for any value of C, is used to construct many coefficients of the infiltration series without requiring any numerical integration. In particular, for either C - 1 small or 1/C small, several infiltration series coefficients are constructed as formal power series in C - 1 or in 1/C, for which we construct a number of terms explicitly. In the limit as the diffusivity approaches a delta function, the infiltration coefficients are obtained in simpler closed form. All but the sorptivity depend on the form of the conductivity function.
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.
NASA Astrophysics Data System (ADS)
Farzanehpour, M.; Tokatly, I. V.
2016-05-01
We use analytic (current) density-potential maps of time-dependent (current) density-functional theory [TD(C)DFT] to inverse engineer analytically solvable time-dependent quantum problems. In this approach the driving potential (the control signal) and the corresponding solution of the Schrödinger equation are parametrized analytically in terms of the basic TD(C)DFT observables. We describe the general reconstruction strategy and illustrate it with a number of explicit examples. First we consider the real space one-particle dynamics driven by a time-dependent electromagnetic field and recover, from the general TDDFT reconstruction formulas, the known exact solution for a driven oscillator with a time-dependent frequency. Then we use analytic maps of the lattice TD(C)DFT to control quantum dynamics in a discrete space. As a first example we construct a time-dependent potential which generates prescribed dynamics on a tight-binding chain. Then our method is applied to the dynamics of spin-1/2 driven by a time-dependent magnetic field. We design an analytic control pulse that transfers the system from the ground to excited state and vice versa. This pulse generates the spin flip thus operating as a quantum not gate.
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
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.
Alem, Mehdi; Soto, Marcelo A; Thévenaz, Luc
2015-11-16
Modulation instability is thoroughly investigated and a simple analytical model for its power critically modifying the wave properties in terms of system parameters is derived and experimentally validated. The differences on the modulation instability gain spectrum in lossless and lossy optical fibers are analyzed based on theoretical models and numerical simulations. In particular the impact of background noise on the behavior of modulation instability is studied analytically and verified by measurements and simulations. The proposed analytical model is experimentally validated by monitoring the wave propagation along an optical fiber using a Brillouin optical time-domain analyzer. This way, the evolution of the optical signal traveling through optical fibers, especially, the pump depletion and the recurrence phenomenon are investigated. PMID:26698435
ATOMIC AND MOLECULAR PHYSICS: Four-parameter analytical local model potential for atoms
NASA Astrophysics Data System (ADS)
Yu, Fei; Sun, Jiu-Xun; Tian, Rong-Gang; Yang, Wei
2009-10-01
Analytical local model potential for modeling the interaction in an atom reduces the computational effort in electronic structure calculations significantly. A new four-parameter analytical local model potential is proposed for atoms Li through Lr, and the values of four parameters are shell-independent and obtained by fitting the results of Xa method. At the same time, the energy eigenvalues, the radial wave functions and the total energies of electrons are obtained by solving the radial Schrödinger equation with a new form of potential function by Numerov's numerical method. The results show that our new form of potential function is suitable for high, medium and low Z atoms. A comparison among the new potential function and other analytical potential functions shows the greater flexibility and greater accuracy of the present new potential function.
An analytically resolved model of a potato's thermal processing using Heun functions
NASA Astrophysics Data System (ADS)
Vargas Toro, Agustín.
2014-05-01
A potato's thermal processing model is solved analytically. The model is formulated using the equation of heat diffusion in the case of a spherical potato processed in a furnace, and assuming that the potato's thermal conductivity is radially modulated. The model is solved using the method of the Laplace transform, applying Bromwich Integral and Residue Theorem. The temperatures' profile in the potato is presented as an infinite series of Heun functions. All computations are performed with computer algebra software, specifically Maple. Using the numerical values of the thermal parameters of the potato and geometric and thermal parameters of the processing furnace, the time evolution of the temperatures in different regions inside the potato are presented analytically and graphically. The duration of thermal processing in order to achieve a specified effect on the potato is computed. It is expected that the obtained analytical results will be important in food engineering and cooking engineering.
Anisotropic Multishell Analytical Modeling of an Intervertebral Disk Subjected to Axial Compression.
Demers, Sébastien; Nadeau, Sylvie; Bouzid, Abdel-Hakim
2016-04-01
Studies on intervertebral disk (IVD) response to various loads and postures are essential to understand disk's mechanical functions and to suggest preventive and corrective actions in the workplace. The experimental and finite-element (FE) approaches are well-suited for these studies, but validating their findings is difficult, partly due to the lack of alternative methods. Analytical modeling could allow methodological triangulation and help validation of FE models. This paper presents an analytical method based on thin-shell, beam-on-elastic-foundation and composite materials theories to evaluate the stresses in the anulus fibrosus (AF) of an axisymmetric disk composed of multiple thin lamellae. Large deformations of the soft tissues are accounted for using an iterative method and the anisotropic material properties are derived from a published biaxial experiment. The results are compared to those obtained by FE modeling. The results demonstrate the capability of the analytical model to evaluate the stresses at any location of the simplified AF. It also demonstrates that anisotropy reduces stresses in the lamellae. This novel model is a preliminary step in developing valuable analytical models of IVDs, and represents a distinctive groundwork that is able to sustain future refinements. This paper suggests important features that may be included to improve model realism. PMID:26833355
A Semi-Analytical Model for Short Range Dispersion From Ground Sources
NASA Astrophysics Data System (ADS)
Gavze, E.; Fattal, E.; Reichman, R.
2014-12-01
A semi-analytical model for dispersion of passive scalars from ground sources up to distances of a few hundred meters is presented. Most widely used analytical models are Gaussian models which assume both a uniform wind field and homogeneous turbulence. These assumptions are not valid when ground sources are involved since both the wind and the turbulence depend on height. The model presented here is free of these two assumptions. The formulation of the vertical dispersion is based on approximating the vertical profiles of the wind and the the vertical diffusion coefficient, based on Monin Obukhov Similarity Theory, as power laws. One advantage of this approach is that it allows for non Gaussian vertical profiles of the concentration which better fit the experimental data. For the lateral dispersion the model still assumes a Gaussian form. A system of equations was developed to compute the cloud width. This system of equations is based on an analytical solution of a Langevin equation which takes into account the non-homogeneity of the wind and the turbulence in the vertical direction. The model was tested against two field experiments. Comparison with a Gaussian model showed that it performed much better in predicting both the integrated cross wind ground concentration and the cloud width. Analytical, or semi-analytical models are useful as they are simple to use and require only a short computation time, compared, for example, to Lagrangian Stochastic Models. The presented model is very efficient from the computational point of view. As such it is suitable for cases in which repeated computations of the concentration field are required, as for example in risk assessments and in the inverse problem of source determination.
Analytical and numerical modeling of non-collinear shear wave mixing at an imperfect interface.
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 additional 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. PMID:26482394
WFR-2D: an analytical model for PWAS-generated 2D ultrasonic guided wave propagation
NASA Astrophysics Data System (ADS)
Shen, Yanfeng; Giurgiutiu, Victor
2014-03-01
This paper presents WaveFormRevealer 2-D (WFR-2D), an analytical predictive tool for the simulation of 2-D ultrasonic guided wave propagation and interaction with damage. The design of structural health monitoring (SHM) systems and self-aware smart structures requires the exploration of a wide range of parameters to achieve best detection and quantification of certain types of damage. Such need for parameter exploration on sensor dimension, location, guided wave characteristics (mode type, frequency, wavelength, etc.) can be best satisfied with analytical models which are fast and efficient. The analytical model was constructed based on the exact 2-D Lamb wave solution using Bessel and Hankel functions. Damage effects were inserted in the model by considering the damage as a secondary wave source with complex-valued directivity scattering coefficients containing both amplitude and phase information from wave-damage interaction. The analytical procedure was coded with MATLAB, and a predictive simulation tool called WaveFormRevealer 2-D was developed. The wave-damage interaction coefficients (WDICs) were extracted from harmonic analysis of local finite element model (FEM) with artificial non-reflective boundaries (NRB). The WFR-2D analytical simulation results were compared and verified with full scale multiphysics finite element models and experiments with scanning laser vibrometer. First, Lamb wave propagation in a pristine aluminum plate was simulated with WFR-2D, compared with finite element results, and verified by experiments. Then, an inhomogeneity was machined into the plate to represent damage. Analytical modeling was carried out, and verified by finite element simulation and experiments. This paper finishes with conclusions and suggestions for future work.
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.
Prasher, Ravi; Tong, Tao; Majumdar, Arun
2008-01-01
We introduce simple approximate analytical models for phonon specific heat and ballistic thermal conductance of nanowires. The analytical model is in excellent agreement with the detailed numerical calculations based on the solution of the elastic wave equation and is also in good agreement with the ballistic thermal conductance data by Schwab et al. (Nature 2000, 404, 974). Finally, we propose a demarcating criterion in terms of temperature, dimension, and material properties to capture the dimensional crossover from a three-dimensional (3D) bulk system to a one-dimensional (1D) system.
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.
Useful measures and models for analytical quality management in medical laboratories.
Westgard, James O
2016-02-01
The 2014 Milan Conference "Defining analytical performance goals 15 years after the Stockholm Conference" initiated a new discussion of issues concerning goals for precision, trueness or bias, total analytical error (TAE), and measurement uncertainty (MU). Goal-setting models are critical for analytical quality management, along with error models, quality-assessment models, quality-planning models, as well as comprehensive models for quality management systems. There are also critical underlying issues, such as an emphasis on MU to the possible exclusion of TAE and a corresponding preference for separate precision and bias goals instead of a combined total error goal. This opinion recommends careful consideration of the differences in the concepts of accuracy and traceability and the appropriateness of different measures, particularly TAE as a measure of accuracy and MU as a measure of traceability. TAE is essential to manage quality within a medical laboratory and MU and trueness are essential to achieve comparability of results across laboratories. With this perspective, laboratory scientists can better understand the many measures and models needed for analytical quality management and assess their usefulness for practical applications in medical laboratories.
Analytical Model for Prediction of Reduced Strain Energy Release Rate of Single-Side-Patched Plates
NASA Astrophysics Data System (ADS)
Kwon, Y. W.; Lee, W. Y.; McGee, A. S.; Hart, D. C.; Loup, D. C.; Rasmussen, E. A.
2013-12-01
A study was undertaken to develop an analytical model that can predict how much reduction in Strain Energy Release Rate (SERR) can be achieved by repairing a cracked plate using a single-side bonded patch. The plate may be subjected to inplane or out-of-plane bending loading. Furthermore, the plate may be flat or curved in a cylindrical shape. The model helps to select patch material (i.e., elastic modulus of the material) and the appropriate patch size in order to reduce the SERR at the crack tip of the patched base plate. In other words, the analytical model can be utilized to select the patch material and patch dimensions required to achieve the desired SERR for a cracked base plate with known modulus, thickness, and crack size. The model is based on axial and bending stresses of the single-side strap joint configuration, which are related to the SERR at the crack tip of a plate with a single-side patch repair. In order to verify the analytical model, finite element analyses were conducted to determine stresses as well as SERR in many different patched plates. The numerical study confirmed the validity of the analytical model in predicting the reduction ratio of SERR resulting from the single-side patch repair.
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.
Analytical coupled vibroacoustic modeling of membrane-type acoustic metamaterials: membrane model.
Chen, Yangyang; Huang, Guoliang; Zhou, Xiaoming; Hu, Gengkai; Sun, Chin-Teh
2014-09-01
Membrane-type acoustic metamaterials (MAMs) have demonstrated unusual capacity in controlling low-frequency sound transmission/reflection. In this paper, an analytical vibroacoustic membrane model is developed to study sound transmission behavior of the MAM under a normal incidence. The MAM is composed of a prestretched elastic membrane with attached rigid masses. To accurately capture finite-dimension rigid mass effects on the membrane deformation, the point matching approach is adopted by applying a set of distributed point forces along the interfacial boundary between masses and the membrane. The accuracy and capability of the theoretical model is verified through the comparison with the finite element method. In particular, microstructure effects such as weight, size, and eccentricity of the attached mass, pretension, and thickness of the membrane on the resulting transmission peak and dip frequencies of the MAM are quantitatively investigated. New peak and dip frequencies are found for the MAM with one and multiple eccentric attached masses. The developed model can be served as an efficient tool for design of such membrane-type metamaterials. PMID:25190372
NASA Astrophysics Data System (ADS)
Mori, Takuro; Nakatani, Makoto; Tesfamariam, Solomon
2015-12-01
This paper presents analytical and numerical models for semirigid timber frame with Lagscrewbolt (LSB) connections. A series of static and reverse cyclic experimental tests were carried out for different beam sizes (400, 500, and 600 mm depth) and column-base connections with different numbers of LSBs (4, 5, 8). For the beam-column connections, with increase in beam depth, moment resistance and stiffness values increased, and ductility factor reduced. For the column-base connection, with increase in the number of LSBs, the strength, stiffness, and ductility values increased. A material model available in OpenSees, Pinching4 hysteretic model, was calibrated for all connection test results. Finally, analytical model of the portal frame was developed and compared with the experimental test results. Overall, there was good agreement with the experimental test results, and the Pinching4 hysteretic model can readily be used for full-scale structural model.
Towards an Analytical Age-Dependent Model of Contrast Sensitivity Functions for an Ageing Society.
Joulan, Karine; Brémond, Roland; Hautière, Nicolas
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
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
Analytical Solutions Involving Shock Waves for Testing Debris Avalanche Numerical Models
NASA Astrophysics Data System (ADS)
Mungkasi, Sudi; Roberts, Stephen Gwyn
2012-10-01
Analytical solutions to debris avalanche problems involving shock waves are derived. The debris avalanche problems are described in two different coordinate systems, namely, the standard Cartesian and topography-linked coordinate systems. The analytical solutions can then be used to test debris avalanche numerical models. In this article, finite volume methods are applied as the numerical models. We compare the performance of the finite volume method with reconstruction of the conserved quantities based on stage, height, and velocity to that of the conserved quantities based on stage, height, and momentum for solving the debris avalanche problems involving shock waves. The numerical solutions agree with the analytical solution. In addition, both reconstructions lead to similar numerical results. This article is an extension of the work of Mangeney et al. (Pure Appl Geophys 157(6-8):1081-1096, 2000).
NASA Astrophysics Data System (ADS)
Shi, Xun; Komatsu, Eiichiro; Nelson, Kaylea; Nagai, Daisuke
2015-03-01
Turbulent gas motion inside galaxy clusters provides a non-negligible non-thermal pressure support to the intracluster gas. If not corrected, it leads to a systematic bias in the estimation of cluster masses from X-ray and Sunyaev-Zel'dovich (SZ) observations assuming hydrostatic equilibrium, and affects interpretation of measurements of the SZ power spectrum and observations of cluster outskirts from ongoing and upcoming large cluster surveys. Recently, Shi & Komatsu developed an analytical model for predicting the radius, mass, and redshift dependence of the non-thermal pressure contributed by the kinetic random motions of intracluster gas sourced by the cluster mass growth. In this paper, we compare the predictions of this analytical model to a state-of-the-art cosmological hydrodynamics simulation. As different mass growth histories result in different non-thermal pressure, we perform the comparison on 65 simulated galaxy clusters on a cluster-by-cluster basis. We find an excellent agreement between the modelled and simulated non-thermal pressure profiles. Our results open up the possibility of using the analytical model to correct the systematic bias in the mass estimation of galaxy clusters. We also discuss tests of the physical picture underlying the evolution of intracluster non-thermal gas motions, as well as a way to further improve the analytical modelling, which may help achieve a unified understanding of non-thermal phenomena in galaxy clusters.
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…
Comparing factor analytic models of the DSM-IV personality disorders.
Huprich, Steven K; Schmitt, Thomas A; Richard, David C S; Chelminski, Iwona; Zimmerman, Mark A
2010-01-01
There is little agreement about the latent factor structure of the Diagnostic and Statistical Manual of Mental Disorders (DSM) personality disorders (PDs). Factor analytic studies over the past 2 decades have yielded different results, in part reflecting differences in factor analytic technique, the measure used to assess the PDs, and the changing DSM criteria. In this study, we explore the latent factor structure of the DSM (4th ed.; IV) PDs in a sample of 1200 psychiatric outpatients evaluated with the Structured Interview for DSM-IV PDs (B. Pfohl, N. Blum, & M. Zimmerman, 1997). We first evaluated 2 a priori models of the PDs with confirmatory factor analysis (CFA), reflecting their inherent organization in the DSM-IV: a 3-factor model and a 10-factor model. Fit statistics did not suggest that these models yielded an adequate fit. We then evaluated the latent structure with exploratory factor analysis (EFA). Multiple solutions produced more statistically and theoretically reasonable results, as well as providing clinically useful findings. On the basis of fit statistics and theory, 3 models were evaluated further--the 4-, 5-, and 10-factor models. The 10-factor model, which did not resemble the 10-factor model of the CFA, was determined to be the strongest of all 3 models. Future research should use contemporary methods of evaluating factor analytic results in order to more thoroughly compare various factor solutions.
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.
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. 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.
Efficient computation of net analyte signal vector in inverse multivariate calibration models.
Faber, N K
1998-12-01
The net analyte signal vector has been defined by Lorber as the part of a mixture spectrum that is unique for the analyte of interest; i.e., it is orthogonal to the spectra of the interferences. It plays a key role in the development of multivariate analytical figures of merit. Applications have been reported that imply its utility for spectroscopic wavelength selection as well as calibration method comparison. Currently available methods for computing the net analyte signal vector in inverse multivariate calibration models are based on the evaluation of projection matrices. Due to the size of these matrices (p × p, with p the number of wavelengths) the computation may be highly memory- and time-consuming. This paper shows that the net analyte signal vector can be obtained in a highly efficient manner by a suitable scaling of the regression vector. Computing the scaling factor only requires the evaluation of an inner product (p multiplications and additions). The mathematical form of the newly derived expression is discussed, and the generalization to multiway calibration models is briefly outlined.
NASA Astrophysics Data System (ADS)
Nastac, L.; Stefanescu, D. M.
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.
Sanderson, Ruth M; Catton, Philip P
2011-05-01
This paper presents an analytical modeling technique for the simulation of long-range ultrasonic guided waves in structures. The model may be used to predict the displacement field in a prismatic structure arising from any excitation arrangement and may therefore be used as a tool to design new inspection systems. It is computationally efficient and relatively simple to implement, yet gives accuracy similar to finite element analysis and semi-analytical finite element analysis methods. The model has many potential applications; one example is the optimization of part-circumferential arrays where access to the full circumference of the pipe is restricted. The model has been successfully validated by comparison with finite element solutions. Experimental validation has also been carried out using an array of piezoelectric transducer elements to measure the displacement field arising from a single transducer element in an 88.9-mm-diameter pipe. Good agreement has been obtained between the two models and the experimental data.
NASA Astrophysics Data System (ADS)
Lin, Zer-Ming; Lin, Horng-Chih; Liu, Keng-Ming; Huang, Tiao-Yuan
2012-02-01
In this study, we derive an analytical model of an electric potential of a double-gated (DG) fully depleted (FD) junctionless (J-less) transistor by solving the two-dimensional Poisson's equation. On the basis of this two-dimensional electric potential model, subthreshold current and swing can be calculated. Threshold voltage roll-off can also be estimated with analytical forms derived using the above model. The calculated results of electric potential, subthreshold current and threshold voltage roll-off are all in good agreement with the results of technology computer aided design (TCAD) simulation. The model proposed in this paper may help in the development of a compact model for simulation program with integrated circuit emphasis (SPICE) simulation and in providing deeper insights into the characteristics of short-channel J-less transistors.
Teaching Students to Write Literature Reviews: A Meta-Analytic Model.
ERIC Educational Resources Information Center
Froese, Arnold D.; Gantz, Brandon S.; Henry, Amanda L.
1998-01-01
Presents an integrated model for teaching students to write psychology literature reviews. Outlines a series of five writing tasks incorporating meta-analytical techniques. Describes a series of writing problems and provides solutions. Argues that such instruction, presented early in undergraduates' training, prepares them to write formal papers…
Analytic models of ducted turbomachinery tone noise sources. Volume 2: Subprogram documentation
NASA Technical Reports Server (NTRS)
Clark, T. L.; Ganz, U. W.; Graf, G. A.; Westall, J. S.
1974-01-01
Analytical models were developed for computing the periodic sound pressures of subsonic fans in an infinite hardwall annular duct with uniform flow. The computer programs are described which are used for numerical computations of sound pressure mode amplitudes. The data are applied to the acoustic properties of turbomachinery.
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…
Analytical Advection-Dispersion Model for Transport and Plant Uptake of Solutes in the Root Zone
Technology Transfer Automated Retrieval System (TEKTRAN)
We develop an advective-dispersive solute transport equation that includes plant uptake of water and solute, and present an analytical solution. Assumptions underlying the transport model include linear solute sorption, first-order plant uptake, and a uniform soil water content. We examine the lat...
ERIC Educational Resources Information Center
Bozdogan, Hamparsum
1987-01-01
This paper studies the general theory of Akaike's Information Criterion (AIC) and provides two analytical extensions. The extensions make AIC asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the two models. The criteria are applied in two Monte Carlo experiments. (Author/GDC)
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
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 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)
A semi-analytic model for localized variable charge dust acoustic waves
Tribeche, Mouloud; Gougam, Leila Ait; Aoutou, Kamal
2006-09-15
A semi-analytic model for nonlinear variable charge dust acoustic waves is outlined. It is shown that rarefactive variable charge dust acoustic solitons involving cusped density humps can exist. The effects of dust dynamics as well as equilibrium dust charge on these nonlinear localized structures are briefly discussed.
NASA Technical Reports Server (NTRS)
Friedmann, P. P.; Venkatesan, C.
1988-01-01
The results of an analytical study aimed at predicting the aeromechanical stability of a helicopter in ground resonance, with the inclusion of aerodynamic forces are presented. The theoretical results are found to be in good agreement with the experimental results, available in literature, indicating that the coupled rotor/fuselage system can be represented by a reasonably simple mathematical model.