Analytically solvable processes on networks.
Smilkov, Daniel; Kocarev, Ljupco
2011-07-01
We introduce a broad class of analytically solvable processes on networks. In the special case, they reduce to random walk and consensus process, the two most basic processes on networks. Our class differs from previous models of interactions (such as the stochastic Ising model, cellular automata, infinite particle systems, and the voter model) in several ways, the two most important being (i) the model is analytically solvable even when the dynamical equation for each node may be different and the network may have an arbitrary finite graph and influence structure and (ii) when local dynamics is described by the same evolution equation, the model is decomposable, with the equilibrium behavior of the system expressed as an explicit function of network topology and node dynamics. PMID:21867254
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.
NASA Astrophysics Data System (ADS)
Makarov, Dmitrii E.
2013-01-01
Conformational rearrangements in biomolecules (such as protein folding or enzyme-ligand binding) are often interpreted in terms of low-dimensional models of barrier crossing such as Kramers' theory. Dimensionality reduction, however, entails memory effects; as a result, the effective frictional drag force along the reaction coordinate nontrivially depends on the time scale of the transition. Moreover, when both solvent and "internal" friction effects are important, their interplay results in a highly nonlinear dependence of the effective friction on solvent viscosity that is not captured by common phenomenological models of barrier crossing. Here, these effects are illustrated using an analytically solvable toy model of an unstructured polymer chain involved in an inter- or intramolecular transition. The transition rate is calculated using the Grote-Hynes and Langer theories, which—unlike Kramers' theory—account for memory. The resulting effective frictional force exerted by the polymer along the reaction coordinate can be rationalized in terms of the effective number of monomers engaged in the transition. Faster transitions (relative to the polymer reconfiguration time scale) involve fewer monomers and, correspondingly, lower friction forces, because the polymer chain does not have enough time to reconfigure in response to the transition.
Novel quasi-exactly solvable models with anharmonic singular potentials
Agboola, Davids Zhang, Yao-Zhong
2013-03-15
We present new quasi-exactly solvable models with inverse quartic, sextic, octic and decatic power potentials, respectively. We solve these models exactly by means of the functional Bethe ansatz method. For each case, we give closed-form solutions for the energies and the wave functions as well as analytical expressions for the allowed potential parameters in terms of the roots of a set of algebraic equations. - Highlights: Black-Right-Pointing-Pointer The quasi-exactly solvable treatments of a class of singular anharmonic models. Black-Right-Pointing-Pointer Exact solutions to a class of integer power singular potential. Black-Right-Pointing-Pointer Solutions obtained in terms of the roots to the Bethe ansatz equations. Black-Right-Pointing-Pointer Results useful in describing diatomic molecules and elastic differential cross sections for high energy scattering.
Diffraction in time: An exactly solvable model
NASA Astrophysics Data System (ADS)
Goussev, Arseni
2014-03-01
In optics, diffraction is typically portrayed as deflection of light incident upon an obstacle with sharp boundaries, that can not be accounted for by reflection or refraction. Interestingly, quantum mechanics allows for an additional, intrinsically time-dependent manifestation of the phenomenon: Owing to the dispersive nature of quantum matter waves, sudden changes in boundary conditions may cause the particle wave function to develop interference fringes akin to those in stationary (optical) diffraction problems. This phenomenon, pioneered in 1952 by Moshinsky [Phys. Rev. 88, 625 (1952)] and presently referred to as ``diffraction in time,'' is at the heart of a vibrant area of experimental and theoretical research concerned with quantum transients. In my talk, I will introduce a new versatile exactly-solvable model of diffraction in time. The model describes dynamics of a quantum particle in the presence of an absorbing time-dependent barrier, and enables a quantitative description of diffraction and interference patterns in a large variety of setups.
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
Band structure analysis of an analytically solvable Hill equation with continuous potential
NASA Astrophysics Data System (ADS)
Morozov, G. V.; Sprung, D. W. L.
2015-03-01
This paper concerns analytically solvable cases of Hill’s equation containing a continuously differentiable periodic potential. We outline a procedure for constructing the Floquet-Bloch fundamental system, and analyze the band structure of the system. The similarities to, and differences from, the cases of a piecewise constant periodic potential and the Mathieu potential, are illuminated.
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. PMID:15323678
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.
Planar hydrogen-like atom in inhomogeneous magnetic fields: Exactly or quasi-exactly solvable models
NASA Astrophysics Data System (ADS)
Liu, Liyan; Hao, Qinghai
2015-05-01
We use a simple mathematical method to solve the problem of a two-dimensional hydrogen-like atom in the inhomogeneous magnetic fields B = ( k/ r)z and B = ( k/ r 3)z. We construct a Hamiltonian that takes the same form as the Hamiltonian of a hydrogen-like atom in the homogeneous magnetic fields and obtain the energy spectrum by comparing the Hamiltonians. The results show that the whole spectrum of the atom in the magnetic field B = ( k/ r)z can be obtained, and the problem is exactly solvable in this case. We find analytic solutions of the Schrödinger equation for the atom in the magnetic field B = ( k/ r 3)z for particular values of the magnetic strength k and thus present a quasi-exactly solvable model.
Simplified Exactly Solvable Model for β-Amyloid Aggregation
NASA Astrophysics Data System (ADS)
Zamparo, M.; Trovato, A.; Maritan, A.
2010-09-01
We propose an exactly solvable simplified statistical mechanical model for the thermodynamics of β-amyloid aggregation, generalizing a well-studied model for protein folding. The monomer concentration is explicitly taken into account as well as a nontrivial dependence on the microscopic degrees of freedom of the single peptide chain, both in the α-helix folded isolated state and in the fibrillar one. The phase diagram of the model is studied and compared to the outcome of fibril formation experiments which is qualitatively reproduced.
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.
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. PMID:26931585
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.
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.
Decoherence and Exponential Law: A Solvable Model
NASA Technical Reports Server (NTRS)
Pascazio, Saverio; Namiki, Mikio
1996-01-01
We analyze a modified version of the 'AgBr' Hamiltonian, solve exactly the equations of motion in terms of SU(2) coherent states, and study the weak-coupling, macroscopic limit of the model, obtaining an exponential behavior at all times. The asymptotic dominance of the exponential behavior is representative of a purely stochastic evolution and can be derived quantum mechanically in the so-called van Hove's limit (which is a weak-coupling, macroscopic limit). At the same time, a temporal behavior of the exponential type, yielding a 'probability dissipation' is closely related to dephasing ('decoherence') effects and one can expect a close connection with a dissipative and irreversible behavior. We stress the central relevance of the problem of dissipation to the quantum measurement theory and to the general topic of decoherence.
An Exactly Solvable Supersymmetric Model of Semimagic Nuclei
Balantekin, A. B.; Gueven, Nurtac; Pehlivan, Yamac
2008-11-11
A simple model of nucleons coupled to angular momentum zero (s-pairs) occupying the valance shell of a semi-magic nuclei is considered. The model has a separable, orbit dependent pairing interaction which dominates over the kinetic term. It is shown that such an interaction leads to an exactly solvable model whose (0{sup +}) eigenstates and energies can be computed very easily with the help of the algebraic Bethe ansatz method. It is also shown that the model has a supersymmetry which connects the spectra of some semimagic nuclei. The results obtained from this model for the semimagic Ni isotopes from {sup 58}Ni to {sup 68}Ni are given. In addition, a new and easier technique for calculating the energy eigenvalues from the Bethe ansatz equations is also presented.
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 four-state Landau-Zener model of two interacting qubits with path interference
NASA Astrophysics Data System (ADS)
Sinitsyn, N. A.
2015-11-01
I identify a nontrivial four-state Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. The model describes an experimentally accessible system of two interacting qubits, such as a localized state in a Dirac material with both valley and spin degrees of freedom or a singly charged quantum dot (QD) molecule with spin orbit coupling. Application of the linearly time-dependent magnetic field induces a sequence of quantum level crossings with possibility of interference of different trajectories in a semiclassical picture. I argue that this system satisfies the criteria of integrability in the multistate Landau-Zener theory, which allows one to derive explicit exact analytical expressions for the transition probability matrix. I also argue that this model is likely a special case of a larger class of solvable systems, and present a six-state generalization as an example.
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.
NASA Astrophysics Data System (ADS)
Ben-Zion, Daniel; Das, Diptarka; McGreevy, John
2016-04-01
We develop a scheme to make exactly solvable gauge theories whose electric flux lines host (1+1)-dimensional topological phases. We use this exact "decorated-string-net" framework to construct several classes of interesting models. In particular, we construct an exactly solvable model of a quantum spin liquid whose (gapped) elementary excitations form doublets under an internal symmetry, and hence may be regarded as spin-carrying spinons. The model may be formulated, and is solvable, in any number of dimensions on any bipartite graph. Another example, in any dimension, has Z2 topological order and anyons which are Kramers' doublets of time-reversal symmetry. Further, we make exactly solvable models of three-dimensional topological paramagnets.
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.
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.
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}
Entanglement, decoherence and thermal relaxation in exactly solvable models
NASA Astrophysics Data System (ADS)
Lychkovskiy, Oleg
2011-07-01
Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression describing the evolution of the reduced density matrix. This expression proves to be tractable when the combined closed system (i.e. open system plus environment) is integrable. Then we focus on comparing decoherence and thermalization timescales in the XX chain. We find that for a single spin these timescales are comparable, in contrast to what should be expected for a macroscopic body. This indicates that the process of quantum relaxation of a system with few accessible states can not be separated in two distinct stages - decoherence and thermalization. Finally, we turn to finite-size effects in the time evolution of a single spin in the XY chain. We observe three consecutive stages of the evolution: regular evolution, partial revivals, irregular (apparently chaotic) evolution. The duration of the regular stage is proportional to the number of spins in the chain. We observe a "quiet and cold period" in the end of the regular stage, which breaks up abruptly at some threshold time.
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
Non-cooperative Brownian donkeys: A solvable 1D model
NASA Astrophysics Data System (ADS)
Jiménez de Cisneros, B.; Reimann, P.; Parrondo, J. M. R.
2003-12-01
A paradigmatic 1D model for Brownian motion in a spatially symmetric, periodic system is tackled analytically. Upon application of an external static force F the system's response is an average current which is positive for F < 0 and negative for F > 0 (absolute negative mobility). Under suitable conditions, the system approaches 100% efficiency when working against the external force F.
Localized Majorana-Like Modes in a Number-Conserving Setting: An Exactly Solvable Model
NASA Astrophysics Data System (ADS)
Iemini, Fernando; Mazza, Leonardo; Rossini, Davide; Fazio, Rosario; Diehl, Sebastian
2015-10-01
In this Letter we present, in a number conserving framework, a model of interacting fermions in a two-wire geometry supporting nonlocal zero-energy Majorana-like edge excitations. The model has an exactly solvable line, on varying the density of fermions, described by a topologically nontrivial ground state wave function. Away from the exactly solvable line we study the system by means of the numerical density matrix renormalization group. We characterize its topological properties through the explicit calculation of a degenerate entanglement spectrum and of the braiding operators which are exponentially localized at the edges. Furthermore, we establish the presence of a gap in its single particle spectrum while the Hamiltonian is gapless, and compute the correlations between the edge modes as well as the superfluid correlations. The topological phase covers a sizable portion of the phase diagram, the solvable line being one of its boundaries.
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
On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations
Zhang, Yao-Zhong
2013-10-15
We study the solvability of the time-independent matrix Schrödinger differential equations of the quantum Rabi model and its 2-photon and two-mode generalizations in Bargmann Hilbert spaces of entire functions. We show that the Rabi model and its 2-photon and two-mode analogs are quasi-exactly solvable. We derive the exact, closed-form expressions for the energies and the allowed model parameters for all the three cases in the solvable subspaces. Up to a normalization factor, the eigenfunctions for these models are given by polynomials whose roots are determined by systems of algebraic equations.
A solvable model of hard rods with gravitational interactions
NASA Astrophysics Data System (ADS)
Champion, M.; Alastuey, A.
2015-01-01
We consider a simple 1D model of hard rods with gravitational interactions. First, we consider the situation where the sytem is enclosed in a box with finite size and we exactly compute the equilibrium thermodynamical quantities. Thanks to the confining nature of gravity in 1D which prevents evaporation, the box can be released and we can study an open system with its center of mass fixed. Then, we exactly compute the corresponding equilibrium density profile within the microcanonical ensemble. All those analytical results are discussed in connection with the general issue of ensemble inequivalences for systems with long-range interactions. They also provide specific tests for the reliability of the hydrostatic approach combined with a mean-field treatment of gravitational interactions. In particular, the hydrostatic approach is shown to fail for energies close to the collapse energy where a core-halo structure emerges.
Quasi-exactly solvable relativistic soft-core Coulomb models
Agboola, Davids Zhang, Yao-Zhong
2012-09-15
By considering a unified treatment, we present quasi exact polynomial solutions to both the Klein-Gordon and Dirac equations with the family of soft-core Coulomb potentials V{sub q}(r)=-Z/(r{sup q}+{beta}{sup q}){sup 1/q}, Z>0, {beta}>0, q{>=}1. We consider cases q=1 and q=2 and show that both cases are reducible to the same basic ordinary differential equation. A systematic and closed form solution to the basic equation is obtained using the Bethe ansatz method. For each case, the expressions for the energies and the allowed parameters are obtained analytically and the wavefunctions are derived in terms of the roots of a set of Bethe ansatz equations. - Highlights: Black-Right-Pointing-Pointer The relativistic bound-state solutions of the soft-core Coulomb models. Black-Right-Pointing-Pointer Quasi-exact treatments of the Dirac and Klein-Gordon equations for the soft-core Coulomb models. Black-Right-Pointing-Pointer Solutions obtained in terms of the roots to the Bethe ansatz equations. Black-Right-Pointing-Pointer The hidden Lie algebraic structure discussed for the models. Black-Right-Pointing-Pointer Results useful in describing mesonic atoms and interaction of intense laser fields with atom.
Isovector Pairing within the so(5) Richardson-Gaudin Exactly Solvable Model
Dimitrova, S S; Dukelsky, J; Gueorguiev, V G; Van Isacker, P
2005-10-10
Properties of a nucleon system interacting via isovector proton-neutron pairing can be described within the so(5) generalized Richardson-Gaudin exactly-solvable model [1]. We present results for a system of 12 nucleon pairs within the full f{sub p} + g{sub 9/2} shell-model space. We discuss coupling constant dependence of the pair energies, total energy of the system, and the occupation numbers.
Universal Finite Size Corrections and the Central Charge in Non-solvable Ising Models
NASA Astrophysics Data System (ADS)
Giuliani, Alessandro; Mastropietro, Vieri
2013-11-01
We investigate a non-solvable two-dimensional ferromagnetic Ising model with nearest neighbor plus weak finite range interactions of strength λ. We rigorously establish one of the predictions of Conformal Field Theory (CFT), namely the fact that at the critical temperature the finite size corrections to the free energy are universal, in the sense that they are exactly independent of the interaction. The corresponding central charge, defined in terms of the coefficient of the first subleading term to the free energy, as proposed by Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2 for all and λ 0 a small but finite convergence radius. This is one of the very few cases where the predictions of CFT can be rigorously verified starting from a microscopic non solvable statistical model. The proof uses a combination of rigorous renormalization group methods with a novel partition function inequality, valid for ferromagnetic interactions.
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
Analytically solvable two-level quantum systems and Landau-Zener interferometry
NASA Astrophysics Data System (ADS)
Barnes, Edwin
2013-07-01
A simple algorithm is presented based on a type of partial reverse engineering that generates an unlimited number of exact analytical solutions to the Schrödinger equation for a general time-dependent two-level Hamiltonian. I demonstrate this method by deriving exact solutions corresponding to fast control pulses that contain arbitrarily many tunable parameters. It is shown that the formalism is naturally suited to generating analytical control protocols that perform precise nonadiabatic rapid passage and Landau-Zener interferometry near the quantum speed limit. A general, exact formula for Landau-Zener interference patterns is derived.
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.
Numerically Solvable Model for Resonant Collisions of Electronswith Diatomic Molecules
Houfek, Karel; Rescigno, T.N.; McCurdy, C.W.
2006-01-27
We describe a simple model for electron-molecule collisions that has one nuclear and one electronic degree of freedom and that can be solved to arbitrarily high precision, without making the Born-Oppenheimer approximation, by employing a combination of the exterior complex scaling method and a finite-element implementation of the discrete variable representation. We compare exact cross sections for vibrational excitation and dissociative attachment with results obtained using the local complex potential approximation as commonly applied in the ''boomerang'' model, and suggest how this two-dimensional model can be used to test the underpinnings of contemporary nonlocal approximations to resonant collisions.
Solvable null model for the distribution of word frequencies
NASA Astrophysics Data System (ADS)
Fontanari, J. F.; Perlovsky, L. I.
2004-10-01
Zipf’s law asserts that in all natural languages the frequency of a word is inversely proportional to its rank. The significance, if any, of this result for language remains a mystery. Here we examine a null hypothesis for the distribution of word frequencies, a so-called discourse-triggered word choice model, which is based on the assumption that the more a word is used, the more likely it is to be used again. We argue that this model is equivalent to the neutral infinite-alleles model of population genetics and so the degeneracy of the different words composing a sample of text is given by the celebrated Ewens sampling formula [Theor. Pop. Biol. 3, 87 (1972)], which we show to produce an exponential distribution of word frequencies.
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.
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
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.
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
2016-01-01
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
Alternative solvable description of the E(5) critical point symmetry in the interacting boson model
NASA Astrophysics Data System (ADS)
Pan, Feng; Zhang, Yu; Xu, Hao-Cheng; Dai, Lian-Rong; Draayer, J. P.
2015-03-01
A solvable extended Hamiltonian that includes multipair interactions among s and d bosons up to infinite order within the framework of the interacting boson model (IBM) is proposed to gain a better description of E(5) model results for finite-N systems. Numerical fits to low-lying energy levels and reduced E 2 transition rates within this extended version of the theory are presented for various N values. The fits show that the extended Hamiltonian within the IBM provides a better description of the E(5) model results for small-N cases, while the results of the model in the large-N cases are close to those of the E (5 )-β2 n type models studied previously.
Microcanonical work and fluctuation relations for an open system: An exactly solvable model.
Subaşı, Y; Jarzynski, C
2013-10-01
We calculate the probability distribution of work for an exactly solvable model of a system interacting with its environment. The system of interest is a harmonic oscillator with a time-dependent control parameter, the environment is modeled by N-independent harmonic oscillators with arbitrary frequencies, and the system-environment coupling is bilinear and not necessarily weak. The initial conditions of the combined system and environment are sampled from a microcanonical distribution and the system is driven out of equilibrium by changing the control parameter according to a prescribed protocol. In the limit of infinitely large environment, i.e., N→∞, we recover the nonequilibrium work relation and Crooks's fluctuation relation. Moreover, the microcanonical Crooks relation is verified for finite environments. Finally, we show the equivalence of multitime correlation functions of the system in the infinite environment limit for canonical and microcanonical ensembles. PMID:24229144
A set of exactly solvable Ising models with half-odd-integer spin
NASA Astrophysics Data System (ADS)
Rojas, Onofre; de Souza, S. M.
2009-03-01
We present a set of exactly solvable Ising models, with half-odd-integer spin- S on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed half-odd-integer spin- (S,1/2) and only nearest-neighbor interaction, allow us to map this system either onto a purely spin-1/2 lattice or onto a purely spin- S lattice. By imposing the condition that the mixed half-odd-integer spin- (S,1/2) lattice must have an exact solution, we found a set of exact solutions that satisfy the free fermion condition of the eight vertex model. The number of solutions for a general half-odd-integer spin- S is given by S+1/2. Therefore we conclude that this transformation is equivalent to a simple spin transformation which is independent of the coordination number.
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 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)
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
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.
NASA Astrophysics Data System (ADS)
Bogolubov, N. N.; Prykarpatsky, Y. A.
2013-03-01
An approach to describing nonlinear Lax type integrable dynamical systems of modern mathematical and theoretical physics, based on the Marsden-Weinstein reduction method on canonically symplectic manifolds with group symmetry, is proposed. Its natural relationship with the well-known Adler-Kostant-Souriau-Berezin-Kirillov method and the associated R-matrix approach is analyzed. A new generalized exactly solvable spatially one-dimensional quantum superradiance model, describing a charged fermionic medium interacting with external electromagnetic field, is suggested. The Lax type operator spectral problem is presented, the related R-structure is calculated. The Hamilton operator renormalization procedure subject to a physically stable vacuum is described, the quantum excitations and quantum solitons, related with the thermodynamical equilibrity of the model, are discussed.
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
NASA Astrophysics Data System (ADS)
Boyer, D.; Romo-Cruz, J. C. R.
2014-10-01
Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random-walk model with long-range memory for which not only the mean-square displacement (MSD) but also the propagator can be obtained exactly in the asymptotic limit. The model consists of a random walker on a lattice, which, at a constant rate, stochastically relocates at a site occupied at some earlier time. This time in the past is chosen randomly according to a memory kernel, whose temporal decay can be varied via an exponent parameter. In the weakly non-Markovian regime, memory reduces the diffusion coefficient from the bare value. When the mean backward jump in time diverges, the diffusion coefficient vanishes and a transition to an anomalous subdiffusive regime occurs. Paradoxically, at the transition, the process is an anticorrelated Lévy flight. Although in the subdiffusive regime the model exhibits some features of the continuous time random walk with infinite mean waiting time, it belongs to another universality class. If memory is very long-ranged, a second transition takes place to a regime characterized by a logarithmic growth of the MSD with time. In this case the process is asymptotically Gaussian and effectively described as a scaled Brownian motion with a diffusion coefficient decaying as 1 /t .
Schulze-Halberg, Axel; García-Ravelo, Jesús; Pacheco-García, Christian; Juan Peña Gil, José
2013-06-15
We consider the Schrödinger equation in the Thomas–Fermi field, a model that has been used for describing electron systems in δ-doped semiconductors. It is shown that the problem becomes exactly-solvable if a particular effective (position-dependent) mass distribution is incorporated. Orthogonal sets of normalizable bound state solutions are constructed in explicit form, and the associated energies are determined. We compare our results with the corresponding findings on the constant-mass problem discussed by Ioriatti (1990) [13]. -- Highlights: ► We introduce an exactly solvable, position-dependent mass model for the Thomas–Fermi potential. ► Orthogonal sets of solutions to our model are constructed in closed form. ► Relation to delta-doped semiconductors is discussed. ► Explicit subband bottom energies are calculated and compared to results obtained in a previous study.
NASA Astrophysics Data System (ADS)
Fakhri, H.; Chenaghlou, A.
2007-05-01
Introducing p - 1 new parameters into the multilinear relations, we extend the standard unitary parasupersymmetry algebra of order p so that by embedding the quantum solvable models possessing gl(2, c) Lie algebra symmetry into it, the partitions of integer numbers p - 1 and \\frac{1}{2}p(p-1) are established. These two partitions are performed by the new parameters and the product of new parameters with their labels, respectively. The former partition is just necessary for the real form h4; however, both of them are essential for the real forms u(2) and u(1, 1). By occupying these parameters with arbitrary values, the energy spectra are determined by the mean value of proposed parameters for the real form h4 with their label weight function as well as for the real forms u(2) and u(1, 1) with the weight function of their squared label. So for the given energies, the multilinear behaviour of parasupercharges is not specified uniquely by varying the new parameters continuously.
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.
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
Exactly Solvable Wormhole and Cosmological Models with a Barotropic Equation of State
NASA Astrophysics Data System (ADS)
Kuhfittig, P. K. F.
An exact solution of the Einstein field equations given the barotropic equation of state $p=\\omega\\rho$ yields two possible models: (1) if $\\omega <-1$, we obtain the most general possible anisotropic model for wormholes supported by phantom energy and (2) if $\\omega >0$, we obtain a model for galactic rotation curves. Here the equation of state represents a perfect fluid which may include dark matter. These results illustrate the power and usefulness of exact solutions.
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.
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.
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)] and the information refrigerator [Phys. Rev. Lett. 111, 030602 (2013)], 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. PMID:26172671
An exactly solvable spherical mean-field plus extended monopole pairing model
NASA Astrophysics Data System (ADS)
Pan, Feng; Ding, Xiaoxue; Launey, Kristina D.; Li, Hui; Xu, Xinxin; Draayer, Jerry P.
2016-03-01
An extended pairing Hamiltonian that describes pairing interactions among monopole nucleon pairs up to an infinite order in a spherical mean field, such as the spherical shell model, is proposed based on the local E˜2 algebraic structure, which includes the extended pairing interaction within a deformed mean-field theory (Pan et al., 2004) [19] as a special case. The advantage of the model lies in the fact that numerical solutions of the model can be obtained more easily and with less computational time than the solutions to the standard pairing model. Thus, open-shell large-scale calculations within the model become feasible. As an example of the application, pairing contribution to the binding energy of 12-28O is estimated in the present model with neutron pairs allowed to occupy a no-core shell model space of 11 j-orbits up to the fifth major harmonic oscillator shell including excitations up to 14 ħω for 12O and up to 40 ħω for 28O. The results for 12O are also compared and found to be in agreement with those of ab initio calculations. It is shown that the pairing energy per particle in 12-28O ranges from 0.4 to 1.8 MeV/A with the strongest one observed for a small number of pairs.
Quantum phase transitions in exactly solvable one-dimensional compass models
NASA Astrophysics Data System (ADS)
You, Wen-Long; Horsch, Peter; Oleś, Andrzej M.
2014-03-01
We present an exact solution for a class of one-dimensional compass models which stand for interacting orbital degrees of freedom in a Mott insulator. By employing the Jordan-Wigner transformation we map these models on noninteracting fermions and discuss how spin correlations, high degeneracy of the ground state, and Z2 symmetry in the quantum compass model are visible in the fermionic language. Considering a zigzag chain of ions with singly occupied eg orbitals (eg orbital model) we demonstrate that the orbital excitations change qualitatively with increasing transverse field, and that the excitation gap closes at the quantum phase transition to a polarized state. This phase transition disappears in the quantum compass model with maximally frustrated orbital interactions which resembles the Kitaev model. Here we find that the finite transverse field destabilizes the orbital-liquid ground state with macroscopic degeneracy, and leads to peculiar behavior of the specific heat and orbital susceptibility at finite temperature. We show that the entropy and the cooling rate at finite temperature exhibit quite different behavior near the critical point for these two models.
Work and information processing in a solvable model of Maxwell’s demon
Mandal, Dibyendu; Jarzynski, Christopher
2012-01-01
We describe a minimal model of an autonomous Maxwell demon, a device that delivers work by rectifying thermal fluctuations while simultaneously writing information to a memory register. We solve exactly for the steady-state behavior of our model, and we construct its phase diagram. We find that our device can also act as a “Landauer eraser”, using externally supplied work to remove information from the memory register. By exposing an explicit, transparent mechanism of operation, our model offers a simple paradigm for investigating the thermodynamics of information processing by small systems. PMID:22753515
University Macro Analytic Simulation Model.
ERIC Educational Resources Information Center
Baron, Robert; Gulko, Warren
The University Macro Analytic Simulation System (UMASS) has been designed as a forecasting tool to help university administrators budgeting decisions. Alternative budgeting strategies can be tested on a computer model and then an operational alternative can be selected on the basis of the most desirable projected outcome. UMASS uses readily…
Analytic Time Depending Galaxy Models
NASA Astrophysics Data System (ADS)
Sala, F.
1990-11-01
RESUMEN. Considerando las hip6tesis de Chandrasekhar para el estudjo de la GalActicaq se han desarrollado varios modelos analiticos integrables con simetria axial y dependientes del . . By considering Chandrasekhar hypotheses +or the study o+ Galactic Dynamics, several integrable analytic axisymmetric time-depending galactic models have been developed. Ke ords; GALAXY-DYNAMICS - GALAXY-STRUCTURE
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.
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
Correlation effects in sequential energy branching: an exactly solvable model of Fano statistics.
Subashiev, Arsen V; Luryi, Serge
2010-02-01
Correlation effects in the fluctuation of the number of particles in the process of energy branching by sequential impact ionizations are studied using an exactly soluble model of random parking on a line. The Fano factor F calculated in an uncorrelated final-state "shot-glass" model does not give an accurate answer even with the exact gap-distribution statistics. Allowing for the nearest-neighbor correlation effects gives a correction to F that brings F very close to its exact value. We discuss the implications of our results for energy resolution of semiconductor gamma detectors, where the value of F is of the essence. We argue that F is controlled by correlations in the cascade energy branching process and hence the widely used final-state model estimates are not reliable--especially in the practically relevant cases when the energy branching is terminated by competition between impact ionization and phonon emission. PMID:20365546
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…
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.
Statistics of heat generated in a solvable dissipative Landau-Zener model
NASA Astrophysics Data System (ADS)
Ponomarenko, V. V.
2015-07-01
We consider an adiabatic Landau-Zener model of a two-level system diagonally coupled to an Ohmic bosonic bath of large spectral width and, through fermionization, derive its exact solution at a special value of the coupling constant. From this solution we obtain the characteristic function of the distribution of energy transferred to the bath during the evolution of the system ground state as a functional determinant of a single-particle operator. At zero temperature this distribution is further found to be exponential, and at finite temperature the first three moments of the distribution are calculated.
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.
Comparative study of non-Markovianity measures in exactly solvable one- and two-qubit models
NASA Astrophysics Data System (ADS)
Addis, Carole; Bylicka, Bogna; Chruściński, Dariusz; Maniscalco, Sabrina
2014-11-01
In this paper we present a detailed critical study of several recently proposed non-Markovianity measures. We analyze their properties for single-qubit and two-qubit systems in both pure-dephasing and dissipative scenarios. More specifically we investigate and compare their computability, their physical meaning, their Markovian to non-Markovian crossover, and their additivity properties with respect to the number of qubits. The bottom-up approach that we pursue is aimed at identifying similarities and differences in the behavior of non-Markovianity indicators in several paradigmatic open system models. This, in turn, allows us to infer the leading traits of the variegated phenomenon known as non-Markovian dynamics.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Links, Jon; Moghaddam, Amir; Zhang, Yao-Zhong
2013-08-01
We demonstrate the occurrence of free quasi-particle excitations obeying generalized exclusion statistics in a BCS model with asymmetric pair scattering. The results are derived from an exact solution of the Hamiltonian, which was obtained via the algebraic Bethe ansatz utilizing the representation theory of an underlying Yangian algebra. The free quasi-particle excitations are associated with highest weight states of the Yangian algebra, corresponding to a class of analytic solutions of the Bethe ansatz equations.
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.
NASA Astrophysics Data System (ADS)
Schütz, Gunter M.; de Almeida Prado, Fernando Pigeard; Harris, Rosemary J.; Belitsky, Vladimir
2009-10-01
We introduce a stochastic heterogeneous interacting-agent model for the short-time non-equilibrium evolution of excess demand and price in a stylized asset market. We consider a combination of social interaction within peer groups and individually heterogeneous fundamentalist trading decisions which take into account the market price and the perceived fundamental value of the asset. The resulting excess demand is coupled to the market price. Rigorous analysis reveals that this feedback may lead to price oscillations, a single bounce, or monotonic price behaviour. The model is a rare example of an analytically tractable interacting-agent model which allows us to deduce in detail the origin of these different collective patterns. For a natural choice of initial distribution, the results are independent of the graph structure that models the peer network of agents whose decisions influence each other.
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.
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 Antenna Sheaths
NASA Astrophysics Data System (ADS)
D'Ippolito, D. A.; Myra, J. R.
2008-11-01
RF sheaths are generated on ICRF antennas whenever the launched fast wave also drives a slow wave, e.g. when the magnetic field is tilted (not perpendicular to the current straps). A new approach to sheath modeling was recently proposed in which the RF waves are computed using a modified boundary condition at the sheath surface to describe the plasma-sheath coupling. Here, we illustrate the use of the sheath BC for antenna sheaths by a model electromagnetic perturbation calculation, treating the B field tilt as a small parameter. Analytic expressions are obtained for the sheath voltage and the rf electric field parallel to B in both sheath and plasma regions, including the Child-Langmuir (self-consistency) constraint. It is shown that the plasma corrections to the sheath voltage (which screen the rf field) can be important. The simple vacuum-field sheath-voltage estimate is obtained as a limiting case. Implications for antenna codes such as TOPICA will be discussed. D.A. D'Ippolito and J.R. Myra, Phys. Plasmas 13, 102508 (2006). V. Lancellotti et al., Nucl. Fusion 46, S476 (2006).
Znojil, Miloslav
2013-09-15
It is known that the practical use of non-Hermitian (i.e., typically, PT-symmetric) phenomenological quantum Hamiltonians H≠H{sup †} requires an efficient reconstruction of an ad hoc Hilbert-space metric Θ=Θ(H) which would render the time-evolution unitary. Once one considers just the N-dimensional matrix toy models H=H{sup (N)}, the matrix elements of Θ(H) may be defined via a coupled set of N{sup 2} polynomial equations. Their solution is a typical task for computer-assisted symbolic manipulations. The feasibility of such a model-completion construction is illustrated here via a discrete square well model H=p{sup 2}+V endowed with a k-parametric close-to-the-boundary interaction V. The model is shown to possess (possibly, multiply degenerate) exceptional points marking the phase transitions which are attributable, due to the exact solvability of the model at any N<∞, to the loss of the regularity of the metric. In the parameter-dependence of the energy spectrum near these singularities one encounters a broad variety of alternative, topologically non-equivalent scenarios. -- Highlights: •New elementary non-Hermitian quantum Hamiltonians with real spectra proposed. •Exceptional points found and studied. •Non-equivalent stability-loss patterns of phase transition identified. •Hermitization matrices of metrics Θ constructed via symbolic manipulations and extrapolations at all N and k.
ANALYTICAL ELEMENT MODELING OF COASTAL AQUIFERS
Four topics were studied concerning the modeling of groundwater flow in coastal aquifers with analytic elements: (1) practical experience was obtained by constructing a groundwater model of the shallow aquifers below the Delmarva Peninsula USA using the commercial program MVAEM; ...
NASA Astrophysics Data System (ADS)
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.
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.
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.
MPD Thruster Performance Analytic Models
NASA Astrophysics Data System (ADS)
Gilland, James; Johnston, Geoffrey
2003-01-01
Magnetoplasmadynamic (MPD) thrusters are capable of accelerating quasi-neutral plasmas to high exhaust velocities using Megawatts (MW) of electric power. These characteristics make such devices worthy of consideration for demanding, far-term missions such as the human exploration of Mars or beyond. Assessment of MPD thrusters at the system and mission level is often difficult due to their status as ongoing experimental research topics rather than developed thrusters. However, in order to assess MPD thrusters' utility in later missions, some adequate characterization of performance, or more exactly, projected performance, and system level definition are required for use in analyses. The most recent physical models of self-field MPD thrusters have been examined, assessed, and reconfigured for use by systems and mission analysts. The physical models allow for rational projections of thruster performance based on physical parameters that can be measured in the laboratory. The models and their implications for the design of future MPD thrusters are presented.
MPD Thruster Performance Analytic Models
NASA Technical Reports Server (NTRS)
Gilland, James; Johnston, Geoffrey
2007-01-01
Magnetoplasmadynamic (MPD) thrusters are capable of accelerating quasi-neutral plasmas to high exhaust velocities using Megawatts (MW) of electric power. These characteristics make such devices worthy of consideration for demanding, far-term missions such as the human exploration of Mars or beyond. Assessment of MPD thrusters at the system and mission level is often difficult due to their status as ongoing experimental research topics rather than developed thrusters. However, in order to assess MPD thrusters utility in later missions, some adequate characterization of performance, or more exactly, projected performance, and system level definition are required for use in analyses. The most recent physical models of self-field MPD thrusters have been examined, assessed, and reconfigured for use by systems and mission analysts. The physical models allow for rational projections of thruster performance based on physical parameters that can be measured in the laboratory. The models and their implications for the design of future MPD thrusters are presented.
MPD Thruster Performance Analytic Models
NASA Technical Reports Server (NTRS)
Gilland, James; Johnston, Geoffrey
2003-01-01
Magnetoplasmadynamic (MPD) thrusters are capable of accelerating quasi-neutral plasmas to high exhaust velocities using Megawatts (MW) of electric power. These characteristics make such devices worthy of consideration for demanding, far-term missions such as the human exploration of Mars or beyond. Assessment of MPD thrusters at the system and mission level is often difficult due to their status as ongoing experimental research topics rather than developed thrusters. However, in order to assess MPD thrusters utility in later missions, some adequate characterization of performance, or more exactly, projected performance, and system level definition are required for use in analyses. The most recent physical models of self-field MPD thrusters have been examined, assessed, and reconfigured for use by systems and mission analysts. The physical models allow for rational projections of thruster performance based on physical parameters that can be measured in the laboratory. The models and their implications for the design of future MPD thrusters are presented.
Analytic 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
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
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.
Analytical models of slug tests
Karasaki, K.; Long, J.C.S.; Witherspoon, P.A.
1988-01-01
In the present paper, attempts are made to develop solutions to various models of slug tests that may be applicable in analyzing the results of such tests where existing solutions are inadequate. Various geometries that may be encountered in heterogeneous systems such as fractured rocks are considered. Solutions are presented for linear flow, radial flow with boundaries, two layer, and concentric composite models with different flow geometries between the inner and outer region. Solutions are obtained in Laplace space and inverted back to real space numerically. Type curves are presented for each solution. Analyses of the type curves and derivative response curves reveal that many curves have unique shapes only for certain combination of the flow parameters and the distance. Other sets of type curves are similar in shape, although log-log plots and derivative plots may emphasize some features that may not be apparent in semilog plots. These results show that slug tests suffer problems of nonuniqueness to a greater extent than other well tests.
Analytic models of warm plasma dispersion relations
Seough, J. J.; Yoon, P. H.
2009-09-15
The present paper is concerned with analytic models of warm plasma dispersion relations for electromagnetic waves propagating parallel to the ambient magnetic field. Specifically, effects of finite betas on two slow modes, namely, the left-hand circularly polarized ion-cyclotron mode and the right-hand circularly polarized whistler mode, are investigated. Analytic models of the warm plasma dispersion relations are constructed on the basis of conjecture and upon comparisons with numerically found roots. It is shown that the model solutions are good substitutes for actual roots. The significance of the present work in the context of nonlinear plasma research is discussed.
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.
WELLHEAD ANALYTIC ELEMENT MODEL FOR WINDOWS
WhAEM2000 (wellhead analytic element model for Win 98/00/NT/XP) is a public domain, ground-water flow model designed to facilitate capture zone delineation and protection area mapping in support of the State's and Tribe's Wellhead Protection Programs (WHPP) and Source Water Asses...
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 ...
ANALYTIC ELEMENT MODELING OF COASTAL AQUIFERS
Four topics were studied concerning the modeling of ground-water flow in coastal aquifers with analytic elements: (1) practical experience was obtained by constructing a ground-water model of the shallow aquifers below the Delmarva Peninsula USA using the commercial program MVAEM...
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
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.
Bond indices in solids: extended analytical model.
Ponec, Robert
2011-11-15
The analytical model suggested some time ago for the calculation of bond indices in infinite periodical structures was reconsidered and extended so as to provide not only realistic estimate of the extent of electron sharing localized among individual pairs of the atoms in the lattice but also to detect the eventual presence of multicenter bonding in metallic solids. PMID:21823136
Analytical damped-oscillator models for unsteady atmospheric boundary layers
NASA Astrophysics Data System (ADS)
Momen, Mostafa; Bou-Zeid, Elie
2015-11-01
Geophysical flows are dynamical systems that are evolving nonlinearly with time. Non-stationary shear and buoyancy forces are the main sources that drive the unsteadiness of such flows. However, due to their inherent complexity, most previous studies focused on steady-state conditions. In these boundary layers, the pressure gradient, buoyancy, Coriolis, and friction forces interact. The mean PDEs governing the unsteady version of the problem, which emerges when these forces are not in equilibrium, are solvable only for a limited set of forcing variability modes, and the resulting solutions are intricate and difficult to interpret. Here we derive a simpler physical model that reduces the governing RANS equations into a first-order ODE with non-constant coefficients. The origin of the non-stationarity of turbulence can be buoyant stabilization/destabilization and/or unsteady pressure gradient. The reduced model is straightforward and solvable for arbitrary turbulent viscosity variability, and it captures LES results for linearly variable buoyancy and pressure gradient pretty well. The suggested model is thus general and will be useful for elucidating some features of the diurnal cycle, for short-term wind forecast, and in meteorological applications. NSF-PDM under AGS-10266362. Simulations performed at NCAR, and Della server at Princeton University. Cooperative Institute for Climate Science, NOAA-Princeton University under NA08OAR4320752.
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.
Analytic Model for the Rototranslational Torsion Pendulum
NASA Astrophysics Data System (ADS)
De Marchi, F.; Bassan, M.; Pucacco, G.; Marconi, L.; Stanga, R.; Visco, M.
2013-01-01
We develop an analytic model to describe the motion of the RotoTranslational Torsion Pendulum PETER in a wide range of frequencies (from 1mHz up to 10-15Hz). We also try to explain some unexpected features we found in the data with only 1 soft degree of freedom and we estimate values for the misalignment angles and other parameters of the model.
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
Automated statistical modeling of analytical measurement systems
Jacobson, J J
1992-08-01
The statistical modeling of analytical measurement systems at the Idaho Chemical Processing Plant (ICPP) has been completely automated through computer software. The statistical modeling of analytical measurement systems is one part of a complete quality control program used by the Remote Analytical Laboratory (RAL) at the ICPP. The quality control program is an integration of automated data input, measurement system calibration, database management, and statistical process control. The quality control program and statistical modeling program meet the guidelines set forth by the American Society for Testing Materials and American National Standards Institute. A statistical model is a set of mathematical equations describing any systematic bias inherent in a measurement system and the precision of a measurement system. A statistical model is developed from data generated from the analysis of control standards. Control standards are samples which are made up at precise known levels by an independent laboratory and submitted to the RAL. The RAL analysts who process control standards do not know the values of those control standards. The object behind statistical modeling is to describe real process samples in terms of their bias and precision and, to verify that a measurement system is operating satisfactorily. The processing of control standards gives us this ability.
NASA Astrophysics Data System (ADS)
Fakhri, H.; Dehghani, A.; Mojaveri, B.
Using second-order differential operators as a realization of the su(1,1) Lie algebra by the associated Laguerre functions, it is shown that the quantum states of the Calogero-Sutherland, half-oscillator and radial part of a 3D harmonic oscillator constitute the unitary representations for the same algebra. This su(1,1) Lie algebra symmetry leads to derivation of the Barut-Girardello and Klauder-Perelomov coherent states for those models. The explicit compact forms of these coherent states are calculated. Also, to realize the resolution of the identity, their corresponding positive definite measures on the complex plane are obtained in terms of the known functions.
NASA Astrophysics Data System (ADS)
Hilbert, Stefan; Dunkel, Jörn
2006-07-01
We calculate exactly both the microcanonical and canonical thermodynamic functions (TDFs) for a one-dimensional model system with piecewise constant Lennard-Jones type pair interactions. In the case of an isolated N -particle system, the microcanonical TDFs exhibit (N-1) singular (nonanalytic) microscopic phase transitions of the formal order N/2 , separating N energetically different evaporation (dissociation) states. In a suitably designed evaporation experiment, these types of phase transitions should manifest themselves in the form of pressure and temperature oscillations, indicating cooling by evaporation. In the presence of a heat bath (thermostat), such oscillations are absent, but the canonical heat capacity shows a characteristic peak, indicating the temperature-induced dissociation of the one-dimensional chain. The distribution of complex zeros of the canonical partition may be used to identify different degrees of dissociation in the canonical ensemble.
Analytical steam injection model for layered systems
Abdual-Razzaq; Brigham, W.E.; Castanier, L.M.
1993-08-01
Screening, evaluation and optimization of the steam flooding process in homogeneous reservoirs can be performed by using simple analytical predictive models. In the absence of any analytical model for layered reservoirs, at present, only numerical simulators can be used. And these are expensive. In this study, an analytical model has been developed considering two isolated layers of differing permeabilities. The principle of equal flow potential is applied across the two layers. Gajdica`s (1990) single layer linear steam drive model is extended for the layered system. The formulation accounts for variation of heat loss area in the higher permeability layer, and the development of a hot liquid zone in the lower permeability layer. These calculations also account for effects of viscosity, density, fractional flow curves and pressure drops in the hot liquid zone. Steam injection rate variations in the layers are represented by time weighted average rates. For steam zone calculations, Yortsos and Gavalas`s (1981) upper bound method is used with a correction factor. The results of the model are compared with a numerical simulator. Comparable oil and water flow rates, and breakthrough times were achieved for 100 cp oil. Results with 10 cp and 1000 cp oils indicate the need to improve the formulation to properly handle differing oil viscosities.
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.
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.
NASA Astrophysics Data System (ADS)
Lienert, Matthias
2015-04-01
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)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
NASA Astrophysics Data System (ADS)
Choquard, Ph.; Vuffray, M.
2014-10-01
The coupling between dilatation and vorticity, two coexisting and fundamental processes in fluid dynamics (Wu et al., 2006, pp. 3, 6) is investigated here, in the simplest cases of inviscid 2D isotropic Burgers and pressureless Euler-Coriolis fluids respectively modeled by single vortices confined in compressible, local, inertial and global, rotating, environments. The field equations are established, inductively, starting from the equations of the characteristics solved with an initial Helmholtz decomposition of the velocity fields namely a vorticity free and a divergence free part (Wu et al., 2006, Sects. 2.3.2, 2.3.3) and, deductively, by means of a canonical Hamiltonian Clebsch like formalism (Clebsch, 1857, 1859), implying two pairs of conjugate variables. Two vector valued fields are constants of the motion: the velocity field in the Burgers case and the momentum field per unit mass in the Euler-Coriolis one. Taking advantage of this property, a class of solutions for the mass densities of the fluids is given by the Jacobian of their sum with respect to the actual coordinates. Implementation of the isotropy hypothesis entails a radial dependence of the velocity potentials and of the stream functions associated to the compressible and to the rotational part of the fluids and results in the cancellation of the dilatation-rotational cross terms in the Jacobian. A simple expression is obtained for all the radially symmetric Jacobians occurring in the theory. Representative examples of regular and singular solutions are shown and the competition between dilatation and vorticity is illustrated. Inspired by thermodynamical, mean field theoretical analogies, a genuine variational formula is proposed which yields unique measure solutions for the radially symmetric fluid densities investigated. We stress that this variational formula, unlike the Hopf-Lax formula, enables us to treat systems which are both compressible and rotational. Moreover in the one
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.
An analytical model of memristors in plants
Markin, Vladislav S; Volkov, Alexander G; Chua, Leon
2014-01-01
The memristor, a resistor with memory, was postulated by Chua in 1971 and the first solid-state memristor was built in 2008. Recently, we found memristors in vivo in plants. Here we propose a simple analytical model of 2 types of memristors that can be found within plants. The electrostimulation of plants by bipolar periodic waves induces electrical responses in the Aloe vera and Mimosa pudica with fingerprints of memristors. Memristive properties of the Aloe vera and Mimosa pudica are linked to the properties of voltage gated K+ ion channels. The potassium channel blocker TEACl transform plant memristors to conventional resistors. The analytical model of a memristor with a capacitor connected in parallel exhibits different characteristic behavior at low and high frequency of applied voltage, which is the same as experimental data obtained by cyclic voltammetry in vivo. PMID:25482769
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.
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.
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.
Analytical modeling of worldwide medical radiation use
Mettler, F.A. Jr.; Davis, M.; Kelsey, C.A.; Rosenberg, R.; Williams, A.
1987-02-01
An analytical model was developed to estimate the availability and frequency of medical radiation use on a worldwide basis. This model includes medical and dental x-ray, nuclear medicine, and radiation therapy. The development of an analytical model is necessary as the first step in estimating the radiation dose to the world's population from this source. Since there is no data about the frequency of medical radiation use in more than half the countries in the world and only fragmentary data in an additional one-fourth of the world's countries, such a model can be used to predict the uses of medical radiation in these countries. The model indicates that there are approximately 400,000 medical x-ray machines worldwide and that approximately 1.2 billion diagnostic medical x-ray examinations are performed annually. Dental x-ray examinations are estimated at 315 million annually and approximately 22 million in-vivo diagnostic nuclear medicine examinations. Approximately 4 million radiation therapy procedures or courses of treatment are undertaken annually.
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.
Analytic models of plausible gravitational lens potentials
Baltz, Edward A.; Marshall, Phil; Oguri, Masamune E-mail: pjm@physics.ucsb.edu
2009-01-15
Gravitational lenses on galaxy scales are plausibly modelled 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. Emphasising 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 modelled, 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.
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.
Analytical Performance Models for Geologic Repositories
Chambre, P.L.; Pigford, T.H.; Fujita, A.; Kanki, T.; Kobayashi,A.; Lung, H.; Ting, D.; Sato, Y.; Savoshy, S.J.
1982-10-01
This report presents analytical solutions of the dissolution and hydrogeologic transport of radionuclides in geologic repositories. Numerical examples are presented to demonstrate the equations resulting from these analyses. The subjects treated in the present report are: (a) Solubility-limited transport with transverse dispersion (Chapter 2); (b) Transport of a radionuclide chain with nonequilibrium chemical reactions (Chapter 3); (c) Advective transport in a two-dimensional flow field (Chapter 4); (d) Radionuclide.transport in fractured media (Chapter 5); (e) A mathematical model for EPA's analysis of generic repositories (Chapter 6); and (f) Dissolution of radionuclides from solid waste (Chapter 7).
Analytic Modeling of Pressurization and Cryogenic Propellant
NASA Technical Reports Server (NTRS)
Corpening, Jeremy H.
2010-01-01
An analytic model for pressurization and cryogenic propellant conditions during all mission phases of any liquid rocket based vehicle has been developed and validated. The model assumes the propellant tanks to be divided into five nodes and also implements an empirical correlation for liquid stratification if desired. The five nodes include a tank wall node exposed to ullage gas, an ullage gas node, a saturated propellant vapor node at the liquid-vapor interface, a liquid node, and a tank wall node exposed to liquid. The conservation equations of mass and energy are then applied across all the node boundaries and, with the use of perfect gas assumptions, explicit solutions for ullage and liquid conditions are derived. All fluid properties are updated real time using NIST Refprop.1 Further, mass transfer at the liquid-vapor interface is included in the form of evaporation, bulk boiling of liquid propellant, and condensation given the appropriate conditions for each. Model validation has proven highly successful against previous analytic models and various Saturn era test data and reasonably successful against more recent LH2 tank self pressurization ground test data. Finally, this model has been applied to numerous design iterations for the Altair Lunar Lander, Ares V Core Stage, and Ares V Earth Departure Stage in order to characterize Helium and autogenous pressurant requirements, propellant lost to evaporation and thermodynamic venting to maintain propellant conditions, and non-uniform tank draining in configurations utilizing multiple LH2 or LO2 propellant tanks. In conclusion, this model provides an accurate and efficient means of analyzing multiple design configurations for any cryogenic propellant tank in launch, low-acceleration coast, or in-space maneuvering and supplies the user with pressurization requirements, unusable propellants from evaporation and liquid stratification, and general ullage gas, liquid, and tank wall conditions as functions of time.
Analytical model of batch magnetophoretic separation
NASA Astrophysics Data System (ADS)
Kashevsky, S. B.; Kashevsky, B. E.
2013-06-01
Magnetophoresis (the motion of magnetic particles driven by the nonuniform magnetic field), that for a long time has been used for extracting magnetically susceptible objects in diverse industries, now attracts interest to develop more sophisticated microfluidic and batch techniques for separation and manipulation of biological particles, and magnetically assisted absorption and catalysis in organic chemistry, biochemistry, and petrochemistry. A deficiency of magnetic separation science is the lack of simple analytical models imitating real processes of magnetic separation. We have studied the motion of superparamagnetic (generally, soft magnetic) particles in liquid in the three-dimensional field of the diametrically polarized permanent cylindrical magnet; this geometry is basically representative of the batch separation mode. In the limit of the infinite-length magnet, we found the particle magnetophoresis proceeds independently of the magnet polarization direction, following the simple analytical relation incorporating all the relevant physical and geometrical parameters of the particle-magnet system. In experiments with a finite-length magnet we have shown applicability of the developed theory as to analyze the performance of the real batch separation systems in the noncooperative mode, and finally, we have presented an example of such analysis for the case of immunomagnetic cell separation and developed a criterion of the model limitation imposed by the magnetic aggregation of particles.
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.
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.
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.
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.
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.
Simple analytic model for astrophysical S factors
Yakovlev, D. G.; Beard, M.; Gasques, L. R.; Wiescher, M.
2010-10-15
We propose a physically transparent analytic model of astrophysical S factors as a function of a center-of-mass energy E of colliding nuclei (below and above the Coulomb barrier) for nonresonant fusion reactions. For any given reaction, the S(E) model contains four parameters [two of which approximate the barrier potential, U(r)]. They are easily interpolated along many reactions involving isotopes of the same elements; they give accurate practical expressions for S(E) with only several input parameters for many reactions. The model reproduces the suppression of S(E) at low energies (of astrophysical importance) due to the shape of the low-r wing of U(r). The model can be used to reconstruct U(r) from computed or measured S(E). For illustration, we parametrize our recent calculations of S(E) (using the Sao Paulo potential and the barrier penetration formalism) for 946 reactions involving stable and unstable isotopes of C, O, Ne, and Mg (with nine parameters for all reactions involving many isotopes of the same elements, e.g., C+O). In addition, we analyze astrophysically important {sup 12}C+{sup 12}C reaction, compare theoretical models with experimental data, and discuss the problem of interpolating reliably known S(E) values to low energies (E < or approx. 2-3 MeV).
The Immediate Exchange model: an analytical investigation
NASA Astrophysics Data System (ADS)
Katriel, Guy
2015-01-01
We study the Immediate Exchange model, recently introduced by Heinsalu and Patriarca [Eur. Phys. J. B 87, 170 (2014)], who showed by simulations that the wealth distribution in this model converges to a Gamma distribution with shape parameter 2. Here we justify this conclusion analytically, in the infinite-population limit. An infinite-population version of the model is derived, describing the evolution of the wealth distribution in terms of iterations of a nonlinear operator on the space of probability densities. It is proved that the Gamma distributions with shape parameter 2 are fixed points of this operator, and that, starting with an arbitrary wealth distribution, the process converges to one of these fixed points. We also discuss the mixed model introduced in the same paper, in which exchanges are either bidirectional or unidirectional with fixed probability. We prove that, although, as found by Heinsalu and Patriarca, the equilibrium distribution can be closely fit by Gamma distributions, the equilibrium distribution for this model is not a Gamma distribution.
ANALYTIC 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.
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 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...
One-dimensional quasi-exactly solvable Schrödinger equations
NASA Astrophysics Data System (ADS)
Turbiner, Alexander V.
2016-06-01
Quasi-Exactly Solvable Schrödinger Equations occupy an intermediate place between exactly-solvable (e.g. the harmonic oscillator and Coulomb problems, etc.) and non-solvable ones. Mainly, they were discovered in the 1980s. Their major property is an explicit knowledge of several eigenstates while the remaining ones are unknown. Many of these problems are of the anharmonic oscillator type with a special type of anharmonicity. The Hamiltonians of quasi-exactly-solvable problems are characterized by the existence of a hidden algebraic structure but do not have any hidden symmetry properties. In particular, all known one-dimensional (quasi)-exactly-solvable problems possess a hidden sl(2, R) -Lie algebra. They are equivalent to the sl(2, R) Euler-Arnold quantum top in a constant magnetic field. Quasi-Exactly Solvable problems are highly non-trivial, they shed light on the delicate analytic properties of the Schrödinger Equations in coupling constant, they lead to a non-trivial class of potentials with the property of Energy-Reflection Symmetry. The Lie-algebraic formalism allows us to make a link between the Schrödinger Equations and finite-difference equations on uniform and/or exponential lattices, it implies that the spectra is preserved. This link takes the form of quantum canonical transformation. The corresponding isospectral problems for finite-difference operators are described. The underlying Fock space formalism giving rise to this correspondence is uncovered. For a quite general class of perturbations of unperturbed problems with the hidden Lie algebra property we can construct an algebraic perturbation theory, where the wavefunction corrections are of polynomial nature, thus, can be found by algebraic means. In general, Quasi-Exact-Solvability points to the existence of a hidden algebra formalism which ranges from quantum mechanics to 2-dimensional conformal field theories.
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.
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
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.}
Analytic Models of High-Temperature Hohlraums
Stygar, W.A.; Olson, R.E.; Spielman, R.B.; Leeper, R.J.
2000-11-29
A unified set of high-temperature-hohlraum models has been developed. For a simple hohlraum, P{sub s} = [A{sub s}+(1{minus}{alpha}{sub W})A{sub W}+A{sub H}]{sigma}T{sub R}{sup 4} + (4V{sigma}/c)(dT{sub R}{sup r}/dt) where P{sub S} is the total power radiated by the source, A{sub s} is the source area, A{sub W} is the area of the cavity wall excluding the source and holes in the wall, A{sub H} is the area of the holes, {sigma} is the Stefan-Boltzmann constant, T{sub R} is the radiation brightness temperature, V is the hohlraum volume, and c is the speed of light. The wall albedo {alpha}{sub W} {triple_bond} (T{sub W}/T{sub R}){sup 4} where T{sub W} is the brightness temperature of area A{sub W}. The net power radiated by the source P{sub N} = P{sub S}-A{sub S}{sigma}T{sub R}{sup 4}, which suggests that for laser-driven hohlraums the conversion efficiency {eta}{sub CE} be defined as P{sub N}/P{sub LASER}. The characteristic time required to change T{sub R}{sup 4} in response to a change in P{sub N} is 4V/C[(l{minus}{alpha}{sub W})A{sub W}+A{sub H}]. Using this model, T{sub R}, {alpha}{sub W}, and {eta}{sub CE} can be expressed in terms of quantities directly measurable in a hohlraum experiment. For a steady-state hohlraum that encloses a convex capsule, P{sub N} = {l_brace}(1{minus}{alpha}{sub W})A{sub W}+A{sub H}+[(1{minus}{alpha}{sub C})(A{sub S}+A{sub W}{alpha}{sub W})A{sub C}/A{sub T}]{r_brace}{sigma}T{sub RC}{sup 4} where {alpha}{sub C} is the capsule albedo, A{sub C} is the capsule area, A{sub T} {triple_bond} (A{sub S}+A{sub W}+A{sub H}), and T{sub RC} is the brightness temperature of the radiation that drives the capsule. According to this relation, the capsule-coupling efficiency of the baseline National-Ignition-Facility (NIF) hohlraum is 15% higher than predicted by previous analytic expressions. A model of a hohlraum that encloses a z pinch is also presented.
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; ...
Automated dynamic analytical model improvement for damped structures
NASA Technical Reports Server (NTRS)
Fuh, J. S.; Berman, A.
1985-01-01
A method is described to improve a linear nonproportionally damped analytical model of a structure. The procedure finds the smallest changes in the analytical model such that the improved model matches the measured modal parameters. Features of the method are: (1) ability to properly treat complex valued modal parameters of a damped system; (2) applicability to realistically large structural models; and (3) computationally efficiency without involving eigensolutions and inversion of a large matrix.
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.
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.
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
Analytic Model For Estimation Of Cold Bulk Metal Forming Simulations
Skunca, Marko; Keran, Zdenka; Math, Miljenko
2007-05-17
Numerical simulation of bulk metal forming plays an important role in predicting a key parameters in cold forging. Comparison of numerical and experimental data is of great importance, but there is always a need of more universal analytical tools. Therefore, many papers besides experiment and simulation of a particular bulk metal forming technology, include an analytic model. In this paper an analytical model for evaluation of commercially available simulation program packages is proposed. Based on elementary theory of plasticity, being only geometry dependent, model represents a good analytical reference to estimate given modeling preferences like; element types, solver, remeshing influence and many others. Obtained, geometry dependent, stress fields compared with numerical data give a clear picture of numerical possibilities and limitations of particular modeling program package.
An analytic performance model of disk arrays and its application
NASA Technical Reports Server (NTRS)
Lee, Edward K.; Katz, Randy H.
1991-01-01
As disk arrays become widely used, tools for understanding and analyzing their performance become increasingly important. In particular, performance models can be invaluable in both configuring and designing disk arrays. Accurate analytic performance models are desirable over other types of models because they can be quickly evaluated, are applicable under a wide range of system and workload parameters, and can be manipulated by a range of mathematical techniques. Unfortunately, analytical performance models of disk arrays are difficult to formulate due to the presence of queuing and fork-join synchronization; a disk array request is broken up into independent disk requests which must all complete to satisfy the original request. We develop, validate, and apply an analytic performance model for disk arrays. We derive simple equations for approximating their utilization, response time, and throughput. We then validate the analytic model via simulation and investigate the accuracy of each approximation used in deriving the analytical model. Finally, we apply the analytical model to derive an equation for the optimal unit of data striping in disk arrays.
Feedbacks Between Numerical and Analytical Models in Hydrogeology
NASA Astrophysics Data System (ADS)
Zlotnik, V. A.; Cardenas, M. B.; Toundykov, D.; Cohn, S.
2012-12-01
Hydrogeology is a relatively young discipline which combines elements of Earth science and engineering. Mature fundamental disciplines (e.g., physics, chemistry, fluid mechanics) have centuries-long history of mathematical modeling even prior to discovery of Darcy's law. Thus, in hydrogeology, relatively few classic analytical models (such those by Theis, Polubarinova-Kochina, Philip, Toth, Henry, Dagan, Neuman) were developed by the early 1970's. The advent of computers and practical demands refocused mathematical models towards numerical techniques. With more diverse but less mathematically-oriented training, most hydrogeologists shifted from analytical methods to use of standardized computational software. Spatial variability in internal properties and external boundary conditions and geometry, and the added complexity of chemical and biological processes will remain major challenges for analytical modeling. Possibly, analytical techniques will play a subordinate role to numerical approaches in many applications. On the other hand, the rise of analytical element modeling of groundwater flow is a strong alternative to numerical models when data demand and computational efficiency is considered. The hallmark of analytical models - transparency and accuracy - will remain indispensable for scientific exploration of complex phenomena and for benchmarking numerical models. Therefore, there will always be feedbacks and complementarities between numerical and analytical techniques, as well as a certain ideological schism among various views to modeling. We illustrate the idea of feedbacks by reviewing evolution of Joszef Toth's analytical model of gravity driven flow systems. Toth's (1963) approach was to reduce the flow domain to a rectangle which allowed for closed-form solution of the governing equations. Succeeding numerical finite-element models by Freeze and Witherspoon (1966-1968) explored the effects of geometry and heterogeneity on regional groundwater flow
Towards an analytical model of water: The octupolar model
NASA Astrophysics Data System (ADS)
Blum, L.; Vericat, F.; Bratko, D.
1995-01-01
A simple potential for the water intermolecular potential, consisting of hard spheres with a point dipole and a potential well with the symmetry of a tetrahedral octupole was proposed by Bratko, Blum, and Luzar some time ago. This structural model was formally solved by Blum, Cummings, and Bratko, and explicit solutions have been recently obtained. We show here that this very simple model agrees surprisingly well with the experimental pair correlation functions of Soper and Phillips. The agreement with the gOH(r) and gHH(r) functions is quite good. For the gOO(r) the agreement is not as good, but this has to do with the hard core nature of the potential. Analytical solutions for soft spherical cores exist.
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.
Demonstration of Detection and Ranging Using Solvable Chaos
NASA Technical Reports Server (NTRS)
Corron, Ned J.; Stahl, Mark T.; Blakely, Jonathan N.
2013-01-01
Acoustic experiments demonstrate a novel approach to ranging and detection that exploits the properties of a solvable chaotic oscillator. This nonlinear oscillator includes an ordinary differential equation and a discrete switching condition. The chaotic waveform generated by this hybrid system is used as the transmitted waveform. The oscillator admits an exact analytic solution that can be written as the linear convolution of binary symbols and a single basis function. This linear representation enables coherent reception using a simple analog matched filter and without need for digital sampling or signal processing. An audio frequency implementation of the transmitter and receiver is described. Successful acoustic ranging measurements are presented to demonstrate the viability of the approach.
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.
Analytical modelling of Thirty Meter Telescope optics polarization
NASA Astrophysics Data System (ADS)
Anche, Ramya M.; Anupama, G. C.; Reddy, Krishna; Sen, Asoke; Sankarasubramanian, K.; Ramaprakash, A. N.; Sengupta, Sujan; Skidmore, Warren; Atwood, Jenny; Tirupathi, Sivarani; Pandey, Shashi Bhushan
2015-06-01
The polarization introduced due to Thirty Meter Telescope (TMT) optics is calculated using an analytical model. Mueller matrices are also generated for each optical element using Zemax, based on which the instrumental polarization due to the entire system at the focal plane is estimated and compared with the analytical model. This study is significant in the estimation of the telescope sensitivity and also has great implications for future instruments.
Analytical Ion Thruster Discharge Performance Model
NASA Technical Reports Server (NTRS)
Goebel, Dan M.; Wirz, Richard E.; Katz, Ira
2006-01-01
A particle and energy balance model of the plasma discharge in magnetic ring-cusp ion thrusters has been developed. The model follows the original work of Brophy in the development of global 0-D discharge models that utilize conservation of particles into and out of the thruster and conservation of energy into the discharge and out of the plasma in the form of charged particles to the walls and beam and plasma radiation. The present model is significantly expanded over Brophy's original work by including self-consistent calculations of the internal neutral pressure, electron temperature, primary electron density, electrostatic ion confinement (due to the ring-cusp fields), plasma potential, discharge stability, and time dependent behavior during recycling. The model only requires information on the thruster geometry, ion optics performance and electrical inputs such as discharge voltage and currents, etc. to produce accurate performance curves of discharge loss versus mass utilization efficiency. The model has been benchmarked against the NEXIS Laboratory Model (LM) and Development Model (DM) thrusters, and successfully predicts the thruster discharge loss as a function of mass utilization efficiency for a variety of thrusters. The discharge performance model will be presented and results showing ion thruster performance and stability given.
Analytical 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.
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.
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.
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.
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.''
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
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.
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.
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
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.
A new analytic model for fracture-dominated reservoirs
Karasaki, K.; Long, J.C.S.; Witherspoon, P.A.
1988-03-01
A new analytic model for analyzing well test data from fracture-dominated reservoirs is presented. It is a concentric composite model with a finite-radius well located in the center. In the inner region the flow is assumed to be linear, and in the outer region the flow is assumed to be radial. Solutions are obtained analytically and type curves for ranges of dimensionless parameters are presented. The model can be used to find the extent and the flow parameters of the fractures near the well and the average values for the entire system provided that wellbore-storage effects do not mask the early-time data.
Analytical modelling of no-vent fill process
NASA Technical Reports Server (NTRS)
Vaughan, David A.; Schmidt, George R.
1990-01-01
An analytical model called FILL is presented which represents the first step in attaining the capability for no-vent fill of cryogens in space. The model's analytical structure is described, including the equations used to calculate transient thermodynamic behavior in different regions of the tank. The code predictions are compared with data from recent no-vent fill ground tests using Freon-114. The results are used to validate the FILL model to evaluate the viability of universal submerged jet theory in predicting system-level condensation effects.
ANALYTIC ELEMENT MODELING OF COASTAL AQUIFERS - PROJECT SUMMARY
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 MVAE...
Experimental verification of the SP-100 TEM pump analytical models
Salamah, S.A.; Miller, D.D.; Sinha, U.N.; Narkiewicz, R.S. )
1993-01-15
Validation of the TEM pump analytical model is conducted via experimental verification of the model prediction. Two key tests that have provided essential information toward this objective are the Magnetic Bench Test (MBT) and the ElectroMagnetic Integration Test (EMIT). The tests are briefly described and experimental results are compared with predictions of simulation models that form part of overall TEM pump performance model.
Semi-analytical modelling of piezoelectric excitation of guided waves
NASA Astrophysics Data System (ADS)
Kalkowski, Michał K.; Rustighi, Emiliano; Waters, Timothy P.
2015-03-01
Piezoelectric elements are a key component of modern non-destructive testing (NDT) and structural health monitoring (SHM) systems and play a significant role in many other areas involving dynamic interaction with the structure such as energy harvesting, active control, power ultrasonics or removal of surface accretions using structural waves. In this paper we present a wave-based technique for modelling waveguides equipped with piezoelectric actuators in which there is no need for common simplifications regarding their dynamic behaviour or mutual interaction with the structure. The proposed approach is based on the semi-analytical finite element (SAFE) method. We developed a new piezoelectric semi-analytical element and employed the analytical wave approach to model the distributed electric excitation and scattering of the waves at discontinuities. The model is successfully validated against an experiment on a beam-like waveguide with emulated anechoic terminations.
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.
Analytical modeling of the radial pn junction nanowire solar cells
NASA Astrophysics Data System (ADS)
Ali, Nouran M.; Allam, Nageh K.; Abdel Haleem, Ashraf M.; Rafat, Nadia H.
2014-07-01
In photovoltaic solar cells, radial p-n junctions have been considered a very promising structure to improve the carrier collection efficiency and accordingly the conversion efficiency. In the present study, the semiconductor equations, namely Poisson's and continuity equations for a cylindrical p-n junction solar cell, have been solved analytically. The analytical model is based on Green's function theory to calculate the current density, open circuit voltage, fill factor, and conversion efficiency. The model has been used to simulate p-n and p-i-n silicon radial solar cells. The validity and accuracy of the present simulator were confirmed through a comparison with previously published experimental and numerical reports.
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.
Helicopter derivative identification from analytic models and flight test data
NASA Technical Reports Server (NTRS)
Molusis, J. H.; Briczinski, S.
1974-01-01
Recent results of stability derivative identification from helicopter analytic models and flight test data are presented. Six and nine degree-of-freedom (DOF) linear models are identified from an analytic nonlinear helicopter simulation using a least square technique. The identified models are compared with the convectional partial differentiation method for obtaining derivatives to form the basis for interpretation of derivatives identified from flight data. Six degree-of-freedom models are identified from CH-53A and CH-54B flight data, using an extended Kalman filter modified to process several maneuvers simultaneously. The a priori derivative estimate is obtained by optimal filtering of the data and then using a least square method. The results demonstrate that a six DOF identified model is sufficient to determine the low frequency modes of motion, but a nine DOF rotor/body model is necessary for proper representation of short-term response.
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.
Analytical modeling for gamma radiation damage on silicon photodiodes
NASA Astrophysics Data System (ADS)
Jafari, H.; Feghhi, S. A. H.
2016-04-01
Radiation-induced damage in PIN silicon photodiode induces degradation of the photodiode parameters. In this work, by presenting an analytical model, the effect of gamma dose on the dark current in a PIN photodiode array was investigated. Geant4 was used to obtain the damage constant as a result of primary incident particle fluence and NIEL distribution calculations. Experimental measurements as well as numerical simulation of the semiconductor with ATLAS were carried out to verify and parameterize the analytical model calculations. A reasonable agreement has been found between analytical results and experimental data for BPX65 silicon photodiodes irradiated by a Co-60 gamma source at total doses up to 500 krad under different reverse voltages. Moreover, the results showed that the dark current of each photodiode array pixel has considerably increased by gamma dose irradiation.
Evaluation of one dimensional analytical models for vegetation canopies
NASA Technical Reports Server (NTRS)
Goel, Narendra S.; Kuusk, Andres
1992-01-01
The SAIL model for one-dimensional homogeneous vegetation canopies has been modified to include the specular reflectance and hot spot effects. This modified model and the Nilson-Kuusk model are evaluated by comparing the reflectances given by them against those given by a radiosity-based computer model, Diana, for a set of canopies, characterized by different leaf area index (LAI) and leaf angle distribution (LAD). It is shown that for homogeneous canopies, the analytical models are generally quite accurate in the visible region, but not in the infrared region. For architecturally realistic heterogeneous canopies of the type found in nature, these models fall short. These shortcomings are quantified.
Large-signal numerical and analytical HBT models
Teeter, D.A.; East, J.R.; Mains, R.K.; Haddad, G.I. )
1993-05-01
Several large-signal HBT models are investigated in this paper to determine their usefulness at millimeter-wave frequencies. The most detailed model involves numerically solving moments of the Boltzmann Transport Equation. A description of the numerical model is given along with several simulated results. The numerical model is then used to evaluate two analytical HBT models, the conventional Gummel-Poon model and a modified Ebers-Moll model. It is found that the commonly used Gummel-Poon model exhibits poor agreement with numerical and experimental data at millimeter-wave frequencies due to neglect of transit-time delays. Improved agreement between measured and modeled data result by including transit-time effects in an Ebers-Moll model. This simple model has direct application to millimeter-wave power amplifier and oscillator design. Several measured results are presented to help verify the simple model.
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.
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.
Modeling Analyte Transport and Capture in Porous Bead Sensors
Chou, Jie; Lennart, Alexis; Wong, Jorge; Ali, Mehnaaz F.; Floriano, Pierre N.; Christodoulides, Nicolaos; Camp, James; McDevitt, John T.
2013-01-01
Porous agarose microbeads, with high surface to volume ratios and high binding densities, are attracting attention as highly sensitive, affordable sensor elements for a variety of high performance bioassays. While such polymer microspheres have been extensively studied and reported on previously and are now moving into real-world clinical practice, very little work has been completed to date to model the convection, diffusion, and binding kinetics of soluble reagents captured within such fibrous networks. Here, we report the development of a three-dimensional computational model and provide the initial evidence for its agreement with experimental outcomes derived from the capture and detection of representative protein and genetic biomolecules in 290μm porous beads. We compare this model to antibody-mediated capture of C-reactive protein and bovine serum albumin, along with hybridization of oligonucleotide sequences to DNA probes. These results suggest that due to the porous interior of the agarose bead, internal analyte transport is both diffusion- and convection-based, and regardless of the nature of analyte, the bead interiors reveal an interesting trickle of convection-driven internal flow. Based on this model, the internal to external flow rate ratio is found to be in the range of 1:3100 to 1:170 for beads with agarose concentration ranging from 0.5% to 8% for the sensor ensembles here studied. Further, both model and experimental evidence suggest that binding kinetics strongly affect analyte distribution of captured reagents within the beads. These findings reveal that high association constants create a steep moving boundary in which unbound analytes are held back at the periphery of the bead sensor. Low association constants create a more shallow moving boundary in which unbound analytes diffuse further into the bead before binding. These models agree with experimental evidence and thus serve as a new tool set for the study of bio-agent transport processes
An analytic spin chain model with fractional revival
NASA Astrophysics Data System (ADS)
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei
2016-08-01
New analytic spin chains with fractional revival are introduced. Their nearest-neighbor couplings and local magnetic fields correspond to the recurrence coefficients of para-Racah polynomials which are orthogonal on quadratic bi-lattices. These models generalize the spin chain associated to the dual-Hahn polynomials. Instances where perfect state transfer also occurs are identified.
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...
Piezoresistive Cantilever Performance-Part I: Analytical Model for Sensitivity.
Park, Sung-Jin; Doll, Joseph C; Pruitt, Beth L
2010-02-01
An accurate analytical model for the change in resistance of a piezoresistor is necessary for the design of silicon piezoresistive transducers. Ion implantation requires a high-temperature oxidation or annealing process to activate the dopant atoms, and this treatment results in a distorted dopant profile due to diffusion. Existing analytical models do not account for the concentration dependence of piezoresistance and are not accurate for nonuniform dopant profiles. We extend previous analytical work by introducing two nondimensional factors, namely, the efficiency and geometry factors. A practical benefit of this efficiency factor is that it separates the process parameters from the design parameters; thus, designers may address requirements for cantilever geometry and fabrication process independently. To facilitate the design process, we provide a lookup table for the efficiency factor over an extensive range of process conditions. The model was validated by comparing simulation results with the experimentally determined sensitivities of piezoresistive cantilevers. We performed 9200 TSUPREM4 simulations and fabricated 50 devices from six unique process flows; we systematically explored the design space relating process parameters and cantilever sensitivity. Our treatment focuses on piezoresistive cantilevers, but the analytical sensitivity model is extensible to other piezoresistive transducers such as membrane pressure sensors. PMID:20336183
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…
Piezoresistive Cantilever Performance—Part I: Analytical Model for Sensitivity
Park, Sung-Jin; Doll, Joseph C.; Pruitt, Beth L.
2010-01-01
An accurate analytical model for the change in resistance of a piezoresistor is necessary for the design of silicon piezoresistive transducers. Ion implantation requires a high-temperature oxidation or annealing process to activate the dopant atoms, and this treatment results in a distorted dopant profile due to diffusion. Existing analytical models do not account for the concentration dependence of piezoresistance and are not accurate for nonuniform dopant profiles. We extend previous analytical work by introducing two nondimensional factors, namely, the efficiency and geometry factors. A practical benefit of this efficiency factor is that it separates the process parameters from the design parameters; thus, designers may address requirements for cantilever geometry and fabrication process independently. To facilitate the design process, we provide a lookup table for the efficiency factor over an extensive range of process conditions. The model was validated by comparing simulation results with the experimentally determined sensitivities of piezoresistive cantilevers. We performed 9200 TSUPREM4 simulations and fabricated 50 devices from six unique process flows; we systematically explored the design space relating process parameters and cantilever sensitivity. Our treatment focuses on piezoresistive cantilevers, but the analytical sensitivity model is extensible to other piezoresistive transducers such as membrane pressure sensors. PMID:20336183
Analytical properties of the anisotropic cubic Ising model
Hansel, D.; Maillard, J.M.; Oitmaa, J.; Velgakis, M.J.
1987-07-01
The authors combine an exact functional relation, the inversion relation, with conventional high-temperature expansions to explore the analytic properties of the anisotropic Ising model on both the square and simple cubic lattice. In particular, they investigate the nature of the singularities that occur in partially resummed expansions of the partition function and of the susceptibility.
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.
Terahertz microstructured optical fibers: An analytical field model
NASA Astrophysics Data System (ADS)
Sharma, Dinesh Kumar; Sharma, Anurag; Varshney, R. K.; Pal, B. P.
2014-10-01
Microstructured optical fibers (MOFs) have wavelength scale periodic microstructure running along their length. Their core and two-dimensional microstructured cladding might be based on varied geometries and materials, enabling light guidance due to different propagation mechanisms over an extremely large wavelength range, extending to the terahertz (THz) frequency region. As a result, these fibers have revolutionized the optical fiber technology by means of creating new degrees of freedom in the fiber design, fabrication and applicability. We analytically study the modal properties of terahertz microstructured optical fiber (THz MOF), by using our analytical field model, developed for optical waveguides.
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 models for electrically thin flat lenses and reflectors.
Ruphuy, Miguel; Ramahi, Omar M
2015-04-01
This work presents analytical models for two-dimensional (2D) and three-dimensional (3D) electrically thin lenses and reflectors. The 2D formulation is based on infinite current line sources, whereas the 3D formulation is based on electrically small dipoles. These models emulate the energy convergence of an electrically thin flat lens and reflector when illuminated by a plane wave with specific polarization. The advantages of these models are twofold: first, prediction of the performance of electrically thin flat lenses and reflectors can be made significantly faster than full-wave simulators, and second, providing insight on the performance of these electrically thin devices. The analytic models were validated by comparison with full-wave simulation for several interesting examples. The validation results show that the focal point of the electrically thin flat lenses and reflectors can be accurately predicted through a design that assumes low coupling between different layers of an inhomogeneous media. PMID:26366759
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 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
A parsimonious analytical model for simulating multispecies plume migration
NASA Astrophysics Data System (ADS)
Chen, J.-S.; Liang, C.-P.; Liu, C.-W.; Li, L. Y.
2015-09-01
A parsimonious analytical model for rapidly predicting the long-term plume behavior of decaying contaminant such as radionuclide and dissolved chlorinated solvent is presented in this study. Generalized analytical solutions in compact format are derived for the two-dimensional advection-dispersion equations coupled with sequential first-order decay reactions involving an arbitrary number of species in groundwater system. The solution techniques involve the sequential applications of the Laplace, finite Fourier cosine, and generalized integral transforms to reduce the coupled partial differential equation system to a set of linear algebraic equations. The system of algebraic equations is next solved for each species in the transformed domain, and the solutions in the original domain are then obtained through consecutive integral transform inversions. Explicit form solutions for a special case are derived using the generalized analytical solutions and are verified against the numerical solutions. The analytical results indicate that the parsimonious analytical solutions are robust and accurate. The solutions are useful for serving as simulation or screening tools for assessing plume behaviors of decaying contaminants including the radionuclides and dissolved chlorinated solvents in groundwater systems.
An analytical model for permeability of isotropic porous media
NASA Astrophysics Data System (ADS)
Yang, Xiaohu; Lu, Tian Jian; Kim, Tongbeum
2014-06-01
We demonstrate that permeability of isotropic porous media e.g., open-cell foams can be analytically presented as a function of two morphological parameters: porosity and pore size. Adopting a cubic unit cell model, an existing tortuosity model from the branching algorithm method is incorporated into a generalized permeability model. The present model shows that dimensionless permeability significantly increases as the porosity of isotropic porous media and unifies the previously reported data in a wide range of porosity (ɛ=0.55-0.98) and pore size (Dp=0.254 mm-5.08 mm).
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. PMID:27136981
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.
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.
Galactic chemical evolution and nucleocosmochronology - Analytic quadratic models
NASA Technical Reports Server (NTRS)
Clayton, D. D.
1985-01-01
Quadratic models of the chemical evolution of the Galaxy for a star formation rate proportional to the square of the gas mass are studied. The search for analytic solutions to the gas mass and star mass for time-dependent rates of gaseous infall onto the disk is examined. The quadratic models are compared to models having linear star formation rates. The mass, metallicity, number of stars, and U-235/U-238 isotopic ratio for the models which are subjected to the same infall rate, the same initial disk mass, and the same final gas fraction are compared. The results of the comparison indicate that: (1) the average dwarf age is greater in the quadratic model, (2) the metallicity grows initially faster in the quadratic model, (3) the quadratic model has a smaller percentage of low-Z dwarfs, and (4) the U-235/U-238 isotopic ratio indicates a younger quadratic model.
An Analytic Function of Lunar Surface Temperature for Exospheric Modeling
NASA Technical Reports Server (NTRS)
Hurley, Dana M.; Sarantos, Menelaos; Grava, Cesare; Williams, Jean-Pierre; Retherford, Kurt D.; Siegler, Matthew; Greenhagen, Benjamin; Paige, David
2014-01-01
We present an analytic expression to represent the lunar surface temperature as a function of Sun-state latitude and local time. The approximation represents neither topographical features nor compositional effects and therefore does not change as a function of selenographic latitude and longitude. The function reproduces the surface temperature measured by Diviner to within +/-10 K at 72% of grid points for dayside solar zenith angles of less than 80, and at 98% of grid points for nightside solar zenith angles greater than 100. The analytic function is least accurate at the terminator, where there is a strong gradient in the temperature, and the polar regions. Topographic features have a larger effect on the actual temperature near the terminator than at other solar zenith angles. For exospheric modeling the effects of topography on the thermal model can be approximated by using an effective longitude for determining the temperature. This effective longitude is randomly redistributed with 1 sigma of 4.5deg. The resulting ''roughened'' analytical model well represents the statistical dispersion in the Diviner data and is expected to be generally useful for future models of lunar surface temperature, especially those implemented within exospheric simulations that address questions of volatile transport.
Secondary metallicity in analytic models of chemical evolution of galaxies
NASA Technical Reports Server (NTRS)
Clayton, D. D.; Pantelaki, I.
1986-01-01
Analytic models of the chemical evolution of galactic regions that grow in mass owing to the continuous infall of matter are characterized, emphasizing the solutions for secondary nuclei (defined as those nuclei whose stellar yields are proportional to the abundance of a primary seed nucleus) in the families of models described by Clayton (1984 and 1985). Wide variations in time dependence of both primary and secondary nuclei as well as in the ratio of secondary to primary are displayed by these model families, confirming again the usefulness of these families as interpretive guides if galaxies do in fact evolve with substantial infall. Additionally, analytic solutions are presented for two other possible interesting systems: the evolution of abundances if the primary metallicity in the infall is increasing in time, and the evolution of abundances if the primary yield changes linearly with time owing to continuous changes in the stellar mass function, the opacity, or other astrophysical agents. Finally, test evaluations of the instantaneous recycling approximation on which these analytic models rely are presented.
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.
Fast micromagnetic simulations using an analytic mathematical model
NASA Astrophysics Data System (ADS)
Tsiantos, Vassilios; Miles, Jim
2006-02-01
In this paper an analytic mathematical model is presented for fast micromagnetic simulations. In dynamic micromagnetic simulations the Landau-Lifshitz-Gilbert (LLG) equation is solved for the observation of the reversal magnetisation mechanisms. In stiff micromagnetic simulations the large system of ordinary differential equations has to be solved with an appropriate method, such as the Backward Differentiation Formulas (BDF) method, which leads to the solution of a large linear system. The latter is solved efficiently employing matrix-free techniques, such as Krylov methods with preconditioning. Within the Krylov methods framework a product of a matrix times a vector is involved which is usually approximated with directional differences. This paper provides an analytic mathematical model to calculate efficiently this product, leading to more accurate calculations and consequently faster micromagnetic simulations due to better convergence properties.
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.
Analytical models quantify the military benefit of collaborative search
NASA Astrophysics Data System (ADS)
Friedman, Melvin H.; Du Bosq, Todd W.; Flug, Eric A.
2010-04-01
Analytical Model 1 describes how long it takes the first observer to find a target when multiple observers search a field of regard using imagery provided by a single sensor. This model, developed using probability concepts, suggests considerable benefits accrue from collaborative search: when P is near one and with ten observers the mean detection time (in reduced time) is reduced by almost an order of magnitude when compared to that of a single observer. To get the instant of detection in clock time we add the delay time td to the reduced time. Empirical fits for td and are also given in the paper. Model 1 was verified/validated by computer simulation and perception experiments. Here ten observers searched sixty computer generated fields of regard (each one was 60 x 20 degrees) for a single military vehicle. Analytical Model 2 describes how the probability of target acquisition increases with the number of observers. The results of Model 2 suggest that probability of target acquisition increases considerably when multiple observers independently search a field of regard. Model 2 was verified by simulation but not by perception experiment. Models 1 and 2 are pertinent to development of search strategies with multiple observers and are expected to find use in wargaming for evaluating the efficacy of networked imaging sensors.
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
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.
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.
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
Aspirating Seal Development: Analytical Modeling and Seal Test Rig
NASA Technical Reports Server (NTRS)
Bagepalli, Bharat
1996-01-01
This effort is to develop large diameter (22 - 36 inch) Aspirating Seals for application in aircraft engines. Stein Seal Co. will be fabricating the 36-inch seal(s) for testing. GE's task is to establish a thorough understanding of the operation of Aspirating Seals through analytical modeling and full-scale testing. The two primary objectives of this project are to develop the analytical models of the aspirating seal system, to upgrade using GE's funds, GE's 50-inch seal test rig for testing the Aspirating Seal (back-to-back with a corresponding brush seal), test the aspirating seal(s) for seal closure, tracking and maneuver transients (tilt) at operating pressures and temperatures, and validate the analytical model. The objective of the analytical model development is to evaluate the transient and steady-state dynamic performance characteristics of the seal designed by Stein. The transient dynamic model uses a multi-body system approach: the Stator, Seal face and the rotor are treated as individual bodies with relative degrees of freedom. Initially, the thirty-six springs are represented as a single one trying to keep open the aspirating face. Stops (Contact elements) are provided between the stator and the seal (to compensate the preload in the fully-open position) and between the rotor face and Seal face (to detect rub). The secondary seal is considered as part of the stator. The film's load, damping and stiffness characteristics as functions of pressure and clearance are evaluated using a separate (NASA) code GFACE. Initially, a laminar flow theory is used. Special two-dimensional interpolation routines are written to establish exact film load and damping values at each integration time step. Additionally, other user-routines are written to read-in actual pressure, rpm, stator-growth and rotor growth data and, later, to transfer these as appropriate loads/motions in the system-dynamic model. The transient dynamic model evaluates the various motions, clearances
Peat pyrolysis and the analytical semi-empirical model
Feng, J.; Green, A.E.S.
2007-07-01
Pyrolysis of peat could convert this material into useful fuels and valuable hydrocarbons. A study of peat pyrolysis can also serve as a useful bridge between studies of coal pyrolysis and biomass pyrolysis. Using an analytical model of pyrolysis that has previously been applied to biomass and to coal, we present here the results of applications of this model to a representative peat. The analysis suggests means of organizing and processing rate and yield data that should be useful in applications of pyrolysis for the production of fuels and chemicals.
Analytical properties of a three-compartmental dynamical demographic model
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.
An Analytic Model for Buoyancy Resonances in Protoplanetary Disks
NASA Astrophysics Data System (ADS)
Lubow, Stephen H.; Zhu, Zhaohuan
2014-04-01
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 ky > h -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.
Multilayer analytic element modeling of radial collector wells.
Bakker, Mark; Kelson, Victor A; Luther, Kenneth H
2005-01-01
A new multilayer approach is presented for the modeling of ground water flow to radial collector wells. The approach allows for the inclusion of all aspects of the unique boundary condition along the lateral arms of a collector well, including skin effect and internal friction losses due to flow in the arms. The hydraulic conductivity may differ between horizontal layers within the aquifer, and vertical anisotropy can be taken into account. The approach is based on the multilayer analytic element method, such that regional flow and local three-dimensional detail may be simulated simultaneously and accurately within one regional model. Horizontal flow inside a layer is computed analytically, while vertical flow is approximated with a standard finite-difference scheme. Results obtained with the proposed approach compare well to results obtained with three-dimensional analytic element solutions for flow in unconfined aquifers. The presented approach may be applied to predict the yield of a collector well in a regional setting and to compute the origin and residence time, and thus the quality, of water pumped by the collector well. As an example, the addition of three lateral arms to a collector well that already has three laterals is investigated. The new arms are added at an elevation of 2 m above the existing laterals. The yield increase of the collector well is computed as a function of the lengths of the three new arms. PMID:16324013